From owner-obm-l@saci.mat.puc-rio.br Mon Mar 3 09:20:08 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m23CInsG022062 for ; Mon, 3 Mar 2008 09:18:50 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m23CIn8n022060 for obm-l-MllGbsmmN; Mon, 3 Mar 2008 09:18:49 -0300 Received: from bay0-omc2-s1.bay0.hotmail.com (bay0-omc2-s1.bay0.hotmail.com [65.54.246.137]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m23CIjsG022028 for ; Mon, 3 Mar 2008 09:18:46 -0300 Received: from BAY135-W6 ([65.55.140.41]) by bay0-omc2-s1.bay0.hotmail.com with Microsoft SMTPSVC(6.0.3790.3959); Sat, 1 Mar 2008 07:31:52 -0800 Message-ID: Content-Type: multipart/alternative; boundary="_9f971faf-0e76-47fa-ad74-93125db61bc3_" X-Originating-IP: [201.9.202.7] From: Rhilbert Rivera To: Subject: [obm-l] Derivada errada? Date: Sat, 1 Mar 2008 15:31:53 +0000 Importance: Normal In-Reply-To: <7e31215a0802291612k288ad47fy71b8a664234fb5b5@mail.gmail.com> References: <000c01c1627c$3420dc00$0b7147bd@pessoal2b51d2e> <7e31215a0802251815w5b44dbdakbbc1fc2275adc506@mail.gmail.com> <7e31215a0802251832m6fea4b5eo41fb7f15aad87c38@mail.gmail.com> <7e31215a0802280647m35f81766w72795953dd05762e@mail.gmail.com> <7e31215a0802280739g44952d61tbe78f0edc5954d31@mail.gmail.com> <7e31215a0802291612k288ad47fy71b8a664234fb5b5@mail.gmail.com> MIME-Version: 1.0 X-OriginalArrivalTime: 01 Mar 2008 15:31:52.0445 (UTC) FILETIME=[5FA9CAD0:01C87BB1] Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Rhilbert Rivera X-Spam-Status: No, hits=4.5 required=5.0 tests=AWL,BIG_FONT,FROM_ENDS_IN_NUMS,IN_REP_TO,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** --_9f971faf-0e76-47fa-ad74-93125db61bc3_ Content-Type: text/plain; charset="Windows-1252" Content-Transfer-Encoding: quoted-printable Um famoso livro de c=E1lculo, demonstra a regra da derivada do quociente da= seguinte maneira: =20 Sejam f e g duas fun=E7=F5es e seja h =3D f/g, definida onde g diferente d= e zero. Ent=E3o f =3D hg, aplicando a regra do produto =E1 fun=E7=E3o f, te= mos que:=20 f=92 =3D h=92g + hg=92 Da=ED, obtemos h=92=3D(f=92 =96hg=92)g. Substituindo o valor de h nesta =FAltima express=E3o, vem: h=92=3D (f=92g =96 fg=92)/g^2 =20 Um outro livro diz que essa demonstra=E7=E3o est=E1 errada, mas n=E3o diz = onde.=20 =C1g=FCem poderia me d=E1 uma dica, porque esse procedimento n=E3o demonstr= a a regra do quociente?Obrigado! _________________________________________________________________ Cansado de espa=E7o para s=F3 50 fotos? Conhe=E7a o Spaces, o site de relac= ionamentos com at=E9 6,000 fotos! http://www.amigosdomessenger.com.br= --_9f971faf-0e76-47fa-ad74-93125db61bc3_ Content-Type: text/html; charset="Windows-1252" Content-Transfer-Encoding: quoted-printable

Um famoso livro de c=E1lculo, demonstra a r= egra da derivada do quociente da seguinte maneira:

 

Sejam f e g  duas fun=E7=F5es e seja h =3D f/g, definida onde= g diferente de zero. Ent=E3o f =3D hg, aplicando a regra do produto =E1 fu= n=E7=E3o f, temos que:

f=92 = ; =3D h=92g + hg=92

Da=ED, obtemos

h=92=3D(f=92 =96hg=92)g.

Substituindo o valor de h nesta =FAltima ex= press=E3o, vem:

  h=92=3D (f=92g =96 fg=92)/g^2

 

Um outro livro diz que  essa demonstra=E7=E3o est=E1 errada, mas n=E3o d= iz onde.

=C1g=FCem poderia me d= =E1 uma dica, porque esse procedimento n=E3o demonstra a regra do quociente= ?


Obrigado!
Encontre o que voc=EA procura com mais= efici=EAncia! Instale j=E1 a Barra de Ferramentas com Windows Desktop Sear= ch! =C9 GR=C1TIS!= = --_9f971faf-0e76-47fa-ad74-93125db61bc3_-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Mon Mar 3 09:20:08 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m23CHnsG021927 for ; Mon, 3 Mar 2008 09:17:49 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m23CHmPg021925 for obm-l-MllGbsmmN; Mon, 3 Mar 2008 09:17:48 -0300 Received: from bay0-omc2-s14.bay0.hotmail.com (bay0-omc2-s14.bay0.hotmail.com [65.54.246.150]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m23CHhsG021914 for ; Mon, 3 Mar 2008 09:17:44 -0300 Received: from BAY112-W45 ([64.4.26.145]) by bay0-omc2-s14.bay0.hotmail.com with Microsoft SMTPSVC(6.0.3790.3959); Sun, 2 Mar 2008 18:59:19 -0800 Message-ID: Content-Type: multipart/alternative; boundary="_18ab6d90-b4ab-4ed0-8107-b5d278c8ad78_" X-Originating-IP: [201.53.49.100] From: Pedro Cardoso To: Subject: [obm-l] Algebra Linear e Desigualdade de Schwarz Date: Mon, 3 Mar 2008 05:59:18 +0300 Importance: Normal In-Reply-To: <7e31215a0802291612k288ad47fy71b8a664234fb5b5@mail.gmail.com> References: <000c01c1627c$3420dc00$0b7147bd@pessoal2b51d2e> <7e31215a0802251815w5b44dbdakbbc1fc2275adc506@mail.gmail.com> <7e31215a0802251832m6fea4b5eo41fb7f15aad87c38@mail.gmail.com> <7e31215a0802280647m35f81766w72795953dd05762e@mail.gmail.com> <7e31215a0802280739g44952d61tbe78f0edc5954d31@mail.gmail.com> <7e31215a0802291612k288ad47fy71b8a664234fb5b5@mail.gmail.com> MIME-Version: 1.0 X-OriginalArrivalTime: 03 Mar 2008 02:59:19.0033 (UTC) FILETIME=[92F56690:01C87CDA] Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Pedro Cardoso X-Spam-Status: No, hits=4.4 required=5.0 tests=AWL,IN_REP_TO,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, REFERENCES,SPAM_PHRASE_00_01,SUPERLONG_LINE,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** --_18ab6d90-b4ab-4ed0-8107-b5d278c8ad78_ Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Caros amigos da lista, =20 sauda=E7=F5es! Queria a ajuda de voc=EAs em dois problemas, nos quais a min= ha d=FAvida consiste em saber com exatid=E3o o que o enunciado exige de mim= . Um =E9 de =E1lgebra linear, outro =E9 de, bem, desigualdade de couchy-sch= warz (que t=F3pico da =E1lgebra isso seria?). =20 1- Determine sistemas lineares de equa=E7=F5es com duas inc=F3gnitas (x,y) = cujas solu=E7=F5es sejam da forma (1,3) (solu=E7=E3o =FAnica), (t,2t),(t,3)= . Coment=E1rio: na verdade, vendo a solu=E7=E3o de uma dessas, acho que ent= enderia o que =E9 para fazer nas outras. At=E9 resolvi, mas a resposta n=E3= o parecia estar bonita e soava =F3bvia demais. =20 2- D=EA a interpreta=E7=E3o geom=E9trica da desigualdade de Couchy-Schwarz = para n=3D2, n=3D3. =20 Abra=E7os, =20 Pedro Laz=E9ra cardoso. =20 _________________________________________________________________ Cansado de espa=E7o para s=F3 50 fotos? Conhe=E7a o Spaces, o site de relac= ionamentos com at=E9 6,000 fotos! http://www.amigosdomessenger.com.br= --_18ab6d90-b4ab-4ed0-8107-b5d278c8ad78_ Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable

Caros amigos da lista,
 
sauda=E7=F5es! Queria a ajuda de voc=EAs em dois problemas, nos quais&= nbsp;a minha d=FAvida consiste em saber com exatid=E3o o que o enunciado ex= ige de mim. Um =E9 de =E1lgebra linear, outro =E9 de, bem, desigualdade de = couchy-schwarz (que t=F3pico da =E1lgebra isso seria?).
 
1- Determine sistemas lineares de equa=E7=F5es com duas inc=F3gnitas (x,y) = cujas solu=E7=F5es sejam da forma (1,3) (solu=E7=E3o =FAnica), (t,2t),(t,3)= . Coment=E1rio: na verdade, vendo a solu=E7=E3o de uma dessas, acho que ent= enderia o que =E9 para fazer nas outras. At=E9 resolvi, mas a resposta n=E3= o parecia estar bonita e soava =F3bvia demais.
 
2- D=EA a interpreta=E7=E3o geom=E9trica da desigualdade de Couchy-Schwarz = para n=3D2, n=3D3.
 
Abra=E7os,
 
Pedro Laz=E9ra cardoso.
 

Encontre o que voc=EA procura com mais efici=EAncia! = Instale j=E1 a Barra de Ferramentas com Windows Desktop Search! =C9 GR=C1TIS! = --_18ab6d90-b4ab-4ed0-8107-b5d278c8ad78_-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Mon Mar 3 11:01:12 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m23DxtsG029247 for ; Mon, 3 Mar 2008 10:59:55 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m23Dxt6O029245 for obm-l-MllGbsmmN; Mon, 3 Mar 2008 10:59:55 -0300 Received: from relay3.bol.com.br (relay3.bol.com.br [200.221.4.107]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m23DxrsG029239 for ; Mon, 3 Mar 2008 10:59:53 -0300 Received: from localhost (localhost [127.0.0.1]) by salsa3.bol.com.br (Postfix) with ESMTP id 7DF56E006450 for ; Sat, 1 Mar 2008 08:07:51 -0300 (BRT) Received: from bol.com.br (whisper8.mail.sys.intranet [172.26.5.83]) by salsa3.bol.com.br (Postfix) with ESMTP id 46DEDE00614F for ; Sat, 1 Mar 2008 08:07:51 -0300 (BRT) Date: Sat, 1 Mar 2008 08:07:51 -0300 Message-Id: Subject: [obm-l] PONTO SELECIONADO MIME-Version: 1.0 X-Sensitivity: 3 Content-Type: multipart/alternative; boundary="_=__=_XaM3_.1204369671.2A.225341.42.25656.52.42.007.1185096967" From: "arkon" To: "obm-l" X-XaM3-API-Version: 4.3(R1) (B10) X-SenderIP: 200.140.133.74 X-SIG5: 47ddf02f5e679b7323fb0a6921b2c595 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "arkon" X-Spam-Status: No, hits=1.3 required=5.0 tests=AWL,BIG_FONT,HTML_50_70,LINES_OF_YELLING, LINES_OF_YELLING_2,SPAM_PHRASE_00_01,TO_LOCALPART_EQ_REAL, X_MAILING_LIST version=2.44 X-Spam-Level: * --_=__=_XaM3_.1204369671.2A.225341.42.25656.52.42.007.1185096967 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable ALGU=C9M PODE RESOLVER ESSA, POR FAVOR (AFA-93/94) Um ponto =E9 selecionado aleatoriamente dentro de um tri=E2ng= ulo eq=FCil=E1tero de lado L =3D 3. A probabilidade de a dist=E2ncia dess= e ponto a qualquer v=E9rtice ser maior do que 1 =E9: a) 1 =96 (2pisqrt3/9). b) 1 =96 (pisqrt3/9). c) 1 =96 (2pisqrt3/27). = d) 1 =96 (pisqrt3/27). Considerar pisqrt3 =3D pi vezes a raiz quadrada de tr=EAs GABARITO LETRA C DESDE J=C1 AGRADE=C7O --_=__=_XaM3_.1204369671.2A.225341.42.25656.52.42.007.1185096967 Content-Type: text/html; charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable

<= B style=3D"mso-bidi-font-weight: normal">ALGU=C9M PODE RESOLVER ESSA, P= OR FAVOR

<= B style=3D"mso-bidi-font-weight: normal"> <= /P>

<= B style=3D"mso-bidi-font-weight: normal">(AFA-93/94) Um ponto =E9 selec= ionado aleatoriamente dentro de um tri=E2ngulo eq=FCil=E1tero de lado L =3D= 3. A probabilidade de a dist=E2ncia desse ponto a qualquer = v=E9rtice ser maior do que 1 =E9:

=

<= B style=3D"mso-bidi-font-weight: normal"> <= /P>

<= B style=3D"mso-bidi-font-weight: normal">a) 1 =96 (2pisqrt3/9).   b) 1 =96 (pisqrt3/9).&nbs= p;  c) 1 =96 (2pisqrt3/27).   d) 1 =96 (pisq= rt3/27).

<= B style=3D"mso-bidi-font-weight: normal"> <= /P>

<= B style=3D"mso-bidi-font-weight: normal">Considerar pisqrt3 =3D pi vezes = a raiz quadrada de tr=EAs

<= B style=3D"mso-bidi-font-weight: normal"> 

<= B style=3D"mso-bidi-font-weight: normal">GABARITO LETRA C

<= B style=3D"mso-bidi-font-weight: normal"> <= /P>

<= B style=3D"mso-bidi-font-weight: normal">DESDE J=C1 AGRADE=C7O

--_=__=_XaM3_.1204369671.2A.225341.42.25656.52.42.007.1185096967-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Mon Mar 3 13:17:45 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m23GGUsG007288 for ; Mon, 3 Mar 2008 13:16:30 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m23GGUgg007286 for obm-l-MllGbsmmN; Mon, 3 Mar 2008 13:16:30 -0300 Received: from rogue.cesp.com.br (rogue.cesp.com.br [201.63.4.194]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m23GFwsG007229; Mon, 3 Mar 2008 13:15:59 -0300 Received: from correio.cesp.com.br (nightcrawler.cesp.com.br [201.63.4.197]) by rogue.cesp.com.br (Postfix) with ESMTP id 5691943B16; Mon, 3 Mar 2008 13:16:18 -0300 (BRT) Received: from x454322e3f5ac4 (unknown [10.136.21.53]) by correio.cesp.com.br (Postfix) with ESMTP id CBD9751407B; Mon, 3 Mar 2008 13:16:19 -0300 (BRT) From: "Rubens Kamimura" To: , References: In-Reply-To: Subject: [SPAM] [obm-l] =?iso-8859-1?Q?=5Bobm-l=5D_Quest=E3o_de_indu=E7=E3o_matem=E1tica?= Date: Mon, 3 Mar 2008 13:16:19 -0300 Organization: CESP - OMPTD Message-ID: <003501c87d49$ea15a1f0$be40e5d0$@kamimura@cesp.com.br> MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" X-Mailer: Microsoft Office Outlook 12.0 Thread-Index: Ach3ys5m3HcJz2jXRO2GK7UheOhAkwADzF3QAVQ1M+AAB7SLwA== Content-Language: pt-br Content-Transfer-Encoding: 7bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m23GFxsG007230 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Rubens Kamimura" X-Spam-Status: Yes, hits=5.8 required=5.0 tests=AWL,INVALID_MSGID,NOSPAM_INC,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ***** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (5.80 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: NOSPAM_INC (-0.2 points) Where are you working at? SPAM: INVALID_MSGID (0.0 points) Message-Id is not valid, according to RFC 2822 SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 197.4.63.201.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 197.4.63.201.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (0.2 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- Olá turma da LISTA!!! Alguém desta LISTA, se habilitariam em me elucidar tal questão? 1. Sabendo, por definição, que: a^0=1 e a^1=a, como poderemos provar por indução matemática sobre n, que a^m.a^n = a^(m+n), para qualquer m,n pertencente ao conjunto dos números naturais? 2. Como podemos provar por indução matemática: 2.1. 1^2+ 2^2+...+n^2 = [n(n+1)(2n+1)]/6, (n maior igual 1); 2.2. 1^3+ 2^3+...+n^3 = (1+2+...+n)^2, (n maior igual 1); 2.3. 1.2+2.3+...+n(n+1) = [n(n+1)(n+2)]/3, (n maior igual 1); Abraços leigo e neófito... ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Mon Mar 3 14:25:13 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m23HNdsG011926 for ; Mon, 3 Mar 2008 14:23:39 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m23HNcwN011923 for obm-l-MllGbsmmN; Mon, 3 Mar 2008 14:23:38 -0300 Received: from wa-out-1112.google.com (wa-out-1112.google.com [209.85.146.183]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m23HNasG011909 for ; Mon, 3 Mar 2008 14:23:37 -0300 Received: by wa-out-1112.google.com with SMTP id m28so155123wag.13 for ; Mon, 03 Mar 2008 09:23:57 -0800 (PST) Received: by 10.114.102.1 with SMTP id z1mr13655702wab.56.1204397357496; Sat, 01 Mar 2008 10:49:17 -0800 (PST) Received: by 10.114.58.13 with HTTP; Sat, 1 Mar 2008 10:49:17 -0800 (PST) Message-ID: <3e7bcb580803011049j3d81dd41k43d4916b54cad6f1@mail.gmail.com> Date: Sat, 1 Mar 2008 15:49:17 -0300 From: "=?ISO-8859-1?Q?Henrique_Renn=F3?=" To: obm-l@mat.puc-rio.br Subject: [obm-l] =?ISO-8859-1?Q?Determinante_de_Matriz_Sim=E9trica?= MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m23HNcsG011921 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "=?ISO-8859-1?Q?Henrique_Renn=F3?=" X-Spam-Status: No, hits=2.0 required=5.0 tests=AWL,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, SIGNATURE_SHORT_SPARSE,SPAM_PHRASE_00_01,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: ** Gostaria de saber se existe alguma propriedade sobre o determinante de uma matriz simétrica, como, por exemplo: o determinante de uma matriz simétrica é a multiplicação dos elementos da diagonal principal. Não sei se o exemplo que dei é verdadeiro, e se for, como isso poderia ser demonstrado. Seja uma matriz simétrica na forma a11 a12 ... a1n a12 a22 ... a2n . a1n a2n ... ann Podemos escrevê-la como a11/2 a12 ... a1n 0 a22/2 ... a2n . 0 0 ... ann/2 + a11/2 0 ... 0 a12 a22/2 ... 0 . a1n a2n ... ann/2 ou seja, a soma de duas matrizes triângulares, para as quais é fácil demonstrar que o determinante é a multiplicação dos elementos da diagonal principal já que a parte superior ou inferior da matriz é nula e isso anula todos os elementos da soma no cálculo do determinante exceto a multiplicação dos elementos da diagonal principal. Há uma forma de demonstrar algo como, e isso se mantém verdadeiro até para dimensões maiores que 3 onde não é aplicada a regra de Sarrus, mas o Teorema de Laplace facilita o cálculo através dos cofatores. det(C) = det(A+B) ou seria de outra forma? -- Henrique ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Mon Mar 3 15:59:36 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m23IvKsG016500 for ; Mon, 3 Mar 2008 15:57:20 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m23IvGHU016496 for obm-l-MllGbsmmN; Mon, 3 Mar 2008 15:57:16 -0300 Received: from web30101.mail.mud.yahoo.com (web30101.mail.mud.yahoo.com [209.191.69.33]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id m23IunsG016480 for ; Mon, 3 Mar 2008 15:56:50 -0300 Received: (qmail 16866 invoked by uid 60001); 3 Mar 2008 18:57:06 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:Date:From:Subject:To:In-Reply-To:MIME-Version:Content-Type:Content-Transfer-Encoding:Message-ID; b=2qMUM9p132LvZOcMw1tTVCRciQcMCcMqhxy77BHqkWgj0pogJwMOk1IRzu6/cR6OM4/3o6TD/GUL+7HTuVlHAacEIByALs2JmhL+GGPO7aLpdkr+YFYb1+EDbi7OY0pZFe16kzMxkEZDK4U+C3LwFTloziW3ygk80QrD41yuiz4=; X-YMail-OSG: eWsiGz0VM1mnEJMocL5zg2nRkGm2XqwzlRutmEyi Received: from [201.63.131.82] by web30101.mail.mud.yahoo.com via HTTP; Mon, 03 Mar 2008 15:57:05 ART Date: Mon, 3 Mar 2008 15:57:05 -0300 (ART) From: Angelo Schranko Subject: [SPAM] =?iso-8859-1?q?Re:=20[obm-l]=20Determinante=20de=20Matriz=20Sim=E9trica?= To: obm-l@mat.puc-rio.br In-Reply-To: <3e7bcb580803011049j3d81dd41k43d4916b54cad6f1@mail.gmail.com> MIME-Version: 1.0 Content-Type: text/plain Content-Transfer-Encoding: 7bit Message-ID: <987662.57709.qm@web30101.mail.mud.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Angelo Schranko X-Spam-Status: Yes, hits=6.8 required=5.0 tests=AWL,FORGED_YAHOO_RCVD,IN_REP_TO,QUOTED_EMAIL_TEXT, RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01, SPAM_REDIRECTOR,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ****** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="0-1753326547-1204570625=:57709" X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (6.80 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: QUOTED_EMAIL_TEXT (-0.8 points) BODY: Contains what looks like a quoted email text SPAM: SPAM_REDIRECTOR (0.4 points) URI: Uses open redirection service SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 33.69.191.209.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 33.69.191.209.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (0.8 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- --0-1753326547-1204570625=:57709 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 8bit > Gostaria de saber se existe alguma propriedade sobre o determinante de > uma matriz simétrica Uma matriz A é simétrica se A = A^T (transposta de A). Sendo A simétrica ou não, vale DetA = DetA^T > Não sei se o exemplo que dei é verdadeiro, e se for, como isso poderia > ser demonstrado. Falso. Seja A= {{1,2},{2,4}}. A é simétrica. Det[{{1,2},{2,4}}] = 0 diferente 4. [ ]´s Angelo --------------------------------- Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-1753326547-1204570625=:57709 Content-Type: text/html; charset=iso-8859-1 Content-Transfer-Encoding: 8bit
> Gostaria de saber se existe alguma propriedade sobre o determinante de
> uma matriz simétrica
 
Uma matriz A é simétrica se A = A^T (transposta de A).
Sendo A simétrica ou não, vale DetA = DetA^T
 
> Não sei se o exemplo que dei é verdadeiro, e se for, como isso poderia
> ser demonstrado.
 
Falso.
 
Seja A= {{1,2},{2,4}}.
A é simétrica.
Det[{{1,2},{2,4}}] = 0 diferente 4.
 
[ ]´s
Angelo

Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-1753326547-1204570625=:57709-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Mon Mar 3 16:35:29 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m23JY3sG018781 for ; Mon, 3 Mar 2008 16:34:03 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m23JY3J4018779 for obm-l-MllGbsmmN; Mon, 3 Mar 2008 16:34:03 -0300 Received: from mu-out-0910.google.com (mu-out-0910.google.com [209.85.134.188]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m23JXlsG018759 for ; Mon, 3 Mar 2008 16:34:02 -0300 Received: by mu-out-0910.google.com with SMTP id w8so307988mue.1 for ; Mon, 03 Mar 2008 11:34:08 -0800 (PST) Received: by 10.82.168.2 with SMTP id q2mr13207186bue.13.1204380747142; Sat, 01 Mar 2008 06:12:27 -0800 (PST) Received: by 10.82.108.5 with HTTP; Sat, 1 Mar 2008 06:12:27 -0800 (PST) Message-ID: <70bb75a50803010612x2b3575actc2309b0322d3312c@mail.gmail.com> Date: Sat, 1 Mar 2008 11:12:27 -0300 From: "Emanuel Valente" To: obm-l@mat.puc-rio.br Subject: [obm-l] =?ISO-8859-1?Q?Polin=F4mio_-_Iezzi_-_(E.E._Lins-66)?= MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m23JY2sG018777 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Emanuel Valente" X-Spam-Status: No, hits=4.6 required=5.0 tests=AWL,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** Olá senhores, estou tendo trabalho pra resolver essa questão. Encontrei valores p=1 e p=-1, mas nunca o resultado do gabarito que é p=0. Calcular p para que o polinômio 4x^4 - 8x^3 + 8x^2 - 4(p+1)x + (p+1)^2 seja o quadrado perfeito de um polinômio racional inteiro em x. Abraços e um bom final de semana a todos! -- Emanuel Valente ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Mon Mar 3 17:31:11 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m23KSVsG021167 for ; Mon, 3 Mar 2008 17:28:31 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m23KSULY021165 for obm-l-MllGbsmmN; Mon, 3 Mar 2008 17:28:30 -0300 Received: from wr-out-0506.google.com (wr-out-0506.google.com [64.233.184.230]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m23KSPsG021146 for ; Mon, 3 Mar 2008 17:28:28 -0300 Received: by wr-out-0506.google.com with SMTP id c37so476201wra.19 for ; Mon, 03 Mar 2008 12:28:46 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=ANSNFLB6o1P6ObZ/q/5Z20gH7lla9XDkbO1bgW57nxk=; b=W5AZ80Ib5+f7YC7TdiUcCDCqrq8H+4/YIqFtrFV0T/7UP+tsZeMuqPIs7wm2TQ517MbaLspvBfjgmpmEq1LsDQzjgHlzDOvEXhmZN9e7DuBMSoRk78wqCQzvMnLdzuw/ZK2sSkL1oyXnaIiZcJW/BfK2rTDDa/+jAs6GV3S9yRQ= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=GZBo340Ox9X98P7XVo0Hg38RVhOzgkVfGpPkCOrl4kCqfcOuGoZ3g151IghNhyMvB0eqCG1RGdYPq48slmj/FKLfrmiwXDpm7YgT3Fv0A+oohw3kRVjw2j+qbBL1YstpLrEH93ZGuJUNIT7t4TFRhRKdw2C8Uw4yEgcdOXn6HDo= Received: by 10.65.83.18 with SMTP id k18mr176510qbl.12.1204575707904; Mon, 03 Mar 2008 12:21:47 -0800 (PST) Received: by 10.65.11.16 with HTTP; Mon, 3 Mar 2008 12:21:47 -0800 (PST) Message-ID: Date: Mon, 3 Mar 2008 17:21:47 -0300 From: "=?ISO-8859-1?Q?Pedro_J=FAnior?=" To: obm-l@mat.puc-rio.br Subject: =?ISO-8859-1?Q?Re:_[obm-l]_Res:_[obm-l]_Re:_[obm-?= =?ISO-8859-1?Q?l]_Eq._do_2=BA_Grau_de_Coef._Inteiros?= In-Reply-To: <273445.20933.qm@web33708.mail.mud.yahoo.com> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_7443_18916900.1204575707892" References: <273445.20933.qm@web33708.mail.mud.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "=?ISO-8859-1?Q?Pedro_J=FAnior?=" X-Spam-Status: No, hits=3.8 required=5.0 tests=AWL,FROM_ENDS_IN_NUMS,IN_REP_TO,JAVASCRIPT_UNSAFE, MAILTO_LINK,MAILTO_TO_SPAM_ADDR,QUOTED_EMAIL_TEXT, RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,REFERENCES, SPAM_PHRASE_00_01,SPAM_REDIRECTOR,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: *** ------=_Part_7443_18916900.1204575707892 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Muito obrigado... Essa foi muito boa... Em 29/02/08, Eduardo Estrada escreveu: > > Ol=E1, > > Consegui uma outra solu=E7=E3o, que, por sinal, tem certa semelhan=E7a: > > Suponha a equa=E7=E3o na forma ax^2+bx+c =3D 0, com discriminante b^2-4ac= =3D 39. > Como 39 =E9 =EDmpar e 4ac =E9 par, devemos ter b^2 =EDmpar, donde b, tamb= =E9m, =EDmpar. > Logo, suponhamos b =3D 2k+1, com k inteiro. Ent=E3o, temos: > > b^2-4ac =3D 39 -> (2k+1)^2-4ac =3D 39 -> 4k^2+4k+1-4ac =3D 39 -> 4(k^2+k-= ac) =3D > 38, > > e, como k^2+k-ac =E9 inteiro, segue que 38 deve ser m=FAltiplo de 4, o qu= e > sabemos n=E3o ser verdade. > > Um abra=E7o, > Eduardo > > ----- Mensagem original ---- > De: Rafael Cano > Para: obm-l@mat.puc-rio.br > Enviadas: Sexta-feira, 29 de Fevereiro de 2008 2:24:53 > Assunto: [obm-l] Re: [obm-l] Eq. do 2=BA Grau de Coef. Inteiros > > Ol=E1 > Primeiro =E9 =FAtil usar o seguinte fato: todo inteiro elevado ao quadrad= o > deixa resto 0 ou 1 na divis=E3o por 3 ou por 4 (tente provar isso...se n= =E3o der > mande outro email). > Seja ax^2+bx+c com a, b, c inteiros. O discriminante =E9: b^2 - 4ac. Supo= nha > por absurdo que b^2 - 4ac =3D 39. Ent=E3o: b^2=3D39+4ac. Veja que dividin= do os > dois lados por 4 temos: (b^2)/4=3D39/4 + ac. Se fosse poss=EDvel encontra= r > inteiros que satisfazem a igualdade, o resto do lado direito deveria ser = 0 > ou 1. Mas 39/4 deixa resto 3. Logo =E9 imposs=EDvel encontrar inteiros qu= e > satisfazem a igualdade, ou seja, o discriminante n=E3o pode ser 39. > Abra=E7os > > ----- Original Message ----- > *From:* Pedro J=FAnior > *To:* obm-l@mat.puc-rio.br > *Sent:* Thursday, February 28, 2008 11:17 PM > *Subject:* [obm-l] Eq. do 2=BA Grau de Coef. Inteiros > > Dada uma equa=E7=E3o do 2=BA Grau, com coeficientes inteiros, mostre que = seu > discriminante n=E3o pode ser igual a 39. > > > Agrade=E7o desde j=E1... > Atenciosamente Pedro Jr (Jo=E3o Pessoa) > > > > ------------------------------ > Abra sua conta no Yahoo! Mail, > o =FAnico sem limite de espa=E7o para armazenamento! > ------=_Part_7443_18916900.1204575707892 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Muito obrigado...
Essa foi muito boa...

Em 29/02/08, Eduardo Estrada <= eestradaitu@yahoo.com.br>= ; escreveu:
Ol=E1,

Consegui uma outra solu=E7=E3o, que, po= r sinal, tem certa semelhan=E7a:

Suponha a equa=E7=E3o na forma ax^2+bx+= c =3D 0, com discriminante b^2-4ac =3D 39. Como 39 =E9 =EDmpar e 4ac= =E9 par, devemos ter b^2 =EDmpar, donde b, tamb=E9m, =EDmpar. Logo, suponh= amos b =3D 2k+1, com k inteiro. Ent=E3o, temos:

b^2-4ac =3D 39 -> (2k+1)^2-4ac =3D 39 -> 4k^2+4k+1-4ac =3D 39 -> 4(k^2+k-ac) =3D 38,

e, como <= /font>k^2+k-ac =E9 inteiro, segue que 38 de= ve ser m=FAltiplo de 4, o que sabemos n=E3o ser verdade.

Um abra=E7o,
Eduardo

----- Mensagem original -= ---
De: Rafael Cano <rafa= elcano@dglnet.com.br>
Para: obm-l@mat.puc-rio.br
E= nviadas: Sexta-feira, 29 de Fevereiro de 2008 2:24:53
Assunto: [obm-l] R= e: [obm-l] Eq. do 2=BA Grau de Coef. Inteiros


=20 =20
Ol=E1
Primeiro =E9 =FAtil usar o seguinte fa= to: todo inteiro=20 elevado ao quadrado deixa resto 0 ou 1 na divis=E3o por 3 ou por 4 (tente p= rovar=20 isso...se n=E3o der mande outro email).
Seja ax^2+bx+c com a, b, c inteiros. O= =20 discriminante =E9: b^2 - 4ac. Suponha por absurdo que b^2 - 4ac =3D 39. Ent=E3o: b^2=3D39+4ac. Veja que=20 dividindo os dois lados por 4 temos: (b^2)/4=3D39/4 + ac. Se fosse poss=EDvel encontrar inteiros que satis= fazem a=20 igualdade, o resto do lado direito deveria ser 0 ou 1. Mas 39/4 deixa resto 3. Logo =E9 imposs=EDvel encontrar = inteiros que=20 satisfazem a igualdade, ou seja, o discriminante n=E3o pode ser 39.<= /div>
Abra=E7os
----- Original Message -----
From:=20 Pedro J=FAnior
Sent: Thursday, February 28, 2008 = 11:17=20 PM
Subject: [obm-l] Eq. do 2=BA Grau = de Coef.=20 Inteiros

Dada uma equa=E7=E3o do 2=BA Grau, com coeficientes inteir= os, mostre=20 que seu discriminante n=E3o pode ser igual a 39.


Agrade=E7o de= sde=20 j=E1...
Atenciosamente Pedro Jr (Jo=E3o Pessoa)

<= br>
Abra sua conta no Yahoo! Mail, o =FAnico sem= limite de espa=E7o para armazenamento!=20

------=_Part_7443_18916900.1204575707892-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Mon Mar 3 17:46:12 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m23KhrsG021780 for ; Mon, 3 Mar 2008 17:43:53 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m23KhrZa021778 for obm-l-MllGbsmmN; Mon, 3 Mar 2008 17:43:53 -0300 Received: from ug-out-1314.google.com (ug-out-1314.google.com [66.249.92.172]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m23KhosG021774 for ; Mon, 3 Mar 2008 17:43:51 -0300 Received: by ug-out-1314.google.com with SMTP id q7so2098167uge.0 for ; Mon, 03 Mar 2008 12:44:12 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; bh=0DVQSA6ZReKJx5WxWMIfTAkG4YVhyS0242vXfVCQYlQ=; b=Xk83wRjwMJeV/sbNViSFaywzJRCK5I3he6WkIetpvLgccGjTgG3SKSNh0puTkYyoMSlK/FjM3Ke+NzsfNJB1HdMtkrntFzNzR0wpOofEjfK7EWXNQD9w+PDmHVUxSF5bP6o78rlrFxx8gBGwD41Tnl1TrME7pZdAwJibb2UwRPg= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; b=Gcil+1fO7Jdw7tX0OA+diXdQLc+97sicnpBwialWnyY8Lu9s1MQDYsa3ImQPJkWmjri4u6VUTs0zZ3anZHCb2wZICSDBGpSScoXWxtlczXvzAEWGofu+/c22bTG2yGbWHQxSOBJCeZyArhVOT6eQb8oqlVY3KlmtpRZDt9iusFI= Received: by 10.67.24.11 with SMTP id b11mr5040505ugj.2.1204575425094; Mon, 03 Mar 2008 12:17:05 -0800 (PST) Received: by 10.66.219.5 with HTTP; Mon, 3 Mar 2008 12:17:04 -0800 (PST) Message-ID: <2d483c770803031217k438c855n4a88bd4012cfe696@mail.gmail.com> Date: Mon, 3 Mar 2008 17:17:04 -0300 From: "Ralph Teixeira" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Derivada errada? In-Reply-To: MIME-Version: 1.0 Content-Type: text/plain; charset=WINDOWS-1252 Content-Disposition: inline References: <000c01c1627c$3420dc00$0b7147bd@pessoal2b51d2e> <7e31215a0802251815w5b44dbdakbbc1fc2275adc506@mail.gmail.com> <7e31215a0802251832m6fea4b5eo41fb7f15aad87c38@mail.gmail.com> <7e31215a0802280647m35f81766w72795953dd05762e@mail.gmail.com> <7e31215a0802280739g44952d61tbe78f0edc5954d31@mail.gmail.com> <7e31215a0802291612k288ad47fy71b8a664234fb5b5@mail.gmail.com> Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m23KhqsG021776 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Ralph Teixeira" X-Spam-Status: No, hits=4.4 required=5.0 tests=AWL,IN_REP_TO,MAILTO_TO_SPAM_ADDR,QUOTED_EMAIL_TEXT, RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,REFERENCES, SPAM_PHRASE_00_01,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** O problema desta demonstração é que ela não prova que h é derivável. A Regra do Produto diz que: "SE h e g forem diferenciáveis num ponto x=a, então hg também é e (hg)'=h'g+hg' Então, quando você passa de f=hg para f'=h'g+hg', você está USANDO que h é derivável, fato que, teoricamente, ainda não está provado. Em outras palavras, o que a gente demonstrou com este argumento (que eu acho bacana!) foi apenas: "Sejam f e g duas funções diferenciáveis no ponto x=a; seja h(x)=f(x)/g(x). **SE** h(x) for diferenciável em x=a, então h'=(f'g-fg')/g^2 neste ponto." Abraço, Ralph 2008/3/1 Rhilbert Rivera : > > > Um famoso livro de cálculo, demonstra a regra da derivada do quociente da > seguinte maneira: > > > > Sejam f e g duas funções e seja h = f/g, definida onde g diferente de zero. > Então f = hg, aplicando a regra do produto á função f, temos que: > > f' = h'g + hg' > > Daí, obtemos > > h'=(f' –hg')g. > > Substituindo o valor de h nesta última expressão, vem: > > h'= (f'g – fg')/g^2 > > > > Um outro livro diz que essa demonstração está errada, mas não diz onde. > > Ágüem poderia me dá uma dica, porque esse procedimento não demonstra a regra > do quociente? > Obrigado! > ________________________________ > Encontre o que você procura com mais eficiência! Instale já a Barra de > Ferramentas com Windows Desktop Search! É GRÁTIS! ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Mon Mar 3 21:41:49 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m240dhsG031835 for ; Mon, 3 Mar 2008 21:39:43 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m240dhDr031832 for obm-l-MllGbsmmN; Mon, 3 Mar 2008 21:39:43 -0300 Received: from wx-out-0506.google.com (wx-out-0506.google.com [66.249.82.230]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m240dfsG031829 for ; Mon, 3 Mar 2008 21:39:41 -0300 Received: by wx-out-0506.google.com with SMTP id t4so577710wxc.18 for ; Mon, 03 Mar 2008 16:40:02 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; bh=9rEvk4Zn2hcgddCQYvL6+xc72XMwuEUEu2MJ0aO/4Xw=; b=sZ68uMR8hCr3U77EjqFlM18/Oy0+VHwUndnzgGeWmehR4hnAPosH58paT9/VO5aQXHaQaNJSH0dzqJW4EB+MWjHf+erTxuPfNWQlSeIPHdjuI1q1mhHk1pFuW4afXeKtsoJQjI6FT/Bfc6KeksNE7vUmbG+FoEqOMeq0VgoWtjY= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; b=GrdDU+RwH/EUjIwasgOBaPkv4pGI9gSHk8wEWZQWyn3zkttiz94Wf1ql1kymEDiQolyM/q1U4QI30b2ALSNn70kpKjUblV6AGXaR1u9xHAg3GxqPYZLv+pENqpv6ctBpM3VPP33Bg2hh3S+Po4+Ho8K7ATUyYni+GTu044r3sCE= Received: by 10.70.48.1 with SMTP id v1mr673800wxv.64.1204591202527; Mon, 03 Mar 2008 16:40:02 -0800 (PST) Received: by 10.70.116.11 with HTTP; Mon, 3 Mar 2008 16:40:02 -0800 (PST) Message-ID: <7e31215a0803031640l38579250k5bd5060317b1366b@mail.gmail.com> Date: Mon, 3 Mar 2008 21:40:02 -0300 From: "Rodrigo Renji" To: obm-l@mat.puc-rio.br Subject: =?ISO-8859-1?Q?Re:_[obm-l]_[obm-l]_Quest=E3o_de_indu=E7=E3o_matem=E1tica?= In-Reply-To: <3034149193991073565@unknownmsgid> MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline References: <3034149193991073565@unknownmsgid> Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m240dgsG031830 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Rodrigo Renji" X-Spam-Status: No, hits=3.9 required=5.0 tests=AWL,IN_REP_TO,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: *** oi, vou tentar te ajudar com esses problemas vou usar uma notação simplificada, a de somatorio, (temo que isso dificulte sua leitura =/) vou escrever o somatorio como soma [k=1, n] f(k) que é o mesmo que informalmente a soma [k=1, n] f(k)= f(1)+f(2)+....+f(n-1)+f(n) que definido por recorrencia por soma [k=1, n+1] f(k)=soma [k=1, n] f(k)= +f(n) com soma [k=1, 1] f(k)= f(1) e soma [k=1, n] f(k)= 0 se n<1, isto é, se o limite superior é menor que o inferior mas o que voce precisa saber realmente é que soma [k=1, n+1] f(k)=soma [k=1, n] f(k)= +f(n) com soma [k=1, 1] f(k)= f(1) soma [k=1, n] f(k)= f(1)+f(2)+....+f(n-1)+f(n) isto é, que esse simbolo soma [k=1, n] f(k)= equivale a toma a soma de f(k), com k variando de 1 até n f(1)+f(2)+....+f(n-1)+f(n) o que vai ser usado nas demonstrações vai ser isso soma [k=1, n+1] f(k)=soma [k=1, n] f(k)= +f(n). (eu considero mais formal e compacto usar a notação de somatorio) agora vamos pra primeira 2.1. 1^2+ 2^2+...+n^2 = [n(n+1)(2n+1)]/6, (n maior igual 1); com a notação de somatorio isso se escreve soma [k=1, n] k^2=[n(n+1)(2n+1)]/6 para n=1 temos soma [k=1, n] k^2= 1^2=1 e no outro lado temos [1(1+1)(2+1)]/6= 1(2)(3)/6=1, entao a base da indução esta provada agora vamos tomar por hipotese de que soma [k=1, n] k^2=[n(n+1)(2n+1)]/6 e provar para (n+1) soma [k=1, n+1] k^2=[(n+1)(n+2)(2n+3)]/6 mas primeiro vamos expandir [(n+1)(n+2)(2n+3)]/6, pois provavelmente nao vamos chegar na forma fatorada bunitinha como esta acima [(n+1)(n+2)(2n+3)]/6=1+13n/6 +3n^2 /2 +n^3/3 vamos expandir tb [n(n+1)(2n+1)]/6 [n(n+1)(2n+1)]/6= n/6 +n^2/2 +n^3/3 agora vamos pra demonstração soma [k=1, n+1] k^2=soma [k=1, n] k^2 + (n+1)^2 (pela definição de somatorio), mas pela hipotese temos soma [k=1, n] k^2 =[n(n+1)(2n+1)]/6 que expandido é = n/6 +n^2/2 +n^3/3 somando com (n+1)^2 = n^2 +2n+1, ficamos com n/6 +n^2/2 +n^3/3 + n^2 +2n+1=n^3/3+ 3n^2/2 +13n/6 +1= [(n+1)(n+2)(2n+3)]/6 =x, tenta fazer o resto se nao conseguir ou nao entender algo, tenta responder o/ 2.2. 1^3+ 2^3+...+n^3 = (1+2+...+n)^2, (n maior igual 1); 2.3. 1.2+2.3+...+n(n+1) = [n(n+1)(n+2)]/3, (n maior igual 1); Em 03/03/08, Rubens Kamimura escreveu: > Olá turma da LISTA!!! > > Alguém desta LISTA, se habilitariam em me elucidar tal questão? > > 1. Sabendo, por definição, que: a^0=1 e a^1=a, como poderemos provar por > indução matemática sobre n, que a^m.a^n = a^(m+n), para qualquer m,n > pertencente ao conjunto dos números naturais? > > 2. Como podemos provar por indução matemática: > 2.1. 1^2+ 2^2+...+n^2 = [n(n+1)(2n+1)]/6, (n maior igual 1); > 2.2. 1^3+ 2^3+...+n^3 = (1+2+...+n)^2, (n maior igual 1); > 2.3. 1.2+2.3+...+n(n+1) = [n(n+1)(n+2)]/3, (n maior igual 1); > > Abraços > > leigo e neófito... > > > ========================================================================= > Instruções para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > ========================================================================= > ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Mon Mar 3 23:22:00 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m242KKsG003417 for ; Mon, 3 Mar 2008 23:20:20 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m242KJZC003415 for obm-l-MllGbsmmN; Mon, 3 Mar 2008 23:20:19 -0300 Received: from smtp.bol.com.br (smtpout2.bol.com.br [200.221.4.213]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m242KIsG003412 for ; Mon, 3 Mar 2008 23:20:18 -0300 Received: from localhost (localhost [127.0.0.1]) by smart6.bol.com.br (Postfix) with ESMTP id 73E956E9 for ; Mon, 3 Mar 2008 23:20:40 -0300 (BRT) Received: from nxgen4 (189-18-161-242.dsl.telesp.net.br [189.18.161.242]) by smart6.bol.com.br (Postfix) with ESMTP id EC9856E3 for ; Mon, 3 Mar 2008 23:20:37 -0300 (BRT) Message-ID: <005a01c87c0b$f5e5ed30$6401a8c0@nxgen4> From: "Anderson Weber" To: References: Subject: [SPAM] Re: [obm-l] PONTO SELECIONADO Date: Sat, 1 Mar 2008 23:20:17 -0300 MIME-Version: 1.0 Content-Type: text/plain X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2900.2180 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.2180 X-SIG5: cf427aa8e032cbebc359bb5a96655506 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Anderson Weber" X-Spam-Status: Yes, hits=8.9 required=5.0 tests=BIG_FONT,DATE_IN_PAST_48_96,HTML_50_70,LINES_OF_YELLING, MAILTO_LINK,RCVD_IN_DSBL,RCVD_IN_OSIRUSOFT_COM,REFERENCES, SPAM_PHRASE_00_01,SUPERLONG_LINE,USER_AGENT_OE, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_NextPart_000_0057_01C87BF2.CFAA3680" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (8.90 hits, 5 required) SPAM: REFERENCES (-0.5 points) Has a valid-looking References header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: USER_AGENT_OE (0.2 points) X-Mailer header indicates a non-spam MUA (Outlook Express) SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: BIG_FONT (0.3 points) BODY: FONT Size +2 and up or 3 and up SPAM: HTML_50_70 (0.3 points) BODY: Message is 50-70% HTML tags SPAM: LINES_OF_YELLING (0.2 points) BODY: A WHOLE LINE OF YELLING DETECTED SPAM: MAILTO_LINK (0.2 points) BODY: Includes a URL link to send an email SPAM: SUPERLONG_LINE (0.0 points) BODY: Contains a line >=199 characters long SPAM: DATE_IN_PAST_48_96 (1.4 points) Date: is 48 to 96 hours before Received: date SPAM: RCVD_IN_DSBL (3.2 points) RBL: Received via a relay in list.dsbl.org SPAM: [RBL check: found 242.161.18.189.list.dsbl.org] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 242.161.18.189.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- This is a multi-part message in MIME format. ------=_NextPart_000_0057_01C87BF2.CFAA3680 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Ol=E1 Uma sugest=E3o =E9 tentar fazer considerando a =E1rea do tri=E2ngulo = como n(E) =3D n=FAmero de elementos do espa=E7o amostral, e usando como = n=FAmero de elementos do seu evento (o que lhe interessa) a ar=E9a total = do tri=E2ngulo menos a soma das =E1reas dos tr=EAs setores circulares, = com centro nos v=E9rtices e raio 1. Um abra=E7o Anderson ----- Original Message -----=20 From: arkon=20 To: obm-l=20 Sent: Saturday, March 01, 2008 8:07 AM Subject: [obm-l] PONTO SELECIONADO ALGU=C9M PODE RESOLVER ESSA, POR FAVOR =20 (AFA-93/94) Um ponto =E9 selecionado aleatoriamente dentro de um = tri=E2ngulo eq=FCil=E1tero de lado L =3D 3. A probabilidade de a = dist=E2ncia desse ponto a qualquer v=E9rtice ser maior do que 1 =E9: =20 a) 1 - (2pisqrt3/9). b) 1 - (pisqrt3/9). c) 1 - (2pisqrt3/27). = d) 1 - (pisqrt3/27).=20 =20 Considerar pisqrt3 =3D pi vezes a raiz quadrada de tr=EAs =20 GABARITO LETRA C =20 DESDE J=C1 AGRADE=C7O ------=_NextPart_000_0057_01C87BF2.CFAA3680 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable
Ol=E1
 
Uma sugest=E3o =E9 tentar fazer = considerando a =E1rea do=20 tri=E2ngulo como n(E) =3D n=FAmero de elementos do espa=E7o amostral, e = usando como=20 n=FAmero de elementos do seu evento (o que lhe interessa) a ar=E9a total = do=20 tri=E2ngulo menos  a soma das =E1reas dos tr=EAs setores = circulares, com centro=20 nos v=E9rtices e raio 1.
 
Um abra=E7o
 
Anderson
----- Original Message -----
From:=20 arkon =
To: obm-l
Sent: Saturday, March 01, 2008 = 8:07=20 AM
Subject: [obm-l] PONTO = SELECIONADO

ALGU=C9M PODE RESOLVER ESSA, = POR=20 FAVOR

 

(AFA-93/94) Um ponto =E9 = selecionado=20 aleatoriamente dentro de um tri=E2ngulo eq=FCil=E1tero de lado L =3D=20 3. = A=20 probabilidade de a dist=E2ncia desse ponto a qualquer v=E9rtice ser = maior do que 1=20 =E9:

 

a) 1 =96 = (2pisqrt3/9).   b) 1 =96 (pisqrt3/9).   c) 1 =96=20 (2pisqrt3/27).   d) 1 =96 (pisqrt3/27). =

 

Considerar pisqrt3 =3D pi = vezes a raiz=20 quadrada de tr=EAs

 

GABARITO LETRA=20 C

 

DESDE J=C1=20 = AGRADE=C7O

------=_NextPart_000_0057_01C87BF2.CFAA3680-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Tue Mar 4 08:33:49 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m24BVtsG008723 for ; Tue, 4 Mar 2008 08:31:55 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m24BVtBN008721 for obm-l-MllGbsmmN; Tue, 4 Mar 2008 08:31:55 -0300 Received: from rogue.cesp.com.br (rogue.cesp.com.br [201.63.4.194]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m24BVOsG008678; Tue, 4 Mar 2008 08:31:24 -0300 Received: from correio.cesp.com.br (nightcrawler.cesp.com.br [201.63.4.197]) by rogue.cesp.com.br (Postfix) with ESMTP id 82FA1441AA; Tue, 4 Mar 2008 08:31:44 -0300 (BRT) Received: from x454322e3f5ac4 (unknown [10.136.21.53]) by correio.cesp.com.br (Postfix) with ESMTP id 5858151407B; Tue, 4 Mar 2008 08:31:46 -0300 (BRT) From: To: , References: <3034149193991073565@unknownmsgid> <7e31215a0803031640l38579250k5bd5060317b1366b@mail.gmail.com> In-Reply-To: <7e31215a0803031640l38579250k5bd5060317b1366b@mail.gmail.com> Subject: [SPAM] [obm-l] =?UTF-8?Q?RES:_=5Bobm-l=5D_=5Bobm-l=5D_Quest=C3=A3o_de_?= =?UTF-8?Q?indu=C3=A7=C3=A3o_matem=C3=A1tica?= Date: Tue, 4 Mar 2008 08:31:46 -0300 Organization: CESP - OMPTD Message-ID: <002f01c87deb$5428dd90$fc7a98b0$@kamimura@cesp.com.br> MIME-Version: 1.0 Content-Type: text/plain; charset="UTF-8" X-Mailer: Microsoft Office Outlook 12.0 Thread-Index: Ach9kR/13iLjRvoJTxi3j2MsHq9uTQAWaodw Content-Language: pt-br Content-Transfer-Encoding: 7bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m24BVOsG008682 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: X-Spam-Status: Yes, hits=5.2 required=5.0 tests=AWL,INVALID_MSGID,IN_REP_TO,NOSPAM_INC,NO_REAL_NAME, QUOTED_EMAIL_TEXT,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, REFERENCES,SIGNATURE_LONG_SPARSE,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ***** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (5.20 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: REFERENCES (-0.5 points) Has a valid-looking References header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: NOSPAM_INC (-0.2 points) Where are you working at? SPAM: NO_REAL_NAME (1.3 points) From: does not include a real name SPAM: INVALID_MSGID (0.0 points) Message-Id is not valid, according to RFC 2822 SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: QUOTED_EMAIL_TEXT (-0.8 points) BODY: Contains what looks like a quoted email text SPAM: SIGNATURE_LONG_SPARSE (-0.3 points) Long signature present (empty lines) SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 197.4.63.201.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 197.4.63.201.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (0.7 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- Caro Rodrigo Renji e toda LISTA; 1. Bom dia; 2. Muito grato pela resposta; 3. Pelo fato já exposto anteriormente, sou iniciante na matéria, ... agora vou decifrar a tua explicação. Sds, Rubens Kamimura Assistente Técnico III - CREA/SP 5062246285 CESP - Companhia Energética de São Paulo OMPTD - Capacitação e Desenvolvimento Caixa Postal, 58 - CEP 15385-000 Ilha Solteira/SP - Brasil Tel. +55-18-3704-4240 ramal 136/137 Tel./Fax +55-18-3704-6800 www.cesp.com.br email: rubens.kamimura@cesp.com.br Mens In Corpore Tantun Molen Regit UNYK : 132 XOU ï Antes de imprimir pense em sua responsabilidade e compromisso com o MEIO AMBIENTE. -----Mensagem original----- De: owner-obm-l@mat.puc-rio.br [mailto:owner-obm-l@mat.puc-rio.br] Em nome de Rodrigo Renji Enviada em: segunda-feira, 3 de março de 2008 21:40 Para: obm-l@mat.puc-rio.br Assunto: Re: [obm-l] [obm-l] Questão de indução matemática oi, vou tentar te ajudar com esses problemas vou usar uma notação simplificada, a de somatorio, (temo que isso dificulte sua leitura =/) vou escrever o somatorio como soma [k=1, n] f(k) que é o mesmo que informalmente a soma [k=1, n] f(k)= f(1)+f(2)+....+f(n-1)+f(n) que definido por recorrencia por soma [k=1, n+1] f(k)=soma [k=1, n] f(k)= +f(n) com soma [k=1, 1] f(k)= f(1) e soma [k=1, n] f(k)= 0 se n<1, isto é, se o limite superior é menor que o inferior mas o que voce precisa saber realmente é que soma [k=1, n+1] f(k)=soma [k=1, n] f(k)= +f(n) com soma [k=1, 1] f(k)= f(1) soma [k=1, n] f(k)= f(1)+f(2)+....+f(n-1)+f(n) isto é, que esse simbolo soma [k=1, n] f(k)= equivale a toma a soma de f(k), com k variando de 1 até n f(1)+f(2)+....+f(n-1)+f(n) o que vai ser usado nas demonstrações vai ser isso soma [k=1, n+1] f(k)=soma [k=1, n] f(k)= +f(n). (eu considero mais formal e compacto usar a notação de somatorio) agora vamos pra primeira 2.1. 1^2+ 2^2+...+n^2 = [n(n+1)(2n+1)]/6, (n maior igual 1); com a notação de somatorio isso se escreve soma [k=1, n] k^2=[n(n+1)(2n+1)]/6 para n=1 temos soma [k=1, n] k^2= 1^2=1 e no outro lado temos [1(1+1)(2+1)]/6= 1(2)(3)/6=1, entao a base da indução esta provada agora vamos tomar por hipotese de que soma [k=1, n] k^2=[n(n+1)(2n+1)]/6 e provar para (n+1) soma [k=1, n+1] k^2=[(n+1)(n+2)(2n+3)]/6 mas primeiro vamos expandir [(n+1)(n+2)(2n+3)]/6, pois provavelmente nao vamos chegar na forma fatorada bunitinha como esta acima [(n+1)(n+2)(2n+3)]/6=1+13n/6 +3n^2 /2 +n^3/3 vamos expandir tb [n(n+1)(2n+1)]/6 [n(n+1)(2n+1)]/6= n/6 +n^2/2 +n^3/3 agora vamos pra demonstração soma [k=1, n+1] k^2=soma [k=1, n] k^2 + (n+1)^2 (pela definição de somatorio), mas pela hipotese temos soma [k=1, n] k^2 =[n(n+1)(2n+1)]/6 que expandido é = n/6 +n^2/2 +n^3/3 somando com (n+1)^2 = n^2 +2n+1, ficamos com n/6 +n^2/2 +n^3/3 + n^2 +2n+1=n^3/3+ 3n^2/2 +13n/6 +1= [(n+1)(n+2)(2n+3)]/6 =x, tenta fazer o resto se nao conseguir ou nao entender algo, tenta responder o/ 2.2. 1^3+ 2^3+...+n^3 = (1+2+...+n)^2, (n maior igual 1); 2.3. 1.2+2.3+...+n(n+1) = [n(n+1)(n+2)]/3, (n maior igual 1); Em 03/03/08, Rubens Kamimura escreveu: > Olá turma da LISTA!!! > > Alguém desta LISTA, se habilitariam em me elucidar tal questão? > > 1. Sabendo, por definição, que: a^0=1 e a^1=a, como poderemos provar por > indução matemática sobre n, que a^m.a^n = a^(m+n), para qualquer m,n > pertencente ao conjunto dos números naturais? > > 2. Como podemos provar por indução matemática: > 2.1. 1^2+ 2^2+...+n^2 = [n(n+1)(2n+1)]/6, (n maior igual 1); > 2.2. 1^3+ 2^3+...+n^3 = (1+2+...+n)^2, (n maior igual 1); > 2.3. 1.2+2.3+...+n(n+1) = [n(n+1)(n+2)]/3, (n maior igual 1); > > Abraços > > leigo e neófito... > > > ========================================================================= > Instruções para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > ========================================================================= > ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= -- Esta mensagem foi verificada pelo sistema de antivírus e acredita-se estar livre de perigo. ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Tue Mar 4 13:01:57 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m24FxcsG022795 for ; Tue, 4 Mar 2008 12:59:38 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m24Fxb5P022793 for obm-l-MllGbsmmN; Tue, 4 Mar 2008 12:59:37 -0300 Received: from relay2.bol.com.br (relay2.bol.com.br [200.221.4.106]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m24FxasG022786 for ; Tue, 4 Mar 2008 12:59:36 -0300 Received: from bol.com.br (whisper8.mail.sys.intranet [172.26.5.83]) by salsa2.bol.com.br (Postfix) with ESMTP id 868D9E006357 for ; Tue, 4 Mar 2008 12:59:59 -0300 (BRT) Date: Tue, 4 Mar 2008 12:59:59 -0300 Message-Id: Subject: [obm-l] ALTURA DO TETRAEDRO MIME-Version: 1.0 X-Sensitivity: 3 Content-Type: multipart/alternative; boundary="_=__=_XaM3_.1204646399.2A.489082.42.13644.52.42.007.653787707" From: "arkon" To: "obm-l" X-XaM3-API-Version: 4.3(R1) (B10) X-SenderIP: 200.140.133.73 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "arkon" X-Spam-Status: No, hits=4.1 required=5.0 tests=AWL,BIG_FONT,HTML_50_70,LINES_OF_YELLING, LINES_OF_YELLING_2,LINES_OF_YELLING_3,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01, TO_LOCALPART_EQ_REAL,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** --_=__=_XaM3_.1204646399.2A.489082.42.13644.52.42.007.653787707 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable ALGU=C9M PODE ME ENVIAR A SOLU=C7=C3O DESSA, POR FAVOR (IME-45/46) Um tetraedro, cujos lados da base medem 6, 10 e 8 metros, tem= arestas laterais com comprimento de 13 metros cada uma. Calcular a altur= a desse poliedro em rela=E7=E3o =E0 base considerada: DESDE J=C1 MUITO OBRIGADO --_=__=_XaM3_.1204646399.2A.489082.42.13644.52.42.007.653787707 Content-Type: text/html; charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable

<= B style=3D"mso-bidi-font-weight: normal">ALGU=C9M PODE ME ENVIAR A SOLU= =C7=C3O DESSA, POR FAVOR

<= B style=3D"mso-bidi-font-weight: normal"> 

<= B style=3D"mso-bidi-font-weight: normal">(IME-45/46) Um tetraedro, cujos lados da base medem 6, 10 e= 8 me= tros, tem arestas laterais com comprimento de 13 metros cada uma. Calcular a altura desse poliedro em rela=E7=E3o =E0 = base considerada:

<= B style=3D"mso-bidi-font-weight: normal"> <= /P>

<= B style=3D"mso-bidi-font-weight: normal">DESDE J=C1 MUITO OBRIGADO=

--_=__=_XaM3_.1204646399.2A.489082.42.13644.52.42.007.653787707-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Tue Mar 4 13:58:52 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m24GvjsG025449 for ; Tue, 4 Mar 2008 13:57:45 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m24GvjeJ025446 for obm-l-MllGbsmmN; Tue, 4 Mar 2008 13:57:45 -0300 Received: from ug-out-1314.google.com (ug-out-1314.google.com [66.249.92.171]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m24GvhsG025441 for ; Tue, 4 Mar 2008 13:57:43 -0300 Received: by ug-out-1314.google.com with SMTP id q7so2638879uge.0 for ; Tue, 04 Mar 2008 08:58:05 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; bh=ebj+4N0Q45H5J0A4S5si29s6a9jMcz1l5GAp1QPiSlU=; b=gn3gG0lcWV4vYnqp4PttCsggcmUS6okg0zQMvfaQsDhPnENM7aY5lSYCcNG4TH3j7xQQ4GDHHoDFlfvliADDgYmad7/9V+Tj+yLYIXo3h8zLrzGFes4Vg1qkRzQWGCC3Jf9WKwh6tdcE55Lax5PiytHtpyV1+m/9Pak1FOsvnWY= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; b=MCOIqFGTfHnAumgkeFiSInx1m1pJI8CBwpJiBXz4fnfpvtUtlVuyjvQkKHDahcJ2twfmpjfZIT1AAQU/mrgjXauSf7oB6kzWm3yKXhua0o6Xim9/IlTtCoeF22cemhScKw3MP3MD700d4SXsQ5Sm5Xge4jsLSHt6UQ04YvNtFhA= Received: by 10.78.203.15 with SMTP id a15mr3563617hug.57.1204649884281; Tue, 04 Mar 2008 08:58:04 -0800 (PST) Received: by 10.78.179.18 with HTTP; Tue, 4 Mar 2008 08:58:04 -0800 (PST) Message-ID: Date: Tue, 4 Mar 2008 13:58:04 -0300 From: "Marcos Martinelli" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] ALTURA DO TETRAEDRO In-Reply-To: MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline References: Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m24GvisG025444 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Marcos Martinelli" X-Spam-Status: No, hits=4.5 required=5.0 tests=IN_REP_TO,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,REFERENCES, SPAM_PHRASE_00_01,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** A projeção do vértice deve coincidir com o circuncentro do triângulo da base. Devemos calcular o raio desse círculo. S = a * b * c / ( 4 * R ) -> 6 * 8 / 2 = 6 * 8 * 10 / ( 4 * R ) -> R = 5. Portanto, a altura é um cateto de um triângulo retângulo de hipotenusa 13 e outro cateto 5. Logo, a altura vale 12. ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Tue Mar 4 14:31:34 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m24HTTsG027697 for ; Tue, 4 Mar 2008 14:29:29 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m24HTPgo027688 for obm-l-MllGbsmmN; Tue, 4 Mar 2008 14:29:25 -0300 Received: from el-out-1112.google.com (el-out-1112.google.com [209.85.162.178]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m24HSmsG027656 for ; Tue, 4 Mar 2008 14:28:51 -0300 Received: by el-out-1112.google.com with SMTP id o28so1247542ele.3 for ; Tue, 04 Mar 2008 09:29:10 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=0a5fMDSu5L6rMWg0GsqwtlPDA5UdBhCUD1OEk70M8ws=; b=upeWrqNrx2/gH25qNkuRC94Jil6J8+GaULiB0lyKQxtBum0igczrc6GHoUGrc4/2d8FeCldL0772ZFX0QDzNOErXIog3iBnFmnM2XUU/s6emAEy1HfiAiuznbCwfhyshbZ/J9ng09olrFH+nEuI1f+dOKbjyS2Xlx4iL3RPkRgs= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=wyySgDbRE4ZzYws9F+uGy4CPOMtssi54a9Rckgte3eXFLykTy48TJ89cZmCyphZdCc0aOpDpNBE50guV8lgU9wM5MgS13iM3paffOvvO3lvdkwSxYBggd62v/CcBi1fXo33cxtA6n+lAecbhyqQ/ywyvc6NO5O7yI5TyP7xSbL8= Received: by 10.114.135.1 with SMTP id i1mr2522187wad.88.1204651747912; Tue, 04 Mar 2008 09:29:07 -0800 (PST) Received: by 10.114.136.9 with HTTP; Tue, 4 Mar 2008 09:29:07 -0800 (PST) Message-ID: <3bd00efc0803040929k5d9f7b84y13bdad30b8bf0db0@mail.gmail.com> Date: Tue, 4 Mar 2008 14:29:07 -0300 From: "Marcelo Salhab Brogliato" To: obm-l@mat.puc-rio.br Subject: =?ISO-8859-1?Q?Re:_[obm-l]_[obm-l]_Quest=E3o_de_indu=E7=E3o_matem=E1tica?= In-Reply-To: <3034149193991073565@unknownmsgid> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_32636_5428282.1204651747897" References: <3034149193991073565@unknownmsgid> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Marcelo Salhab Brogliato" X-Spam-Status: No, hits=4.0 required=5.0 tests=AWL,IN_REP_TO,MAILTO_LINK,MIME_EXCESSIVE_QP, QUOTED_EMAIL_TEXT,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, REFERENCES,SPAM_PHRASE_00_01,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** ------=_Part_32636_5428282.1204651747897 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Ol=E1 Rubens, Essas demonstra=E7=F5es seguem todas a mesma id=E9ia... vou fazer apenas o 2.1 veja que para n=3D1 =E9 v=E1lido vamos supor valido para K e vamos mostrar que vale para K+1. isto =E9: Hip=F3tese: 1^2 + 2^2 + ... + k^2 =3D [k(k+1)(2k+1)]/6 Tese: 1^2 + 2^2 + ... + k^2 + (k+1)^2 =3D (k+1)(k+2)(2k+3)/6 Demo: Sabemos que: 1^2 + 2^2 + .. + k^2 =3D k(k+1)(2k+1)/6 somando (k+1)^2 em ambos os lados, temos: 1^2 + 2^2 + ... + k^2 + (k+1)^2 =3D k(k+1)(2k+1)/6 + (k+1)^2 vamos apenas fatorar o lado direito, e mostrar que ele =E9 igual a (k+1)(k+2)(2k+3)/6 =3D (k+1)(2k^2 + 7k + 6)/6 k(k+1)(2k+1)/6 + (k+1)^2 =3D (k+1)[ k(2k+1)/6 + (k+1) ] =3D (k+1)[ 2k^2 + k= + 6k + 6 ]/6 =3D (k+1)(2k^2 + 7k + 6)/6 logo, est=E1 provado por indu=E7=E3o. abra=E7os, Salhab 2008/3/3 Rubens Kamimura : > Ol=E1 turma da LISTA!!! > > Algu=E9m desta LISTA, se habilitariam em me elucidar tal quest=E3o? > > 1. Sabendo, por defini=E7=E3o, que: a^0=3D1 e a^1=3Da, como poderemos pro= var por > indu=E7=E3o matem=E1tica sobre n, que a^m.a^n =3D a^(m+n), para qualquer = m,n > pertencente ao conjunto dos n=FAmeros naturais? > > 2. Como podemos provar por indu=E7=E3o matem=E1tica: > 2.1. 1^2+ 2^2+...+n^2 =3D [n(n+1)(2n+1)]/6, (n maior igual 1); > 2.2. 1^3+ 2^3+...+n^3 =3D (1+2+...+n)^2, (n maior igual 1); > 2.3. 1.2+2.3+...+n(n+1) =3D [n(n+1)(n+2)]/3, (n maior igual 1); > > Abra=E7os > > leigo e ne=F3fito... > > > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > Instru=E7=F5es para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > ------=_Part_32636_5428282.1204651747897 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Ol=E1 Rubens,

Essas demonstra=E7=F5es seguem todas a mesma id=E9ia..= .
vou fazer apenas o 2.1
veja que para n=3D1 =E9 v=E1lido

vamo= s supor valido para K e vamos mostrar que vale para K+1.
isto =E9:
Hi= p=F3tese: 1^2 + 2^2 + ... + k^2 =3D [k(k+1)(2k+1)]/6
Tese: 1^2 + 2^2 + ... + k^2 + (k+1)^2 =3D (k+1)(k+2)(2k+3)/6

Demo:Sabemos que: 1^2 + 2^2 + .. + k^2 =3D k(k+1)(2k+1)/6
somando (k+1)^2 e= m ambos os lados, temos:
1^2 + 2^2 + ... + k^2 + (k+1)^2 =3D k(k+1)(2k+1= )/6 + (k+1)^2

vamos apenas fatorar o lado direito, e mostrar que ele =E9 igual a (k+1= )(k+2)(2k+3)/6 =3D (k+1)(2k^2 + 7k + 6)/6
k(k+1)(2k+1)/6 + (k+1)^2 =3D (= k+1)[ k(2k+1)/6 + (k+1) ] =3D (k+1)[ 2k^2 + k + 6k + 6 ]/6 =3D (k+1)(2k^2 += 7k + 6)/6

logo, est=E1 provado por indu=E7=E3o.

abra=E7os,
Salhab


2008/3/3 Rubens Kamimura <rubens.kamimura@cesp.com.br>= :
Ol=E1 turma da LISTA!!!

Algu=E9m desta LISTA, se habilitariam em me elucidar tal quest=E3o?

1. Sabendo, por defini=E7=E3o, que: a^0=3D1 e a^1=3Da, como poderemos prova= r por
indu=E7=E3o matem=E1tica sobre n, que a^m.a^n =3D a^(m+n), para qualquer m,= n
pertencente ao conjunto dos n=FAmeros naturais?

2. Como podemos provar por indu=E7=E3o matem=E1tica:
2.1. 1^2+ 2^2+...+n^2 =3D [n(n+1)(2n+1)]/6, (n maior igual 1);
2.2. 1^3+ 2^3+...+n^3 =3D (1+2+...+n)^2, (n maior igual 1);
2.3. 1.2+2.3+...+n(n+1) =3D [n(n+1)(n+2)]/3, (n maior igual 1);

Abra=E7os

leigo e ne=F3fito...


=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D
Instru=E7=F5es para entrar na lista, sair da lista e usar a lista em
http://www.mat.puc-rio.br/~obmlistas/obm-l.html
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D

------=_Part_32636_5428282.1204651747897-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Tue Mar 4 15:36:11 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m24IXnsG031011 for ; Tue, 4 Mar 2008 15:33:49 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m24IXnnU031009 for obm-l-MllGbsmmN; Tue, 4 Mar 2008 15:33:49 -0300 Received: from rogue.cesp.com.br (rogue.cesp.com.br [201.63.4.194]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m24IXisG030994 for ; Tue, 4 Mar 2008 15:33:45 -0300 Received: from correio.cesp.com.br (nightcrawler.cesp.com.br [201.63.4.197]) by rogue.cesp.com.br (Postfix) with ESMTP id 1D65F4420E; Tue, 4 Mar 2008 15:33:48 -0300 (BRT) Received: from x454322e3f5ac4 (unknown [10.136.21.53]) by correio.cesp.com.br (Postfix) with ESMTP id C2DB7514087; Tue, 4 Mar 2008 15:33:48 -0300 (BRT) From: "Rubens Kamimura" To: Cc: "'Evandro'" References: <3034149193991073565@unknownmsgid> <3bd00efc0803040929k5d9f7b84y13bdad30b8bf0db0@mail.gmail.com> In-Reply-To: <3bd00efc0803040929k5d9f7b84y13bdad30b8bf0db0@mail.gmail.com> Subject: [SPAM] [obm-l] =?iso-8859-1?Q?RES:_=5Bobm-l=5D_=5Bobm-l=5D_Quest=E3o_de_indu=E7=E3o_mate?= =?iso-8859-1?Q?m=E1tica?= Date: Tue, 4 Mar 2008 15:33:48 -0300 Organization: CESP - OMPTD Message-ID: <001e01c87e26$49b42960$dd1c7c20$@kamimura@cesp.com.br> MIME-Version: 1.0 Content-Type: text/plain X-Mailer: Microsoft Office Outlook 12.0 thread-index: Ach+HuvJkO1QlN1MTROS3z5htVhrQgABzKAg Content-Language: pt-br Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Rubens Kamimura" X-Spam-Status: Yes, hits=5.3 required=5.0 tests=AWL,HTML_50_70,INVALID_MSGID,IN_REP_TO,MAILTO_LINK, NOSPAM_INC,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,REFERENCES, SPAM_PHRASE_00_01,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ***** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_NextPart_000_001F_01C87E0D.2466F160" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. 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SPAM: INVALID_MSGID (0.0 points) Message-Id is not valid, according to RFC 2822 SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: HTML_50_70 (0.3 points) BODY: Message is 50-70% HTML tags SPAM: MAILTO_LINK (0.2 points) BODY: Includes a URL link to send an email SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 197.4.63.201.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 197.4.63.201.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (0.5 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- Esta é uma mensagem em várias partes no formato MIME. ------=_NextPart_000_001F_01C87E0D.2466F160 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Ol=E1 Marcelo Salhab, =20 Muito grato. =20 Sds =20 Rubens Kamimura=20 Assistente T=E9cnico III - CREA/SP 5062246285 CESP - Companhia Energ=E9tica de S=E3o Paulo OMPTD - Capacita=E7=E3o e Desenvolvimento Caixa Postal, 58 - CEP 15385-000 Ilha Solteira/SP - Brasil Tel. +55-18-3704-4240 ramal 136/137 Tel./Fax +55-18-3704-6800 www.cesp.com.br email: rubens.kamimura@cesp.com.br=20 Mens In Corpore Tantun Molen Regit UNYK : 132 XOU P Antes de imprimir pense em sua responsabilidade e compromisso com o = MEIO AMBIENTE. =20 =20 =20 De: owner-obm-l@mat.puc-rio.br [mailto:owner-obm-l@mat.puc-rio.br] Em = nome de Marcelo Salhab Brogliato Enviada em: ter=E7a-feira, 4 de mar=E7o de 2008 14:29 Para: obm-l@mat.puc-rio.br Assunto: Re: [obm-l] [obm-l] Quest=E3o de indu=E7=E3o matem=E1tica =20 Ol=E1 Rubens, Essas demonstra=E7=F5es seguem todas a mesma id=E9ia... vou fazer apenas o 2.1 veja que para n=3D1 =E9 v=E1lido vamos supor valido para K e vamos mostrar que vale para K+1. isto =E9: Hip=F3tese: 1^2 + 2^2 + ... + k^2 =3D [k(k+1)(2k+1)]/6 Tese: 1^2 + 2^2 + ... + k^2 + (k+1)^2 =3D (k+1)(k+2)(2k+3)/6 Demo: Sabemos que: 1^2 + 2^2 + .. + k^2 =3D k(k+1)(2k+1)/6 somando (k+1)^2 em ambos os lados, temos: 1^2 + 2^2 + ... + k^2 + (k+1)^2 =3D k(k+1)(2k+1)/6 + (k+1)^2 vamos apenas fatorar o lado direito, e mostrar que ele =E9 igual a (k+1)(k+2)(2k+3)/6 =3D (k+1)(2k^2 + 7k + 6)/6 k(k+1)(2k+1)/6 + (k+1)^2 =3D (k+1)[ k(2k+1)/6 + (k+1) ] =3D (k+1)[ 2k^2 = + k + 6k + 6 ]/6 =3D (k+1)(2k^2 + 7k + 6)/6 logo, est=E1 provado por indu=E7=E3o. abra=E7os, Salhab 2008/3/3 Rubens Kamimura : Ol=E1 turma da LISTA!!! Algu=E9m desta LISTA, se habilitariam em me elucidar tal quest=E3o? 1. Sabendo, por defini=E7=E3o, que: a^0=3D1 e a^1=3Da, como poderemos = provar por indu=E7=E3o matem=E1tica sobre n, que a^m.a^n =3D a^(m+n), para qualquer = m,n pertencente ao conjunto dos n=FAmeros naturais? 2. Como podemos provar por indu=E7=E3o matem=E1tica: 2.1. 1^2+ 2^2+...+n^2 =3D [n(n+1)(2n+1)]/6, (n maior igual 1); 2.2. 1^3+ 2^3+...+n^3 =3D (1+2+...+n)^2, (n maior igual 1); 2.3. 1.2+2.3+...+n(n+1) =3D [n(n+1)(n+2)]/3, (n maior igual 1); Abra=E7os leigo e ne=F3fito... =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D Instru=E7=F5es para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html =20 =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D --=20 Esta mensagem foi verificada pelo sistema de antiv=EDrus e=20 acredita-se estar livre de perigo.=20 ------=_NextPart_000_001F_01C87E0D.2466F160 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable

Ol=E1 Marcelo Salhab,

 

Muito grato.

 

Sds

 

Rubens Kamimura

Assistente T=E9cnico III - CREA/SP = 5062246285

CESP - Companhia Energ=E9tica de S=E3o = Paulo

OMPTD - Capacita=E7=E3o e = Desenvolvimento

Caixa Postal, 58 - CEP 15385-000

Ilha Solteira/SP - Brasil

Tel. +55-18-3704-4240 ramal 136/137

Tel./Fax +55-18-3704-6800

www.cesp.com.br

=

email: rubens.kamimura@cesp.com.br

Mens In Corpore Tantun Molen = Regit

UNYK : 132 XOU

P Antes de imprimir pense em sua responsabilidade e = compromisso com o MEIO AMBIENTE.

 

 

 

De: owner-obm-l@mat.puc-rio.br [mailto:owner-obm-l@mat.puc-rio.br] Em = nome de Marcelo Salhab Brogliato
Enviada em: ter=E7a-feira, 4 de mar=E7o de 2008 14:29
Para: obm-l@mat.puc-rio.br
Assunto: Re: [obm-l] [obm-l] Quest=E3o de indu=E7=E3o = matem=E1tica

 

Ol=E1 Rubens,

Essas demonstra=E7=F5es seguem todas a mesma id=E9ia...
vou fazer apenas o 2.1
veja que para n=3D1 =E9 v=E1lido

vamos supor valido para K e vamos mostrar que vale para K+1.
isto =E9:
Hip=F3tese: 1^2 + 2^2 + ... + k^2 =3D [k(k+1)(2k+1)]/6
Tese: 1^2 + 2^2 + ... + k^2 + (k+1)^2 =3D (k+1)(k+2)(2k+3)/6

Demo:
Sabemos que: 1^2 + 2^2 + .. + k^2 =3D k(k+1)(2k+1)/6
somando (k+1)^2 em ambos os lados, temos:
1^2 + 2^2 + ... + k^2 + (k+1)^2 =3D k(k+1)(2k+1)/6 + (k+1)^2

vamos apenas fatorar o lado direito, e mostrar que ele =E9 igual a (k+1)(k+2)(2k+3)/6 =3D (k+1)(2k^2 + 7k + 6)/6
k(k+1)(2k+1)/6 + (k+1)^2 =3D (k+1)[ k(2k+1)/6 + (k+1) ] =3D (k+1)[ 2k^2 = + k + 6k + 6 ]/6 =3D (k+1)(2k^2 + 7k + 6)/6

logo, est=E1 provado por indu=E7=E3o.

abra=E7os,
Salhab


2008/3/3 Rubens Kamimura <rubens.kamimura@cesp.com.br>:

Ol=E1 turma da LISTA!!!

Algu=E9m desta LISTA, se habilitariam em me elucidar tal quest=E3o?

1. Sabendo, por defini=E7=E3o, que: a^0=3D1 e a^1=3Da, como poderemos = provar por
indu=E7=E3o matem=E1tica sobre n, que a^m.a^n =3D a^(m+n), para qualquer = m,n
pertencente ao conjunto dos n=FAmeros naturais?

2. Como podemos provar por indu=E7=E3o matem=E1tica:
2.1. 1^2+ 2^2+...+n^2 =3D [n(n+1)(2n+1)]/6, (n maior igual 1);
2.2. 1^3+ 2^3+...+n^3 =3D (1+2+...+n)^2, (n maior igual 1);
2.3. 1.2+2.3+...+n(n+1) =3D [n(n+1)(n+2)]/3, (n maior igual 1);

Abra=E7os

leigo e ne=F3fito...


=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D
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--
Esta mensagem foi verificada pelo sistema de antiv=EDrus e
acredita-se estar livre de perigo.

------=_NextPart_000_001F_01C87E0D.2466F160-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Tue Mar 4 18:06:27 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m24L2usG008064 for ; Tue, 4 Mar 2008 18:02:56 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m24L2u5i008061 for obm-l-MllGbsmmN; Tue, 4 Mar 2008 18:02:56 -0300 Received: from rv-out-0910.google.com (rv-out-0910.google.com [209.85.198.184]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m24L2nsG008029 for ; Tue, 4 Mar 2008 18:02:51 -0300 Received: by rv-out-0910.google.com with SMTP id c27so775023rvf.9 for ; Tue, 04 Mar 2008 13:03:11 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; bh=StdJl9K8H7TWc3dcdiZKcsbosGTpyspQwEkwuBozSPY=; b=luwRw7Bli3DyDvUkezgKblSytSRt49UzIyALgnIDMbj2zh5uMyejDr3s7c/sJBt1dsx/hNeJDuv5TjwEewAj9L9aWTXgSXaaTOoDVEUz83ry2kGvQzmcKA5O0QBCRbP4sFlGwNEnZgRNP4173K+CC8auy3AiNX/Cfs/SdXdBT08= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; b=uf7ui/WewvH9y1lHFaCQ4/uWUlrQ5BILTeiVyfz47Iz25KrL+zyhwbHQepPqeFJRO2p+s26EeqnJKtVQJL0jf8eSUJ6R7QO4jzG8QuArvfmJOzUSDQGmo3Eh1BBus0LAO6g3n6h6WCiMP/n5eNidNsLXdqqIHJeDkrb3GTxW8M8= Received: by 10.141.68.12 with SMTP id v12mr978669rvk.111.1204664591765; Tue, 04 Mar 2008 13:03:11 -0800 (PST) Received: by 10.70.116.11 with HTTP; Tue, 4 Mar 2008 13:03:10 -0800 (PST) Message-ID: <7e31215a0803041303y66dd7c5cr38282e78d6358c3c@mail.gmail.com> Date: Tue, 4 Mar 2008 18:03:10 -0300 From: "Rodrigo Renji" To: obm-l@mat.puc-rio.br Subject: =?ISO-8859-1?Q?Re:_[obm-l]_RES:_[obm-l]_[obm-l?= =?ISO-8859-1?Q?]_Quest=E3o_de_indu=E7=E3o_matem=E1tica?= In-Reply-To: <-1248285056949373452@unknownmsgid> MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline References: <3034149193991073565@unknownmsgid> <3bd00efc0803040929k5d9f7b84y13bdad30b8bf0db0@mail.gmail.com> <-1248285056949373452@unknownmsgid> Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m24L2rsG008038 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Rodrigo Renji" X-Spam-Status: No, hits=3.9 required=5.0 tests=AWL,IN_REP_TO,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: *** bem saiu um simbolo errado no texto que eu escrevi ao inves de soma [k=1, n+1] f(k)=soma [k=1, n] f(k)= +f(n) com soma [k=1, 1] f(k)= f(1) é soma [k=1, n+1] f(k)=soma [k=1, n] f(k) +f(n) com soma [k=1, 1] f(k)= f(1) apareceu um "=" a mais na primeira que não era pra ter eu costumo usar sempre essa definição acima, para demonstrar problemas de somatórios acho a notação de pontinhos (a1+...+an) informal, tento não usar apesar de dar uma "visão" as vezes do que esta acontecendo com o somatorio, mas acho que se pode desenvolver as técnicas de somatorio o suficiente para nao precisar abrir em pontinhos =P (abrindo as vezes, o primeiro, ou ultimo termo apenas nas demonstrações) se precisar de mais alguma ajuda só postar abraços o/ Em 04/03/08, Rubens Kamimura escreveu: > > > > > Olá Marcelo Salhab, > > > > Muito grato. > > > > Sds > > > > Rubens Kamimura > > Assistente Técnico III - CREA/SP 5062246285 > > CESP - Companhia Energética de São Paulo > > OMPTD - Capacitação e Desenvolvimento > > Caixa Postal, 58 - CEP 15385-000 > > Ilha Solteira/SP - Brasil > > Tel. +55-18-3704-4240 ramal 136/137 > > Tel./Fax +55-18-3704-6800 > > www.cesp.com.br > > email: rubens.kamimura@cesp.com.br > > Mens In Corpore Tantun Molen Regit > > UNYK : 132 XOU > > P Antes de imprimir pense em sua responsabilidade e compromisso com o MEIO > AMBIENTE. > > > > > > > > > De: owner-obm-l@mat.puc-rio.br [mailto:owner-obm-l@mat.puc-rio.br] Em nome > de Marcelo Salhab Brogliato > Enviada em: terça-feira, 4 de março de 2008 14:29 > Para: obm-l@mat.puc-rio.br > Assunto: Re: [obm-l] [obm-l] Questão de indução matemática > > > > > Olá Rubens, > > Essas demonstrações seguem todas a mesma idéia... > vou fazer apenas o 2.1 > veja que para n=1 é válido > > vamos supor valido para K e vamos mostrar que vale para K+1. > isto é: > Hipótese: 1^2 + 2^2 + ... + k^2 = [k(k+1)(2k+1)]/6 > Tese: 1^2 + 2^2 + ... + k^2 + (k+1)^2 = (k+1)(k+2)(2k+3)/6 > > Demo: > Sabemos que: 1^2 + 2^2 + .. + k^2 = k(k+1)(2k+1)/6 > somando (k+1)^2 em ambos os lados, temos: > 1^2 + 2^2 + ... + k^2 + (k+1)^2 = k(k+1)(2k+1)/6 + (k+1)^2 > > vamos apenas fatorar o lado direito, e mostrar que ele é igual a > (k+1)(k+2)(2k+3)/6 = (k+1)(2k^2 + 7k + 6)/6 > k(k+1)(2k+1)/6 + (k+1)^2 = (k+1)[ k(2k+1)/6 + (k+1) ] = (k+1)[ 2k^2 + k + > 6k + 6 ]/6 = (k+1)(2k^2 + 7k + 6)/6 > > logo, está provado por indução. > > abraços, > Salhab > > > > > > 2008/3/3 Rubens Kamimura : > > Olá turma da LISTA!!! > > Alguém desta LISTA, se habilitariam em me elucidar tal questão? > > 1. Sabendo, por definição, que: a^0=1 e a^1=a, como poderemos provar por > indução matemática sobre n, que a^m.a^n = a^(m+n), para qualquer m,n > pertencente ao conjunto dos números naturais? > > 2. Como podemos provar por indução matemática: > 2.1. 1^2+ 2^2+...+n^2 = [n(n+1)(2n+1)]/6, (n maior igual 1); > 2.2. 1^3+ 2^3+...+n^3 = (1+2+...+n)^2, (n maior igual 1); > 2.3. 1.2+2.3+...+n(n+1) = [n(n+1)(n+2)]/3, (n maior igual 1); > > Abraços > > leigo e neófito... > > > ========================================================================= > Instruções para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > ========================================================================= > > > > -- > Esta mensagem foi verificada pelo sistema de antivírus e > acredita-se estar livre de perigo. ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Mar 5 00:12:26 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m251A2t0019521 for ; Tue, 4 Mar 2008 22:11:02 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m24FBJhm020685 for obm-l-MllGbsmmN; Tue, 4 Mar 2008 12:11:19 -0300 Received: from fg-out-1718.google.com (fg-out-1718.google.com [72.14.220.156]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m24FAdsG020553 for ; Tue, 4 Mar 2008 12:10:45 -0300 Received: by fg-out-1718.google.com with SMTP id e12so2071205fga.3 for ; Tue, 04 Mar 2008 07:11:00 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=Mui/xfB5q9Csklk+jmvdcwHMuQyO1D/zTvpwlveDUMM=; b=JxV6M8GH9Xnp5H/528X16ROV3nb1Obhcjxutt7+F2jVaFPHzQ0ZhhzXsCjWS3WoREbXZJtkgqHxt1vlIPwuF5T7B7oQ+V1cEBDu1eDT0eScQEtq4CK7xf3GEYTLpcWyrJJshr9AKbbMQ62JvIbxkJgQg9ZO+njOtvw24bQO9uO8= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=gCKPvQT1T7LTijxqNfAL0sKtmoJHR6fIiI0+FcmnBQQtB3V9rQ43VE1W7aa+coaujRd/WRncezkWCzuR/rnwBgXsL19nZcB1mQ9JNi8hSJS9Y+Hh17uF3nk2rdvpbYO8tcldoZU9XPoYn8ihBk8LaF4+vqNxqC+aZcMTI6eAQY4= Received: by 10.86.86.12 with SMTP id j12mr1380506fgb.33.1204643460740; Tue, 04 Mar 2008 07:11:00 -0800 (PST) Received: by 10.86.54.14 with HTTP; Tue, 4 Mar 2008 07:11:00 -0800 (PST) Message-ID: Date: Tue, 4 Mar 2008 12:11:00 -0300 From: "saulo nilson" To: obm-l@mat.puc-rio.br Subject: =?ISO-8859-1?Q?Re:_[obm-l]_Polin=F4mio_-_Iezzi_-_(E.E._Lins-66)?= In-Reply-To: <70bb75a50803010612x2b3575actc2309b0322d3312c@mail.gmail.com> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_1015_10852123.1204643460751" References: <70bb75a50803010612x2b3575actc2309b0322d3312c@mail.gmail.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "saulo nilson" X-Spam-Status: No, hits=-0.2 required=5.0 tests=AWL,HTML_FONT_COLOR_GRAY,HTML_FONT_COLOR_UNSAFE,IN_REP_TO, MAILTO_LINK,MIME_EXCESSIVE_QP,QUOTED_EMAIL_TEXT,REFERENCES, SPAM_PHRASE_00_01,X_MAILING_LIST version=2.44 X-Spam-Level: ------=_Part_1015_10852123.1204643460751 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline (2x^2+ax+(p+1))^^2=3D 4x^4+a^2x^2+(p+1)^2+2(2ax^3+2(p+1)x^2+a(p+1)x)=3D =3D4x^4+4ax^3+x^2(a^2+4(p+1))+2a(p+1)x+(p+1)^2 a=3D-2 4+4(p+1)=3D8 p+1=3D1 p=3D0 2008/3/1 Emanuel Valente : > Ol=E1 senhores, estou tendo trabalho pra resolver essa quest=E3o. > Encontrei valores p=3D1 e p=3D-1, mas nunca o resultado do gabarito que = =E9 > p=3D0. > > Calcular p para que o polin=F4mio > > 4x^4 - 8x^3 + 8x^2 - 4(p+1)x + (p+1)^2 > > seja o quadrado perfeito de um polin=F4mio racional inteiro em x. > > Abra=E7os e um bom final de semana a todos! > > -- > Emanuel Valente > > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > Instru=E7=F5es para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > ------=_Part_1015_10852123.1204643460751 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline
(2x^2+ax+(p+1))^^2=3D
4x^4+a^2x^2+(p+1)^2+2(2ax^3+2(p+1)x^2+a(p+1)x)=3D
=3D4x^4+4ax^3+x^2(a^2+4(p+1))+2a(p+1)x+(p+1)^2
a=3D-2
4+4(p+1)=3D8
p+1=3D1
p=3D0

2008/3/1 Emanuel Valente <emanuelvalente@gmail.com>:
Ol=E1 senhores, estou tendo trab= alho pra resolver essa quest=E3o.
Encontrei valores p=3D1 e p=3D-1, mas = nunca o resultado do gabarito que =E9
p=3D0.

Calcular p para que o polin=F4mio

4x^4 - 8x^3 + 8x^2 -= 4(p+1)x + (p+1)^2

seja o quadrado perfeito de um polin=F4mio racion= al inteiro em x.

Abra=E7os e um bom final de semana a todos!

--
Emanuel Valente

=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D
Instru=E7=F5es para entrar na lista, sair da li= sta e usar a lista em
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------=_Part_1015_10852123.1204643460751-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Mar 5 12:22:18 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m25FJPsG018353 for ; Wed, 5 Mar 2008 12:19:25 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m25FJPc1018351 for obm-l-MllGbsmmN; Wed, 5 Mar 2008 12:19:25 -0300 Received: from web63115.mail.re1.yahoo.com (web63115.mail.re1.yahoo.com [69.147.97.10]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id m25FJNsG018330 for ; Wed, 5 Mar 2008 12:19:24 -0300 Received: (qmail 36536 invoked by uid 60001); 5 Mar 2008 15:19:42 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:Date:From:Subject:To:MIME-Version:Content-Type:Content-Transfer-Encoding:Message-ID; b=uQ97wVBKvv23weyusxxj8WDoSFTPoqCN14pcy5S7P2HxVWJTJ0eMfj0pzwFo0Y+t0o5TjQ5tAgpGvuczzHZo0tVHYXPDTvhoQ/h7MAZwJe2zCGAP/7gIwTU1F60dhma453gX/WtA0MLRj9U5zNB3xA+TZFshLcrli+Rt8cX59g8=; X-YMail-OSG: Se5IodIVM1ke05jiHCbIGispjf_y5P__Q6_pKuxmJDj788vKAkjO4TkkvQIPxey.rKK5lsuEwZ8MO7kO9Cq5oHwoCLZuuovo_EM- Received: from [143.107.205.8] by web63115.mail.re1.yahoo.com via HTTP; Wed, 05 Mar 2008 12:19:42 ART Date: Wed, 5 Mar 2008 12:19:42 -0300 (ART) From: Adriano Dutra Teixeira Subject: [SPAM] [obm-l] =?iso-8859-1?q?Quest=E3o=20de=20Probabilidade?= To: obm-l@mat.puc-rio.br MIME-Version: 1.0 Content-Type: text/plain Content-Transfer-Encoding: 7bit Message-ID: <402124.36529.qm@web63115.mail.re1.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Adriano Dutra Teixeira X-Spam-Status: Yes, hits=7.6 required=5.0 tests=FORGED_YAHOO_RCVD,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, SPAM_PHRASE_00_01,SPAM_REDIRECTOR,SUPERLONG_LINE, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******* X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="0-1081819514-1204730382=:36529" X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (7.60 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: SUPERLONG_LINE (0.0 points) BODY: Contains a line >=199 characters long SPAM: SPAM_REDIRECTOR (0.4 points) URI: Uses open redirection service SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 10.97.147.69.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 10.97.147.69.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- --0-1081819514-1204730382=:36529 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 8bit Olá pessoal, Um probleminha de Probabilidade: Considere uma urna com 5 bolas: uma azul, uma verde, uma amarela, uma vermelha e uma branca. Sabe-se que há reposição das bolas e a ordem que sai as cores não importa, o que importa é quantas bolas saem de cada cor. De quantas maneiras podemos selecionar 12(doze) bolas? Desde já, muito obrigado. Adriano. --------------------------------- Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-1081819514-1204730382=:36529 Content-Type: text/html; charset=iso-8859-1 Content-Transfer-Encoding: 8bit
Olá pessoal,
 
Um probleminha de Probabilidade:
Considere uma urna com 5 bolas: uma azul, uma verde, uma amarela, uma vermelha e uma branca. Sabe-se que há reposição das bolas e a ordem que sai as cores não importa, o que importa é quantas bolas saem de cada cor. De quantas maneiras podemos selecionar 12(doze) bolas?   
 
Desde já, muito obrigado.
 
Adriano.

Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-1081819514-1204730382=:36529-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Mar 5 14:12:01 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m25HA2ss025861 for ; Wed, 5 Mar 2008 14:10:49 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m25GBB6u022160 for obm-l-MllGbsmmN; Wed, 5 Mar 2008 13:11:11 -0300 Received: from rogue.cesp.com.br (rogue.cesp.com.br [201.63.4.194]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m25GAtsG022027 for ; Wed, 5 Mar 2008 13:10:57 -0300 Received: from correio.cesp.com.br (nightcrawler.cesp.com.br [201.63.4.197]) by rogue.cesp.com.br (Postfix) with ESMTP id C19A9446DE for ; Wed, 5 Mar 2008 13:11:15 -0300 (BRT) Received: from x454322e3f5ac4 (unknown [10.136.21.53]) by correio.cesp.com.br (Postfix) with ESMTP id 5ABCD51407B for ; Wed, 5 Mar 2008 13:11:17 -0300 (BRT) From: "Rubens Kamimura" To: References: <3034149193991073565@unknownmsgid> <3bd00efc0803040929k5d9f7b84y13bdad30b8bf0db0@mail.gmail.com> <-1248285056949373452@unknownmsgid> <7e31215a0803041303y66dd7c5cr38282e78d6358c3c@mail.gmail.com> In-Reply-To: <7e31215a0803041303y66dd7c5cr38282e78d6358c3c@mail.gmail.com> Subject: [obm-l] =?iso-8859-1?Q?RES:_=5Bobm-l=5D_RES:_=5Bobm-l=5D_=5Bobm-l=5D_Quest=E3o_de?= =?iso-8859-1?Q?_indu=E7=E3o_matem=E1tica?= Date: Wed, 5 Mar 2008 13:11:16 -0300 Organization: CESP - OMPTD Message-ID: <003601c87edb$8aa277a0$9fe766e0$@kamimura@cesp.com.br> MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" X-Mailer: Microsoft Office Outlook 12.0 Thread-Index: Ach+PSKuVb6XAeJ7Q5etGCIKBVi3LgAnlYIQ Content-Language: pt-br Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m25GB6sG022107 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Rubens Kamimura" X-Spam-Status: No, hits=4.4 required=5.0 tests=AWL,INVALID_MSGID,IN_REP_TO,NOSPAM_INC,QUOTED_EMAIL_TEXT, RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,REFERENCES, SIGNATURE_LONG_SPARSE,SPAM_PHRASE_00_01,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** Renji, 1. grato pelo retorno, valeu. Sds Rubens -----Mensagem original----- De: owner-obm-l@mat.puc-rio.br [mailto:owner-obm-l@mat.puc-rio.br] Em nome de Rodrigo Renji Enviada em: terça-feira, 4 de março de 2008 18:03 Para: obm-l@mat.puc-rio.br Assunto: Re: [obm-l] RES: [obm-l] [obm-l] Questão de indução matemática bem saiu um simbolo errado no texto que eu escrevi ao inves de soma [k=1, n+1] f(k)=soma [k=1, n] f(k)= +f(n) com soma [k=1, 1] f(k)= f(1) é soma [k=1, n+1] f(k)=soma [k=1, n] f(k) +f(n) com soma [k=1, 1] f(k)= f(1) apareceu um "=" a mais na primeira que não era pra ter eu costumo usar sempre essa definição acima, para demonstrar problemas de somatórios acho a notação de pontinhos (a1+...+an) informal, tento não usar apesar de dar uma "visão" as vezes do que esta acontecendo com o somatorio, mas acho que se pode desenvolver as técnicas de somatorio o suficiente para nao precisar abrir em pontinhos =P (abrindo as vezes, o primeiro, ou ultimo termo apenas nas demonstrações) se precisar de mais alguma ajuda só postar abraços o/ Em 04/03/08, Rubens Kamimura escreveu: > > > > > Olá Marcelo Salhab, > > > > Muito grato. > > > > Sds > > > > Rubens Kamimura > > Assistente Técnico III - CREA/SP 5062246285 > > CESP - Companhia Energética de São Paulo > > OMPTD - Capacitação e Desenvolvimento > > Caixa Postal, 58 - CEP 15385-000 > > Ilha Solteira/SP - Brasil > > Tel. +55-18-3704-4240 ramal 136/137 > > Tel./Fax +55-18-3704-6800 > > www.cesp.com.br > > email: rubens.kamimura@cesp.com.br > > Mens In Corpore Tantun Molen Regit > > UNYK : 132 XOU > > P Antes de imprimir pense em sua responsabilidade e compromisso com o MEIO > AMBIENTE. > > > > > > > > > De: owner-obm-l@mat.puc-rio.br [mailto:owner-obm-l@mat.puc-rio.br] Em nome > de Marcelo Salhab Brogliato > Enviada em: terça-feira, 4 de março de 2008 14:29 > Para: obm-l@mat.puc-rio.br > Assunto: Re: [obm-l] [obm-l] Questão de indução matemática > > > > > Olá Rubens, > > Essas demonstrações seguem todas a mesma idéia... > vou fazer apenas o 2.1 > veja que para n=1 é válido > > vamos supor valido para K e vamos mostrar que vale para K+1. > isto é: > Hipótese: 1^2 + 2^2 + ... + k^2 = [k(k+1)(2k+1)]/6 > Tese: 1^2 + 2^2 + ... + k^2 + (k+1)^2 = (k+1)(k+2)(2k+3)/6 > > Demo: > Sabemos que: 1^2 + 2^2 + .. + k^2 = k(k+1)(2k+1)/6 > somando (k+1)^2 em ambos os lados, temos: > 1^2 + 2^2 + ... + k^2 + (k+1)^2 = k(k+1)(2k+1)/6 + (k+1)^2 > > vamos apenas fatorar o lado direito, e mostrar que ele é igual a > (k+1)(k+2)(2k+3)/6 = (k+1)(2k^2 + 7k + 6)/6 > k(k+1)(2k+1)/6 + (k+1)^2 = (k+1)[ k(2k+1)/6 + (k+1) ] = (k+1)[ 2k^2 + k + > 6k + 6 ]/6 = (k+1)(2k^2 + 7k + 6)/6 > > logo, está provado por indução. > > abraços, > Salhab > > > > > > 2008/3/3 Rubens Kamimura : > > Olá turma da LISTA!!! > > Alguém desta LISTA, se habilitariam em me elucidar tal questão? > > 1. Sabendo, por definição, que: a^0=1 e a^1=a, como poderemos provar por > indução matemática sobre n, que a^m.a^n = a^(m+n), para qualquer m,n > pertencente ao conjunto dos números naturais? > > 2. Como podemos provar por indução matemática: > 2.1. 1^2+ 2^2+...+n^2 = [n(n+1)(2n+1)]/6, (n maior igual 1); > 2.2. 1^3+ 2^3+...+n^3 = (1+2+...+n)^2, (n maior igual 1); > 2.3. 1.2+2.3+...+n(n+1) = [n(n+1)(n+2)]/3, (n maior igual 1); > > Abraços > > leigo e neófito... > > > ========================================================================= > Instruções para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > ========================================================================= > > > > -- > Esta mensagem foi verificada pelo sistema de antivírus e > acredita-se estar livre de perigo. ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= -- This message has been scanned for viruses and dangerous content by MailScanner, and is believed to be clean. ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Mar 5 16:44:11 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m25JfjsG003505 for ; Wed, 5 Mar 2008 16:41:45 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m25Jfil3003499 for obm-l-MllGbsmmN; Wed, 5 Mar 2008 16:41:44 -0300 Received: from c350a-7.friendster.com ([209.11.169.67]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m25JfcsG003478 for ; Wed, 5 Mar 2008 16:41:41 -0300 Date: Wed, 5 Mar 2008 16:41:38 -0300 Received: from unknown (HELO mailmergebatch1) ([10.16.72.3]) by c350a-7.friendster.com with ESMTP; 05 Mar 2008 11:41:56 -0800 Message-Id: <6mttp9$1hlhcol@c350a.gbxsc.friendster.com> From: Jamil Silva Subject: [SPAM] [obm-l] Jamil Silva has invited you to join Friendster To: obm-l@mat.puc-rio.br X-Campaign-ID: 3 X-Campaign-Type: 5 X-Message-Ref: c4aHaNyZaCTYTqDciq12iXB7cgtgnkAqTmX4dbTBof0* Content-Type: text/plain MIME-Version: 1.0 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Jamil Silva X-Spam-Status: Yes, hits=9.0 required=5.0 tests=BIG_FONT,CLICK_BELOW,EXCUSE_14,HTML_FONT_COLOR_CYAN, HTML_FONT_COLOR_GRAY,HTML_FONT_COLOR_UNSAFE, MSG_ID_ADDED_BY_MTA_3,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, SPAM_PHRASE_03_05,WEB_BUGS,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ********* X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----_=_FSter_001_3251204748571466" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. 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------_=_FSter_001_3251204748571466-- Date: Wed, 5 Mar 2008 12:22:52 -0800 Message-Id: <1204748572.29032@mailmergebatch1> ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Mar 5 17:04:39 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m25K33sG005075 for ; Wed, 5 Mar 2008 17:03:03 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m25K330O005073 for obm-l-MllGbsmmN; Wed, 5 Mar 2008 17:03:03 -0300 Received: from wf-out-1314.google.com (wf-out-1314.google.com [209.85.200.170]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m25K30sG005069 for ; Wed, 5 Mar 2008 17:03:01 -0300 Received: by wf-out-1314.google.com with SMTP id 27so2129048wfd.18 for ; Wed, 05 Mar 2008 12:03:22 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; bh=cvW0BuVDXdgOSJHQegqPXK76cQlnMjpuvtlLMShObd8=; b=BQxyFQIBfoL9bPbaabQfHFRx+Q6wGtIcsyBkOKo88zGTND1W+eZcNONo643eIXo5GAo7VIhdLjGN9KzWLh0s6EijRyquxvG1iUkQapKvFaa+z2qJ+RLBDtRKNpXka3wsFhNhb9NQiQrVW7M8CytJCJELb4e9JzxYplO7crKuKO0= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; b=gAQ/A8Q7/AJEkrHBOx3ugO/G/YrHwaGgkI7suESk0DG/L52aYwoeYLef5KIl1cpOdeqGJ6JDYoQvLm3416qFWG+bXWhhdj36LvXoiT7UGMC4gm7KDoH5okY5DnuGSSyRs77TmwVP1zF3ZRHYoVDQboqWKzmbmxgH9YPFQrXGjP4= Received: by 10.142.48.14 with SMTP id v14mr1007587wfv.121.1204747401466; Wed, 05 Mar 2008 12:03:21 -0800 (PST) Received: by 10.70.116.11 with HTTP; Wed, 5 Mar 2008 12:03:21 -0800 (PST) Message-ID: <7e31215a0803051203q5d1e967bqbf17c9cda00868d2@mail.gmail.com> Date: Wed, 5 Mar 2008 17:03:21 -0300 From: "Rodrigo Renji" To: obm-l@mat.puc-rio.br Subject: =?ISO-8859-1?Q?Re:_[obm-l]_RES:_[obm-l]_RES:_[obm-l]?= =?ISO-8859-1?Q?_[obm-l]_Quest=E3o_de_indu=E7=E3o_matem=E1tica?= In-Reply-To: <-8589676258403532532@unknownmsgid> MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline References: <3034149193991073565@unknownmsgid> <3bd00efc0803040929k5d9f7b84y13bdad30b8bf0db0@mail.gmail.com> <-1248285056949373452@unknownmsgid> <7e31215a0803041303y66dd7c5cr38282e78d6358c3c@mail.gmail.com> <-8589676258403532532@unknownmsgid> Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m25K32sG005071 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Rodrigo Renji" X-Spam-Status: No, hits=3.9 required=5.0 tests=AWL,IN_REP_TO,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: *** agora me lembrei de outra coisa tb... tem um tempo eu fiz uma página de internet com propriedades básicas de somatório (bem básicas mesmo!! hehehe) o link abaixo se quiser ver http://iishp.5gbfree.com/matematica/soma/somas.html depois vou escrever mais (incluindo aplicação nos problema desse email) e colocar em outra página abraços o/ Em 05/03/08, Rubens Kamimura escreveu: > Renji, > > 1. grato pelo retorno, valeu. > > Sds > > Rubens > > -----Mensagem original----- > > De: owner-obm-l@mat.puc-rio.br [mailto:owner-obm-l@mat.puc-rio.br] Em nome > > de Rodrigo Renji > Enviada em: terça-feira, 4 de março de 2008 18:03 > > Para: obm-l@mat.puc-rio.br > > Assunto: Re: [obm-l] RES: [obm-l] [obm-l] Questão de indução matemática > > > bem saiu um simbolo errado no texto que eu escrevi > ao inves de > > soma [k=1, n+1] f(k)=soma [k=1, n] f(k)= +f(n) > com > soma [k=1, 1] f(k)= f(1) > > > é > > > soma [k=1, n+1] f(k)=soma [k=1, n] f(k) +f(n) > com > soma [k=1, 1] f(k)= f(1) > > apareceu um "=" a mais na primeira que não era pra ter > > eu costumo usar sempre essa definição acima, para demonstrar problemas > de somatórios > acho a notação de pontinhos (a1+...+an) informal, tento não usar > apesar de dar uma "visão" as vezes do que esta acontecendo com o > somatorio, mas acho que se pode desenvolver as técnicas de somatorio o > suficiente para nao precisar abrir em pontinhos =P (abrindo as vezes, > o primeiro, ou ultimo termo apenas nas demonstrações) > > se precisar de mais alguma ajuda só postar > abraços o/ > Em 04/03/08, Rubens Kamimura escreveu: > > > > > > > > > > Olá Marcelo Salhab, > > > > > > > > Muito grato. > > > > > > > > Sds > > > > > > > > Rubens Kamimura > > > > Assistente Técnico III - CREA/SP 5062246285 > > > > CESP - Companhia Energética de São Paulo > > > > OMPTD - Capacitação e Desenvolvimento > > > > Caixa Postal, 58 - CEP 15385-000 > > > > Ilha Solteira/SP - Brasil > > > > Tel. +55-18-3704-4240 ramal 136/137 > > > > Tel./Fax +55-18-3704-6800 > > > > www.cesp.com.br > > > > email: rubens.kamimura@cesp.com.br > > > > Mens In Corpore Tantun Molen Regit > > > > UNYK : 132 XOU > > > > P Antes de imprimir pense em sua responsabilidade e compromisso com o MEIO > > AMBIENTE. > > > > > > > > > > > > > > > > > > De: owner-obm-l@mat.puc-rio.br [mailto:owner-obm-l@mat.puc-rio.br] Em nome > > de Marcelo Salhab Brogliato > > Enviada em: terça-feira, 4 de março de 2008 14:29 > > Para: obm-l@mat.puc-rio.br > > Assunto: Re: [obm-l] [obm-l] Questão de indução matemática > > > > > > > > > > Olá Rubens, > > > > Essas demonstrações seguem todas a mesma idéia... > > vou fazer apenas o 2.1 > > veja que para n=1 é válido > > > > vamos supor valido para K e vamos mostrar que vale para K+1. > > isto é: > > Hipótese: 1^2 + 2^2 + ... + k^2 = [k(k+1)(2k+1)]/6 > > Tese: 1^2 + 2^2 + ... + k^2 + (k+1)^2 = (k+1)(k+2)(2k+3)/6 > > > > Demo: > > Sabemos que: 1^2 + 2^2 + .. + k^2 = k(k+1)(2k+1)/6 > > somando (k+1)^2 em ambos os lados, temos: > > 1^2 + 2^2 + ... + k^2 + (k+1)^2 = k(k+1)(2k+1)/6 + (k+1)^2 > > > > vamos apenas fatorar o lado direito, e mostrar que ele é igual a > > (k+1)(k+2)(2k+3)/6 = (k+1)(2k^2 + 7k + 6)/6 > > k(k+1)(2k+1)/6 + (k+1)^2 = (k+1)[ k(2k+1)/6 + (k+1) ] = (k+1)[ 2k^2 + k + > > 6k + 6 ]/6 = (k+1)(2k^2 + 7k + 6)/6 > > > > logo, está provado por indução. > > > > abraços, > > Salhab > > > > > > > > > > > > 2008/3/3 Rubens Kamimura : > > > > Olá turma da LISTA!!! > > > > Alguém desta LISTA, se habilitariam em me elucidar tal questão? > > > > 1. Sabendo, por definição, que: a^0=1 e a^1=a, como poderemos provar por > > indução matemática sobre n, que a^m.a^n = a^(m+n), para qualquer m,n > > pertencente ao conjunto dos números naturais? > > > > 2. Como podemos provar por indução matemática: > > 2.1. 1^2+ 2^2+...+n^2 = [n(n+1)(2n+1)]/6, (n maior igual 1); > > 2.2. 1^3+ 2^3+...+n^3 = (1+2+...+n)^2, (n maior igual 1); > > 2.3. 1.2+2.3+...+n(n+1) = [n(n+1)(n+2)]/3, (n maior igual 1); > > > > Abraços > > > > leigo e neófito... > > > > > > ========================================================================= > > Instruções para entrar na lista, sair da lista e usar a lista em > > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > > ========================================================================= > > > > > > > > -- > > Esta mensagem foi verificada pelo sistema de antivírus e > > acredita-se estar livre de perigo. > > ========================================================================= > Instruções para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > ========================================================================= > > -- > > This message has been scanned for viruses and > dangerous content by MailScanner, and is > believed to be clean. > > > > ========================================================================= > Instruções para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > ========================================================================= > ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Mar 5 18:54:46 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m25LrEsG011555 for ; Wed, 5 Mar 2008 18:53:14 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m25LrEoq011553 for obm-l-MllGbsmmN; Wed, 5 Mar 2008 18:53:14 -0300 Received: from wa-out-1112.google.com (wa-out-1112.google.com [209.85.146.182]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m25LrAsG011550 for ; Wed, 5 Mar 2008 18:53:11 -0300 Received: by wa-out-1112.google.com with SMTP id m28so1944794wag.13 for ; Wed, 05 Mar 2008 13:53:33 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=F2z/zosrv533jkp+Xu+gpMp/Df/0p8unbqPGay6w2+8=; b=CYzc9aWpZx+JWfvG8NBC+lo5wkbuo8nnZJP+C6HY1ocEIzo0u4CRBpRB80Epslg6E1/apoiquQMljPzceo79qdS9wlC01N5YmRCyiI2vjNT9/Si3k9XIjcnVxtbQPA10M7TBWEJ6ljadF+IYnLsmjpD7E7WWrILxm0Kf41n1oPE= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=dwE+9Jg4lAHve0ALWC9cyC/9W2zfu8enWTRHGO+Y7kH0N/NmkqAPLj9D2R9CzvFUYf8p+meHapbQiDiIyOFE0DlA/niG4XGm2ksQ6MmaGrTDoh2boKl+VozrNhCIk6EiVqJhOdPxMSLTvkHbHYz5Pui9aVQCquFHSkmcz2SGnws= Received: by 10.114.160.1 with SMTP id i1mr5462011wae.49.1204754013516; Wed, 05 Mar 2008 13:53:33 -0800 (PST) Received: by 10.114.136.9 with HTTP; Wed, 5 Mar 2008 13:53:33 -0800 (PST) Message-ID: <3bd00efc0803051353s45634fabub3a69a952fa5072e@mail.gmail.com> Date: Wed, 5 Mar 2008 18:53:33 -0300 From: "Marcelo Salhab Brogliato" To: obm-l@mat.puc-rio.br Subject: =?ISO-8859-1?Q?Re:_[obm-l]_RES:_[obm-l]_[obm-l?= =?ISO-8859-1?Q?]_Quest=E3o_de_indu=E7=E3o_matem=E1tica?= In-Reply-To: <7e31215a0803041303y66dd7c5cr38282e78d6358c3c@mail.gmail.com> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_5644_29040145.1204754013513" References: <3034149193991073565@unknownmsgid> <3bd00efc0803040929k5d9f7b84y13bdad30b8bf0db0@mail.gmail.com> <-1248285056949373452@unknownmsgid> <7e31215a0803041303y66dd7c5cr38282e78d6358c3c@mail.gmail.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Marcelo Salhab Brogliato" X-Spam-Status: No, hits=4.0 required=5.0 tests=AWL,IN_REP_TO,MAILTO_LINK,MIME_EXCESSIVE_QP, QUOTED_EMAIL_TEXT,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, REFERENCES,SPAM_PHRASE_00_01,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** ------=_Part_5644_29040145.1204754013513 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Ol=E1 Renji, concordo que sempre =E9 poss=EDvel demonstrar usando a nota=E7=E3o de somat= =F3rio, mas n=E3o concordo com a informalidade dos tr=EAs pontinhos. Veja que =E9 apena= s uma quest=E3o de nota=E7=E3o, e existe uma "bije=E7=E3o" entre elas... isto =E9= , representam exatamente a mesma coisa. Sum[i=3Da .. b] { f(i) } =3D=3D f(a) + f(a+1) + ... + (b) =C9 o mesmo que escrevermos df(x)/dx ao inv=E9s de f'(x). abra=E7os, Salhab 2008/3/4 Rodrigo Renji : > bem saiu um simbolo errado no texto que eu escrevi > ao inves de > > soma [k=3D1, n+1] f(k)=3Dsoma [k=3D1, n] f(k)=3D +f(n) > com > soma [k=3D1, 1] f(k)=3D f(1) > > > =E9 > > > soma [k=3D1, n+1] f(k)=3Dsoma [k=3D1, n] f(k) +f(n) > com > soma [k=3D1, 1] f(k)=3D f(1) > > apareceu um "=3D" a mais na primeira que n=E3o era pra ter > > eu costumo usar sempre essa defini=E7=E3o acima, para demonstrar problema= s > de somat=F3rios > acho a nota=E7=E3o de pontinhos (a1+...+an) informal, tento n=E3o usar > apesar de dar uma "vis=E3o" as vezes do que esta acontecendo com o > somatorio, mas acho que se pode desenvolver as t=E9cnicas de somatorio o > suficiente para nao precisar abrir em pontinhos =3DP (abrindo as vezes, > o primeiro, ou ultimo termo apenas nas demonstra=E7=F5es) > > se precisar de mais alguma ajuda s=F3 postar > abra=E7os o/ > Em 04/03/08, Rubens Kamimura escreveu: > > > > > > > > > > Ol=E1 Marcelo Salhab, > > > > > > > > Muito grato. > > > > > > > > Sds > > > > > > > > Rubens Kamimura > > > > Assistente T=E9cnico III - CREA/SP 5062246285 > > > > CESP - Companhia Energ=E9tica de S=E3o Paulo > > > > OMPTD - Capacita=E7=E3o e Desenvolvimento > > > > Caixa Postal, 58 - CEP 15385-000 > > > > Ilha Solteira/SP - Brasil > > > > Tel. +55-18-3704-4240 ramal 136/137 > > > > Tel./Fax +55-18-3704-6800 > > > > www.cesp.com.br > > > > email: rubens.kamimura@cesp.com.br > > > > Mens In Corpore Tantun Molen Regit > > > > UNYK : 132 XOU > > > > P Antes de imprimir pense em sua responsabilidade e compromisso com o > MEIO > > AMBIENTE. > > > > > > > > > > > > > > > > > > De: owner-obm-l@mat.puc-rio.br [mailto:owner-obm-l@mat.puc-rio.br] Em > nome > > de Marcelo Salhab Brogliato > > Enviada em: ter=E7a-feira, 4 de mar=E7o de 2008 14:29 > > Para: obm-l@mat.puc-rio.br > > Assunto: Re: [obm-l] [obm-l] Quest=E3o de indu=E7=E3o matem=E1tica > > > > > > > > > > Ol=E1 Rubens, > > > > Essas demonstra=E7=F5es seguem todas a mesma id=E9ia... > > vou fazer apenas o 2.1 > > veja que para n=3D1 =E9 v=E1lido > > > > vamos supor valido para K e vamos mostrar que vale para K+1. > > isto =E9: > > Hip=F3tese: 1^2 + 2^2 + ... + k^2 =3D [k(k+1)(2k+1)]/6 > > Tese: 1^2 + 2^2 + ... + k^2 + (k+1)^2 =3D (k+1)(k+2)(2k+3)/6 > > > > Demo: > > Sabemos que: 1^2 + 2^2 + .. + k^2 =3D k(k+1)(2k+1)/6 > > somando (k+1)^2 em ambos os lados, temos: > > 1^2 + 2^2 + ... + k^2 + (k+1)^2 =3D k(k+1)(2k+1)/6 + (k+1)^2 > > > > vamos apenas fatorar o lado direito, e mostrar que ele =E9 igual a > > (k+1)(k+2)(2k+3)/6 =3D (k+1)(2k^2 + 7k + 6)/6 > > k(k+1)(2k+1)/6 + (k+1)^2 =3D (k+1)[ k(2k+1)/6 + (k+1) ] =3D (k+1)[ 2k^= 2 + k > + > > 6k + 6 ]/6 =3D (k+1)(2k^2 + 7k + 6)/6 > > > > logo, est=E1 provado por indu=E7=E3o. > > > > abra=E7os, > > Salhab > > > > > > > > > > > > 2008/3/3 Rubens Kamimura : > > > > Ol=E1 turma da LISTA!!! > > > > Algu=E9m desta LISTA, se habilitariam em me elucidar tal quest=E3o? > > > > 1. Sabendo, por defini=E7=E3o, que: a^0=3D1 e a^1=3Da, como poderemos = provar > por > > indu=E7=E3o matem=E1tica sobre n, que a^m.a^n =3D a^(m+n), para qualqu= er m,n > > pertencente ao conjunto dos n=FAmeros naturais? > > > > 2. Como podemos provar por indu=E7=E3o matem=E1tica: > > 2.1. 1^2+ 2^2+...+n^2 =3D [n(n+1)(2n+1)]/6, (n maior igual 1); > > 2.2. 1^3+ 2^3+...+n^3 =3D (1+2+...+n)^2, (n maior igual 1); > > 2.3. 1.2+2.3+...+n(n+1) =3D [n(n+1)(n+2)]/3, (n maior igual 1); > > > > Abra=E7os > > > > leigo e ne=F3fito... > > > > > > > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > > Instru=E7=F5es para entrar na lista, sair da lista e usar a lista em > > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > > > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > > > > > > > > -- > > Esta mensagem foi verificada pelo sistema de antiv=EDrus e > > acredita-se estar livre de perigo. > > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > Instru=E7=F5es para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > ------=_Part_5644_29040145.1204754013513 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Ol=E1 Renji,

concordo que sempre =E9 poss=EDvel demonstrar usando a = nota=E7=E3o de somat=F3rio, mas n=E3o concordo com a informalidade dos tr= =EAs pontinhos. Veja que =E9 apenas uma quest=E3o de nota=E7=E3o, e existe = uma "bije=E7=E3o" entre elas... isto =E9, representam exatamente = a mesma coisa.

Sum[i=3Da .. b] { f(i) } =3D=3D f(a) + f(a+1) + ... + (b)

=C9 o = mesmo que escrevermos df(x)/dx ao inv=E9s de f'(x).

abra=E7os,Salhab




2008/3/4 Rodrigo Ren= ji <rodrigo.uff.math@gmail= .com>:
bem saiu um simbo= lo errado no texto que eu escrevi
ao inves de

soma [k=3D1, n+1] f(k)=3Dsoma [k=3D1, n] f(k)=3D +f(n)
com
soma [k=3D1, 1] f(k)=3D f(1)


=E9


soma [k=3D1, n+1] f(k)=3Dsoma [k=3D1, n] f(k) +f(n)
com
soma [k=3D1, 1] f(k)=3D f(1)

apareceu um "=3D" a mais na primeira que n=E3o era pra ter<= br>
eu costumo usar sempre essa defini=E7=E3o acima, para demonstrar problemas<= br> de somat=F3rios
acho a nota=E7=E3o de pontinhos (a1+...+an) informal, tento n=E3o usar
apesar de dar uma "vis=E3o" as vezes do que esta acontecendo com = o
somatorio, mas acho que se pode desenvolver as t=E9cnicas de somatorio o suficiente para nao precisar abrir em pontinhos =3DP (abrindo as vezes,
o primeiro, ou ultimo termo apenas nas demonstra=E7=F5es)

se precisar de mais alguma ajuda s=F3 postar
abra=E7os o/
Em 04/03/08, Rubens Kamimura<rubens.kamimura@cesp.com.br> escreveu:
>
>
>
>
> Ol=E1 Marcelo Salhab,
>
>
>
> Muito grato.
>
>
>
> Sds
>
>
>
> Rubens Kamimura
>
> Assistente T=E9cnico III - CREA/SP 5062246285
>
> CESP - Companhia Energ=E9tica de S=E3o Paulo
>
> OMPTD - Capacita=E7=E3o e Desenvolvimento
>
> Caixa Postal, 58 - CEP 15385-000
>
> Ilha Solteira/SP - Brasil
>
> Tel. +55-18-3704-4240 ramal 136/137
>
> Tel./Fax +55-18-3704-6800
>
> www.cesp.com.br
>
> email: rubens.kamimura@= cesp.com.br
>
> Mens In Corpore Tantun Molen Regit
>
> UNYK : 132 XOU
>
> P Antes de imprimir pense em sua responsabilidade e compromisso com o = MEIO
> AMBIENTE.
>
>
>
>
>
>
>
>
> De: owner-obm-l@mat.puc-= rio.br [mailto:owner-obm-= l@mat.puc-rio.br] Em nome
> de Marcelo Salhab Brogliato
>  Enviada em: ter=E7a-feira, 4 de mar=E7o de 2008 14:29
>  Para: obm-l@mat.puc-rio.= br
>  Assunto: Re: [obm-l] [obm-l] Quest=E3o de indu=E7=E3o matem=E1ti= ca
>
>
>
>
> Ol=E1 Rubens,
>
>  Essas demonstra=E7=F5es seguem todas a mesma id=E9ia...
>  vou fazer apenas o 2.1
>  veja que para n=3D1 =E9 v=E1lido
>
>  vamos supor valido para K e vamos mostrar que vale para K+1.
>  isto =E9:
>  Hip=F3tese: 1^2 + 2^2 + ... + k^2 =3D [k(k+1)(2k+1)]/6
>  Tese: 1^2 + 2^2 + ... + k^2 + (k+1)^2 =3D (k+1)(k+2)(2k+3)/6
>
>  Demo:
>  Sabemos que: 1^2 + 2^2 + .. + k^2 =3D k(k+1)(2k+1)/6
>  somando (k+1)^2 em ambos os lados, temos:
>  1^2 + 2^2 + ... + k^2 + (k+1)^2 =3D k(k+1)(2k+1)/6 + (k+1)^2
>
>  vamos apenas fatorar o lado direito, e mostrar que ele =E9 igual= a
> (k+1)(k+2)(2k+3)/6 =3D (k+1)(2k^2 + 7k + 6)/6
>  k(k+1)(2k+1)/6 + (k+1)^2 =3D (k+1)[ k(2k+1)/6 + (k+1) ] =3D (k+1= )[ 2k^2 + k +
> 6k + 6 ]/6 =3D (k+1)(2k^2 + 7k + 6)/6
>
>  logo, est=E1 provado por indu=E7=E3o.
>
>  abra=E7os,
>  Salhab
>
>
>
>
>
> 2008/3/3 Rubens Kamimura <rubens.kamimura@cesp.com.br>:
>
> Ol=E1 turma da LISTA!!!
>
>  Algu=E9m desta LISTA, se habilitariam em me elucidar tal quest= =E3o?
>
>  1. Sabendo, por defini=E7=E3o, que: a^0=3D1 e a^1=3Da, como pode= remos provar por
>  indu=E7=E3o matem=E1tica sobre n, que a^m.a^n =3D a^(m+n), para = qualquer m,n
>  pertencente ao conjunto dos n=FAmeros naturais?
>
>  2. Como podemos provar por indu=E7=E3o matem=E1tica:
>  2.1. 1^2+ 2^2+...+n^2 =3D [n(n+1)(2n+1)]/6, (n maior igual 1); >  2.2. 1^3+ 2^3+...+n^3 =3D (1+2+...+n)^2, (n maior igual 1);
>  2.3. 1.2+2.3+...+n(n+1) =3D [n(n+1)(n+2)]/3, (n maior igual 1);<= br> >
>  Abra=E7os
>
>  leigo e ne=F3fito...
>
>
> =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
>  Instru=E7=F5es para entrar na lista, sair da lista e usar a list= a em
>  http://www.mat.puc-rio.br/~obmlistas/obm-l.html
> =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
>
>
>
>  --
>  Esta mensagem foi verificada pelo sistema de antiv=EDrus e
>  acredita-se estar livre de perigo.

=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D
Instru=E7=F5es para entrar na lista, sair da lista e usar a lista em
http://www.mat.puc-rio.br/~obmlistas/obm-l.html
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D

------=_Part_5644_29040145.1204754013513-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Mar 5 19:57:21 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m25MtjsG014249 for ; Wed, 5 Mar 2008 19:55:45 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m25MtiG8014247 for obm-l-MllGbsmmN; Wed, 5 Mar 2008 19:55:44 -0300 Received: from web33802.mail.mud.yahoo.com (web33802.mail.mud.yahoo.com [209.191.69.165]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id m25MtgsG014240 for ; Wed, 5 Mar 2008 19:55:43 -0300 Received: (qmail 13607 invoked by uid 60001); 5 Mar 2008 22:56:04 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:X-Mailer:Date:From:Subject:To:MIME-Version:Content-Type:Message-ID; b=l/tjpJJhvgR+LFaNXJr2dJJROchG3StaEUaTtUlXs/PTVgAv4HltdZGUfa6K33AyCvEqD2+hdJgPpzDRLgec/vDVmSRDSwQmqQM6VHU3xoFjijeJUjdvI2op6GCE2zdOT8ZHe868Xhu/KdYK7DSN6X4wlKY+WGo6GHWuoJrxtMU=; X-YMail-OSG: BjVGTMIVM1koI0TeKCwaZyGGm6mjmzXi6emhU7arP6ViV2seywve239TbrbQj7WHuiy_vNWkJKnJ4FdNPSAcHJBsMfsk5lhjEQfmWSfB7CzamZ6wWWu1RbIxCSo8Aw-- Received: from [201.51.127.74] by web33802.mail.mud.yahoo.com via HTTP; Wed, 05 Mar 2008 14:56:04 PST X-Mailer: YahooMailRC/902.35 YahooMailWebService/0.7.162 Date: Wed, 5 Mar 2008 14:56:04 -0800 (PST) From: Klaus Ferraz Subject: [SPAM] [obm-l] Marte To: obm-l@mat.puc-rio.br MIME-Version: 1.0 Content-Type: text/plain Message-ID: <694285.12003.qm@web33802.mail.mud.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Klaus Ferraz X-Spam-Status: Yes, hits=8.3 required=5.0 tests=AWL,FORGED_YAHOO_RCVD,MIME_BOUND_DIGITS_5,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01,SPAM_REDIRECTOR, SUPERLONG_LINE,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="0-797474094-1204757764=:12003" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (8.30 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: MIME_BOUND_DIGITS_5 (1.7 points) Spam tool pattern in MIME boundary SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: SUPERLONG_LINE (0.0 points) BODY: Contains a line >=199 characters long SPAM: SPAM_REDIRECTOR (0.4 points) URI: Uses open redirection service SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 165.69.191.209.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 165.69.191.209.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-1.0 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- --0-797474094-1204757764=:12003 Content-Type: text/plain; charset=utf-8 Content-Transfer-Encoding: quoted-printable A primeira expedicao a Marte encontrou somente as ruinas de uma civilizacao= . Os exploradores concluiram dos artefatos e desenhos que as criaturas que = produziram esta civilizacao tinham quatro pernas, cada uma terminada em um = conjunto de garras parecidas com dedos. Ap=C3=B3s muito estudo foram capaze= s de traduzir a matematica marciana. Eles encontraram a seguinte equacao:= =0A5x^2-50x+125=3D0=0AEsta era uma matematica estranha. O valor x=3D5 parec= ia correto, mas x=3D8 n=C3=A3o. Entao os exploradores lembraram a maneira c= omo o nosso sistema de numeracao foi desenvolvido e encontraram evidencias = de que o sistema marciano teve uma historia analoga. Quantos dedos tinham o= s marcianos?=0A=0A=0A Abra sua conta no Yahoo! Mail, o =C3=BAnico sem = limite de espa=C3=A7o para armazenamento!=0Ahttp://br.mail.yahoo.com/ --0-797474094-1204757764=:12003 Content-Type: text/html; charset=utf-8 Content-Transfer-Encoding: quoted-printable
A primeira expedicao a Marte encontrou somente as= ruinas de uma civilizacao. Os exploradores concluiram dos artefatos e dese= nhos que as criaturas que produziram esta civilizacao tinham quatro pe= rnas, cada uma terminada em um conjunto de garras parecidas com dedos. Ap= =C3=B3s muito estudo foram capazes de traduzir a matematica marciana. Eles = encontraram a seguinte equacao:
=0A
5x^2-50x+125=3D0
=0A
= Esta era uma matematica estranha. O valor x=3D5 parecia correto, mas x=3D8 = n=C3=A3o. Entao os exploradores lembraram a maneira como o nosso sistema de= numeracao foi desenvolvido e encontraram evidencias de que o sistema marci= ano teve uma historia analoga. Quantos dedos tinham os marcianos?

=0A=0A=0A
Abra sua conta no Yahoo! Mail, = o =C3=BAnico sem limite de espa=C3=A7o para armazenamento! =0A --0-797474094-1204757764=:12003-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Mar 5 20:26:05 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m25NP0sG015786 for ; Wed, 5 Mar 2008 20:25:00 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m25NOx6S015784 for obm-l-MllGbsmmN; Wed, 5 Mar 2008 20:24:59 -0300 Received: from smtp2.oi.com.br (smtp5.oi.com.br [200.222.115.129]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m25NOwsG015779 for ; Wed, 5 Mar 2008 20:24:59 -0300 Received: from smtp2.oi.com.br (localhost.localdomain [127.0.0.1]) by smtp2.oi.com.br (Postfix) with ESMTP id 90F4170012EF for ; Wed, 5 Mar 2008 20:25:17 -0300 (BRT) Received: from pessoal2b51d2e (unknown [189.71.123.215]) by smtp2.oi.com.br (Postfix) with SMTP id BECA87000DC8 for ; Wed, 5 Mar 2008 20:25:16 -0300 (BRT) Message-ID: <000801c162a5$306250c0$d77b47bd@pessoal2b51d2e> From: "Pedro " To: Subject: [SPAM] [obm-l] =?iso-8859-1?B?RXF1Yefjbw==?= Date: Thu, 1 Nov 2001 05:16:54 -0200 MIME-Version: 1.0 Content-Type: text/plain X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2900.2180 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.2180 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Pedro " X-Spam-Status: Yes, hits=8.4 required=5.0 tests=AWL,BIG_FONT,DATE_IN_PAST_96_XX,FROM_ENDS_IN_NUMS, RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01, USER_AGENT_OE,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_NextPart_000_0005_01C16294.6BC1CF30" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (8.40 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: FROM_ENDS_IN_NUMS (0.9 points) From: ends in numbers SPAM: USER_AGENT_OE (0.2 points) X-Mailer header indicates a non-spam MUA (Outlook Express) SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: BIG_FONT (0.3 points) BODY: FONT Size +2 and up or 3 and up SPAM: DATE_IN_PAST_96_XX (1.5 points) Date: is 96 hours or more before Received: date SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 215.123.71.189.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 215.123.71.189.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-0.3 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- This is a multi-part message in MIME format. ------=_NextPart_000_0005_01C16294.6BC1CF30 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Amigos, min d=EA uma id=E9ia para essa equa=E7=E3o : Encontre todas as solu=E7=F5es inteiras (x,y) da equa=E7=E3o=20 x^(2006)Y + 1 =3D Y^(2007) + X. ------=_NextPart_000_0005_01C16294.6BC1CF30 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable
Amigos, min d=EA uma id=E9ia = para essa=20 equa=E7=E3o :
 
Encontre todas as = solu=E7=F5es inteiras (x,y)=20 da equa=E7=E3o
x^(2006)Y + 1 =3D Y^(2007) + = X.
------=_NextPart_000_0005_01C16294.6BC1CF30-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Mar 5 21:10:57 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2609UsG017448 for ; Wed, 5 Mar 2008 21:09:30 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2609UpV017446 for obm-l-MllGbsmmN; Wed, 5 Mar 2008 21:09:30 -0300 Received: from rn-out-0910.google.com (rn-out-0910.google.com [64.233.170.188]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2609SsG017443 for ; Wed, 5 Mar 2008 21:09:28 -0300 Received: by rn-out-0910.google.com with SMTP id e11so676505rng.7 for ; Wed, 05 Mar 2008 16:09:51 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=hFoMY4vL/RXl4rvecFDjG/lG7RQFR8/2gTi7CCA2LCY=; b=EizBHpjEt2yjSq8ty9KphG9j38syK1Cl5loZ5alHY0I7uNkoVWdv4N9IpP91gV0XEjeKoDMyP1ITuN20nJHNdgkQJf2JOZF6QR15sCxj4Ho3IvQEkWG2QzddK3YkoHNMqSxGZCt4uw5mJcA+ZLc8VRIvdm03NmE/nDv8+cccNfs= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=ADcfhlzRau8cDcTIVkUYsboDzP8h8AYy0k2+9OZdb7bdgsi/mrmxb2tapWMn/fEpmHQs57fHdCs14MBmHDyaOr1UHnoA6abCujCPcPK/ShW7smnqdg1S82wHkQQyX9VGnMUxsG83MeraXZg4ch6exbuwnb91r8m5KieGdh3QBK0= Received: by 10.115.58.1 with SMTP id l1mr5633749wak.110.1204762190758; Wed, 05 Mar 2008 16:09:50 -0800 (PST) Received: by 10.114.136.9 with HTTP; Wed, 5 Mar 2008 16:09:50 -0800 (PST) Message-ID: <3bd00efc0803051609o5c2c6c1ew99878d35af676a46@mail.gmail.com> Date: Wed, 5 Mar 2008 21:09:50 -0300 From: "Marcelo Salhab Brogliato" To: obm-l@mat.puc-rio.br Subject: =?ISO-8859-1?Q?Re:_[obm-l]_Equa=E7=E3o?= In-Reply-To: <000801c162a5$306250c0$d77b47bd@pessoal2b51d2e> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_6230_24901720.1204762190748" References: <000801c162a5$306250c0$d77b47bd@pessoal2b51d2e> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Marcelo Salhab Brogliato" X-Spam-Status: No, hits=4.5 required=5.0 tests=AWL,BIG_FONT,IN_REP_TO,MAILTO_LINK,MAILTO_TO_SPAM_ADDR, RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,REFERENCES, SPAM_PHRASE_00_01,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** ------=_Part_6230_24901720.1204762190748 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Ol=E1 Pedro, vamos a algumas solu=E7=F5es triviais: (0, 1), (1, 1), (1, -1) x^(2006)y + 1 =3D y^(2007) + x y[x^(2006) - y^(2006)] + 1 =3D x y(x^(1003) - y^(1003))(x^(1003) + y^(1003)) + 1 =3D x analisando a equacao modx, temos: 1 =3D=3D y^(2007) (mod x) agora, analisando mody, temos: 1 =3D=3D x (mod y) logo: x =3D a*y + 1 portanto, a equa=E7=E3o fica: [(a*y+1)^2006]*y =3D y^(2007) + a*y assim, temos: y*[(a*y+1)^(2006) - y^(2006) - a] =3D 0 hmm, ainda nao tive nenhuma boa id=E9ia.. assim que tiver eu mando! abra=E7os, Salhab deste modo, temos: y^(2007) 2001/11/1 Pedro : > Amigos, min d=EA uma id=E9ia para essa equa=E7=E3o : > > Encontre todas as solu=E7=F5es inteiras (x,y) da equa=E7=E3o > x^(2006)Y + 1 =3D Y^(2007) + X. > ------=_Part_6230_24901720.1204762190748 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Ol=E1 Pedro,

vamos a algumas solu=E7=F5es triviais: (0, 1), (1, 1), = (1, -1)

x^(2006)y + 1 =3D y^(2007) + x
y[x^(2006) - y^(2006)] + 1= =3D x
y(x^(1003) - y^(1003))(x^(1003) + y^(1003)) + 1 =3D x

anal= isando a equacao modx, temos: 1 =3D=3D y^(2007) (mod x)
agora, analisando mody, temos: 1 =3D=3D x (mod y)
logo: x =3D a*y + 1portanto, a equa=E7=E3o fica: [(a*y+1)^2006]*y =3D y^(2007) + a*y
assim= , temos: y*[(a*y+1)^(2006) - y^(2006) - a] =3D 0

hmm, ainda nao tive= nenhuma boa id=E9ia..
assim que tiver eu mando!

abra=E7os,
Salhab




de= ste modo, temos: y^(2007)


2001/11/1 P= edro <npc1972@oi.com.br>:
Amigos, min d=EA uma id=E9ia para essa=20 equa=E7=E3o :
 
Encontre todas as solu=E7=F5es inteiras (x,y)= =20 da equa=E7=E3o
x^(2006)Y + 1 =3D Y^(2007) + X.

------=_Part_6230_24901720.1204762190748-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Mar 5 23:34:47 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m262WpsG023700 for ; Wed, 5 Mar 2008 23:32:51 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m262Wpkt023698 for obm-l-MllGbsmmN; Wed, 5 Mar 2008 23:32:51 -0300 Received: from fg-out-1718.google.com (fg-out-1718.google.com [72.14.220.158]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m262WnsG023682 for ; Wed, 5 Mar 2008 23:32:50 -0300 Received: by fg-out-1718.google.com with SMTP id e12so8520732fga.3 for ; Wed, 05 Mar 2008 18:33:12 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=7LBByVNHZmk/0Q29o09405gDHxYiCkTBXqOmci7AbGs=; b=f3VjVH9mqyhbPM29YnP1VPYywLAcY1TEuLxBpB5tDmXlEBhQwyb+9ePRFj54o4xwgJsf+qFFBSkS/V0A8bGdRYaio4aUD0IAreY0IluXVRYWV/0Qq0EJ+qRORe6y4OavTEwk/+nPStWDgFA6JAcXqDGxNxvpyonzpeqUu2igLvM= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=HHf/3OK+1CZCPR/hw/Gux5NkGpQoLRMaE0jOCpEhohjkJDNRXnG4AESHYDEkEx7iYMDQoOCIF3dDtfjaAzWXl8NvbarDOEV2bmj4A7sLu/1xwOuMu3UywqACdKb19vJsfasXuBatmuhjp2y2z7/J0M1fSdwvDJiwh7VJjGr1WWI= Received: by 10.86.31.18 with SMTP id e18mr3936927fge.38.1204770792401; Wed, 05 Mar 2008 18:33:12 -0800 (PST) Received: by 10.86.54.14 with HTTP; Wed, 5 Mar 2008 18:33:12 -0800 (PST) Message-ID: Date: Wed, 5 Mar 2008 22:33:12 -0400 From: "saulo nilson" To: obm-l@mat.puc-rio.br Subject: =?ISO-8859-1?Q?Re:_[obm-l]_Quest=E3o_de_Probabilidade?= In-Reply-To: <402124.36529.qm@web63115.mail.re1.yahoo.com> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_4978_24744211.1204770792355" References: <402124.36529.qm@web63115.mail.re1.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "saulo nilson" X-Spam-Status: No, hits=-0.7 required=5.0 tests=AWL,IN_REP_TO,JAVASCRIPT_UNSAFE,MAILTO_LINK, QUOTED_EMAIL_TEXT,REFERENCES,SPAM_PHRASE_01_02, SPAM_REDIRECTOR,X_MAILING_LIST version=2.44 X-Spam-Level: ------=_Part_4978_24744211.1204770792355 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline x+y+z+w+v=3D12 C13,5 On 3/5/08, Adriano Dutra Teixeira wrote: > > Ol=E1 pessoal, > > Um probleminha de Probabilidade: > *Considere uma urna com 5 bolas: uma azul, uma verde, uma amarela, uma > vermelha e uma branca. Sabe-se que h=E1 reposi=E7=E3o das bolas e a ordem= que sai > as cores n=E3o importa, o que importa =E9 quantas bolas saem de cada cor.= De > quantas maneiras podemos selecionar 12(doze) bolas? * > > Desde j=E1, muito obrigado. > > Adriano. > > ------------------------------ > Abra sua conta no Yahoo! Mail, > o =FAnico sem limite de espa=E7o para armazenamento! > > ------=_Part_4978_24744211.1204770792355 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline
x+y+z+w+v=3D12
C13,5

 
On 3/5/08, A= driano Dutra Teixeira <adtdri= @yahoo.com.br> wrote:
Ol=E1 pessoal,
 
Um probleminha de Probabilidade:
Considere uma urna com 5 bolas: uma azul, uma verde, uma = amarela, uma vermelha e uma branca. Sabe-se que h=E1 reposi=E7=E3o das= bolas e a ordem que sai as cores n=E3o importa, o que importa =E9 qua= ntas bolas saem de cada cor. De quantas maneiras podemos selecionar 12(doze= ) bolas?   
 
Desde j=E1, muito obrigado.
 
Adriano.

Abra sua conta no Yahoo! Mail, o =FAnico sem l= imite de espa=E7o para armazenamento!


------=_Part_4978_24744211.1204770792355-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Mar 5 23:34:47 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m262XCsG023711 for ; Wed, 5 Mar 2008 23:33:12 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m262XCVb023709 for obm-l-MllGbsmmN; Wed, 5 Mar 2008 23:33:12 -0300 Received: from nf-out-0910.google.com (nf-out-0910.google.com [64.233.182.187]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m262XAsG023704 for ; Wed, 5 Mar 2008 23:33:11 -0300 Received: by nf-out-0910.google.com with SMTP id k4so1690377nfd.19 for ; Wed, 05 Mar 2008 18:33:33 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=YtMgor8YXLGJLEqcavfc4OHCqQ7xaPRzUVef9nxAfwg=; b=dJLqSqtwPMvmoEQiqjeq3PCduBSSVu0xWkTm1ucVzrpUz4J4t2JAvO8cYtGFh1tTw8wOsWiP5rv62ohVLoVpNRiGctYRAOKbgD3t6x8rgAyvdYufkzvfsAXG/tevLHdC3wMnHe8IzaHvc7XC8fLto9fokbqAEjbGbR7oNV2vvPg= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=UG6aC+xyb7PtoKOCK1sDI0djJJX+LYvklVXxya8SfOOW0GsrzmyYKR4x2Xfc6SOO9HXeU7xNCc2q6RT2rq2Pj89XjTpep8/Oq3sa/aXbqIBy6RHQw6HWgNQ9RXBk4lFsm0axy/I+J0FdFEOse2smfvsTISos32EoETvcrKiFsyM= Received: by 10.86.59.2 with SMTP id h2mr3906100fga.63.1204770813502; Wed, 05 Mar 2008 18:33:33 -0800 (PST) Received: by 10.86.54.14 with HTTP; Wed, 5 Mar 2008 18:33:33 -0800 (PST) Message-ID: Date: Wed, 5 Mar 2008 22:33:33 -0400 From: "saulo nilson" To: obm-l@mat.puc-rio.br Subject: =?ISO-8859-1?Q?Re:_[obm-l]_Quest=E3o_de_Probabilidade?= In-Reply-To: <402124.36529.qm@web63115.mail.re1.yahoo.com> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_4980_13298470.1204770813463" References: <402124.36529.qm@web63115.mail.re1.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "saulo nilson" X-Spam-Status: No, hits=1.1 required=5.0 tests=AWL,EMAIL_ATTRIBUTION,IN_REP_TO,JAVASCRIPT_UNSAFE, MAILTO_LINK,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_01_02, SPAM_REDIRECTOR,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: * ------=_Part_4980_13298470.1204770813463 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline C13,4 On 3/5/08, Adriano Dutra Teixeira wrote: > > Ol=E1 pessoal, > > Um probleminha de Probabilidade: > *Considere uma urna com 5 bolas: uma azul, uma verde, uma amarela, uma > vermelha e uma branca. Sabe-se que h=E1 reposi=E7=E3o das bolas e a ordem= que sai > as cores n=E3o importa, o que importa =E9 quantas bolas saem de cada cor.= De > quantas maneiras podemos selecionar 12(doze) bolas? * > > Desde j=E1, muito obrigado. > > Adriano. > > ------------------------------ > Abra sua conta no Yahoo! Mail, > o =FAnico sem limite de espa=E7o para armazenamento! > > ------=_Part_4980_13298470.1204770813463 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline C13,4

On 3/5/08, A= driano Dutra Teixeira <adtdri= @yahoo.com.br> wrote:
Ol=E1 pessoal,
 
Um probleminha de Probabilidade:
Considere uma urna com 5 bolas: uma azul, uma verde, uma = amarela, uma vermelha e uma branca. Sabe-se que h=E1 reposi=E7=E3o das= bolas e a ordem que sai as cores n=E3o importa, o que importa =E9 qua= ntas bolas saem de cada cor. De quantas maneiras podemos selecionar 12(doze= ) bolas?   
 
Desde j=E1, muito obrigado.
 
Adriano.

Abra sua conta no Yahoo! Mail, o =FAnico sem l= imite de espa=E7o para armazenamento!


------=_Part_4980_13298470.1204770813463-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Mar 5 23:49:21 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m262mEsG024352 for ; Wed, 5 Mar 2008 23:48:14 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m262mEhY024350 for obm-l-MllGbsmmN; Wed, 5 Mar 2008 23:48:14 -0300 Received: from ti-out-0910.google.com (ti-out-0910.google.com [209.85.142.187]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m262mAsG024343 for ; Wed, 5 Mar 2008 23:48:12 -0300 Received: by ti-out-0910.google.com with SMTP id y6so2510604tia.13 for ; Wed, 05 Mar 2008 18:48:33 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=kyvTzqLjMUL7sHt39SPLfYza7L0Dllx13vSCYRc0vFE=; b=VlywCGwDPaELd+4x9bEqHZOecA2vlTJcE16xWTqImPRRe6TWFGWxbKH4KL11Sy8PDZckrFeUQqIgeNrGl6UmHWxov8H7yiOzERT5ex1tWcisT1OPByuebo5C4i1yHKJbDej+lE8SzeYd9jAljlBluUNL/EEJQYFah2ZkSbER3wk= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=kUJTHkzwm/C+xRoM3cunC7nzqUmG5yv5sw1ryhXUFAkOcL3A7Vp+MghX7Ot66/JrLqmO+EjhZzLQBgOnvVs80b9NAqgcJ78cyo8GhKRxnYPLhrZ0tfttcF1Pt7IHBmD1pjqxKxnzOJFZYQXkxUAP9C7UUEj9IoRI+4wehgnQ2x0= Received: by 10.151.44.18 with SMTP id w18mr1631659ybj.184.1204771711742; Wed, 05 Mar 2008 18:48:31 -0800 (PST) Received: by 10.150.158.20 with HTTP; Wed, 5 Mar 2008 18:48:31 -0800 (PST) Message-ID: <5bb472220803051848u23734971s622bc7698b067144@mail.gmail.com> Date: Wed, 5 Mar 2008 23:48:31 -0300 From: "Joao Victor Brasil" To: obm-l@mat.puc-rio.br Subject: =?ISO-8859-1?Q?Re:_[obm-l]_Quest=E3o_de_Probabilidade?= In-Reply-To: MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_2264_21853863.1204771711731" References: <402124.36529.qm@web63115.mail.re1.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Joao Victor Brasil" X-Spam-Status: No, hits=4.5 required=5.0 tests=AWL,IN_REP_TO,JAVASCRIPT_UNSAFE,MAILTO_LINK, QUOTED_EMAIL_TEXT,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, REFERENCES,SPAM_PHRASE_00_01,SPAM_REDIRECTOR, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** ------=_Part_2264_21853863.1204771711731 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline me desculpe, mas como posso selecionar selecionar 12 bolas se a urna s=F3 t= em 5??? On 3/5/08, saulo nilson wrote: > > C13,4 > > On 3/5/08, Adriano Dutra Teixeira wrote: > > > > Ol=E1 pessoal, > > > > Um probleminha de Probabilidade: > > *Considere uma urna com 5 bolas: uma azul, uma verde, uma amarela, uma > > vermelha e uma branca. Sabe-se que h=E1 reposi=E7=E3o das bolas e a ord= em que sai > > as cores n=E3o importa, o que importa =E9 quantas bolas saem de cada co= r. De > > quantas maneiras podemos selecionar 12(doze) bolas? * > > > > Desde j=E1, muito obrigado. > > > > Adriano. > > > > ------------------------------ > > Abra sua conta no Yahoo! Mail, > > o =FAnico sem limite de espa=E7o para armazenamento! > > > > > ------=_Part_2264_21853863.1204771711731 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline
me desculpe, mas como posso selecionar selecionar 12 bolas se a urna s= =F3 tem 5???


 
On 3/5/08, s= aulo nilson <saulo.nilson@= gmail.com> wrote:
C13,4=20


On 3/5/08, A= driano Dutra Teixeira <adtdri= @yahoo.com.br> wrote:=20
Ol=E1 pessoal,
 
Um probleminha de Probabilidade:
Considere uma urna com 5 bolas: uma azul, uma verde, uma = amarela, uma vermelha e uma branca. Sabe-se que h=E1 reposi=E7=E3o das= bolas e a ordem que sai as cores n=E3o importa, o que importa =E9 qua= ntas bolas saem de cada cor. De quantas maneiras podemos selecionar 12(doze= ) bolas?   
 
Desde j=E1, muito obrigado.
 
Adriano.

Abra sua conta no Yahoo! Mail, o =FAnico sem limite de espa= =E7o para armazenamento!



------=_Part_2264_21853863.1204771711731-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Mar 6 00:18:04 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m263H6sG026217 for ; Thu, 6 Mar 2008 00:17:06 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m263H58M026215 for obm-l-MllGbsmmN; Thu, 6 Mar 2008 00:17:05 -0300 Received: from fg-out-1718.google.com (fg-out-1718.google.com [72.14.220.156]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m263H2sG026178 for ; Thu, 6 Mar 2008 00:17:02 -0300 Received: by fg-out-1718.google.com with SMTP id e12so8635441fga.3 for ; Wed, 05 Mar 2008 19:17:25 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=TQIetZN6oDZUtzgiZbs1i/jrogEPSrupWdOKIzFUsZA=; b=Fnbb7Ojpdcrw39Jf67cBm3b+WINlRVYvoF+4zabZUCzqSo+IEqpx13GDymy6RDw89dHKf3wioLFtUHALVohW8MFr1ON5FkQt68Wx908l87TJ59eMLraAHNPhKe9jn1KnAH8G74rQWX//7zW7iSc34zKOhvQMBAwNoA6mfClv988= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=mfMHEEn3qd31WmTAAZAj/PVINfwc8O4M96LxmLp0fjy/XW0ePtIwKjZzPHtPBLAYa1WrDy/84uoMoFzLOG5wrXNo0x2x2VaqfIRegFdrbmU3EQVvNQwO7OX04KJZ3zToks883jzYCn9e+HxRHIGDpGoWtR2B2BKC8i2D0DaImP8= Received: by 10.86.84.5 with SMTP id h5mr3857627fgb.27.1204773445212; Wed, 05 Mar 2008 19:17:25 -0800 (PST) Received: by 10.86.54.14 with HTTP; Wed, 5 Mar 2008 19:17:25 -0800 (PST) Message-ID: Date: Wed, 5 Mar 2008 23:17:25 -0400 From: "saulo nilson" To: obm-l@mat.puc-rio.br Subject: =?ISO-8859-1?Q?Re:_[obm-l]_Quest=E3o_de_Probabilidade?= In-Reply-To: <5bb472220803051848u23734971s622bc7698b067144@mail.gmail.com> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_5064_4068096.1204773445212" References: <402124.36529.qm@web63115.mail.re1.yahoo.com> <5bb472220803051848u23734971s622bc7698b067144@mail.gmail.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "saulo nilson" X-Spam-Status: No, hits=-0.3 required=5.0 tests=AWL,IN_REP_TO,JAVASCRIPT_UNSAFE,MAILTO_LINK, QUOTED_EMAIL_TEXT,REFERENCES,SPAM_PHRASE_00_01, SPAM_REDIRECTOR,X_MAILING_LIST version=2.44 X-Spam-Level: ------=_Part_5064_4068096.1204773445212 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline e com reposi=E7ao On 3/5/08, Joao Victor Brasil wrote: > > me desculpe, mas como posso selecionar selecionar 12 bolas se a urna s=F3 > tem 5??? > > > > On 3/5/08, saulo nilson wrote: > > > > C13,4 > > > > On 3/5/08, Adriano Dutra Teixeira wrote: > > > > > > Ol=E1 pessoal, > > > > > > Um probleminha de Probabilidade: > > > *Considere uma urna com 5 bolas: uma azul, uma verde, uma amarela, um= a > > > vermelha e uma branca. Sabe-se que h=E1 reposi=E7=E3o das bolas e a o= rdem que sai > > > as cores n=E3o importa, o que importa =E9 quantas bolas saem de cada = cor. De > > > quantas maneiras podemos selecionar 12(doze) bolas? * > > > > > > Desde j=E1, muito obrigado. > > > > > > Adriano. > > > > > > ------------------------------ > > > Abra sua conta no Yahoo! Mail, > > > o =FAnico sem limite de espa=E7o para armazenamento! > > > > > > > > > ------=_Part_5064_4068096.1204773445212 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline
e com reposi=E7ao


 
On 3/5/08, J= oao Victor Brasil <jvbrasil@gm= ail.com> wrote:
me desculpe, mas como posso selecionar selecionar 12 bolas se a urna s= =F3 tem 5???


 
On 3/5/08, s= aulo nilson <saulo.nilson@= gmail.com> wrote:=20
C13,4=20


On 3/5/08, A= driano Dutra Teixeira <adtdri= @yahoo.com.br> wrote:=20
Ol=E1 pessoal,
 
Um probleminha de Probabilidade:
Considere uma urna com 5 bolas: uma azul, uma verde, uma = amarela, uma vermelha e uma branca. Sabe-se que h=E1 reposi=E7=E3o das= bolas e a ordem que sai as cores n=E3o importa, o que importa =E9 qua= ntas bolas saem de cada cor. De quantas maneiras podemos selecionar 12(doze= ) bolas?   
 
Desde j=E1, muito obrigado.
 
Adriano.

Abra sua conta no Yahoo! Mail, o =FAnico sem limite de espa= =E7o para armazenamento!




------=_Part_5064_4068096.1204773445212-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Mar 6 00:18:59 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m263I5sG026247 for ; Thu, 6 Mar 2008 00:18:05 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m263I5KG026245 for obm-l-MllGbsmmN; Thu, 6 Mar 2008 00:18:05 -0300 Received: from nf-out-0910.google.com (nf-out-0910.google.com [64.233.182.184]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m263I2sG026235 for ; Thu, 6 Mar 2008 00:18:03 -0300 Received: by nf-out-0910.google.com with SMTP id k4so1703266nfd.19 for ; Wed, 05 Mar 2008 19:18:26 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; bh=ep3BlAX9LWr0817QgvueAIU3Jti49aeIz9k5k0qrG8Y=; b=FIfxj2xrlCz/zpWtKu6Gm5UmgRm0hla78isyl2uzNtprGzutmAsGdnwlVXLMe0K/p8Q2ueakD71oDZkpb3Ws5ecslgG/IAtyfG+OvHrotCHY+Yb/l+v8B1rN4/FaD25y+gW7tSVEDAoU7HGTuaX1blkSwoDp4DDm5u/2uHpjoCg= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; b=UoiBPM3+a3Ye8gu0gZp+5L0x+ebtWfNdgx3rZSZ7x7k7oSpuGSB8BYufJpdXaHRDjipFHeqRUQXkQocQd4lU6CRObB/sEVslQkYkjQrSpevVZXx6uNL6nXTjZZbaiLGrzupwKfkA8mkZ83GTK/kUZdS3IWO3eRdCG9AijomBULA= Received: by 10.78.146.11 with SMTP id t11mr8712147hud.71.1204773505777; Wed, 05 Mar 2008 19:18:25 -0800 (PST) Received: by 10.78.42.5 with HTTP; Wed, 5 Mar 2008 19:18:25 -0800 (PST) Message-ID: <8994b830803051918j1f74dd34vfbb272c92826e3af@mail.gmail.com> Date: Thu, 6 Mar 2008 00:18:25 -0300 From: "=?ISO-8859-1?Q?Maur=EDcio_Collares?=" To: obm-l@mat.puc-rio.br Subject: =?ISO-8859-1?Q?Re:_[obm-l]_Quest=E3o_de_Probabilidade?= In-Reply-To: <5bb472220803051848u23734971s622bc7698b067144@mail.gmail.com> MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline References: <402124.36529.qm@web63115.mail.re1.yahoo.com> <5bb472220803051848u23734971s622bc7698b067144@mail.gmail.com> Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m263I4sG026236 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "=?ISO-8859-1?Q?Maur=EDcio_Collares?=" X-Spam-Status: No, hits=4.2 required=5.0 tests=AWL,IN_REP_TO,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, REFERENCES,SPAM_PHRASE_00_01,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** O enunciado informa que há reposição das bolas. Em outras palavras, a bola é recolocada na caixa depois do sorteio. -- Abraços, Maurício 2008/3/5 Joao Victor Brasil : > me desculpe, mas como posso selecionar selecionar 12 bolas se a urna só tem > 5??? ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Mar 6 08:39:34 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m26BaqsG018197 for ; Thu, 6 Mar 2008 08:36:52 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m26Baqgt018195 for obm-l-MllGbsmmN; Thu, 6 Mar 2008 08:36:52 -0300 Received: from relay1.bol.com.br (relay1.bol.com.br [200.221.4.105]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m26BapsG018192 for ; Thu, 6 Mar 2008 08:36:51 -0300 Received: from localhost (localhost [127.0.0.1]) by salsa1.bol.com.br (Postfix) with ESMTP id 4661F50187 for ; Thu, 6 Mar 2008 08:37:15 -0300 (BRT) Received: from bol.com.br (whisper5.mail.sys.intranet [172.26.5.77]) by salsa1.bol.com.br (Postfix) with ESMTP id 233C250DAD for ; Thu, 6 Mar 2008 08:37:15 -0300 (BRT) Date: Thu, 6 Mar 2008 09:37:15 -0200 Message-Id: Subject: Re:[obm-l] Jamil Silva has invited you to join Friendster MIME-Version: 1.0 X-Sensitivity: 3 Content-Type: text/plain; charset=iso-8859-1 From: "fernandobarcel" To: "obm-l" X-XaM3-API-Version: 4.3(R1) (B10) X-SenderIP: 201.53.24.72 X-SIG5: 03d0644771df6ccb2320ee90a894710f Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m26BapsG018193 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "fernandobarcel" X-Spam-Status: No, hits=-0.1 required=5.0 tests=AWL,GAPPY_TEXT,SPAM_PHRASE_00_01,TO_LOCALPART_EQ_REAL, X_MAILING_LIST version=2.44 X-Spam-Level: Jamil,Jamil,Jamil, todo mundo percebeu, só você que não viu! Jamil,Jamil,Jamil, Pra esse tipo de convite, há outras listas no Brasil. Jamil,Jamil,Jamil, eu poderia dizer qualquer coisa, mas preferi uma resposta gentil. Jamil,Jamil,Jamil, minha esperança é a de todos: acho que sua ficha caiu. -x-x-x-x-x-x-x- PS:e fique alegre que eu tô bom de rima hoje ---------- Início da mensagem original ----------- Data: Wed, 5 Mar 2008 16:41:38 -0300 Assunto: [obm-l] Jamil Silva has invited you to join Friendster > You're invited to join Jamil Silva's network of friends. > > By joining Friendster, you can reconnect with old > friends, meet new friends, start a blog, build a custom > profile, keep track of birthdays, and so > much more! ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Mar 6 08:42:43 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m26BelsG018470 for ; Thu, 6 Mar 2008 08:40:47 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m26BekCp018467 for obm-l-MllGbsmmN; Thu, 6 Mar 2008 08:40:46 -0300 Received: from ti-out-0910.google.com (ti-out-0910.google.com [209.85.142.189]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m26BehsG018455 for ; Thu, 6 Mar 2008 08:40:44 -0300 Received: by ti-out-0910.google.com with SMTP id y6so2706692tia.13 for ; Thu, 06 Mar 2008 03:41:06 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=3MjoVCxo1FdIvVe9P6/znYYMM12DumdbiUfwJnnR+G8=; b=tpYWRxcRP/yKMDK4qTq5tEDKfE5z/yKa/mWCAZbUa+UFAaJA4NIw4R+33YV4dPFLI4bunyWgjnUWsxfjQXaXvzfWZaWDqOVUDu/6dLdvRoMCROhF6Cgd7OxQ9H272/8KJeDCpYQXGe6z01PB0sOA8gfvUifonuUNKQqXrD6uv/s= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=PGE5W9Za/+dZn+RtfmNN/fn6aXyQllBwnP1QZkWV4gBSiKufK+qSHh/1vF9CEjjuMmeigbk6K1qEKWAGDadUW15PX/kAXcKUVwl4+Fp+EBkqnEdIObmdls0Gc7jLo9Sk2YxqPKmJC3u2joEI8nAsCPQ4Q4/YZzXgZdKH08ekF/8= Received: by 10.150.195.21 with SMTP id s21mr1882563ybf.114.1204803664599; Thu, 06 Mar 2008 03:41:04 -0800 (PST) Received: by 10.150.158.20 with HTTP; Thu, 6 Mar 2008 03:41:04 -0800 (PST) Message-ID: <5bb472220803060341k7cddfe08t5f58fdd1f8dc9c27@mail.gmail.com> Date: Thu, 6 Mar 2008 08:41:04 -0300 From: "Joao Victor Brasil" To: obm-l@mat.puc-rio.br Subject: =?ISO-8859-1?Q?Re:_[obm-l]_Quest=E3o_de_Probabilidade?= In-Reply-To: <8994b830803051918j1f74dd34vfbb272c92826e3af@mail.gmail.com> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_2960_10690045.1204803664572" References: <402124.36529.qm@web63115.mail.re1.yahoo.com> <5bb472220803051848u23734971s622bc7698b067144@mail.gmail.com> <8994b830803051918j1f74dd34vfbb272c92826e3af@mail.gmail.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Joao Victor Brasil" X-Spam-Status: No, hits=4.7 required=5.0 tests=AWL,IN_REP_TO,MAILTO_LINK,MIME_EXCESSIVE_QP, QUOTED_EMAIL_TEXT,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, REFERENCES,SPAM_PHRASE_00_01,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** ------=_Part_2960_10690045.1204803664572 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Desculpa, n=E3o prestei aten=E7=E3o nesse fato. Achei que n=E3o havia repos= i=E7=E3o. On 3/6/08, Maur=EDcio Collares wrote: > > O enunciado informa que h=E1 reposi=E7=E3o das bolas. Em outras palavras,= a > bola =E9 recolocada na caixa depois do sorteio. > > -- > Abra=E7os, > Maur=EDcio > > 2008/3/5 Joao Victor Brasil : > > me desculpe, mas como posso selecionar selecionar 12 bolas se a urna s= =F3 > tem > > 5??? > > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > Instru=E7=F5es para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > ------=_Part_2960_10690045.1204803664572 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Desculpa, n=E3o prestei aten=E7=E3o nesse fato. Achei que n=E3o havia repos= i=E7=E3o.

On 3/6/08, M= aur=EDcio Collares <mauricioc= @gmail.com> wrote:
O enunciado informa que h=E1 rep= osi=E7=E3o das bolas. Em outras palavras, a
bola =E9 recolocada na caixa= depois do sorteio.

--
Abra=E7os,
Maur=EDcio

2008/3/5 Joao Victor Brasil <<= a href=3D"mailto:jvbrasil@gmail.com">jvbrasil@gmail.com>:
> me= desculpe, mas como posso selecionar selecionar 12 bolas se a urna s=F3 tem=
> 5???

=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D
Instru=E7=F5es para entrar na lista, sair da lista e usar a= lista em
ht= tp://www.mat.puc-rio.br/~obmlistas/obm-l.html
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D

------=_Part_2960_10690045.1204803664572-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Mar 6 08:43:30 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m26BfesG018511 for ; Thu, 6 Mar 2008 08:41:40 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m26BfefH018509 for obm-l-MllGbsmmN; Thu, 6 Mar 2008 08:41:40 -0300 Received: from ti-out-0910.google.com (ti-out-0910.google.com [209.85.142.186]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m26BfbsG018503 for ; Thu, 6 Mar 2008 08:41:38 -0300 Received: by ti-out-0910.google.com with SMTP id y6so2707178tia.13 for ; Thu, 06 Mar 2008 03:42:00 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=cqCG6/168Q29OhYGowAct2VvxiOajNXybmrgPsGWOwQ=; b=sb5TUqrEI4fBRry1pGM+vTEvbm0wQUXYpx1W5GKZ3tCE2sQ+b+N9JaVMTxaljdDxHZa24Mcb91zF6OtUAnwCNRE7ieW5XwjIkp+h20PCuUVuRsTZdoCMJhT4TQdK/TI/MLereJ2iV1h50F0I8w2LElk/vqOZOuhVm3oV6ClgAPo= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=lnbxMs7/x7onTZPCTNgTZooJg+i5Y8c1qE7wD5zBtIZhWPJBjsVlPElCFxMGv2jfmrsGVk8rP+/Q8ETjQx5I/rN0ZcjZJVNgW815pc9mC3r2gUmcFRw2282Inhc+DriNidVH5fCKbxAHXyp3t+gUIQl2A/JD5INptt0RjbjR9Ps= Received: by 10.150.140.6 with SMTP id n6mr1881182ybd.111.1204803718342; Thu, 06 Mar 2008 03:41:58 -0800 (PST) Received: by 10.150.158.20 with HTTP; Thu, 6 Mar 2008 03:41:58 -0800 (PST) Message-ID: <5bb472220803060341o55661828g627d864952e9b770@mail.gmail.com> Date: Thu, 6 Mar 2008 08:41:58 -0300 From: "Joao Victor Brasil" To: obm-l@mat.puc-rio.br Subject: =?ISO-8859-1?Q?Re:_[obm-l]_Quest=E3o_de_Probabilidade?= In-Reply-To: <5bb472220803060341k7cddfe08t5f58fdd1f8dc9c27@mail.gmail.com> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_2964_21521437.1204803718304" References: <402124.36529.qm@web63115.mail.re1.yahoo.com> <5bb472220803051848u23734971s622bc7698b067144@mail.gmail.com> <8994b830803051918j1f74dd34vfbb272c92826e3af@mail.gmail.com> <5bb472220803060341k7cddfe08t5f58fdd1f8dc9c27@mail.gmail.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Joao Victor Brasil" X-Spam-Status: No, hits=4.9 required=5.0 tests=AWL,IN_REP_TO,JAVASCRIPT_UNSAFE,MAILTO_LINK, MIME_EXCESSIVE_QP,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** ------=_Part_2964_21521437.1204803718304 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Saulo, Pq C13,5??? On 3/6/08, Joao Victor Brasil wrote: > > Desculpa, n=E3o prestei aten=E7=E3o nesse fato. Achei que n=E3o havia rep= osi=E7=E3o. > > On 3/6/08, Maur=EDcio Collares wrote: > > > > O enunciado informa que h=E1 reposi=E7=E3o das bolas. Em outras palavra= s, a > > bola =E9 recolocada na caixa depois do sorteio. > > > > -- > > Abra=E7os, > > Maur=EDcio > > > > 2008/3/5 Joao Victor Brasil : > > > me desculpe, mas como posso selecionar selecionar 12 bolas se a urna > > s=F3 tem > > > 5??? > > > > > > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > > Instru=E7=F5es para entrar na lista, sair da lista e usar a lista em > > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > > > > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > > > > ------=_Part_2964_21521437.1204803718304 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline
Saulo,
Pq C13,5???
 
On 3/6/08, J= oao Victor Brasil <jvbrasil@gm= ail.com> wrote:
Desculpa, n=E3o prestei aten=E7= =E3o nesse fato. Achei que n=E3o havia reposi=E7=E3o.=20


On 3/6/08, M= aur=EDcio Collares <mauricioc= @gmail.com> wrote:=20
O enunciado informa que h=E1 rep= osi=E7=E3o das bolas. Em outras palavras, a
bola =E9 recolocada na caixa= depois do sorteio.

--
Abra=E7os,
Maur=EDcio

2008/3/5 Joao Victor Brasil <<= a onclick=3D"return top.js.OpenExtLink(window,event,this)" href=3D"mailto:j= vbrasil@gmail.com" target=3D"_blank">jvbrasil@gmail.com>:
> me= desculpe, mas como posso selecionar selecionar 12 bolas se a urna s=F3 tem=
> 5???

=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D
Instru=E7=F5es para entrar na lista, sair da lista e usar a= lista em
ht= tp://www.mat.puc-rio.br/~obmlistas/obm-l.html
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D


------=_Part_2964_21521437.1204803718304-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Mar 6 08:55:23 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m26BrKsG018966 for ; Thu, 6 Mar 2008 08:53:20 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m26BrKW3018964 for obm-l-MllGbsmmN; Thu, 6 Mar 2008 08:53:20 -0300 Received: from ti-out-0910.google.com (ti-out-0910.google.com [209.85.142.186]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m26BrHsG018961 for ; Thu, 6 Mar 2008 08:53:18 -0300 Received: by ti-out-0910.google.com with SMTP id y6so2712965tia.13 for ; Thu, 06 Mar 2008 03:53:41 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=IDkJggPBopEB5LpMyayrbvPa+iJxInoOGB3vtpUvtDw=; b=Q/tCGS/xWWRnLtF7BOLUOSfw1Jzlf7+Ir9qtqmzneJgh5hlPRC3lofp1zGjAQqxI6lVqARp8B9xhGtjq7EU3of6oZLHUV2zOw9amRD3jPBHupmdWsxJFmly5gSCcGGswlzZv8mzAVry+yP1GS8Fy5cJj7morLCwH0Azm9oeKqnI= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=WvyDkiXC6eZYl1JzjkfXNnnsQpGNje0+cMZSCxC5wmEsQvXbqO4g/s6mOiAtavQT2e7rCLtbzZ9saHMjMY2UOUQWN59EphC23xe3eL4zIKjw2kNjwrZGRJiZC0syqB0qqodRmnY4Rg2vafGbOwZiqCN0+XV4lDRUw/CS7ZSSg4w= Received: by 10.150.157.11 with SMTP id f11mr1904340ybe.54.1204804418960; Thu, 06 Mar 2008 03:53:38 -0800 (PST) Received: by 10.150.158.20 with HTTP; Thu, 6 Mar 2008 03:53:38 -0800 (PST) Message-ID: <5bb472220803060353s4fa6d9caj8db9c693685d520a@mail.gmail.com> Date: Thu, 6 Mar 2008 08:53:38 -0300 From: "Joao Victor Brasil" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Marte In-Reply-To: <694285.12003.qm@web33802.mail.mud.yahoo.com> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_2998_8381591.1204804418920" References: <694285.12003.qm@web33802.mail.mud.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Joao Victor Brasil" X-Spam-Status: No, hits=3.8 required=5.0 tests=AWL,EMAIL_ATTRIBUTION,IN_REP_TO,JAVASCRIPT_UNSAFE, MAILTO_LINK,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, SPAM_REDIRECTOR,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: *** ------=_Part_2998_8381591.1204804418920 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Quando completamos 10 unidades transformamos em uma dezena. Como no sistema de base 10, usamos at=E9 o algarismo 9; o sistema marciano tolera o algaris= mo 5 como unidade e n=E3o tolera o 8. Logo os marcianos devem ter 6 ou 7 dedos nas m=E3os. On 3/5/08, Klaus Ferraz wrote: > > A primeira expedicao a Marte encontrou somente as ruinas de uma > civilizacao. Os exploradores concluiram dos artefatos e desenhos que as > criaturas que produziram esta civilizacao tinham quatro pernas, cada uma > terminada em um conjunto de garras parecidas com dedos. Ap=F3s muito estu= do > foram capazes de traduzir a matematica marciana. Eles encontraram a segui= nte > equacao: > 5x^2-50x+125=3D0 > Esta era uma matematica estranha. O valor x=3D5 parecia correto, mas x=3D= 8 > n=E3o. Entao os exploradores lembraram a maneira como o nosso sistema de > numeracao foi desenvolvido e encontraram evidencias de que o sistema > marciano teve uma historia analoga. Quantos dedos tinham os marcianos? > > ------------------------------ > Abra sua conta no Yahoo! Mail, > o =FAnico sem limite de espa=E7o para armazenamento! > ------=_Part_2998_8381591.1204804418920 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Quando completamos 10 unidades transformamos em uma dezena. Como no sistema= de base 10, usamos at=E9 o algarismo 9; o sistema marciano tolera o algari= smo 5 como unidade e n=E3o tolera o 8. Logo os marcianos devem ter 6 o= u 7 dedos nas m=E3os. 

On 3/5/08, K= laus Ferraz <klausferraz= @yahoo.com.br> wrote:
A primeira expedicao a Marte encontrou somente as ruinas de uma c= ivilizacao. Os exploradores concluiram dos artefatos e desenhos que as= criaturas que produziram esta civilizacao tinham quatro pernas, cada uma t= erminada em um conjunto de garras parecidas com dedos. Ap=F3s muito estudo = foram capazes de traduzir a matematica marciana. Eles encontraram a seguint= e equacao:
5x^2-50x+125=3D0
Esta era uma matematica estranha. O valor x=3D5 parecia correto, mas x= =3D8 n=E3o. Entao os exploradores lembraram a maneira como o nosso sistema = de numeracao foi desenvolvido e encontraram evidencias de que o sistema mar= ciano teve uma historia analoga. Quantos dedos tinham os marcianos?

Abra sua conta no Yahoo! Mail, o =FAnico sem limite de espa=E7o p= ara armazenamento!

------=_Part_2998_8381591.1204804418920-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Mar 6 14:47:52 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m26HimsG017756 for ; Thu, 6 Mar 2008 14:44:48 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m26HilvE017754 for obm-l-MllGbsmmN; Thu, 6 Mar 2008 14:44:47 -0300 Received: from web33704.mail.mud.yahoo.com (web33704.mail.mud.yahoo.com [68.142.201.201]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id m26HijsG017745 for ; Thu, 6 Mar 2008 14:44:46 -0300 Received: (qmail 26420 invoked by uid 60001); 6 Mar 2008 17:45:03 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:X-Mailer:Date:From:Subject:To:MIME-Version:Content-Type:Message-ID; b=lTN92WCryEdVtBjVF6/i4kIHodsSFPivjRq5LuwL3n66I3zuYu1Mty2ElGbPLHQFk9e8kfaFi1XkfEx3qzXWCmIBcU6TWJAYBrNjUwqddxsnlMpsEjJuJdKln7OQO/zBuRr8spi46UalPos+Taqpy88R8InBje2xS65NQZlg+Ko=; X-YMail-OSG: gpxBDqMVM1mCShCgUFc3f82nDqD3ziDSN92LZVtGP.V.uaSnMDBNujIjCpzBJgbTqD2viyhJZDDuP8J4o0SfIA2LQlOg0kCk4FtyMpSGCrVWIc5MJhzftyVDr61U2A-- Received: from [201.92.92.134] by web33704.mail.mud.yahoo.com via HTTP; Thu, 06 Mar 2008 09:45:03 PST X-Mailer: YahooMailRC/902.35 YahooMailWebService/0.7.162 Date: Thu, 6 Mar 2008 09:45:03 -0800 (PST) From: Eduardo Estrada Subject: [SPAM] [obm-l] Problema das Vigas To: obm-l@mat.puc-rio.br MIME-Version: 1.0 Content-Type: text/plain Message-ID: <350805.25765.qm@web33704.mail.mud.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Eduardo Estrada X-Spam-Status: Yes, hits=9.3 required=5.0 tests=FORGED_YAHOO_RCVD,MIME_BOUND_DIGITS_5,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01,SPAM_REDIRECTOR, SUPERLONG_LINE,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ********* X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="0-326908975-1204825503=:25765" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (9.30 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: MIME_BOUND_DIGITS_5 (1.7 points) Spam tool pattern in MIME boundary SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: SUPERLONG_LINE (0.0 points) BODY: Contains a line >=199 characters long SPAM: SPAM_REDIRECTOR (0.4 points) URI: Uses open redirection service SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 201.201.142.68.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 201.201.142.68.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- --0-326908975-1204825503=:25765 Content-Type: text/plain; charset=utf-8 Content-Transfer-Encoding: quoted-printable Ol=C3=A1,=0A=0AAlgu=C3=A9m conhece uma solu=C3=A7=C3=A3o simples para o Pro= blema das Vigas? Consiste no seguinte:=0A=0A"Imagine a seguinte figura:=0A= =0A | |=0A A | = |=0A | |= =0A | |=0A | = | D=0A | = |=0A | |=0A |__________= ________|=0A B C=0A =0A=0AAC= =3D 30 m, BD =3D 20 m, AC e BD interceptam-se em P, que dista 8 m de BC. P= ede-se, calcular o tamanho de BC. Aparentemente simples, para resolver este= problema, ca=C3=ADmos numa equa=C3=A7=C3=A3o de grau maior do que 2. Ent= =C3=A3o, a pergunta, existe alguma solu=C3=A7=C3=A3o simples?=0A=0AUm abra= =C3=A7o,=0AEduardo=0A=0A=0A=0A=0A Abra sua conta no Yahoo! Mail, o =C3= =BAnico sem limite de espa=C3=A7o para armazenamento!=0Ahttp://br.mail.yaho= o.com/ --0-326908975-1204825503=:25765 Content-Type: text/html; charset=utf-8 Content-Transfer-Encoding: quoted-printable
Ol=C3=A1,

Algu=C3=A9m conhece uma solu=C3=A7=C3= =A3o simples para o Problema das Vigas? Consiste no seguinte:

"Imagi= ne a seguinte figura:

       &nbs= p; |            = ;            &n= bsp;           |
 = ;   A  |        &nbs= p;            &= nbsp;           &nbs= p;  |
         |            &= nbsp;           &nbs= p;           |
=0A&nbs= p;        |     = ;            &n= bsp;            = ;      |
=0A      = ;   |          =             &nb= sp;            = | D
=0A         |  &n= bsp;            = ;            &n= bsp;        |
=0A   &n= bsp;     |       &nb= sp;            =             &nb= sp;   |
=0A         |_= _________________|
       =0AB &= nbsp;           &nbs= p;            &= nbsp;        C
    &nb= sp; 

AC =3D 30 m, BD =3D 20 m, AC e BD interceptam-se em P, q= ue dista 8 m de BC. Pede-se, calcular o tamanho de BC. Aparentemente simple= s, para resolver este problema, ca=C3=ADmos numa equa=C3=A7=C3=A3o de grau = maior do que 2. Ent=C3=A3o, a pergunta, existe alguma solu=C3=A7=C3=A3o sim= ples?

Um abra=C3=A7o,
Eduardo

=0A=0A=0A <= hr size=3D1>Abra sua conta no Yahoo! Mail, o =C3=BAnico sem limit= e de espa=C3=A7o para armazenamento! =0A --0-326908975-1204825503=:25765-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Mar 6 15:49:13 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m26IkVsG021403 for ; Thu, 6 Mar 2008 15:46:32 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m26IkN4r021393 for obm-l-MllGbsmmN; Thu, 6 Mar 2008 15:46:23 -0300 Received: from gv-out-0910.google.com (gv-out-0910.google.com [216.239.58.184]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m26Ik4sG021374 for ; Thu, 6 Mar 2008 15:46:05 -0300 Received: by gv-out-0910.google.com with SMTP id u5so1617303gve.25 for ; Thu, 06 Mar 2008 10:46:28 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=z+OkKfT0wIPCG0Aw6a7+G5D280CCU20R5URENbcqvoo=; b=bC+Kr1ZeBL6tpsVcjfVq8QrITO59DpNuGyAhaWYBZPplEirXiJ0mNds0rM3pMcNKVzOFFUOTn47n7RB10YPZ8DeM/akUbFfc6B9LoeOUu1onPe+x8AI3aksSLyL8exAbniLIZFrUEjOLqy1HsHEZbsbHCT/z5mZU60ck1Gr23EA= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=iNbHIo/WQu5G9GosQPEWuKt0BMSb5KYALFg06z+CmeTUCt0IS+CcHL2XsUeaLEOrvVrDvHKRFU6Mw3hoCIG00Hcddfc7smtMbNWDovfDh6nG7pN5RQ9aPP87ZfXmT/IaIB3AnLWl/r5KixqKRVrpvh2NSDiPAlND2sSXgpsss/I= Received: by 10.150.140.6 with SMTP id n6mr66976ybd.111.1204829186897; Thu, 06 Mar 2008 10:46:26 -0800 (PST) Received: by 10.150.158.20 with HTTP; Thu, 6 Mar 2008 10:46:26 -0800 (PST) Message-ID: <5bb472220803061046g44753003r3fecfb5fd845e186@mail.gmail.com> Date: Thu, 6 Mar 2008 15:46:26 -0300 From: "Joao Victor Brasil" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Problema das Vigas In-Reply-To: <350805.25765.qm@web33704.mail.mud.yahoo.com> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_4257_17489635.1204829186883" References: <350805.25765.qm@web33704.mail.mud.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Joao Victor Brasil" X-Spam-Status: No, hits=3.6 required=5.0 tests=AWL,EMAIL_ATTRIBUTION,IN_REP_TO,JAVASCRIPT_UNSAFE, MAILTO_LINK,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_01_02, SPAM_REDIRECTOR,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: *** ------=_Part_4257_17489635.1204829186883 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline AB=3DCD??? On 3/6/08, Eduardo Estrada wrote: > > Ol=E1, > > Algu=E9m conhece uma solu=E7=E3o simples para o Problema das Vigas? Consi= ste no > seguinte: > > "Imagine a seguinte figura: > > | | > A | | > | | > | | > | | D > | | > | | > |__________________| > B C > > > AC =3D 30 m, BD =3D 20 m, AC e BD interceptam-se em P, que dista 8 m de B= C. > Pede-se, calcular o tamanho de BC. Aparentemente simples, para resolver e= ste > problema, ca=EDmos numa equa=E7=E3o de grau maior do que 2. Ent=E3o, a pe= rgunta, > existe alguma solu=E7=E3o simples? > > Um abra=E7o, > Eduardo > > ------------------------------ > Abra sua conta no Yahoo! Mail, > o =FAnico sem limite de espa=E7o para armazenamento! > ------=_Part_4257_17489635.1204829186883 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline AB=3DCD???

On 3/6/08, E= duardo Estrada <eestrada= itu@yahoo.com.br> wrote:
Ol=E1,

Algu=E9m conhece uma solu=E7=E3o simples para o Proble= ma das Vigas? Consiste no seguinte:

"Imagine a seguinte figura:=

         |    &= nbsp;           &nbs= p;            &= nbsp;      |
    A  | =             &nb= sp;            =           |
  &nb= sp;      |      &nbs= p;            &= nbsp;           &nbs= p;    |
         = |            &n= bsp;            = ;           |
 &n= bsp;       |     &nb= sp;            =             &nb= sp;     | D
         |    &= nbsp;           &nbs= p;            &= nbsp;      |
     &nbs= p;   |          = ;            &n= bsp;            = ; |
         |__________________= |
        B    &n= bsp;            = ;            &n= bsp;     C
      

A= C =3D 30 m, BD =3D 20 m, AC e BD interceptam-se em P, que dista 8 m de BC. = Pede-se, calcular o tamanho de BC. Aparentemente simples, para resolver est= e problema, ca=EDmos numa equa=E7=E3o de grau maior do que 2. Ent=E3o, a pe= rgunta, existe alguma solu=E7=E3o simples?

Um abra=E7o,
Eduardo

Abra sua conta no Yahoo! Mail, o =FAnico sem limite de espa=E7o p= ara armazenamento!

------=_Part_4257_17489635.1204829186883-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Mar 6 16:47:13 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m26JjlsG028406 for ; Thu, 6 Mar 2008 16:45:47 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m26JjlGV028404 for obm-l-MllGbsmmN; Thu, 6 Mar 2008 16:45:47 -0300 Received: from web33702.mail.mud.yahoo.com (web33702.mail.mud.yahoo.com [68.142.201.199]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id m26JjhsG028398 for ; Thu, 6 Mar 2008 16:45:45 -0300 Received: (qmail 4131 invoked by uid 60001); 6 Mar 2008 19:46:06 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:X-Mailer:Date:From:Subject:To:MIME-Version:Content-Type:Message-ID; b=JxO2o+jOCw3nLgLb6RdN+iZziM1y5io5hhAfCr9sJhe6whme+nO/GHZmJyo4dgOu+c7JqceyHpkpk+X0m/aq27kOwCAZTrpKg+txNMBabypE589TINbqNiTCc2E5mp+yZDi910t0pZBoTvBl4D0Q5pDJ/OCbaag3DnAvP4JZX8o=; X-YMail-OSG: jqnixokVM1n7DIQX7ALoxcybr2dZyd8GAj7TCmbcSPNW3X47PoT5Gt.3IRC8YT8VoiNuSKEX_KJZ_LKVeRoqLu6to4aDJBdR5do_iR3eBPDxhChk2Tw- Received: from [201.92.92.134] by web33702.mail.mud.yahoo.com via HTTP; Thu, 06 Mar 2008 11:46:06 PST X-Mailer: YahooMailRC/902.35 YahooMailWebService/0.7.162 Date: Thu, 6 Mar 2008 11:46:06 -0800 (PST) From: Eduardo Estrada Subject: [SPAM] Res: [obm-l] Problema das Vigas To: obm-l@mat.puc-rio.br MIME-Version: 1.0 Content-Type: text/plain Message-ID: <282599.1800.qm@web33702.mail.mud.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Eduardo Estrada X-Spam-Status: Yes, hits=7.6 required=5.0 tests=AWL,EMAIL_ATTRIBUTION,FORGED_YAHOO_RCVD,MAILTO_LINK, RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_01_02, SPAM_REDIRECTOR,SUPERLONG_LINE,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******* X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="0-378812290-1204832766=:1800" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (7.60 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: EMAIL_ATTRIBUTION (-1.6 points) BODY: Contains what looks like an email attribution SPAM: SPAM_PHRASE_01_02 (0.5 points) BODY: Spam phrases score is 01 to 02 (low) SPAM: [score: 1] SPAM: MAILTO_LINK (0.2 points) BODY: Includes a URL link to send an email SPAM: SUPERLONG_LINE (0.0 points) BODY: Contains a line >=199 characters long SPAM: SPAM_REDIRECTOR (0.4 points) URI: Uses open redirection service SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 199.201.142.68.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 199.201.142.68.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (1.7 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- --0-378812290-1204832766=:1800 Content-Type: text/plain; charset=utf-8 Content-Transfer-Encoding: quoted-printable N=C3=A3o, pois os =C3=A2ngulos inferiores, na figura, s=C3=A3o retos.=0A=0A= ----- Mensagem original ----=0ADe: Joao Victor Brasil = =0APara: obm-l@mat.puc-rio.br=0AEnviadas: Quinta-feira, 6 de Mar=C3=A7o de = 2008 15:46:26=0AAssunto: Re: [obm-l] Problema das Vigas=0A=0AAB=3DCD???=0A= =0AOn 3/6/08, Eduardo Estrada wrote:Ol=C3=A1,=0A= =0AAlgu=C3=A9m conhece uma solu=C3=A7=C3=A3o simples para o Problema das Vi= gas? Consiste no seguinte:=0A=0A"Imagine a seguinte figura:=0A=0A |= |=0A A | = |=0A | |=0A | = |=0A | = | D=0A | |=0A |= |=0A |__________________|=0A = B C=0A =0A=0AAC =3D 30 m, BD = =3D 20 m, AC e BD interceptam-se em P, que dista 8 m de BC. Pede-se, calcul= ar o tamanho de BC. Aparentemente simples, para resolver este problema, ca= =C3=ADmos numa equa=C3=A7=C3=A3o de grau maior do que 2. Ent=C3=A3o, a perg= unta, existe alguma solu=C3=A7=C3=A3o simples?=0A=0AUm abra=C3=A7o,=0AEduar= do=0A=0A=0A=0AAbra sua conta no Yahoo! Mail, o =C3=BAnico sem limite de esp= a=C3=A7o para armazenamento! =0A=0A=0A=0A=0A=0A=0A=0A=0A Abra sua cont= a no Yahoo! Mail, o =C3=BAnico sem limite de espa=C3=A7o para armazenamento= !=0Ahttp://br.mail.yahoo.com/ --0-378812290-1204832766=:1800 Content-Type: text/html; charset=utf-8 Content-Transfer-Encoding: quoted-printable
N=C3=A3o, pois os =C3=A2ngulos inferiores, na figura, = s=C3=A3o retos.

----- Mensagem original ----
De: Joao Vic= tor Brasil <jvbrasil@gmail.com>
Para: obm-l@mat.puc-rio.br
Envi= adas: Quinta-feira, 6 de Mar=C3=A7o de 2008 15:46:26
Assunto: Re: [obm-l= ] Problema das Vigas

AB=3DCD???

=0A
On 3/6/08, Eduardo Estrada <eestradaitu@yahoo.com.br&g= t; wrote:=0A
=0A
Ol=C3=A1,

Algu=C3=A9m conhece uma so= lu=C3=A7=C3=A3o simples para o Problema das Vigas? Consiste no seguinte:
"Imagine a seguinte figura:

=0A     &n= bsp;   |         &nb= sp;            =             &nb= sp; |
    A  |      &n= bsp;            = ;            &n= bsp;    |
        = ; |            =             &nb= sp;           |
 =         |            &= nbsp;           &nbs= p;           |
 &= nbsp;       |     &n= bsp;            = ;            &n= bsp;     | D
=0A      =    |          &= nbsp;           &nbs= p;             = |
         |   &n= bsp;            = ;            &n= bsp;       |
     = ;    |__________________|
     &= nbsp;  B          &n= bsp;            = ;            C
&n= bsp;     

AC =3D 30 m, BD =3D 20 m, AC e BD int= erceptam-se em P, que dista 8 m de BC. Pede-se, calcular o tamanho de BC. Aparentemente simples, para resolve= r este problema, ca=C3=ADmos numa equa=C3=A7=C3=A3o de grau maior do que 2.= Ent=C3=A3o, a pergunta, existe alguma solu=C3=A7=C3=A3o simples?
=0AUm abra=C3=A7o,
Eduardo

=0A
=0AAbra sua conta no Yahoo! Mail, o =C3=BAnico sem limite de espa=C3= =A7o para armazenamento!
=0A

=0A
=0A=0A=0A
Abra sua conta no Yahoo= ! Mail, o =C3=BAnico sem limite de espa=C3=A7o para armazenamento! =0A<= /body> --0-378812290-1204832766=:1800-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Mar 6 18:29:05 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m26LRBsG003013 for ; Thu, 6 Mar 2008 18:27:11 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m26LRBtn003011 for obm-l-MllGbsmmN; Thu, 6 Mar 2008 18:27:11 -0300 Received: from smtp.bol.com.br (smtpout1.bol.com.br [200.221.4.212]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m26LRAsG003007 for ; Thu, 6 Mar 2008 18:27:10 -0300 Received: from localhost (localhost [127.0.0.1]) by smart5.bol.com.br (Postfix) with ESMTP id 0EBDF442 for ; Thu, 6 Mar 2008 18:27:35 -0300 (BRT) Received: from pai (unknown [201.88.134.242]) by smart5.bol.com.br (Postfix) with ESMTP id 2E580596 for ; Thu, 6 Mar 2008 18:27:33 -0300 (BRT) Message-ID: <005201c87fd1$15ff3b80$6701a8c0@pai> From: "Tio Cabri st" To: Subject: [SPAM] [obm-l] dicas diferente das dicas Date: Thu, 6 Mar 2008 18:28:53 -0300 MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: 7bit X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2800.1478 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2800.1478 X-SIG5: 397c211ea79816c418d1175c96c4dc62 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Tio Cabri st" X-Spam-Status: Yes, hits=6.0 required=5.0 tests=AWL,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01, USER_AGENT_OE,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ****** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (6.00 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: USER_AGENT_OE (0.2 points) X-Mailer header indicates a non-spam MUA (Outlook Express) SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 242.134.88.201.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 242.134.88.201.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (0.0 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- Caros colegas, boa tarde. A minha dúvida está na última linha. Não me recordo a data mas sei que os inúmeros altruístas que participam dessa lista me ajudaram e muito, obrigado. Gostaria de retribuir ao TENTAR ajudar alguns colegas de trabalho que foram obrigados a usar o LaTex. Escrevendo textos matemáticos. Pontos que destaco: Estava pensando em preparar um preâmbulo com quase tudo que eles usarão como esse ======================================= \documentclass[12pt]{article} \usepackage[latin1]{inputenc} \usepackage[brazil]{babel} \usepackage{fancybox,color,amsmath,float,amssymb,amsfonts)} ======================================= e coisas que acho importante: - os passos da instalação (ordem) miktex , gs, gsv, acrobat, teXnic. - uso do comentário (%) - o comando \input (mostrando a possibilidade do doc ser feito em vários arquivos) - \newcommand - \def - o uso do ambiente matemático alguns cuidados como: a_1 e a_{123} =============================================== Gostaria de saber se: está de bom tamanho, estou me excedendo ou é muito pouco? Qualquer comentário será muito bem vindo. Agradeço Cabri ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Mar 6 20:27:17 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m26NPUsG008833 for ; Thu, 6 Mar 2008 20:25:30 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m26NPTg1008830 for obm-l-MllGbsmmN; Thu, 6 Mar 2008 20:25:29 -0300 Received: from fg-out-1718.google.com (fg-out-1718.google.com [72.14.220.154]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m26NPOsG008817 for ; Thu, 6 Mar 2008 20:25:24 -0300 Received: by fg-out-1718.google.com with SMTP id e12so1013207fga.3 for ; Thu, 06 Mar 2008 15:25:48 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=JK2k3NbBQ3YcuYvtKWhuI5hRgeOA2nwGiebZnDNJ+4Q=; b=ec8CXmRcV8ciiEEVW7x47NVah1BVSGM+dRiFGwN9AYxyzS2Ghb2UGA/ndqwwainOSwe7Gg8U3xRAwJIZ80sZ2Yp6ta7u4JvRBRX+WJGjsmiBQVyBqP1NDQPI13xoxVePxdX/DPduyUCUK5WSY7siJpNcG3CH7qXvH3QJEOqSju4= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=bR/S9VMXjWaTmNWku2feXvygxR/oW+yGzkGkj/AhmCOl7Gp//aO0FosSdr7CpoODVzdO9C0mA4xReANnS/70WbMOhgrLbQZKDm6683Fawd+u9ELi73pd0jbuw0+iibg7tY3I+8l02WthwBhxu+VjnwFkqwkxg6aPHgJGSQb9sA0= Received: by 10.86.3.4 with SMTP id 4mr441725fgc.69.1204845948007; Thu, 06 Mar 2008 15:25:48 -0800 (PST) Received: by 10.86.74.8 with HTTP; Thu, 6 Mar 2008 15:25:47 -0800 (PST) Message-ID: Date: Thu, 6 Mar 2008 20:25:47 -0300 From: "saulo nilson" To: obm-l@mat.puc-rio.br Subject: =?ISO-8859-1?Q?Re:_[obm-l]_Quest=E3o_de_Probabilidade?= In-Reply-To: <5bb472220803060341o55661828g627d864952e9b770@mail.gmail.com> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_15308_32585860.1204845948004" References: <402124.36529.qm@web63115.mail.re1.yahoo.com> <5bb472220803051848u23734971s622bc7698b067144@mail.gmail.com> <8994b830803051918j1f74dd34vfbb272c92826e3af@mail.gmail.com> <5bb472220803060341k7cddfe08t5f58fdd1f8dc9c27@mail.gmail.com> <5bb472220803060341o55661828g627d864952e9b770@mail.gmail.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "saulo nilson" X-Spam-Status: No, hits=-0.1 required=5.0 tests=AWL,IN_REP_TO,JAVASCRIPT_UNSAFE,MAILTO_LINK, MIME_EXCESSIVE_QP,QUOTED_EMAIL_TEXT,REFERENCES, SPAM_PHRASE_00_01,X_MAILING_LIST version=2.44 X-Spam-Level: ------=_Part_15308_32585860.1204845948004 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline e o numero de solu=E7oes do sistema abaixo a+b+c+d+e=3D12 On 3/6/08, Joao Victor Brasil wrote: > > Saulo, > Pq C13,5??? > > On 3/6/08, Joao Victor Brasil wrote: > > > > Desculpa, n=E3o prestei aten=E7=E3o nesse fato. Achei que n=E3o havia r= eposi=E7=E3o. > > > > > > On 3/6/08, Maur=EDcio Collares wrote: > > > > > > O enunciado informa que h=E1 reposi=E7=E3o das bolas. Em outras palav= ras, a > > > bola =E9 recolocada na caixa depois do sorteio. > > > > > > -- > > > Abra=E7os, > > > Maur=EDcio > > > > > > 2008/3/5 Joao Victor Brasil : > > > > me desculpe, mas como posso selecionar selecionar 12 bolas se a urn= a > > > s=F3 tem > > > > 5??? > > > > > > > > > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > > > Instru=E7=F5es para entrar na lista, sair da lista e usar a lista em > > > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > > > > > > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > > > > > > > > ------=_Part_15308_32585860.1204845948004 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline
e o numero de solu=E7oes do sistema abaixo
a+b+c+d+e=3D12

 
On 3/6/08, J= oao Victor Brasil <jvbrasil@gm= ail.com> wrote:
Saulo,
Pq C13,5???
 
On 3/6/08, J= oao Victor Brasil <jvbrasil@gm= ail.com> wrote:=20
Desculpa, n=E3o prestei aten=E7= =E3o nesse fato. Achei que n=E3o havia reposi=E7=E3o.=20


On 3/6/08, M= aur=EDcio Collares <mauricioc= @gmail.com> wrote:=20
O enunciado informa que h=E1 rep= osi=E7=E3o das bolas. Em outras palavras, a
bola =E9 recolocada na caixa= depois do sorteio.

--
Abra=E7os,
Maur=EDcio

2008/3/5 Joao Victor Brasil <<= a onclick=3D"return top.js.OpenExtLink(window,event,this)" href=3D"mailto:j= vbrasil@gmail.com" target=3D"_blank">jvbrasil@gmail.com>:
> me= desculpe, mas como posso selecionar selecionar 12 bolas se a urna s=F3 tem=
> 5???

=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D
Instru=E7=F5es para entrar na lista, sair da lista e usar a= lista em
ht= tp://www.mat.puc-rio.br/~obmlistas/obm-l.html
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D



------=_Part_15308_32585860.1204845948004-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Mar 6 21:44:49 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m270gvsG012990 for ; Thu, 6 Mar 2008 21:42:57 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m270gvfc012988 for obm-l-MllGbsmmN; Thu, 6 Mar 2008 21:42:57 -0300 Received: from zeus.hotlink.com.br (zeus.hotlink.com.br [189.1.1.250]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m270gtsG012983 for ; Thu, 6 Mar 2008 21:42:56 -0300 Received: by zeus.hotlink.com.br (Postfix, from userid 1002) id BDC7F48AA82; Thu, 6 Mar 2008 21:45:27 -0300 (BRT) Received: from windows5095252 (veloz-1-2-22.hotlink.com.br [189.1.2.22]) by zeus.hotlink.com.br (Postfix) with SMTP id 6C65C48A9B3 for ; Thu, 6 Mar 2008 21:45:27 -0300 (BRT) Message-ID: <003b01c87fec$3fa7cc70$5700a8c0@windows5095252> From: "Gustavo Duarte" To: References: <402124.36529.qm@web63115.mail.re1.yahoo.com> <5bb472220803051848u23734971s622bc7698b067144@mail.gmail.com> <8994b830803051918j1f74dd34vfbb272c92826e3af@mail.gmail.com> <5bb472220803060341k7cddfe08t5f58fdd1f8dc9c27@mail.gmail.com> <5bb472220803060341o55661828g627d864952e9b770@mail.gmail.com> Subject: [SPAM] [obm-l] =?iso-8859-1?Q?Re:_=5Bobm-l=5D_Quest=E3o_de_Probabilidade?= Date: Thu, 6 Mar 2008 21:43:23 -0300 MIME-Version: 1.0 Content-Type: text/plain X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2900.3138 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.3198 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Gustavo Duarte" X-Spam-Status: Yes, hits=6.2 required=5.0 tests=AWL,HTML_FONT_COLOR_BLUE,HTML_FONT_COLOR_RED, JAVASCRIPT_UNSAFE,MAILTO_LINK,MIME_EXCESSIVE_QP, RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,REFERENCES, SPAM_PHRASE_00_01,SUPERLONG_LINE,USER_AGENT_OE, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ****** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_NextPart_000_0038_01C87FD3.1A36B8C0" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (6.20 hits, 5 required) SPAM: REFERENCES (-0.5 points) Has a valid-looking References header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: USER_AGENT_OE (0.2 points) X-Mailer header indicates a non-spam MUA (Outlook Express) SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: HTML_FONT_COLOR_RED (0.3 points) BODY: HTML font color is red SPAM: HTML_FONT_COLOR_BLUE (0.2 points) BODY: HTML font color is blue SPAM: JAVASCRIPT_UNSAFE (0.3 points) BODY: Easily-executed JavaScript code SPAM: MAILTO_LINK (0.2 points) BODY: Includes a URL link to send an email SPAM: SUPERLONG_LINE (0.0 points) BODY: Contains a line >=199 characters long SPAM: MIME_EXCESSIVE_QP (1.0 points) RAW: Excessive quoted-printable encoding in body SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 250.1.1.189.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 250.1.1.189.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-1.3 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- This is a multi-part message in MIME format. ------=_NextPart_000_0038_01C87FD3.1A36B8C0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Desculpe, mas o n=FAmero de solu=E7=E3o da eq a+b+c+d+e =3D12 n=E3o = seria C 16,4 =3D 1820 ou ainda fazendo ponto (p) barra (b), seria 12 = pontos e 4 barras, por exemplo : ppbppbpppbppppbp que poderia ser = tamb=E9m permuta=E7=E3ode 16 elementos com repeti=E7=E3o de um elemento = 4 vz e de outro 12 vz . ? ----- Original Message -----=20 From: saulo nilson=20 To: obm-l@mat.puc-rio.br=20 Sent: Thursday, March 06, 2008 8:25 PM Subject: Re: [obm-l] Quest=E3o de Probabilidade e o numero de solu=E7oes do sistema abaixo a+b+c+d+e=3D12 =20 On 3/6/08, Joao Victor Brasil wrote:=20 Saulo,=20 Pq C13,5??? =20 On 3/6/08, Joao Victor Brasil wrote:=20 Desculpa, n=E3o prestei aten=E7=E3o nesse fato. Achei que n=E3o = havia reposi=E7=E3o.=20 On 3/6/08, Maur=EDcio Collares wrote:=20 O enunciado informa que h=E1 reposi=E7=E3o das bolas. Em outras = palavras, a bola =E9 recolocada na caixa depois do sorteio. -- Abra=E7os, Maur=EDcio 2008/3/5 Joao Victor Brasil : > me desculpe, mas como posso selecionar selecionar 12 bolas se = a urna s=F3 tem > 5??? = =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D Instru=E7=F5es para entrar na lista, sair da lista e usar a = lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html = =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D ------=_NextPart_000_0038_01C87FD3.1A36B8C0 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable
Desculpe, mas o n=FAmero de solu=E7=E3o = da eq a+b+c+d+e=20 =3D12 n=E3o seria C 16,4 = =3D 1820 ou ainda=20 fazendo ponto (p) barra = (b), seria 12 pontos e 4 barras, = por=20 exemplo : ppbppbpppbppppbp que poderia=20 ser tamb=E9m permuta=E7=E3ode 16 elementos  com = repeti=E7=E3o de um elemento 4=20 vz e de outro 12 vz  . ?
----- Original Message -----
From:=20 saulo=20 nilson
Sent: Thursday, March 06, 2008 = 8:25=20 PM
Subject: Re: [obm-l] Quest=E3o = de=20 Probabilidade

e o numero de solu=E7oes do sistema abaixo
a+b+c+d+e=3D12

 
On 3/6/08, Joao Victor=20 Brasil <jvbrasil@gmail.com>=20 wrote:=20
Saulo,
Pq C13,5???
 
On 3/6/08, Joao=20 Victor Brasil <jvbrasil@gmail.com>=20 wrote:=20
Desculpa,=20 n=E3o prestei aten=E7=E3o nesse fato. Achei que n=E3o havia = reposi=E7=E3o.=20


On 3/6/08, Maur=EDcio=20 Collares <mauricioc@gmail.com> wrote:=20
O=20 enunciado informa que h=E1 reposi=E7=E3o das bolas. Em outras = palavras,=20 a
bola =E9 recolocada na caixa depois do=20 sorteio.

--
Abra=E7os,
Maur=EDcio

2008/3/5 = Joao Victor=20 Brasil <jvbrasil@gmail.com>:
> me desculpe, = mas como=20 posso selecionar selecionar 12 bolas se a urna s=F3 tem
>=20 = 5???

=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D
Instru=E7=F5es=20 para entrar na lista, sair da lista e usar a lista em
http://www.mat.puc-rio.br/~obmlistas/obm-l.html
=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D



------=_NextPart_000_0038_01C87FD3.1A36B8C0-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Mar 6 23:10:43 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m27293sG016746 for ; Thu, 6 Mar 2008 23:09:03 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m27292Ds016744 for obm-l-MllGbsmmN; Thu, 6 Mar 2008 23:09:02 -0300 Received: from web90503.mail.mud.yahoo.com (web90503.mail.mud.yahoo.com [216.252.100.170]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id m27290sG016740 for ; Thu, 6 Mar 2008 23:09:01 -0300 Received: (qmail 901 invoked by uid 60001); 7 Mar 2008 02:09:23 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:X-Mailer:Date:From:Subject:To:MIME-Version:Content-Type:Content-Transfer-Encoding:Message-ID; b=5MKNnJn42UqpFtTSrYNGmwVpG9Y0DQYS5qiVr+2aECWr/DRScIir2IflETH81RqjdDpVtDwnVKuT1biTomERyQ4utw01sHxXpaka5CVDfyFkxirwzgUkoWtHVzOPSwGsW1iqFniEEMgpL8aRQT7vkym+GTmNdxa32ICOgVuTOmo=; X-YMail-OSG: kdT6gm8VM1nj5o4_tIQcRiBfHeYq7vD2QxJ6YiGjeic3kZwOGlx.FsO8oWtz0UhyGQ-- Received: from [201.36.162.177] by web90503.mail.mud.yahoo.com via HTTP; Thu, 06 Mar 2008 18:09:22 PST X-Mailer: YahooMailRC/902.35 YahooMailWebService/0.7.162 Date: Thu, 6 Mar 2008 18:09:22 -0800 (PST) From: Eric Campos Bastos Guedes Subject: [SPAM] [obm-l] Probabilidade Surreal To: obm-l@mat.puc-rio.br MIME-Version: 1.0 Content-Type: text/plain; charset=iso-8859-1 Message-ID: <114874.878.qm@web90503.mail.mud.yahoo.com> Content-Transfer-Encoding: 7bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m27292sG016742 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Eric Campos Bastos Guedes X-Spam-Status: Yes, hits=8.7 required=5.0 tests=AWL,FORGED_YAHOO_RCVD,FROM_ENDS_IN_NUMS, MAILTO_TO_SPAM_ADDR,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, SPAM_PHRASE_00_01,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (8.70 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: FROM_ENDS_IN_NUMS (0.9 points) From: ends in numbers SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: MAILTO_TO_SPAM_ADDR (0.7 points) URI: Includes a link to a likely spammer email address SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 170.100.252.216.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 170.100.252.216.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-0.1 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- QUESTAO DESCONCERTANTE: Qual a probabilidade de um analista de sistemas ter sido morto numa clinica psiquiatrica em Sao Goncalo / RJ no ano de 2007 e alguem, de nome "Eric Campos Bastos Guedes" estar tentando a meses denunciar o fato as autoridades e a midia, sem exito? MINHA RESPOSTA: Essa probabilidade estah bastante proxima de 1. Por favor, ENTREM EM CONTATO. Como matematico e membro da SBM PECO A AJUDA DE VOCES. A midia SABE e IGNORA. ============================================= Eric Campos Bastos Guedes Formulas para primos http://geocities.yahoo.com.br/mathfire2001 http://br.geocities.com/mathfire2001/ Projeto Matematica para Todos mathfire2001@yahoo.com.br MSN: fator-n@hotmail.com Celular: 0xx-21-8131-7542 ============================================= Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! http://br.mail.yahoo.com/ ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Mar 6 23:23:15 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m272M9sG017505 for ; Thu, 6 Mar 2008 23:22:09 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m272M8Ya017503 for obm-l-MllGbsmmN; Thu, 6 Mar 2008 23:22:08 -0300 Received: from fg-out-1718.google.com (fg-out-1718.google.com [72.14.220.153]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m272M5sG017488 for ; Thu, 6 Mar 2008 23:22:05 -0300 Received: by fg-out-1718.google.com with SMTP id e12so1892223fga.3 for ; Thu, 06 Mar 2008 18:22:29 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=dLfCQle6MU9eb+1O2a1QvM0VRxaQasRpFSGjvBCWR/A=; b=dI6cEDvQiRA7nwg4v/no0HTtbmEzH6uG7bIz1a3Cd8N+bIsXyAz/wVkzarIvouQO+3oWT5rcSvJV8ef3JStSkj5siavyexCKrVeIHNPopCgsFNfbef1U/jSNlIYyYgDUnPJoiE9/lQjokVEnjo0uZO57XU9+JuKn2OAa4OcjSbg= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=YuBh7KhYfq51yyUQsfnArn4DtBeS3cetQOei8YhbeX2LYzz0NhU5/ADu4nuQwnFKPQA0aVDSJcwNXrIHcoF3nFq7vCfkDe0kM92VgWSWwL40NvheZbGcvA5zSoWAytaSCBkMm3uu2DELZGQsCdnZEXVTSnCIT+7QuMHa7nrRlMc= Received: by 10.86.28.5 with SMTP id b5mr683518fgb.47.1204856549256; Thu, 06 Mar 2008 18:22:29 -0800 (PST) Received: by 10.86.74.8 with HTTP; Thu, 6 Mar 2008 18:22:29 -0800 (PST) Message-ID: Date: Thu, 6 Mar 2008 22:22:29 -0400 From: "saulo nilson" To: obm-l@mat.puc-rio.br Subject: =?ISO-8859-1?Q?Re:_[obm-l]_Re:_[obm-l]_Quest=E3o_de_Probabilidade?= In-Reply-To: <003b01c87fec$3fa7cc70$5700a8c0@windows5095252> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_15509_27620982.1204856549274" References: <402124.36529.qm@web63115.mail.re1.yahoo.com> <5bb472220803051848u23734971s622bc7698b067144@mail.gmail.com> <8994b830803051918j1f74dd34vfbb272c92826e3af@mail.gmail.com> <5bb472220803060341k7cddfe08t5f58fdd1f8dc9c27@mail.gmail.com> <5bb472220803060341o55661828g627d864952e9b770@mail.gmail.com> <003b01c87fec$3fa7cc70$5700a8c0@windows5095252> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "saulo nilson" X-Spam-Status: No, hits=-0.6 required=5.0 tests=AWL,EMAIL_ATTRIBUTION,HTML_FONT_COLOR_BLUE, HTML_FONT_COLOR_RED,IN_REP_TO,JAVASCRIPT_UNSAFE, MAILTO_LINK,MIME_EXCESSIVE_QP,QUOTED_EMAIL_TEXT,REFERENCES, SPAM_PHRASE_00_01,X_MAILING_LIST version=2.44 X-Spam-Level: ------=_Part_15509_27620982.1204856549274 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline vc permuta somente os bs entre os 13 espa=E7os existentes entre os ps, sena= o ocorre repeti=E7ao exemplo permutando p vc obtem bpp ppb mas depois vc permuta os dois ps de novo ai vc volta para configura=E7ao original. On 3/6/08, Gustavo Duarte wrote: > > Desculpe, mas o n=FAmero de solu=E7=E3o da eq a+b+c+d+e =3D12 n=E3o seri= a *C 16,4 *=3D > 1820 ou ainda fazendo ponto (*p*) barra (*b*), seria 12 pontos e 4 barras= , > por exemplo : pp*b*pp*b*ppp*b*pppp*b*p que poderia ser tamb=E9m permuta= =E7=E3ode > 16 elementos com repeti=E7=E3o de um elemento 4 vz e de outro 12 vz . ? > > ----- Original Message ----- > *From:* saulo nilson > *To:* obm-l@mat.puc-rio.br > *Sent:* Thursday, March 06, 2008 8:25 PM > *Subject:* Re: [obm-l] Quest=E3o de Probabilidade > > > e o numero de solu=E7oes do sistema abaixo > a+b+c+d+e=3D12 > > > On 3/6/08, Joao Victor Brasil wrote: > > > > Saulo, > > Pq C13,5??? > > > > On 3/6/08, Joao Victor Brasil wrote: > > > > > > Desculpa, n=E3o prestei aten=E7=E3o nesse fato. Achei que n=E3o havia > > > reposi=E7=E3o. > > > > > > On 3/6/08, Maur=EDcio Collares wrote: > > > > > > > > O enunciado informa que h=E1 reposi=E7=E3o das bolas. Em outras pal= avras, > > > > a > > > > bola =E9 recolocada na caixa depois do sorteio. > > > > > > > > -- > > > > Abra=E7os, > > > > Maur=EDcio > > > > > > > > 2008/3/5 Joao Victor Brasil : > > > > > me desculpe, mas como posso selecionar selecionar 12 bolas se a > > > > urna s=F3 tem > > > > > 5??? > > > > > > > > > > > > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D > > > > Instru=E7=F5es para entrar na lista, sair da lista e usar a lista e= m > > > > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > > > > > > > > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D > > > > > > > > > > > > > ------=_Part_15509_27620982.1204856549274 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline

vc permuta somente os bs entre os 13 espa=E7os existentes entre os= ps, senao ocorre repeti=E7ao
exemplo
permutando p vc obtem
bpp
ppb
mas depois vc permuta os dois ps de novo ai vc volta para configura=E7= ao original.
 
On 3/6/08, G= ustavo Duarte <gvduarte@h= otlink.com.br> wrote:
Desculpe, mas o n=FAmero de solu=E7=E3= o da eq a+b+c+d+e =3D12 n=E3o seria C 16,4 =3D 1820 ou ainda fazendo ponto (p) barra (b<= /font>), seria 12 pontos e 4 barras, por exemplo : = ppbppbpppbppppbp que poderia ser tamb=E9m permuta=E7=E3ode 16 elementos  = ;com repeti=E7=E3o de um elemento 4 vz e de outro 12 vz  . ?
----- Original Message -----
Sent: Thursday, March 06, 2008 8:25 = PM
Subject: Re: [obm-l] Quest=E3o de Pr= obabilidade

 
e o numero de solu=E7oes do sistema abaixo
a+b+c+d+e=3D12

 
On 3/6/08, J= oao Victor Brasil <jvbrasil@gm= ail.com> wrote:=20
Saulo,
Pq C13,5???
 
On 3/6/08, J= oao Victor Brasil <jvbrasil@gm= ail.com> wrote:=20
Desculpa, n=E3o prestei aten=E7= =E3o nesse fato. Achei que n=E3o havia reposi=E7=E3o.=20


On 3/6/08, M= aur=EDcio Collares <mauricioc= @gmail.com> wrote:=20
O enunciado informa que h=E1 rep= osi=E7=E3o das bolas. Em outras palavras, a
bola =E9 recolocada na caixa= depois do sorteio.

--
Abra=E7os,
Maur=EDcio

2008/3/5 Joao Victor Brasil <<= a onclick=3D"return top.js.OpenExtLink(window,event,this)" href=3D"mailto:j= vbrasil@gmail.com" target=3D"_blank">jvbrasil@gmail.com>:
> me= desculpe, mas como posso selecionar selecionar 12 bolas se a urna s=F3 tem=
> 5???

=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D
Instru=E7=F5es para entrar na lista, sair da lista e usar a= lista em
ht= tp://www.mat.puc-rio.br/~obmlistas/obm-l.html
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D




------=_Part_15509_27620982.1204856549274-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Fri Mar 7 11:48:10 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m27EjnsG024792 for ; Fri, 7 Mar 2008 11:45:49 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m27EjnEo024790 for obm-l-MllGbsmmN; Fri, 7 Mar 2008 11:45:49 -0300 Received: from ti-out-0910.google.com (ti-out-0910.google.com [209.85.142.187]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m27EjjsG024787 for ; Fri, 7 Mar 2008 11:45:47 -0300 Received: by ti-out-0910.google.com with SMTP id y6so480467tia.13 for ; Fri, 07 Mar 2008 06:46:10 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=gZWlh+C2/iVXekX+LLJ6EyZ7ZCLhWjTjnInKM9vOKEY=; b=RSXHvFHtsBgeR6aNKc05LMr5ifHFETomJNls6ID8Ft3vGClAaR/I/M+G01QNzXQAhJn5zPHNlXaMxzOJgohdAm7K6uikI/G54TPt9DQwQHIC5FBwbdKfhZ1nfN7QwCOn8YsSWyhPfPSvD6b9ZtqXTbokzYI+YmNXWEZl2Y6bRYU= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=M8+Y0NXTI+y7bYz1kmBwCd/1hCOB7gf9n0v51WEFXlLwrmukzQaFSEWlNB4B5Y2l3tWfGDRS+QVWbfkKDjBtQHwZsivDA0lYOkLKmPdJm9dmubE8YuSLKUKS9h/M15pXRjfxhisSIsq0Bxr6hLmWNjv/2/K25hSllHaks8G/fnU= Received: by 10.150.196.5 with SMTP id t5mr546189ybf.109.1204901168173; Fri, 07 Mar 2008 06:46:08 -0800 (PST) Received: by 10.150.92.5 with HTTP; Fri, 7 Mar 2008 06:46:08 -0800 (PST) Message-ID: <822488170803070646r145be050rfde75df9d2471ac5@mail.gmail.com> Date: Fri, 7 Mar 2008 11:46:08 -0300 From: "Rafael Dimas" To: obm-l@mat.puc-rio.br Subject: [SPAM] =?ISO-8859-1?Q?[obm-l]_D=FAvidas_de_An=E1lise?= In-Reply-To: <822488170803070639r7758c18ard00020eb169b430@mail.gmail.com> MIME-Version: 1.0 Content-Type: text/plain References: <822488170803070639r7758c18ard00020eb169b430@mail.gmail.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Rafael Dimas" X-Spam-Status: Yes, hits=5.4 required=5.0 tests=FROM_ENDS_IN_NUMS,GAPPY_TEXT,IN_REP_TO,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ***** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_Part_30699_7689413.1204901168164" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (5.40 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: REFERENCES (-0.5 points) Has a valid-looking References header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: FROM_ENDS_IN_NUMS (0.9 points) From: ends in numbers SPAM: GAPPY_TEXT (0.0 points) BODY: Contains 'G.a.p.p.y-T.e.x.t' SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 187.142.85.209.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 187.142.85.209.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- ------=_Part_30699_7689413.1204901168164 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Bom dia!! Algu=E9m poderia me ajudar? Empaquei nessas quatro quest=F5es do livro de An=E1lise II do Elon. Desde j=E1, agrade=E7o. 1) Seja f: U -> R^n, onde U =E9 um subconjunto de R^m, uma fun=E7=E3o diferenci=E1vel no aberto U. Se para algum B pertencente a R^n, a imagem inversa de B possui um ponto de acumula=E7=E3o A pertencente a pertencente= a U ent=E3o f' (A): R^m -> R^n n=E3o =E9 injetiva. 2) Sejam f: U -> R^n lipschitiziana no aberto U de R^m, com A pertencente a U, e g: V -> R^p diferenci=E1vel no aberto V de R^n, com f(U) contido em V = e B=3Df(A). Mostre que se g'(B) =3D 0 ent=E3o (g(f(x)): U -> R^p =E9 diferenc= i=E1vel no ponto A com (g(f(x))'(A) =3D 0. 3) Se f: U -> R^3 =E9 de classe C^1 e tem posto 3 em todos os pontos do abe= rto U de R^4 ent=E3o |f(x)| n=E3o assume m=E1ximo em X pertencente a U. Na quest=E3o abaixo, D representa delta, |f - g|_1 =E9 para ser considerado= o "1" com indice e f|K representa f restrita a K. 4)Sejam f.g: U -> R^n diferenci=E1veis no aberto U de R^m, D um real positi= vo e X subconjunto de U. Dizemos que f e g s=E3o delta pr=F3ximas na norma C^1= em X e escrevemos |f - g|_1 < D em X quando vale |f(x) - g(x)| < D e |f'(x) - g'(x)| < Dpara todo x pertencente a X. Seja K um subconjunto compacto de U = e f:U -> R^n de classe C^1, tal que f|K =E9 uma imers=E3o. Prove que existe D= > 0 tal que se a aplica=E7=E3o g: U -> R^n =E9 de classe C^1 e |g - f|_1 < D e= m K, ent=E3o g|K =E9 uma imers=E3o. ------=_Part_30699_7689413.1204901168164 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Bom dia!!

Algu=E9m poderia me ajudar? Empaquei nessas quatro quest=F5es do livro d= e An=E1lise II do Elon.

Desde j=E1, agrade=E7o.

1) Seja f: U -> R^n, onde U =E9 um subconjunto de R^m, uma fun=E7=E3o= diferenci=E1vel no aberto U. Se para algum B pertencente a R^n, a imagem i= nversa de B possui um ponto de acumula=E7=E3o A pertencente a  pertenc= ente a U ent=E3o f' (A): R^m -> R^n n=E3o =E9 injetiva.

2) Sejam f: U -> R^n lipschitiziana no aberto U de R^m, com A pertenc= ente a U, e g: V -> R^p diferenci=E1vel no aberto V de R^n, com f(U) con= tido em V e B=3Df(A). Mostre que se g'(B) =3D 0 ent=E3o (g(f(x)): U -&g= t; R^p =E9 diferenci=E1vel no ponto A com (g(f(x))'(A) =3D 0.

3) Se f: U -> R^3 =E9 de classe C^1 e tem posto 3 em todos os pontos = do aberto U de R^4 ent=E3o |f(x)| n=E3o assume m=E1ximo em X pertencente a = U.

 
Na quest=E3o abaixo, D representa delta, |f - g|_1 =E9 para ser consid= erado o "1" com indice e f|K representa f restrita a K.
 =
4)Sejam f.g: U -> R^n diferenci=E1veis no aberto U de R^m, D um rea= l positivo e X subconjunto de U. Dizemos que f e g s=E3o delta pr=F3ximas n= a norma C^1 em X e escrevemos |f - g|_1 < D em X quando vale |f(x) - g(x= )| < D e |f'(x) - g'(x)| < Dpara todo x pertencente a X. Seja= K um subconjunto compacto de U e f:U -> R^n de classe C^1, tal que f|K = =E9 uma imers=E3o. Prove que existe D > 0 tal que se a aplica=E7=E3o g: = U -> R^n =E9 de classe C^1 e |g - f|_1  < D em K, ent=E3o g|K = =E9 uma imers=E3o.
------=_Part_30699_7689413.1204901168164-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sat Mar 8 13:26:22 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m28GNVsG028328 for ; Sat, 8 Mar 2008 13:23:31 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m28GNVmv028326 for obm-l-MllGbsmmN; Sat, 8 Mar 2008 13:23:31 -0300 Received: from web32201.mail.mud.yahoo.com (web32201.mail.mud.yahoo.com [68.142.207.132]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id m28GNTsG028313 for ; Sat, 8 Mar 2008 13:23:29 -0300 Received: (qmail 49925 invoked by uid 60001); 8 Mar 2008 16:23:48 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:Date:From:Subject:To:In-Reply-To:MIME-Version:Content-Type:Content-Transfer-Encoding:Message-ID; b=W8FkgrTTMAIZXlxvy9n6/Dth9Rtw8GNbXLlMI/UTVF1y58cPqU6+RIPIBjYq2XGZei/f/L5Jo9yt8nVnS3awMiS7v1KDfF32HAy1X6uyJN3pcdV9/KaT4DhFnSIBgM5Sl0c1jhRx+7kOjlaOG8VFM6sVe1bVw7y5V6O59EVs07Q=; X-YMail-OSG: HTcPiVoVM1nK4IgNtz56jBV43Ls2qSHj1WnVqyEV0NQvp9WO8MxUZu8.9I9mG0vlmxqz5AMZac5sESVJyWZDYyCYQov0DBT2BzNLEHPcIX4EjRvbpfTOkBf_sQrmSQ-- Received: from [189.25.13.92] by web32201.mail.mud.yahoo.com via HTTP; Sat, 08 Mar 2008 14:23:48 ARST Date: Sat, 8 Mar 2008 14:23:48 -0200 (ARST) From: Claudio Gustavo Subject: [SPAM] Re: [obm-l] Marte To: obm-l@mat.puc-rio.br In-Reply-To: <5bb472220803060353s4fa6d9caj8db9c693685d520a@mail.gmail.com> MIME-Version: 1.0 Content-Type: text/plain Content-Transfer-Encoding: 7bit Message-ID: <770528.49540.qm@web32201.mail.mud.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Claudio Gustavo X-Spam-Status: Yes, hits=7.3 required=5.0 tests=FORGED_YAHOO_RCVD,IN_REP_TO,JAVASCRIPT_UNSAFE,MAILTO_LINK, RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01, SPAM_REDIRECTOR,SUPERLONG_LINE,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******* X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="0-89048212-1204993428=:49540" X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (7.30 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: JAVASCRIPT_UNSAFE (0.3 points) BODY: Easily-executed JavaScript code SPAM: MAILTO_LINK (0.2 points) BODY: Includes a URL link to send an email SPAM: SUPERLONG_LINE (0.0 points) BODY: Contains a line >=199 characters long SPAM: SPAM_REDIRECTOR (0.4 points) URI: Uses open redirection service SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 132.207.142.68.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 132.207.142.68.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- --0-89048212-1204993428=:49540 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 8bit Os marcianos tinham 13 dedos. Pois passando os coeficientes da equação para o sistema decimal teremos: i) 5 = 5 ii) 50 = 5.13 = 65 iii) 125 = 1.13^2 + 2.13 + 5 = 169 + 26 + 5 = 200 Logo, no sistema decimal, a equação fica: 5x^2 - 65x + 200 = 0. E o x=8 é raiz: 5.8^2 - 65.8 +200 = 320 - 520 + 200 = 0. Abraço, Claudio Gustavo. Joao Victor Brasil escreveu: Quando completamos 10 unidades transformamos em uma dezena. Como no sistema de base 10, usamos até o algarismo 9; o sistema marciano tolera o algarismo 5 como unidade e não tolera o 8. Logo os marcianos devem ter 6 ou 7 dedos nas mãos. On 3/5/08, Klaus Ferraz wrote: A primeira expedicao a Marte encontrou somente as ruinas de uma civilizacao. Os exploradores concluiram dos artefatos e desenhos que as criaturas que produziram esta civilizacao tinham quatro pernas, cada uma terminada em um conjunto de garras parecidas com dedos. Após muito estudo foram capazes de traduzir a matematica marciana. Eles encontraram a seguinte equacao: 5x^2-50x+125=0 Esta era uma matematica estranha. O valor x=5 parecia correto, mas x=8 não. Entao os exploradores lembraram a maneira como o nosso sistema de numeracao foi desenvolvido e encontraram evidencias de que o sistema marciano teve uma historia analoga. Quantos dedos tinham os marcianos? --------------------------------- Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --------------------------------- Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-89048212-1204993428=:49540 Content-Type: text/html; charset=iso-8859-1 Content-Transfer-Encoding: 8bit
  Os marcianos tinham 13 dedos. Pois passando os coeficientes da equação para o sistema decimal teremos:
 i) 5 = 5
 ii) 50 = 5.13 = 65
 iii) 125 = 1.13^2 + 2.13 + 5 = 169 + 26 + 5 = 200
  Logo, no sistema decimal, a equação fica: 5x^2 - 65x + 200 = 0.
  E o x=8 é raiz: 5.8^2 - 65.8 +200 = 320 - 520 + 200 = 0.
 
  Abraço,
Claudio Gustavo.
 

Joao Victor Brasil <jvbrasil@gmail.com> escreveu:
Quando completamos 10 unidades transformamos em uma dezena. Como no sistema de base 10, usamos até o algarismo 9; o sistema marciano tolera o algarismo 5 como unidade e não tolera o 8. Logo os marcianos devem ter 6 ou 7 dedos nas mãos. 

On 3/5/08, Klaus Ferraz <klausferraz@yahoo.com.br> wrote:
A primeira expedicao a Marte encontrou somente as ruinas de uma civilizacao. Os exploradores concluiram dos artefatos e desenhos que as criaturas que produziram esta civilizacao tinham quatro pernas, cada uma terminada em um conjunto de garras parecidas com dedos. Após muito estudo foram capazes de traduzir a matematica marciana. Eles encontraram a seguinte equacao:
5x^2-50x+125=0
Esta era uma matematica estranha. O valor x=5 parecia correto, mas x=8 não. Entao os exploradores lembraram a maneira como o nosso sistema de numeracao foi desenvolvido e encontraram evidencias de que o sistema marciano teve uma historia analoga. Quantos dedos tinham os marcianos?

Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento!


Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-89048212-1204993428=:49540-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sat Mar 8 15:45:27 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m28IhjsG004885 for ; Sat, 8 Mar 2008 15:43:45 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m28IhidH004882 for obm-l-MllGbsmmN; Sat, 8 Mar 2008 15:43:44 -0300 Received: from fg-out-1718.google.com (fg-out-1718.google.com [72.14.220.152]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m28IhgsG004876 for ; Sat, 8 Mar 2008 15:43:42 -0300 Received: by fg-out-1718.google.com with SMTP id e12so7449741fga.3 for ; Sat, 08 Mar 2008 10:44:07 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=rVu3o/8J6CehFilyOfKAJCrXNEcy3D1G3RsCQDathZg=; b=FixuUD1oM22yL9PMJ4SpiZ9yAs6N75P+GNkfiZD7WbE3l25+H7U5xWJjveGiGvojr9rcLjAmMpcIxfYdT1h3+K5iMnxLeNcX9L6VsLDpereJpzgVTV/XzBt8ZFEHO6mwKO85ZUlN/WRxqeW/7bqp/f60rLiD13FHjWEX8MPKUso= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=VQdV9qxCNFIZfnScWcmsIJdjaiI1+ga8FIY3A6HAEjbPvjHqnh7f0Tq80vIVEyOSOaLMQzLy0BiC/8Q5h8u/w1e5LtaIs76MOPlz1fm9bdBXbBrWRyS+4Fd06YWFuKNJ5OvAMaT7u8I+ZROcttUcuQ2Rc9g0i2c5vqbVBWrDMZo= Received: by 10.86.99.9 with SMTP id w9mr3528058fgb.22.1205001846593; Sat, 08 Mar 2008 10:44:06 -0800 (PST) Received: by 10.86.74.8 with HTTP; Sat, 8 Mar 2008 10:44:06 -0800 (PST) Message-ID: Date: Sat, 8 Mar 2008 15:44:06 -0300 From: "saulo nilson" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Marte In-Reply-To: <770528.49540.qm@web32201.mail.mud.yahoo.com> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_17849_32113524.1205001846599" References: <5bb472220803060353s4fa6d9caj8db9c693685d520a@mail.gmail.com> <770528.49540.qm@web32201.mail.mud.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "saulo nilson" X-Spam-Status: No, hits=-0.7 required=5.0 tests=AWL,IN_REP_TO,MAILTO_LINK,QUOTED_EMAIL_TEXT,REFERENCES, SPAM_PHRASE_01_02,SPAM_REDIRECTOR,X_MAILING_LIST version=2.44 X-Spam-Level: ------=_Part_17849_32113524.1205001846599 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline vc passou para base 13, mas como pode ter 4 pernas e 13 dedos? nao tem que ser simetrico? 2008/3/8 Claudio Gustavo : > Os marcianos tinham 13 dedos. Pois passando os coeficientes da equa=E7= =E3o > para o sistema decimal teremos: > i) 5 =3D 5 > ii) 50 =3D 5.13 =3D 65 > iii) 125 =3D 1.13^2 + 2.13 + 5 =3D 169 + 26 + 5 =3D 200 > Logo, no sistema decimal, a equa=E7=E3o fica: 5x^2 - 65x + 200 =3D 0. > E o x=3D8 =E9 raiz: 5.8^2 - 65.8 +200 =3D 320 - 520 + 200 =3D 0. > > Abra=E7o, > Claudio Gustavo. > > > *Joao Victor Brasil * escreveu: > > Quando completamos 10 unidades transformamos em uma dezena. Como no > sistema de base 10, usamos at=E9 o algarismo 9; o sistema marciano tolera= o > algarismo 5 como unidade e n=E3o tolera o 8. Logo os marcianos devem ter = 6 ou > 7 dedos nas m=E3os. > > On 3/5/08, Klaus Ferraz wrote: > > > > A primeira expedicao a Marte encontrou somente as ruinas de uma > > civilizacao. Os exploradores concluiram dos artefatos e desenhos que as > > criaturas que produziram esta civilizacao tinham quatro pernas, cada um= a > > terminada em um conjunto de garras parecidas com dedos. Ap=F3s muito es= tudo > > foram capazes de traduzir a matematica marciana. Eles encontraram a seg= uinte > > equacao: > > 5x^2-50x+125=3D0 > > Esta era uma matematica estranha. O valor x=3D5 parecia correto, mas x= =3D8 > > n=E3o. Entao os exploradores lembraram a maneira como o nosso sistema d= e > > numeracao foi desenvolvido e encontraram evidencias de que o sistema > > marciano teve uma historia analoga. Quantos dedos tinham os marcianos? > > > > ------------------------------ > > Abra sua conta no Yahoo! Mail, > > o =FAnico sem limite de espa=E7o para armazenamento! > > > > > ------------------------------ > Abra sua conta no Yahoo! Mail, > o =FAnico sem limite de espa=E7o para armazenamento! > > ------=_Part_17849_32113524.1205001846599 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline vc passou para base 13, mas como pode ter 4 pernas e 13 dedos? nao tem que = ser simetrico?

2008/3/8 Claudio Gustavo <claudioggll@yahoo.com.br>:
  Os marcianos tinham 13 dedos. Pois passando os coeficientes da = equa=E7=E3o para o sistema decimal teremos:
 i) 5 =3D 5
 ii) 50 =3D 5.13 =3D 65
 iii) 125 =3D 1.13^2 + 2.13 + 5 =3D 169 + 26 + 5 =3D 200
  Logo, no sistema decimal, a equa=E7=E3o fica: 5x^2 - 65x += 200 =3D 0.
  E o x=3D8 =E9 raiz: 5.8^2 - 65.8 +200 =3D 320 - 520 + 200 =3D 0= .
 
  Abra=E7o,
Claudio Gustavo.
 

Joao Victor Brasil <jvbrasil@gmail.com> escreveu:
Quando completamos 10 unidades transformamos em uma dezena. = Como no sistema de base 10, usamos at=E9 o algarismo 9; o sistema marciano = tolera o algarismo 5 como unidade e n=E3o tolera o 8. Logo os marciano= s devem ter 6 ou 7 dedos nas m=E3os. 

On 3/5/08, K= laus Ferraz <klausferraz@yahoo.com.br> wrote:=20
A primeira expedicao a Marte encontrou somente as ruinas de uma c= ivilizacao. Os exploradores concluiram dos artefatos e desenhos que as= criaturas que produziram esta civilizacao tinham quatro pernas, cada uma t= erminada em um conjunto de garras parecidas com dedos. Ap=F3s muito estudo = foram capazes de traduzir a matematica marciana. Eles encontraram a seguint= e equacao:
5x^2-50x+125=3D0
Esta era uma matematica estranha. O valor x=3D5 parecia correto, mas x= =3D8 n=E3o. Entao os exploradores lembraram a maneira como o nosso sistema = de numeracao foi desenvolvido e encontraram evidencias de que o sistema mar= ciano teve uma historia analoga. Quantos dedos tinham os marcianos?

Abra sua conta no Yahoo! Mail, o =FAnico sem li= mite de espa=E7o para armazenamento!


Abra sua conta no Yahoo! Mail, o =FAnico sem li= mite de espa=E7o para armazenamento!=20


------=_Part_17849_32113524.1205001846599-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sat Mar 8 15:51:26 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m28IoOsG005191 for ; Sat, 8 Mar 2008 15:50:24 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m28IoOWj005189 for obm-l-MllGbsmmN; Sat, 8 Mar 2008 15:50:24 -0300 Received: from fg-out-1718.google.com (fg-out-1718.google.com [72.14.220.153]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m28IoLsG005184 for ; Sat, 8 Mar 2008 15:50:22 -0300 Received: by fg-out-1718.google.com with SMTP id e12so7451448fga.3 for ; Sat, 08 Mar 2008 10:50:46 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=VTVMFLnsO1ofuW+ONh4bEXI/9pg2qL7Vrg9/CEqCpGg=; b=OhCZwLP1jqbEFp5CxjKPWmG0anWhCbhwoX+VIVnebnASyGkiRvP45GwxA99X+BhVmdoOn+IbH0i+AUD+h3iaVA4llCANgQgMqi4pEdfdwlGt5swZd7ItixoDYNXeNjQh9BZmWxXAZe4hJ7xHN+NITsuDfzIeDoGOd3ZeN7q0YXk= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=q00VxScC9J/Ct6F7Gopl6a0ityIoJEFEUeo6tvaVprDs7brvlT3ia+jvthDnPfKW6td/AlIsvbygTOZY+z+c0ss21zRE6yezkAkjC7P+sEc9TUlQ5ckZlqo0Mw+H6Le0RwdEz0W+03EBI24wDU3NnNaEkIB/JJFVI2sXvP8N2mg= Received: by 10.86.3.4 with SMTP id 4mr3501061fgc.55.1205002246687; Sat, 08 Mar 2008 10:50:46 -0800 (PST) Received: by 10.86.74.8 with HTTP; Sat, 8 Mar 2008 10:50:46 -0800 (PST) Message-ID: Date: Sat, 8 Mar 2008 15:50:46 -0300 From: "saulo nilson" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Marte In-Reply-To: MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_17851_27479085.1205002246683" References: <5bb472220803060353s4fa6d9caj8db9c693685d520a@mail.gmail.com> <770528.49540.qm@web32201.mail.mud.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "saulo nilson" X-Spam-Status: No, hits=-0.7 required=5.0 tests=AWL,IN_REP_TO,MAILTO_LINK,QUOTED_EMAIL_TEXT,REFERENCES, SPAM_PHRASE_00_01,SPAM_REDIRECTOR,X_MAILING_LIST version=2.44 X-Spam-Level: ------=_Part_17851_27479085.1205002246683 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline ou sao 13 em cada perna? 2008/3/8 saulo nilson : > vc passou para base 13, mas como pode ter 4 pernas e 13 dedos? nao tem qu= e > ser simetrico? > > 2008/3/8 Claudio Gustavo : > > Os marcianos tinham 13 dedos. Pois passando os coeficientes da equa=E7= =E3o > > para o sistema decimal teremos: > > i) 5 =3D 5 > > ii) 50 =3D 5.13 =3D 65 > > iii) 125 =3D 1.13^2 + 2.13 + 5 =3D 169 + 26 + 5 =3D 200 > > Logo, no sistema decimal, a equa=E7=E3o fica: 5x^2 - 65x + 200 =3D 0. > > E o x=3D8 =E9 raiz: 5.8^2 - 65.8 +200 =3D 320 - 520 + 200 =3D 0. > > > > Abra=E7o, > > Claudio Gustavo. > > > > > > *Joao Victor Brasil * escreveu: > > > > Quando completamos 10 unidades transformamos em uma dezena. Como no > > sistema de base 10, usamos at=E9 o algarismo 9; o sistema marciano tole= ra o > > algarismo 5 como unidade e n=E3o tolera o 8. Logo os marcianos devem te= r 6 ou > > 7 dedos nas m=E3os. > > > > On 3/5/08, Klaus Ferraz wrote: > > > > > > A primeira expedicao a Marte encontrou somente as ruinas de uma > > > civilizacao. Os exploradores concluiram dos artefatos e desenhos que = as > > > criaturas que produziram esta civilizacao tinham quatro pernas, cada = uma > > > terminada em um conjunto de garras parecidas com dedos. Ap=F3s muito = estudo > > > foram capazes de traduzir a matematica marciana. Eles encontraram a s= eguinte > > > equacao: > > > 5x^2-50x+125=3D0 > > > Esta era uma matematica estranha. O valor x=3D5 parecia correto, mas = x=3D8 > > > n=E3o. Entao os exploradores lembraram a maneira como o nosso sistema= de > > > numeracao foi desenvolvido e encontraram evidencias de que o sistema > > > marciano teve uma historia analoga. Quantos dedos tinham os marcianos= ? > > > > > > ------------------------------ > > > Abra sua conta no Yahoo! Mail, > > > o =FAnico sem limite de espa=E7o para armazenamento! > > > > > > > > > ------------------------------ > > Abra sua conta no Yahoo! Mail, > > o =FAnico sem limite de espa=E7o para armazenamento! > > > > > ------=_Part_17851_27479085.1205002246683 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline ou sao 13 em cada perna?
Sent: Sunday, March 09, 2008 = 11:05=20 AM
Subject: Re: [obm-l] = Equa=E7=E3o em=20 Complexo

Ol=E1 Gustavo,

=E9 quase a mesma coisa:
x^4 = =3D -36 =3D 36=20 cis(180 + 360k)

assim, x =3D rz(6) cis(45 + 90k)
que sao: x = =3D rz(6)=20 cis(45), rz(6) cis(135), rz(6) cis(225), rz(6) cis(315)

agora, = basta=20 passar pra forma retangular.. por exemplo:
x =3D rz(6) cis(45) =3D = rz(6) [=20 rz(2)/2 + i rz(2)/2 ] =3D rz(3) + i = rz(3)

abra=E7os,
Salhab


2008/3/8 saulo nilson <saulo.nilson@gmail.com>:
vc passou para base 13, mas como= pode ter 4 pernas e 13 dedos? nao tem que ser simetrico?

2008/3/8 Claudio Gustavo <claudioggll@yahoo.com.br>= :=20

  Os marcianos tinham 13 dedos. Pois passando os coeficientes da = equa=E7=E3o para o sistema decimal teremos:
 i) 5 =3D 5
 ii) 50 =3D 5.13 =3D 65
 iii) 125 =3D 1.13^2 + 2.13 + 5 =3D 169 + 26 + 5 =3D 200
  Logo, no sistema decimal, a equa=E7=E3o fica: 5x^2 - 65x += 200 =3D 0.
  E o x=3D8 =E9 raiz: 5.8^2 - 65.8 +200 =3D 320 - 520 + 200 =3D 0= .
 
  Abra=E7o,
Claudio Gustavo.
 

Joao Victor Brasil <jvbrasil@gmail.com> escreveu:
Quando completamos 10 unidades transformamos em uma dezena. = Como no sistema de base 10, usamos at=E9 o algarismo 9; o sistema marciano = tolera o algarismo 5 como unidade e n=E3o tolera o 8. Logo os marciano= s devem ter 6 ou 7 dedos nas m=E3os. 

On 3/5/08, K= laus Ferraz <klausferraz@yahoo.com.br> wrote:=20
A primeira expedicao a Marte encontrou somente as ruinas de uma c= ivilizacao. Os exploradores concluiram dos artefatos e desenhos que as= criaturas que produziram esta civilizacao tinham quatro pernas, cada uma t= erminada em um conjunto de garras parecidas com dedos. Ap=F3s muito estudo = foram capazes de traduzir a matematica marciana. Eles encontraram a seguint= e equacao:
5x^2-50x+125=3D0
Esta era uma matematica estranha. O valor x=3D5 parecia correto, mas x= =3D8 n=E3o. Entao os exploradores lembraram a maneira como o nosso sistema = de numeracao foi desenvolvido e encontraram evidencias de que o sistema mar= ciano teve uma historia analoga. Quantos dedos tinham os marcianos?

Abra sua conta no Yahoo! Mail, o =FAnico sem li= mite de espa=E7o para armazenamento!


Abra sua conta no Yahoo! Mail, o =FAnico sem li= mite de espa=E7o para armazenamento!=20



------=_Part_17851_27479085.1205002246683-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sat Mar 8 23:00:36 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m291wtsG029641 for ; Sat, 8 Mar 2008 22:58:55 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m291wtrh029639 for obm-l-MllGbsmmN; Sat, 8 Mar 2008 22:58:55 -0300 Received: from web32205.mail.mud.yahoo.com (web32205.mail.mud.yahoo.com [68.142.207.136]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id m291wqsG029636 for ; Sat, 8 Mar 2008 22:58:53 -0300 Received: (qmail 94437 invoked by uid 60001); 9 Mar 2008 01:59:17 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:Date:From:Subject:To:In-Reply-To:MIME-Version:Content-Type:Content-Transfer-Encoding:Message-ID; b=6n3tqemikHLnxUHn8xEm1TmDIGuF/GfzPmos6+iWuYwu98aIsjoc6P+ryKcdC5XAG9NEwU5FRUALT0u69FHU3qpkr7Q42kF3YZ4L1nmuoqTCdiny1A84wkDsmJMwhfr7Fw756udxg98DAnxbr1saprloWt3w75exTKfEwXgV2fk=; X-YMail-OSG: qjJr1KEVM1m6JAHyg_qrmoILfr4G0qdjwnl170rfGz6M6L1ynAEckgq_67tVuYDUFUV1rsjRlswkBP8slEsM9nAV_.zyfKo.TVSsVUss8BFqSnd5dhs- Received: from [189.25.120.9] by web32205.mail.mud.yahoo.com via HTTP; Sat, 08 Mar 2008 23:59:17 ARST Date: Sat, 8 Mar 2008 23:59:17 -0200 (ARST) From: Claudio Gustavo Subject: [SPAM] Re: [obm-l] Marte To: obm-l@mat.puc-rio.br In-Reply-To: MIME-Version: 1.0 Content-Type: text/plain Content-Transfer-Encoding: 7bit Message-ID: <790450.92074.qm@web32205.mail.mud.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Claudio Gustavo X-Spam-Status: Yes, hits=7.8 required=5.0 tests=AWL,FORGED_YAHOO_RCVD,IN_REP_TO,MAILTO_LINK, MIME_BOUND_DIGITS_5,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, SPAM_PHRASE_01_02,SPAM_REDIRECTOR,SUPERLONG_LINE, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******* X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="0-105274796-1205027957=:92074" X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (7.80 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: MIME_BOUND_DIGITS_5 (1.7 points) Spam tool pattern in MIME boundary SPAM: SPAM_PHRASE_01_02 (0.5 points) BODY: Spam phrases score is 01 to 02 (low) SPAM: [score: 1] SPAM: MAILTO_LINK (0.2 points) BODY: Includes a URL link to send an email SPAM: SUPERLONG_LINE (0.0 points) BODY: Contains a line >=199 characters long SPAM: SPAM_REDIRECTOR (0.4 points) URI: Uses open redirection service SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 136.207.142.68.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 136.207.142.68.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-0.6 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- --0-105274796-1205027957=:92074 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 8bit São 13 por membro (total de 4.13=52 dedos). saulo nilson escreveu: ou sao 13 em cada perna? 2008/3/8 saulo nilson : vc passou para base 13, mas como pode ter 4 pernas e 13 dedos? nao tem que ser simetrico? 2008/3/8 Claudio Gustavo : Os marcianos tinham 13 dedos. Pois passando os coeficientes da equação para o sistema decimal teremos: i) 5 = 5 ii) 50 = 5.13 = 65 iii) 125 = 1.13^2 + 2.13 + 5 = 169 + 26 + 5 = 200 Logo, no sistema decimal, a equação fica: 5x^2 - 65x + 200 = 0. E o x=8 é raiz: 5.8^2 - 65.8 +200 = 320 - 520 + 200 = 0. Abraço, Claudio Gustavo. Joao Victor Brasil escreveu: Quando completamos 10 unidades transformamos em uma dezena. Como no sistema de base 10, usamos até o algarismo 9; o sistema marciano tolera o algarismo 5 como unidade e não tolera o 8. Logo os marcianos devem ter 6 ou 7 dedos nas mãos. On 3/5/08, Klaus Ferraz wrote: A primeira expedicao a Marte encontrou somente as ruinas de uma civilizacao. Os exploradores concluiram dos artefatos e desenhos que as criaturas que produziram esta civilizacao tinham quatro pernas, cada uma terminada em um conjunto de garras parecidas com dedos. Após muito estudo foram capazes de traduzir a matematica marciana. Eles encontraram a seguinte equacao: 5x^2-50x+125=0 Esta era uma matematica estranha. O valor x=5 parecia correto, mas x=8 não. Entao os exploradores lembraram a maneira como o nosso sistema de numeracao foi desenvolvido e encontraram evidencias de que o sistema marciano teve uma historia analoga. Quantos dedos tinham os marcianos? --------------------------------- Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --------------------------------- Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --------------------------------- Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-105274796-1205027957=:92074 Content-Type: text/html; charset=iso-8859-1 Content-Transfer-Encoding: 8bit   São 13 por membro (total de 4.13=52 dedos).

saulo nilson <saulo.nilson@gmail.com> escreveu:
ou sao 13 em cada perna?

2008/3/8 saulo nilson <saulo.nilson@gmail.com>:
vc passou para base 13, mas como pode ter 4 pernas e 13 dedos? nao tem que ser simetrico?

2008/3/8 Claudio Gustavo <claudioggll@yahoo.com.br>:

  Os marcianos tinham 13 dedos. Pois passando os coeficientes da equação para o sistema decimal teremos:
 i) 5 = 5
 ii) 50 = 5.13 = 65
 iii) 125 = 1.13^2 + 2.13 + 5 = 169 + 26 + 5 = 200
  Logo, no sistema decimal, a equação fica: 5x^2 - 65x + 200 = 0.
  E o x=8 é raiz: 5.8^2 - 65.8 +200 = 320 - 520 + 200 = 0.
 
  Abraço,
Claudio Gustavo.


Joao Victor Brasil <jvbrasil@gmail.com> escreveu:
Quando completamos 10 unidades transformamos em uma dezena. Como no sistema de base 10, usamos até o algarismo 9; o sistema marciano tolera o algarismo 5 como unidade e não tolera o 8. Logo os marcianos devem ter 6 ou 7 dedos nas mãos. 

On 3/5/08, Klaus Ferraz <klausferraz@yahoo.com.br> wrote:
A primeira expedicao a Marte encontrou somente as ruinas de uma civilizacao. Os exploradores concluiram dos artefatos e desenhos que as criaturas que produziram esta civilizacao tinham quatro pernas, cada uma terminada em um conjunto de garras parecidas com dedos. Após muito estudo foram capazes de traduzir a matematica marciana. Eles encontraram a seguinte equacao:
5x^2-50x+125=0
Esta era uma matematica estranha. O valor x=5 parecia correto, mas x=8 não. Entao os exploradores lembraram a maneira como o nosso sistema de numeracao foi desenvolvido e encontraram evidencias de que o sistema marciano teve uma historia analoga. Quantos dedos tinham os marcianos?

Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento!


Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento!



Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-105274796-1205027957=:92074-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sun Mar 9 10:29:45 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m29DRlsG024878 for ; Sun, 9 Mar 2008 10:27:47 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m29DRk6Z024873 for obm-l-MllGbsmmN; Sun, 9 Mar 2008 10:27:46 -0300 Received: from zeus.hotlink.com.br (zeus.hotlink.com.br [189.1.1.250]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m29DRisG024836 for ; Sun, 9 Mar 2008 10:27:45 -0300 Received: by zeus.hotlink.com.br (Postfix, from userid 1002) id 47780489BF7; Sun, 9 Mar 2008 10:30:27 -0300 (BRT) Received: from windows5095252 (veloz-1-2-22.hotlink.com.br [189.1.2.22]) by zeus.hotlink.com.br (Postfix) with SMTP id 21BA6489B71 for ; Sun, 9 Mar 2008 10:30:27 -0300 (BRT) Message-ID: <000c01c881e9$6c8a5fb0$5700a8c0@windows5095252> From: "Gustavo Duarte" To: =?iso-8859-1?Q?Olimp=EDada?= Subject: [SPAM] [obm-l] =?iso-8859-1?Q?Equa=E7=E3o_em_Complexo?= Date: Sun, 9 Mar 2008 10:28:12 -0300 MIME-Version: 1.0 Content-Type: text/plain X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2900.3138 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.3198 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Gustavo Duarte" X-Spam-Status: Yes, hits=6.1 required=5.0 tests=AWL,BIG_FONT,HTML_FONT_COLOR_RED,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01,SUPERLONG_LINE, USER_AGENT_OE,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ****** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_NextPart_000_0009_01C881D0.4722E8F0" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (6.10 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: USER_AGENT_OE (0.2 points) X-Mailer header indicates a non-spam MUA (Outlook Express) SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: BIG_FONT (0.3 points) BODY: FONT Size +2 and up or 3 and up SPAM: HTML_FONT_COLOR_RED (0.3 points) BODY: HTML font color is red SPAM: SUPERLONG_LINE (0.0 points) BODY: Contains a line >=199 characters long SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 250.1.1.189.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 250.1.1.189.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-0.5 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- This is a multi-part message in MIME format. ------=_NextPart_000_0009_01C881D0.4722E8F0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable x^4 - 36 =3D 0, tudo bem,encontrei como raizes : + rz(6), -rz(6),+rz(6)i = e -rz(6)i com rz(X) >> raiz quadrada de x, por=E9m fiquei pensando no = seguinte caso :x^4 + 36 =3D0, desde j=E1 agrade=E7o alguma ajuda !!! ------=_NextPart_000_0009_01C881D0.4722E8F0 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable
x^4 - 36 =3D 0, tudo = bem,encontrei=20 como raizes : + rz(6), -rz(6),+rz(6)i e=20 -rz(6)i   com  rz(X) >> raiz quadrada de=20 x, por=E9m fiquei pensando no seguinte caso  = :x^4 + 36 =3D0, = desde j=E1=20 agrade=E7o alguma ajuda !!!
 
------=_NextPart_000_0009_01C881D0.4722E8F0-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sun Mar 9 11:05:48 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m29E4hsG005549 for ; Sun, 9 Mar 2008 11:04:43 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m29E4hpP005547 for obm-l-MllGbsmmN; Sun, 9 Mar 2008 11:04:43 -0300 Received: from wa-out-1112.google.com (wa-out-1112.google.com [209.85.146.176]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m29E4esG005499 for ; Sun, 9 Mar 2008 11:04:41 -0300 Received: by wa-out-1112.google.com with SMTP id m28so1858331wag.13 for ; Sun, 09 Mar 2008 07:05:06 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=cDC70aT5fXRIwCfPUirKM3l1P+YRixvwRaplQRd9skk=; b=KQFsmitWsgG9nMe8BKS++AnIKWwywP3KLOQNVVt1WhM2aQ8vLgZ9KGq/2tGA6BLEUQrAcKxEcyeuJvAA4JZCMRA885pUJw2ADIAY9hd0ZF0T7EaZTHZxGWC6nP95rmY1p/gZ8kPrnml8H+WF5N65nwa4M5y5MyII8OGgVLEKPuM= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=O67X1HtGNP0SY/dIa0GhnrTs8TBInxENXJCpWbhMgfuw/btzgFGiFqQqBh2UWKVGUgtl0T/05efF09qTQ73wwqjPfQmPg1/qWnPkR0Lu4Uhi1dSo4mzIvSE09Ygoz1NJ99TzLaOap0JbkQgirk/q/ZMQ4SHOsUhLULOcI9lbMpI= Received: by 10.114.149.2 with SMTP id w2mr4272310wad.29.1205071506394; Sun, 09 Mar 2008 07:05:06 -0700 (PDT) Received: by 10.114.158.9 with HTTP; Sun, 9 Mar 2008 07:05:06 -0700 (PDT) Message-ID: <3bd00efc0803090705n7080c64alcdf5646bdf5664c8@mail.gmail.com> Date: Sun, 9 Mar 2008 11:05:06 -0300 From: "Marcelo Salhab Brogliato" To: obm-l@mat.puc-rio.br Subject: =?ISO-8859-1?Q?Re:_[obm-l]_Equa=E7=E3o_em_Complexo?= In-Reply-To: <000c01c881e9$6c8a5fb0$5700a8c0@windows5095252> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_4823_20672672.1205071506387" References: <000c01c881e9$6c8a5fb0$5700a8c0@windows5095252> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Marcelo Salhab Brogliato" X-Spam-Status: No, hits=3.1 required=5.0 tests=AWL,BIG_FONT,EMAIL_ATTRIBUTION,HTML_FONT_COLOR_RED, IN_REP_TO,MAILTO_LINK,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: *** ------=_Part_4823_20672672.1205071506387 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Ol=E1 Gustavo, =E9 quase a mesma coisa: x^4 =3D -36 =3D 36 cis(180 + 360k) assim, x =3D rz(6) cis(45 + 90k) que sao: x =3D rz(6) cis(45), rz(6) cis(135), rz(6) cis(225), rz(6) cis(315= ) agora, basta passar pra forma retangular.. por exemplo: x =3D rz(6) cis(45) =3D rz(6) [ rz(2)/2 + i rz(2)/2 ] =3D rz(3) + i rz(3) abra=E7os, Salhab On Sun, Mar 9, 2008 at 10:28 AM, Gustavo Duarte wrote: > *x^4 - 36 =3D 0,* tudo bem,encontrei como raizes : + rz(6), -rz(6),+rz(6= )i > e -rz(6)i com *rz(X) >> raiz quadrada de x,** *por=E9m fiquei pensando= no > seguinte caso :*x^4 + 36 =3D0, *desde j=E1 agrade=E7o alguma ajuda !!! > * * > ------=_Part_4823_20672672.1205071506387 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Ol=E1 Gustavo,

=E9 quase a mesma coisa:
x^4 =3D -36 =3D 36 cis(18= 0 + 360k)

assim, x =3D rz(6) cis(45 + 90k)
que sao: x =3D rz(6) c= is(45), rz(6) cis(135), rz(6) cis(225), rz(6) cis(315)

agora, basta = passar pra forma retangular.. por exemplo:
x =3D rz(6) cis(45) =3D rz(6) [ rz(2)/2 + i rz(2)/2 ] =3D rz(3) + i rz(3)
abra=E7os,
Salhab


On Sun, Ma= r 9, 2008 at 10:28 AM, Gustavo Duarte <gvduarte@hotlink.com.br> wrote:
x^4 - 36 =3D 0, tudo bem,encont= rei=20 como raizes : + rz(6), -rz(6),+rz(6)i e=20 -rz(6)i   com  rz(X) >> raiz quadrada de=20 x, por=E9m fiquei pensando no seguinte caso  :x^4 + 36 =3D0, desde j=E1=20 agrade=E7o alguma ajuda !!!
 

------=_Part_4823_20672672.1205071506387-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sun Mar 9 13:37:55 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m29GYTsG030967 for ; Sun, 9 Mar 2008 13:34:29 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m29GYTXd030965 for obm-l-MllGbsmmN; Sun, 9 Mar 2008 13:34:29 -0300 Received: from zeus.hotlink.com.br (zeus.hotlink.com.br [189.1.1.250]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m29GYSsG030953 for ; Sun, 9 Mar 2008 13:34:28 -0300 Received: by zeus.hotlink.com.br (Postfix, from userid 1002) id 3E752489C41; Sun, 9 Mar 2008 13:37:11 -0300 (BRT) Received: from windows5095252 (veloz-1-2-22.hotlink.com.br [189.1.2.22]) by zeus.hotlink.com.br (Postfix) with SMTP id ED3C9489C30 for ; Sun, 9 Mar 2008 13:37:10 -0300 (BRT) Message-ID: <000801c88203$8251a280$5700a8c0@windows5095252> From: "Gustavo Duarte" To: References: <000c01c881e9$6c8a5fb0$5700a8c0@windows5095252> <3bd00efc0803090705n7080c64alcdf5646bdf5664c8@mail.gmail.com> Subject: [SPAM] [obm-l] =?iso-8859-1?Q?Re:_=5Bobm-l=5D_Equa=E7=E3o_em_Complexo?= Date: Sun, 9 Mar 2008 13:34:56 -0300 MIME-Version: 1.0 Content-Type: text/plain X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2900.3138 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.3198 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Gustavo Duarte" X-Spam-Status: Yes, hits=6.0 required=5.0 tests=AWL,BIG_FONT,HTML_FONT_COLOR_RED,MAILTO_LINK,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, SUPERLONG_LINE,USER_AGENT_OE,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ****** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_NextPart_000_0005_01C881EA.5CE326E0" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (6.00 hits, 5 required) SPAM: REFERENCES (-0.5 points) Has a valid-looking References header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: USER_AGENT_OE (0.2 points) X-Mailer header indicates a non-spam MUA (Outlook Express) SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: BIG_FONT (0.3 points) BODY: FONT Size +2 and up or 3 and up SPAM: HTML_FONT_COLOR_RED (0.3 points) BODY: HTML font color is red SPAM: MAILTO_LINK (0.2 points) BODY: Includes a URL link to send an email SPAM: SUPERLONG_LINE (0.0 points) BODY: Contains a line >=199 characters long SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 250.1.1.189.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 250.1.1.189.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-0.3 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- This is a multi-part message in MIME format. ------=_NextPart_000_0005_01C881EA.5CE326E0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Valeu Salhab, muit=EDssimo obrigado, ent=E3o o primeiro caso x^4 - 36 = pude fazer por bi-quadrada, chamando x^2 de um K qualquer, achando K = encontrei os 4 valores de x, por=E9m esse que eu tive d=FAvidas, x^4 + = 36,n=E3o seria uma boa op=E7=E3o (bi-quadrada) fazer a mudan=E7a de = vari=E1vel passando para uma equa=E7=E3o do 2 =BA grau e sim = aplica=E7=E3o direta da segunda f=F3rmula de DE MOIVRE( = radicia=E7=E3o),que eu n=E3o tinha notado !!captei corretamente sua = mensagem ? acho que sim e mais um vz sou grato por socializar o = conhecimento. obg. ----- Original Message -----=20 From: Marcelo Salhab Brogliato=20 To: obm-l@mat.puc-rio.br=20 Sent: Sunday, March 09, 2008 11:05 AM Subject: Re: [obm-l] Equa=E7=E3o em Complexo Ol=E1 Gustavo, =E9 quase a mesma coisa: x^4 =3D -36 =3D 36 cis(180 + 360k) assim, x =3D rz(6) cis(45 + 90k) que sao: x =3D rz(6) cis(45), rz(6) cis(135), rz(6) cis(225), rz(6) = cis(315) agora, basta passar pra forma retangular.. por exemplo: x =3D rz(6) cis(45) =3D rz(6) [ rz(2)/2 + i rz(2)/2 ] =3D rz(3) + i = rz(3) abra=E7os, Salhab On Sun, Mar 9, 2008 at 10:28 AM, Gustavo Duarte = wrote: x^4 - 36 =3D 0, tudo bem,encontrei como raizes : + rz(6), = -rz(6),+rz(6)i e -rz(6)i com rz(X) >> raiz quadrada de x, por=E9m = fiquei pensando no seguinte caso :x^4 + 36 =3D0, desde j=E1 agrade=E7o = alguma ajuda !!! ------=_NextPart_000_0005_01C881EA.5CE326E0 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable
Valeu Salhab, muit=EDssimo obrigado, = ent=E3o o primeiro=20 caso x^4 - 36 pude fazer por bi-quadrada, chamando x^2 de um K qualquer, = achando=20 K encontrei os 4 valores de x, por=E9m esse que eu tive d=FAvidas, = x^4 +=20 36,n=E3o seria uma boa op=E7=E3o (bi-quadrada) fazer a = mudan=E7a de=20 vari=E1vel  passando para uma equa=E7=E3o do 2 =BA grau e sim = aplica=E7=E3o =20 direta da segunda f=F3rmula de  DE MOIVRE( radicia=E7=E3o),que eu = n=E3o tinha=20 notado !!captei corretamente sua mensagem ? acho que sim e mais = um vz=20 sou grato por socializar o conhecimento. obg.
----- Original Message -----
From:=20 Marcelo Salhab=20 Brogliato
On Sun, Mar 9, 2008 at 10:28 AM, Gustavo = Duarte <gvduarte@hotlink.com.br>=20 wrote:
x^4 - 36 =3D 0, tudo = bem,encontrei como=20 raizes : + rz(6), -rz(6),+rz(6)i e=20 -rz(6)i   com  rz(X) >> raiz quadrada = de=20 x, por=E9m fiquei pensando no seguinte caso  :x^4 + 36 =3D0, desde = j=E1 agrade=E7o=20 alguma ajuda !!!
 

------=_NextPart_000_0005_01C881EA.5CE326E0-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sun Mar 9 18:23:10 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m29LLZsG018687 for ; Sun, 9 Mar 2008 18:21:35 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m29LLZW7018683 for obm-l-MllGbsmmN; Sun, 9 Mar 2008 18:21:35 -0300 Received: from fk-out-0910.google.com (fk-out-0910.google.com [209.85.128.187]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m29LLWsG018639 for ; Sun, 9 Mar 2008 18:21:32 -0300 Received: by fk-out-0910.google.com with SMTP id 22so13109399fkq.13 for ; Sun, 09 Mar 2008 14:21:58 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=LBFdSmihIlg5Fod2/hebx1zxNBzGGUU5bgrv8gpDScE=; b=YTvQNbKUXHhefshfwI/8DEmLnqnPIhWGHQDGHYZBbzzh8zLPu/OdEHNnm8dAUGzRsohtDPSyWGDqmYs0m/OYiPY0pZo4gqnoNh5qNHkYon9V+UE6mJ5rx+AAnu6KpQlsv6dycoldyl9gAXCukQmJQEoGAmJ5vxEnFzMhogNyRXU= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=APU3xRDBfEAr5qgm075nyaSvTWsyo0Lgj7OSWwKzTPGkCOPVyAQ+yGfWXaAy57QMtiJag7yL3dwwa412PcctA2OtlSa/PaSmzog4oQwb9aRXLyzmKEkYG0gRYAa5oJbIlUu1XXh3NSaB6xWCwnA0TZbRR+X27+booOg2QGPUZv0= Received: by 10.82.182.1 with SMTP id e1mr10760559buf.21.1205097718066; Sun, 09 Mar 2008 14:21:58 -0700 (PDT) Received: by 10.82.127.13 with HTTP; Sun, 9 Mar 2008 14:21:58 -0700 (PDT) Message-ID: Date: Sun, 9 Mar 2008 18:21:58 -0300 From: "Johann Peter Gustav Lejeune Dirichlet" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Marte In-Reply-To: <790450.92074.qm@web32205.mail.mud.yahoo.com> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_43526_31433597.1205097718030" References: <790450.92074.qm@web32205.mail.mud.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Johann Peter Gustav Lejeune Dirichlet" X-Spam-Status: No, hits=2.5 required=5.0 tests=AWL,FROM_ENDS_IN_NUMS,IN_REP_TO,JAVASCRIPT_UNSAFE, MAILTO_LINK,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_01_02, SPAM_REDIRECTOR,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: ** ------=_Part_43526_31433597.1205097718030 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Levando em conta quie existem algumas civiliza=E7=F5es que usam a bas 5 e o= utras que usam a base 20 para numerar, e logico concluir que eles tinham 13 dedos em cada membro (exceto por anomalias gen=E9ticas, hehe!) Em 08/03/08, Claudio Gustavo escreveu: > > S=E3o 13 por membro (total de 4.13=3D52 dedos). > > *saulo nilson * escreveu: > > ou sao 13 em cada perna? > > 2008/3/8 saulo nilson : > > > vc passou para base 13, mas como pode ter 4 pernas e 13 dedos? nao tem > > que ser simetrico? > > > > 2008/3/8 Claudio Gustavo : > > > > Os marcianos tinham 13 dedos. Pois passando os coeficientes da > > > equa=E7=E3o para o sistema decimal teremos: > > > i) 5 =3D 5 > > > ii) 50 =3D 5.13 =3D 65 > > > iii) 125 =3D 1.13^2 + 2.13 + 5 =3D 169 + 26 + 5 =3D 200 > > > Logo, no sistema decimal, a equa=E7=E3o fica: 5x^2 - 65x + 200 =3D = 0. > > > E o x=3D8 =E9 raiz: 5.8^2 - 65.8 +200 =3D 320 - 520 + 200 =3D 0. > > > > > > Abra=E7o, > > > Claudio Gustavo. > > > > > > > > > *Joao Victor Brasil * escreveu: > > > > > > Quando completamos 10 unidades transformamos em uma dezena. Como no > > > sistema de base 10, usamos at=E9 o algarismo 9; o sistema marciano to= lera o > > > algarismo 5 como unidade e n=E3o tolera o 8. Logo os marcianos devem = ter 6 ou > > > 7 dedos nas m=E3os. > > > > > > On 3/5/08, Klaus Ferraz wrote: > > > > > > > > A primeira expedicao a Marte encontrou somente as ruinas de uma > > > > civilizacao. Os exploradores concluiram dos artefatos e desenhos qu= e as > > > > criaturas que produziram esta civilizacao tinham quatro pernas, cad= a uma > > > > terminada em um conjunto de garras parecidas com dedos. Ap=F3s muit= o estudo > > > > foram capazes de traduzir a matematica marciana. Eles encontraram a= seguinte > > > > equacao: > > > > 5x^2-50x+125=3D0 > > > > Esta era uma matematica estranha. O valor x=3D5 parecia correto, ma= s > > > > x=3D8 n=E3o. Entao os exploradores lembraram a maneira como o nosso= sistema de > > > > numeracao foi desenvolvido e encontraram evidencias de que o sistem= a > > > > marciano teve uma historia analoga. Quantos dedos tinham os marcian= os? > > > > > > > > ------------------------------ > > > > Abra sua conta no Yahoo! Mail, > > > > o =FAnico sem limite de espa=E7o para armazenamento! > > > > > > > > > > > > > ------------------------------ > > > Abra sua conta no Yahoo! Mail, > > > o =FAnico sem limite de espa=E7o para armazenamento! > > > > > > > > > ------------------------------ > Abra sua conta no Yahoo! Mail, > o =FAnico sem limite de espa=E7o para armazenamento! > > --=20 Ideas are bulletproof. V ------=_Part_43526_31433597.1205097718030 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Levando em conta quie existem algumas civiliza=E7=F5es que usam a bas 5 e o= utras que usam a base 20 para numerar, e logico concluir que eles tinham 13= dedos em cada membro (exceto por anomalias gen=E9ticas, hehe!)

Em 08/03/08, Cla= udio Gustavo <claudioggl= l@yahoo.com.br> escreveu:

=20

Abra sua conta no Yahoo! Mail, o =FAnic= o sem limite de espa=E7o para armazenamento!=20




--
Ide= as are bulletproof.

V ------=_Part_43526_31433597.1205097718030-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sun Mar 9 19:02:36 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m29M1VsG029362 for ; Sun, 9 Mar 2008 19:01:31 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m29M1UFk029359 for obm-l-MllGbsmmN; Sun, 9 Mar 2008 19:01:30 -0300 Received: from py-out-1112.google.com (py-out-1112.google.com [64.233.166.179]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m29M1RsG029306 for ; Sun, 9 Mar 2008 19:01:28 -0300 Received: by py-out-1112.google.com with SMTP id f47so1661916pye.14 for ; Sun, 09 Mar 2008 15:01:54 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:mime-version:content-type; bh=9FviIVvY8AicgTXuh2ld1+1XXVLR4ijhEK9Swi8ONwY=; b=dOcAdM5eKeYrpdTKxscrIeYr0p8iUNBwKPq6jymkaMQXw3IUQBHaVXxNPIft/5NuyZDGR21Ex++NCGhofqvaZOrdYGEsfLZx0k/lhL+wOnpyU2RtALUaOO74mQ2DKQBN6fMzeV6XfvhBy/P98av80sHNXC2roj15R8rEEeYfgi4= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:mime-version:content-type; b=GylcGo3qDCUW1epa8WaXgiAkuuG/ijb/uEw9KksFFvC5A+onocRkxbN/XsnpP7RS0Ra1rExi5G9O2i4eB2350SoniGTWJXLVmRHZmo7uY4zM/6MJ6llmYKCInJoPrNqwEpngv1Uq/izoez96L98gXCw2RDevsDlyAGR4vrAZuDQ= Received: by 10.65.73.16 with SMTP id a16mr7609884qbl.85.1205100113888; Sun, 09 Mar 2008 15:01:53 -0700 (PDT) Received: by 10.65.206.20 with HTTP; Sun, 9 Mar 2008 15:01:53 -0700 (PDT) Message-ID: Date: Sun, 9 Mar 2008 19:01:53 -0300 From: "=?ISO-8859-1?Q?Pedro_J=FAnior?=" To: obm-l Subject: [SPAM] [obm-l] =?ISO-8859-1?Q?Teoria_dos_N=FAmeros?= MIME-Version: 1.0 Content-Type: text/plain Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "=?ISO-8859-1?Q?Pedro_J=FAnior?=" X-Spam-Status: Yes, hits=5.1 required=5.0 tests=AWL,FROM_ENDS_IN_NUMS,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, SPAM_PHRASE_00_01,TO_LOCALPART_EQ_REAL,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ***** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_Part_20850_13037010.1205100113868" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (5.10 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: TO_LOCALPART_EQ_REAL (-0.3 points) To: repeats local-part as real name SPAM: FROM_ENDS_IN_NUMS (0.9 points) From: ends in numbers SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 179.166.233.64.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 179.166.233.64.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-1.3 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- ------=_Part_20850_13037010.1205100113868 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Determine a quantidade de n=FAmeros primos p, para que a express=E3o p^1994= + p^1995 seja um quadrado perfeito. Desde j=E1 muito agradecido. Pedro Jr ------=_Part_20850_13037010.1205100113868 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Determine a quantidade de n=FAmeros primos p, para que a express=E3o p^1994= + p^1995 seja um quadrado perfeito.
Desde j=E1 muito agradecido.
Ped= ro Jr
------=_Part_20850_13037010.1205100113868-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sun Mar 9 19:58:22 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m29Mv6sG002582 for ; Sun, 9 Mar 2008 19:57:06 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m29Mv6lX002580 for obm-l-MllGbsmmN; Sun, 9 Mar 2008 19:57:06 -0300 Received: from ug-out-1314.google.com (ug-out-1314.google.com [66.249.92.173]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m29Mv4sG002562 for ; Sun, 9 Mar 2008 19:57:05 -0300 Received: by ug-out-1314.google.com with SMTP id q7so4660177uge.0 for ; Sun, 09 Mar 2008 15:57:30 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; bh=UxGomjl5jvnw2dDwl8gSys5RKF67Lfcx834ugI/qP8E=; b=gnaG1tZqxEJjEG+/1NVl1btdcTrGnuUotr/KuTmYPfR3yGQVX01cJuZdhSBLRpt6zZkh9LV3uVBmnfbyHzjHMAO8uzrhffyXGMyczCsyhI2TNJUM7rhwdio6HNldfml/xtIFcHjwZoEk+8WJzBxDxBgQg/3eDaJrdhoemNo83Qk= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; b=Fk319lrnfyYh0t3SRAauhDvCtczQ35Br49zcF85kF97i36juc2sXBmsuHZpn/7IxkpLFeGct1rEzMerZR3pyISeDsOHpsW0jVks9FfJfrmReFtH/7Oj5wY0qxjHvxRf5R8JnfYN9j11vNPDK7/K5ZtERH50BXONxWgye4l4nfzs= Received: by 10.67.123.19 with SMTP id a19mr3403288ugn.65.1205103450578; Sun, 09 Mar 2008 15:57:30 -0700 (PDT) Received: by 10.66.219.5 with HTTP; Sun, 9 Mar 2008 15:57:30 -0700 (PDT) Message-ID: <2d483c770803091557o1d17f098p1be49398c5ee57f4@mail.gmail.com> Date: Sun, 9 Mar 2008 19:57:30 -0300 From: "Ralph Teixeira" To: obm-l@mat.puc-rio.br Subject: =?ISO-8859-1?Q?Re:_[obm-l]_Teoria_dos_N=FAmeros?= In-Reply-To: MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline References: Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m29Mv5sG002578 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Ralph Teixeira" X-Spam-Status: No, hits=4.8 required=5.0 tests=AWL,IN_REP_TO,MAILTO_TO_SPAM_ADDR,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** p^1994+p^1995=p^1994(p+1) Como p^1994 jah eh um quadrado perfeito (de p^997), a condicao pedida eh equivalente a p+1 ser quadrado perfeito. Mas entao: p+1=k^2 (com k inteiro) p=k^2-1=(k+1)(k-1) Mas se p eh primo, como eh que vai ser o produto de dois inteiros? O unico jeito eh se um deles for 1 e o outro for p; como nao pode ser k+1=1 (pois entao p=0, o que nao serve), tem de ser k-1=1, entao k=2, entao p=3. Assim, ha apenas um numero primo satisfazendo a dita condicao, que eh p=3. De fato: 3^1994+3^1995=3^1994.4=(3^997.2)^2. Abraco, Ralph On Sun, Mar 9, 2008 at 7:01 PM, Pedro Júnior wrote: > Determine a quantidade de números primos p, para que a expressão p^1994 + > p^1995 seja um quadrado perfeito. > Desde já muito agradecido. > Pedro Jr > ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sun Mar 9 20:00:25 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m29MxOsG002727 for ; Sun, 9 Mar 2008 19:59:24 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m29MxNIr002722 for obm-l-MllGbsmmN; Sun, 9 Mar 2008 19:59:23 -0300 Received: from nf-out-0910.google.com (nf-out-0910.google.com [64.233.182.189]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m29MxLsG002708 for ; Sun, 9 Mar 2008 19:59:21 -0300 Received: by nf-out-0910.google.com with SMTP id k4so735605nfd.19 for ; Sun, 09 Mar 2008 15:59:45 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=Z8grARHl21JfSQJX1RgtEoWDUbE7r6WC5urQwAGJC5o=; b=TrgRQ4n4fILGSgNVjLXYCqhJSssqPE5jHjcpIj4xEwKhoL/2525YlIV41aYkPYXZtvFdI8RV5xBevpmqCxPeewnVNZIscbYf0N2ZosEGIMhSWDYz9h7WNC31ovYLwSsbRA6aC9KtwD5nOFTT7Z0zBhRXP3y3iDWplVs3xkt01pY= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=o7JkMdYN215DjjIOZNgQN13fA0wEY1TazKSQqO97EFy6RDH9dcKSSiGkPX/F3jbVGb84IHhYQb9oYxMOvdRhFg7bthLPI3HZgfzxV+RLOmguGtvgU8msrdvpzw+uNIC9XSNWjFaCiAGdrKZtyCPjgpIG+RVnhbAJqxz5tTKup/Q= Received: by 10.78.168.6 with SMTP id q6mr11951545hue.65.1205103585572; Sun, 09 Mar 2008 15:59:45 -0700 (PDT) Received: by 10.78.118.13 with HTTP; Sun, 9 Mar 2008 15:59:45 -0700 (PDT) Message-ID: <29e1bfbd0803091559p31715315r1ee9bc339433f8e5@mail.gmail.com> Date: Sun, 9 Mar 2008 19:59:45 -0300 From: "Felipe Diniz" To: obm-l@mat.puc-rio.br Subject: =?ISO-8859-1?Q?Re:_[obm-l]_Teoria_dos_N=FAmeros?= In-Reply-To: MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_32425_28118474.1205103585562" References: Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Felipe Diniz" X-Spam-Status: No, hits=3.8 required=5.0 tests=AWL,EMAIL_ATTRIBUTION,IN_REP_TO,MAILTO_LINK, MAILTO_TO_SPAM_ADDR,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, REFERENCES,SPAM_PHRASE_00_01,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: *** ------=_Part_32425_28118474.1205103585562 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline p^1994 + p^1995 =3D p^1994 ( p+1) Se p^1994 + p^1995 e quadrado entao p+1 e quadrado assim p+1=3Dx^2 =3D> p=3D(x-1)(x+1), como p e primo devemos ter x-1 =3D 1 =3D> x= =3D2 =3D> p=3D3, assim 3 e o unico primo tal que p^1994 + p^1995 e quadrado On Sun, Mar 9, 2008 at 7:01 PM, Pedro J=FAnior wrote: > Determine a quantidade de n=FAmeros primos p, para que a express=E3o p^19= 94 + > p^1995 seja um quadrado perfeito. > Desde j=E1 muito agradecido. > Pedro Jr > ------=_Part_32425_28118474.1205103585562 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline p^1994 + p^1995 =3D p^1994 ( p+1)
Se p^1994 + p^1995 e quadrado entao p+= 1 e quadrado
assim
p+1=3Dx^2 =3D> p=3D(x-1)(x+1), como p e primo d= evemos ter x-1 =3D 1 =3D> x=3D2 =3D> p=3D3, assim 3 e o unico primo t= al que p^1994 + p^1995 e quadrado

On Sun, Mar 9, 2008 at 7:01 PM, Pedro J=FAni= or <pedromatematico06@gma= il.com> wrote:
Determine a quantidade de n=FAmeros primos p, para que a express=E3o p^1994= + p^1995 seja um quadrado perfeito.
Desde j=E1 muito agradecido.
Ped= ro Jr

------=_Part_32425_28118474.1205103585562-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sun Mar 9 23:04:17 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2A22FsG011976 for ; Sun, 9 Mar 2008 23:02:15 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2A221Ll011961 for obm-l-MllGbsmmN; Sun, 9 Mar 2008 23:02:01 -0300 Received: from smtp.bol.com.br (smtpout2.bol.com.br [200.221.4.213]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2A220sG011957 for ; Sun, 9 Mar 2008 23:02:00 -0300 Received: from localhost (localhost [127.0.0.1]) by smart6.bol.com.br (Postfix) with ESMTP id D7389433 for ; Sun, 9 Mar 2008 23:02:27 -0300 (BRT) Received: from pai (unknown [201.88.134.242]) by smart6.bol.com.br (Postfix) with ESMTP id 6AC66407 for ; Sun, 9 Mar 2008 23:02:27 -0300 (BRT) Message-ID: <000c01c88252$fa804aa0$6701a8c0@pai> From: "Tio Cabri st" To: Subject: [SPAM] [obm-l] =?iso-8859-1?Q?an=E1lise_em_1949?= Date: Sun, 9 Mar 2008 23:03:46 -0300 MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: 7bit X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2800.1478 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2800.1478 X-SIG5: 9cedb15fb72c55f5bcaa204c823f2a80 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Tio Cabri st" X-Spam-Status: Yes, hits=6.0 required=5.0 tests=AWL,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01, USER_AGENT_OE,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ****** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (6.00 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: USER_AGENT_OE (0.2 points) X-Mailer header indicates a non-spam MUA (Outlook Express) SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 242.134.88.201.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 242.134.88.201.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (0.0 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- Boa noite, estou lendo um livro de análise real escrito em 1952. onde ele, o autor, define números reais como um par de classes classe minorante e calsse majorante. Alguém saberia me explicar qual seria a linguagem atual. Obrigado Cabri ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Mon Mar 10 12:37:00 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2AFY8sG014230 for ; Mon, 10 Mar 2008 12:34:10 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2AFY4LF014226 for obm-l-MllGbsmmN; Mon, 10 Mar 2008 12:34:04 -0300 Received: from relay2.bol.com.br (relay2.bol.com.br [200.221.4.106]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2AFXmsG014209 for ; Mon, 10 Mar 2008 12:33:48 -0300 Received: from localhost (localhost [127.0.0.1]) by salsa2.bol.com.br (Postfix) with ESMTP id 9A845E0058E7 for ; Mon, 10 Mar 2008 12:34:15 -0300 (BRT) Received: from bol.com.br (whisper2.mail.sys.intranet [172.26.5.137]) by salsa2.bol.com.br (Postfix) with ESMTP id 664D1E005D5F for ; Mon, 10 Mar 2008 12:34:15 -0300 (BRT) Date: Mon, 10 Mar 2008 12:34:15 -0300 Message-Id: Subject: [obm-l] =?iso-8859-1?b?Q09OQ0VTU0lPTsFSSUEgREUgVkXNQ1VMT1M=?= MIME-Version: 1.0 X-Sensitivity: 3 Content-Type: multipart/alternative; boundary="_=__=_XaM3_.1205163255.2A.376386.42.11561.52.42.007.1148199275" From: "arkon" To: "obm-l" X-XaM3-API-Version: 4.3(R1) (B10) X-SenderIP: 200.140.133.73 X-SIG5: 3a511300da566c26e892b794e102bb02 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "arkon" X-Spam-Status: No, hits=1.2 required=5.0 tests=AWL,BIG_FONT,LINES_OF_YELLING,LINES_OF_YELLING_2, SPAM_PHRASE_00_01,SUPERLONG_LINE,TO_LOCALPART_EQ_REAL, X_MAILING_LIST version=2.44 X-Spam-Level: * --_=__=_XaM3_.1205163255.2A.376386.42.11561.52.42.007.1148199275 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable Algu=E9m pode me enviar a resolu=E7=E3o, por favor: Uma concession=E1ria de ve=EDculos tem um plano de troca de carros usados= por novos de mesma marca e de mesmo modelo. Na negocia=E7=E3o, a concess= ion=E1ria avalia o ve=EDculo usado, depreciando-o a cada ano em 10% em re= la=E7=E3o =E0 avalia=E7=E3o do ano anterior. Por outro lado, devido =E0s = melhorias introduzidas em decorr=EAncia do desenvolvimento tecnol=F3gico,= o pre=E7o de um ve=EDculo novo, de mesma marca e de mesmo modelo, =E9 au= mentado anualmente em 6%. O valor atual de um ve=EDculo novo nessa conces= sion=E1ria =E9 de R$ 28.000,00. Considerando a situa=E7=E3o descrita no texto, calcule, em milhares de re= ais, quanto um cliente dever=E1 desembolsar para trocar por um ve=EDculo = novo, da mesma marca e do mesmo modelo, daqui a 7 anos, um ve=EDculo adqu= irido hoje na concession=E1ria. Despreze, caso exista, a parte fracion=E1= ria do resultado obtido. Resposta: 28. DESDE J=C1 MUITO OBRIGADO. --_=__=_XaM3_.1205163255.2A.376386.42.11561.52.42.007.1148199275 Content-Type: text/html; charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable

<= B style=3D"mso-bidi-font-weight: normal">Algu=E9m pode me enviar a resolu=E7=E3o, por favor:<= o:p>

<= B style=3D"mso-bidi-font-weight: normal"> 

<= B style=3D"mso-bidi-font-weight: normal">Uma concession=E1ria de ve=EDculos tem um plano de troca de= carros usados por novos de mesma marca e de mesmo modelo. Na negocia=E7=E3= o, a concession=E1ria avalia o ve=EDculo usado, depreciando-o a cada ano = em 10% em rela=E7=E3o =E0 avalia=E7=E3o do ano anterior. Por outro lado, = devido =E0s melhorias introduzidas em decorr=EAncia do desenvolvimento te= cnol=F3gico, o pre=E7o de um ve=EDculo novo, de mesma marca e de mesmo mo= delo, =E9 aumentado anualmente em 6%. O valor atual de um ve=EDculo novo = nessa concession=E1ria =E9 de R$ 28.000,00.<= /P>

<= B style=3D"mso-bidi-font-weight: normal"> 

<= B style=3D"mso-bidi-font-weight: normal">Considerando a situa=E7=E3o descrita no texto, calcule, = em milhares de reais, quanto um cliente dever=E1 desembolsar para tro= car por um ve=EDculo novo, da mesma marca e do mesmo modelo, daqui a 7 an= os, um ve=EDculo adquirido hoje na concession=E1ria. Despreze, caso exist= a, a parte fracion=E1ria do resultado obtido.

<= B style=3D"mso-bidi-font-weight: normal"> 

<= FONT size=3D3>Resposta: 28.

 

Amigos, agrade=C3=A7o a ajuda de quem se dispuser.=0A
 
=0A
1.) Um certo tipo de aplica=C3=A7=C3=A3o dupl= ica o valor da aplica=C3=A7=C3=A3o a cada 2 meses. Em quanto tempo essa apl= ica=C3=A7=C3=A3o render=C3=A1 juros de 700%?
=0A
 
=0A2.) Em quantos meses o juro ultrapassar=C3=A1 o valor do capital aplicad= o se a taxa de juro for de 24% a.a, capitalizados trimestralmente?
=0A=
 
=0A
Obrigado.
=0A
 
=0A
Alexand= re Bastos
=0A
 
=0A
 

=0A=0A=0A =
Abra sua conta no Yahoo! Mail, o =C3=BAnico sem= limite de espa=C3=A7o para armazenamento! =0A --0-1270315856-1205164431=:58072-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Mon Mar 10 13:07:14 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2AG5ksG016103 for ; Mon, 10 Mar 2008 13:05:47 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2AG5kfA016101 for obm-l-MllGbsmmN; Mon, 10 Mar 2008 13:05:46 -0300 Received: from ti-out-0910.google.com (ti-out-0910.google.com [209.85.142.184]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2AG5gsG016083 for ; Mon, 10 Mar 2008 13:05:43 -0300 Received: by ti-out-0910.google.com with SMTP id y6so901571tia.13 for ; Mon, 10 Mar 2008 09:06:09 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=3oYltLBBWs9mfnJ6LzSnTPjl5S8OUj3zjoEOjRf+J24=; b=DAn6TAHaiCuurdx7q7sFV8i/xcELM/i4mzFm7nVuZmBZ3p4seuG6K76Zy0ptpNMwYEfHHb8+kB5+XrJF34BduXZpn6eIzpFlAfpJlAL/M0GyhTAQOW36bBQNptf3Ec64VmQg/mJsKxLFDRkxJHCj8lWcCscWS0XwGIWpVwpCP00= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=p4cm+Ump8UE33q6jLUCZuDAVwipaLXmxPL97PuKGVS/Lz9CKxAVjAvplQY3+WrMhDXbR4gXjrz49dA9tw1rYpzeP4XxnMFTt5bw3Con4pyGGLYuECTdl/0BJdxtWD5IdW45YqlfiCbbX+e1ky2E36S6PBt8OnLbD/EBFrOP0iWE= Received: by 10.151.44.18 with SMTP id w18mr2846939ybj.184.1205165167129; Mon, 10 Mar 2008 09:06:07 -0700 (PDT) Received: by 10.150.57.9 with HTTP; Mon, 10 Mar 2008 09:06:07 -0700 (PDT) Message-ID: <5bb472220803100906r796ccef8nf22d23954b7981ec@mail.gmail.com> Date: Mon, 10 Mar 2008 13:06:07 -0300 From: "Joao Victor Brasil" To: obm-l@mat.puc-rio.br Subject: =?ISO-8859-1?Q?Re:_[obm-l]_CONCESSION=C1RIA_DE_VE=CDCULOS?= In-Reply-To: MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_5106_22677799.1205165167129" References: Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Joao Victor Brasil" X-Spam-Status: No, hits=3.5 required=5.0 tests=AWL,BIG_FONT,EMAIL_ATTRIBUTION,IN_REP_TO,LINES_OF_YELLING, MAILTO_LINK,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: *** ------=_Part_5106_22677799.1205165167129 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Valor do carro novo =3D 28000 *(1,06^7) Valor do carro usado =3D 28000 * (0,9^7) VALOR PAGO : R$ 28709,00 (aprox) Quantos milhares foram pagos? 28, porque o 29=B0 n=E3o chegou a ser complet= o. On 3/10/08, arkon wrote: > *Algu=E9m pode me enviar a resolu=E7=E3o, por favor:* > > * * > > *Uma concession=E1ria de ve=EDculos tem um plano de troca de carros usado= s por > novos de mesma marca e de mesmo modelo. Na negocia=E7=E3o, a concession= =E1ria > avalia o ve=EDculo usado, depreciando-o a cada ano em 10% em rela=E7=E3o = =E0 > avalia=E7=E3o do ano anterior. Por outro lado, devido =E0s melhorias intr= oduzidas > em decorr=EAncia do desenvolvimento tecnol=F3gico, o pre=E7o de um ve=EDc= ulo novo, > de mesma marca e de mesmo modelo, =E9 aumentado anualmente em 6%. O valor > atual de um ve=EDculo novo nessa concession=E1ria =E9 de R$ 28.000,00.* > > * * > > *Considerando a situa=E7=E3o descrita no texto, calcule, em milhares de r= eais, > quanto um cliente dever=E1 desembolsar para trocar por um ve=EDculo novo,= da > mesma marca e do mesmo modelo, daqui a 7 anos, um ve=EDculo adquirido hoj= e na > concession=E1ria. Despreze, caso exista, a parte fracion=E1ria do resulta= do > obtido.* > > * * > > *Resposta: 28*. > > * * > > *DESDE J=C1 MUITO OBRIGADO.* > ------=_Part_5106_22677799.1205165167129 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline
Valor do carro novo =3D 28000 *(1,06^7)
Valor do carro usado =3D 28000 * (0,9^7)
 
VALOR PAGO : R$ 28709,00 (aprox)
 
Quantos milhares foram pagos? 28, porque o 29=B0 n=E3o chegou a ser co= mpleto.
 
On 3/10/08, = arkon <arkon@bol.com.br> = wrote:

<= font face=3D"Times New Roman">Algu=E9m pode me enviar a resolu=E7=E3o, por = favor:

 

<= font face=3D"Times New Roman">Uma concession=E1ria de ve=EDculos tem um pla= no de troca de carros usados por novos de mesma marca e de mesmo modelo. Na= negocia=E7=E3o, a concession=E1ria avalia o ve=EDculo usado, depreciando-o= a cada ano em 10% em rela=E7=E3o =E0 avalia=E7=E3o do ano anterior. Por ou= tro lado, devido =E0s melhorias introduzidas em decorr=EAncia do desenvolvi= mento tecnol=F3gico, o pre=E7o de um ve=EDculo novo, de mesma marca e de me= smo modelo, =E9 aumentado anualmente em 6%. O valor atual de um ve=EDculo n= ovo nessa concession=E1ria =E9 de R$ 28.000,00.

 

<= font face=3D"Times New Roman">Considerando a situa=E7=E3o descrita no texto= , calcule, em milhares de reais, quanto um cliente dever=E1 desembol= sar para trocar por um ve=EDculo novo, da mesma marca e do mesmo modelo, da= qui a 7 anos, um ve=EDculo adquirido hoje na concession=E1ria. Despreze, ca= so exista, a parte fracion=E1ria do resultado obtido.

 

Resposta: 28.

 

DESDE J=C1 MUITO OBRIGADO.


------=_Part_5106_22677799.1205165167129-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Mon Mar 10 15:43:39 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2AIeUsG026158 for ; Mon, 10 Mar 2008 15:40:32 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2AIeTfV026152 for obm-l-MllGbsmmN; Mon, 10 Mar 2008 15:40:29 -0300 Received: from fg-out-1718.google.com (fg-out-1718.google.com [72.14.220.157]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2AIdxsG026075 for ; Mon, 10 Mar 2008 15:40:08 -0300 Received: by fg-out-1718.google.com with SMTP id e12so8214066fga.3 for ; Mon, 10 Mar 2008 11:40:26 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=8KYt3gA5TmRJsZPY+sju546l/6sTW23ms+n/ATWbQ+o=; b=bOkB0/uOkHeFUP1PZCAkRYofcQkAYwcuEN/fXbY3KDnnXs0cVXMaUSBrkWU5o5jjiSFlar5o1lBxevuDIg5oob2ONsDjgeyzdg0zEO+3q6tX6J+gIFcIom8afiAyZd2RkPFQJyEIMfXt1nPkIksQIM3PfKTDpmUoOL+fg8WEcr0= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=RvAOnn06ZYiVPESCO0J4VHIcvS/5kp2ydk/1zOU8AHP7CPBfzyUxSKxU+AyocilVDDeQDHKpccOYx5b3PoflNrqIgusekPi8YkEPcBMQ53dKoYI+RPHaEPiBZv8ev4BfPOH/WRfOogbqF3VcH2q7/ESTGovnrEEzE+dC9lJsiB0= Received: by 10.86.26.11 with SMTP id 11mr6891574fgz.17.1205174425090; Mon, 10 Mar 2008 11:40:25 -0700 (PDT) Received: by 10.86.74.8 with HTTP; Mon, 10 Mar 2008 11:40:25 -0700 (PDT) Message-ID: Date: Mon, 10 Mar 2008 15:40:25 -0300 From: "saulo nilson" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Financeira In-Reply-To: <142456.58072.qm@web52205.mail.re2.yahoo.com> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_20289_24870540.1205174425084" References: <142456.58072.qm@web52205.mail.re2.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "saulo nilson" X-Spam-Status: No, hits=-0.2 required=5.0 tests=AWL,HTML_FONT_COLOR_GRAY,HTML_FONT_COLOR_UNSAFE,IN_REP_TO, MAILTO_LINK,MAILTO_TO_SPAM_ADDR,QUOTED_EMAIL_TEXT, REFERENCES,SPAM_PHRASE_01_02,SPAM_REDIRECTOR,X_MAILING_LIST version=2.44 X-Spam-Level: ------=_Part_20289_24870540.1205174425084 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline cn=3Dc0*q^(n)=3Dc0+7c0=3D8c0 2^n=3D8 n=3D3 =3D=3D=3D6 meses 2008/3/10 Alexandre Bastos : > Amigos, agrade=E7o a ajuda de quem se dispuser. > > 1.) Um certo tipo de aplica=E7=E3o duplica o valor da aplica=E7=E3o a cad= a 2 > meses. Em quanto tempo essa aplica=E7=E3o render=E1 juros de 700%? > > 2.) Em quantos meses o juro ultrapassar=E1 o valor do capital aplicado se= a > taxa de juro for de 24% a.a, capitalizados trimestralmente? > > Obrigado. > > Alexandre Bastos > > > > ------------------------------ > Abra sua conta no Yahoo! Mail, > o =FAnico sem limite de espa=E7o para armazenamento! > ------=_Part_20289_24870540.1205174425084 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline
cn=3Dc0*q^(n)=3Dc0+7c0=3D8c0
2^n=3D8
n=3D3 =3D=3D=3D6 meses

2008/3/10 Alexandre Bastos <alexandrebastos78@yahoo.com.br>:
Amigos, agrade=E7o a ajuda de quem se dispuser.
 
1.) Um certo tipo de aplica=E7=E3o duplica o valor da aplica=E7=E3o a = cada 2 meses. Em quanto tempo essa aplica=E7=E3o render=E1 juros de 700%?
 
2.) Em quantos meses o juro ultrapassar=E1 o valor do capital aplicado= se a taxa de juro for de 24% a.a, capitalizados trimestralmente?
 
Obrigado.
 
Alexandre Bastos
 
 

Abra sua conta no Yahoo! Mail, o =FAnico sem li= mite de espa=E7o para armazenamento!

------=_Part_20289_24870540.1205174425084-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Mon Mar 10 18:12:07 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2ALAHsG001994 for ; Mon, 10 Mar 2008 18:10:18 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2ALAGLg001987 for obm-l-MllGbsmmN; Mon, 10 Mar 2008 18:10:16 -0300 Received: from rn-out-0910.google.com (rn-out-0910.google.com [64.233.170.188]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2ALAAsG001924 for ; Mon, 10 Mar 2008 18:10:11 -0300 Received: by rn-out-0910.google.com with SMTP id e11so1480936rng.7 for ; Mon, 10 Mar 2008 14:10:37 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:mime-version:content-type; bh=WxacfgNmAKFVoWnbskwQnal4LUi0MjJJ/uo6u66n/V8=; b=qnuTufGXHlJDhLpkeBedFYgmK2Kluu1hwk9o8zOAdT2At1tQobD43cTd2gSLc/9NEOFXOr7X6+GdWYzA6ylTqOTd99ZJGKhhmjtS+a+duX+xrpJnJttvG1FfWGYee4Atb1Oz1QFT4kqoUOpb23ZyhZkhfinDvPH+vIO9osAX6po= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:mime-version:content-type; b=Jf662ivi4jbEW2FByfPTJ0i72j66ArGt6UhMKNup1l55LD5+6TEF3Y4MU75FpMuMCrJiZEQQrK0G2UtuAKH7c2WrMpJXg823hVm9tc1E0UXQidchNPtjxUFHEBw9cz7HxBBmxTsdpvkhu8RRNRLYzAZXbCe2YQ8+40Uxo1Hkflg= Received: by 10.114.13.1 with SMTP id 1mr3842979wam.60.1205183435425; Mon, 10 Mar 2008 14:10:35 -0700 (PDT) Received: by 10.114.88.8 with HTTP; Mon, 10 Mar 2008 14:10:35 -0700 (PDT) Message-ID: Date: Mon, 10 Mar 2008 18:10:35 -0300 From: MauZ To: obm-l@mat.puc-rio.br Subject: [SPAM] [obm-l] Esfera... problema MIME-Version: 1.0 Content-Type: text/plain Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: MauZ X-Spam-Status: Yes, hits=5.8 required=5.0 tests=RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ***** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_Part_5191_18596901.1205183435400" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (5.80 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 188.170.233.64.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 188.170.233.64.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- ------=_Part_5191_18596901.1205183435400 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Dois pontos na esfera de raio 1 est=E3o conectados por um arco A contido no interior da esfera. Mostre que se o comprimento do arco A =E9 menor do que 2 ent=E3o existe um hemisf=E9rio H que n=E3o intercepta A. ______ Minha ideia at=E9 agora foi simplesmente criar um hemisf=E9rio da seguitne forma: Acho um ponto P coplanar aos dois pontos B e C que seja arco m=E9dio de B e= C. A=ED basta achar o l.g. de P' tal que arco(P,P')=3Dpi/2. ai essa circunfere= ncia determina o hemisferio H. Depois tenho q mostrar que qualquer arco q intercepte esse hemisferio mede 2 ou +. n=E3o sei se esse =E9 o caminho.. mas nao estou cosneguindo formalizar... Obrigado, Maurizio ------=_Part_5191_18596901.1205183435400 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Dois pontos na esfera de raio 1 est=E3o conectados por um arco A contido no= interior da esfera.
 Mostre que se o comprimento do arco A =E9 men= or do que 2 ent=E3o existe um hemisf=E9rio H que n=E3o intercepta A.
______

Minha ideia at=E9 agora foi simplesmente criar um hemisf=E9rio da seguitne = forma:
Acho um ponto P coplanar aos dois pontos B e C que seja arco m=E9= dio de B e C. A=ED basta achar o l.g. de P' tal que arco(P,P')=3Dpi= /2. ai essa circunferencia determina o hemisferio H. Depois tenho q mostrar= que qualquer arco q intercepte esse hemisferio mede 2 ou +.

n=E3o sei se esse =E9 o caminho.. mas nao estou cosneguindo formalizar.= ..

Obrigado,
Maurizio
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Ob= rigado!
------=_Part_5296_2012433.1205183634706-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Mon Mar 10 18:59:25 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2ALvjsG004426 for ; Mon, 10 Mar 2008 18:57:45 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2ALvjbV004424 for obm-l-MllGbsmmN; Mon, 10 Mar 2008 18:57:45 -0300 Received: from py-out-1112.google.com (py-out-1112.google.com [64.233.166.180]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2ALvhsG004421 for ; Mon, 10 Mar 2008 18:57:43 -0300 Received: by py-out-1112.google.com with SMTP id f47so2161433pye.14 for ; Mon, 10 Mar 2008 14:58:10 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=y0T6eniI9LE/XACsbf3uz18udrYcBQDfqGv8/pPYNOI=; b=oUPB+n//3ENIfOfiY7MJqVa7kXjEf9EIk8Mpg9nGCiCqJgodlKKMoD5xlYwSL4c6ov5DqH0uBsacheO1wUZBt3I9OSZd3UmTshFWDNPacCJ5//xgX+OOnmELExCfyu0e6R7XdprveZSqalRbpk+fcQl1VdvquQLriq4gPrr4+2Y= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=UDQqfLGWcyIjea5v3Gy8zM5gu9GslK0or17uI3xsEzgE4gMBNmuf9NNYa6OBZOnMFShFYiO6maeACbB5G0vWdfO8HjkV5CdacU20YqKgVZXhBLMaZdp0PF0zU4LeQ+dGQAyWHRnmkacSqar/12M7gXmJobF3gt7mMQ923GyTOBE= Received: by 10.64.210.3 with SMTP id i3mr11100271qbg.70.1205186279509; Mon, 10 Mar 2008 14:57:59 -0700 (PDT) Received: by 10.65.206.20 with HTTP; Mon, 10 Mar 2008 14:57:59 -0700 (PDT) Message-ID: Date: Mon, 10 Mar 2008 18:57:59 -0300 From: "=?ISO-8859-1?Q?Pedro_J=FAnior?=" To: obm-l@mat.puc-rio.br Subject: =?ISO-8859-1?Q?Re:_[obm-l]_Teoria_dos_N=FAmeros?= In-Reply-To: <29e1bfbd0803091559p31715315r1ee9bc339433f8e5@mail.gmail.com> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_25354_13424993.1205186279445" References: <29e1bfbd0803091559p31715315r1ee9bc339433f8e5@mail.gmail.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "=?ISO-8859-1?Q?Pedro_J=FAnior?=" X-Spam-Status: No, hits=4.8 required=5.0 tests=AWL,EMAIL_ATTRIBUTION,FROM_ENDS_IN_NUMS,IN_REP_TO, JAVASCRIPT_UNSAFE,MAILTO_LINK,MAILTO_TO_SPAM_ADDR, RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,REFERENCES, SPAM_PHRASE_00_01,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** ------=_Part_25354_13424993.1205186279445 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Muito obrigado caros colegas... Boa semana para todos. 2008/3/9, Felipe Diniz : > > p^1994 + p^1995 =3D p^1994 ( p+1) > Se p^1994 + p^1995 e quadrado entao p+1 e quadrado > assim > p+1=3Dx^2 =3D> p=3D(x-1)(x+1), como p e primo devemos ter x-1 =3D 1 =3D> = x=3D2 =3D> p=3D3, > assim 3 e o unico primo tal que p^1994 + p^1995 e quadrado > > On Sun, Mar 9, 2008 at 7:01 PM, Pedro J=FAnior > wrote: > > > Determine a quantidade de n=FAmeros primos p, para que a express=E3o p^= 1994 > > + p^1995 seja um quadrado perfeito. > > Desde j=E1 muito agradecido. > > Pedro Jr > > > > ------=_Part_25354_13424993.1205186279445 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline
Muito obrigado caros colegas...
Boa semana para todos.

 
2008/3/9, Felipe Diniz <edward.elric.br@gmail.com>:
p^1994 + p^199= 5 =3D p^1994 ( p+1)
Se p^1994 + p^1995 e quadrado entao p+1 e qua= drado
assim
p+1=3Dx^2 =3D> p=3D(x-1)(x+1), como p e primo devemos ter x-1 = =3D 1 =3D> x=3D2 =3D> p=3D3, assim 3 e o unico primo tal que p^1994 += p^1995 e quadrado

On Sun, Mar 9, 2008 at 7:01 PM= , Pedro J=FAnior <pedroma= tematico06@gmail.com> wrote:
Determine a quantida= de de n=FAmeros primos p, para que a express=E3o p^1994 + p^1995 seja um qu= adrado perfeito.
Desde j=E1 muito agradecido.
Pedro Jr


------=_Part_25354_13424993.1205186279445-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Mon Mar 10 18:59:25 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2ALwFsG004436 for ; Mon, 10 Mar 2008 18:58:15 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2ALwFTp004434 for obm-l-MllGbsmmN; Mon, 10 Mar 2008 18:58:15 -0300 Received: from wx-out-0506.google.com (wx-out-0506.google.com [66.249.82.231]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2ALwCsG004430 for ; Mon, 10 Mar 2008 18:58:13 -0300 Received: by wx-out-0506.google.com with SMTP id t4so2590802wxc.18 for ; Mon, 10 Mar 2008 14:58:39 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=T49XX0mLV7GVFJ5Jf8F4EYSDxF3LH3PpswHSv02nlUg=; b=nqZTZWSG+QH2joqg8NHzAoRwVdY5tB8gpeSNSXk4XiBxLiSDWpYNNhyX8RosI868Fdf7vj8pT+mjPB3zVLsxXrFpYJYyRKCwDEbodBH0lhJrE/qp74Qx6t3qQdE9hiChi21aGs5iklJV6W7NmoRRta13YSRFMXB5kNI8IFU3QsY= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=leDnckuyfmfFY0jQAvZgzW6ZOASAsFtGsWmG7Su0Vfa3Zsj6mOyQBp+wnJSisByUXkXji7U4kNdkgyVqwOhqgeF7+Yi6gSWo68QPwoWA3Ar1WEyaEOmvWKnu2Pv9KoB53B+lWJaCwsU+3KFOyfVD3TQWHbL+zzsHryNzLy49iy4= Received: by 10.65.95.12 with SMTP id x12mr11104477qbl.35.1205186307766; Mon, 10 Mar 2008 14:58:27 -0700 (PDT) Received: by 10.65.206.20 with HTTP; Mon, 10 Mar 2008 14:58:27 -0700 (PDT) Message-ID: Date: Mon, 10 Mar 2008 18:58:27 -0300 From: "=?ISO-8859-1?Q?Pedro_J=FAnior?=" To: obm-l@mat.puc-rio.br Subject: [SPAM] =?ISO-8859-1?Q?Re:_[obm-l]_Teoria_dos_N=FAmeros?= In-Reply-To: <2d483c770803091557o1d17f098p1be49398c5ee57f4@mail.gmail.com> MIME-Version: 1.0 Content-Type: text/plain References: <2d483c770803091557o1d17f098p1be49398c5ee57f4@mail.gmail.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "=?ISO-8859-1?Q?Pedro_J=FAnior?=" X-Spam-Status: Yes, hits=5.6 required=5.0 tests=AWL,FROM_ENDS_IN_NUMS,IN_REP_TO,MAILTO_LINK, MAILTO_TO_SPAM_ADDR,MIME_EXCESSIVE_QP,QUOTED_EMAIL_TEXT, RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,REFERENCES, SPAM_PHRASE_00_01,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ***** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_Part_25360_7933817.1205186307704" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (5.60 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: REFERENCES (-0.5 points) Has a valid-looking References header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: FROM_ENDS_IN_NUMS (0.9 points) From: ends in numbers SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: QUOTED_EMAIL_TEXT (-0.8 points) BODY: Contains what looks like a quoted email text SPAM: MAILTO_LINK (0.2 points) BODY: Includes a URL link to send an email SPAM: MIME_EXCESSIVE_QP (1.0 points) RAW: Excessive quoted-printable encoding in body SPAM: MAILTO_TO_SPAM_ADDR (0.7 points) URI: Includes a link to a likely spammer email address SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 231.82.249.66.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 231.82.249.66.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-0.9 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- ------=_Part_25360_7933817.1205186307704 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Muito obrigado caros colegas... Boa semana para todos. 2008/3/9, Ralph Teixeira : > > p^1994+p^1995=3Dp^1994(p+1) > > Como p^1994 jah eh um quadrado perfeito (de p^997), a condicao pedida > eh equivalente a p+1 ser quadrado perfeito. Mas entao: > > p+1=3Dk^2 (com k inteiro) > p=3Dk^2-1=3D(k+1)(k-1) > > Mas se p eh primo, como eh que vai ser o produto de dois inteiros? O > unico jeito eh se um deles for 1 e o outro for p; como nao pode ser > k+1=3D1 (pois entao p=3D0, o que nao serve), tem de ser > > k-1=3D1, entao k=3D2, entao p=3D3. > > Assim, ha apenas um numero primo satisfazendo a dita condicao, que eh > p=3D3. De fato: > > 3^1994+3^1995=3D3^1994.4=3D(3^997.2)^2. > > Abraco, > Ralph > > On Sun, Mar 9, 2008 at 7:01 PM, Pedro J=FAnior > wrote: > > Determine a quantidade de n=FAmeros primos p, para que a express=E3o p^= 1994 > + > > p^1995 seja um quadrado perfeito. > > Desde j=E1 muito agradecido. > > Pedro Jr > > > > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > Instru=E7=F5es para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > ------=_Part_25360_7933817.1205186307704 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline
Muito obrigado caros colegas...
Boa semana para todos.
 


2008/3/9, Ralph Teixeira <ralphct@gmail.com>:
p^1994+p^1995=3Dp^1994(p+1)
<= br>Como p^1994 jah eh um quadrado perfeito (de p^997), a condicao pedida eh equivalente a p+1 ser quadrado perfeito. Mas entao:

p+1=3Dk^2 (co= m k inteiro)
p=3Dk^2-1=3D(k+1)(k-1)

Mas se p eh primo, como eh qu= e vai ser o produto de dois inteiros? O
unico jeito eh se um deles for 1= e o outro for p; como nao pode ser
k+1=3D1 (pois entao p=3D0, o que nao serve), tem de ser

k-1=3D1, ent= ao k=3D2, entao p=3D3.

Assim, ha apenas um numero primo satisfazendo= a dita condicao, que eh
p=3D3. De fato:

3^1994+3^1995=3D3^1994.4= =3D(3^997.2)^2.

Abraco,
   Ralph

On Sun, Mar 9, 2008 at 7:01 PM, Pe= dro J=FAnior
<pedromat= ematico06@gmail.com> wrote:
> Determine a quantidade de n=FAme= ros primos p, para que a express=E3o p^1994 +
> p^1995 seja um quadrado perfeito.
> Desde j=E1 muito agradecido.=
> Pedro Jr
>

=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D
Instru=E7=F5es para entrar na lista, sair da= lista e usar a lista em
http://www.mat.= puc-rio.br/~obmlistas/obm-l.html
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D

------=_Part_25360_7933817.1205186307704-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Mon Mar 10 20:11:12 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2AM3VsG004726 for ; Mon, 10 Mar 2008 19:03:35 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2AM3UXt004711 for obm-l-MllGbsmmN; Mon, 10 Mar 2008 19:03:30 -0300 Received: from web32208.mail.mud.yahoo.com (web32208.mail.mud.yahoo.com [68.142.207.139]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id m2AM2jsG004646 for ; Mon, 10 Mar 2008 19:02:48 -0300 Received: (qmail 41332 invoked by uid 60001); 10 Mar 2008 22:03:08 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:Date:From:Subject:To:In-Reply-To:MIME-Version:Content-Type:Content-Transfer-Encoding:Message-ID; b=GFrrA61nlTNPOYfIpbmiTEL2tpOGFVq1slcwz5sqFMeCAxaYQg6FRS7UpNXEXWqxxR0+nCfcWaGid86TjISpfHfWnT4hVPumxpf459Zdk2NtEddb4DNTMzsITBaihzzn2GV8YOhZhg/KqDNR0qfB22G6qzAXrKpPuFs+uR3goCE=; X-YMail-OSG: Rjfc6SUVM1lyDvsxe2hwE6pyyvcBEzTgw8Tp.4bwRM8UyP2Sqt5UOc4ARUAYhPmQ8Hh1AQcl2KDzoYq9j0FqJ3a8kA-- Received: from [189.25.190.107] by web32208.mail.mud.yahoo.com via HTTP; Mon, 10 Mar 2008 20:03:07 ARST Date: Mon, 10 Mar 2008 20:03:07 -0200 (ARST) From: Claudio Gustavo Subject: [SPAM] =?iso-8859-1?q?Re:=20[obm-l]=20soma=20de=20s=E9rie?= To: obm-l@mat.puc-rio.br In-Reply-To: MIME-Version: 1.0 Content-Type: text/plain Content-Transfer-Encoding: 7bit Message-ID: <90300.34643.qm@web32208.mail.mud.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Claudio Gustavo X-Spam-Status: Yes, hits=7.3 required=5.0 tests=AWL,FORGED_YAHOO_RCVD,IN_REP_TO,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01,SPAM_REDIRECTOR, SUPERLONG_LINE,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******* X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="0-2090263396-1205186587=:34643" X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (7.30 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: SUPERLONG_LINE (0.0 points) BODY: Contains a line >=199 characters long SPAM: SPAM_REDIRECTOR (0.4 points) URI: Uses open redirection service SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 139.207.142.68.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 139.207.142.68.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (0.5 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- --0-2090263396-1205186587=:34643 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 8bit Essa é, na verdade, a série harmônica, que diverge. Vc pode demonstrar usando integrais ou usando a desigualdade "1+1/2+...+1/(2^n-1)>n/2". Vc encontra essas demonstrações no livro de Análise do Elon. Abraço. MauZ escreveu: mostrar que 1+1/2+1/3+...+1/n não é inteiro pra qquer N>1. Obrigado! --------------------------------- Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-2090263396-1205186587=:34643 Content-Type: text/html; charset=iso-8859-1 Content-Transfer-Encoding: 8bit
  Essa é, na verdade, a série harmônica, que diverge. Vc pode demonstrar usando integrais ou usando a desigualdade "1+1/2+...+1/(2^n-1)>n/2". Vc encontra essas demonstrações no livro de Análise do Elon.
 
  Abraço.

MauZ <mauz.matematica@gmail.com> escreveu:
mostrar que 1+1/2+1/3+...+1/n não é inteiro pra qquer N>1.

Obrigado!

Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-2090263396-1205186587=:34643-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Mon Mar 10 20:37:57 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2ANaqsG011852 for ; Mon, 10 Mar 2008 20:36:52 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2ANapme011850 for obm-l-MllGbsmmN; Mon, 10 Mar 2008 20:36:51 -0300 Received: from wr-out-0506.google.com (wr-out-0506.google.com [64.233.184.225]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2ANaZsH011832 for ; Mon, 10 Mar 2008 20:36:50 -0300 Received: by wr-out-0506.google.com with SMTP id c30so1090111wra.21 for ; Mon, 10 Mar 2008 16:37:22 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=5L0N2qm3lVn/sZ131j88S/B7VOTOyH4R/JLld98+u5U=; b=OOIyL6DkmNSqVGjboLytTu7vMR4FJitWOqr1FUqgg+AWXEH8N1qRJk0ZLT5jL7N1/QgwsDfXLsPDJ9yq8Nxi5Qt4OojNUaGE1cAi2DEhOTpfTjemfK9y1opUeTuXYmSkIouv5KNacgygtYA7B8wm0eNRl8F4Y7mLHwA/BxG6jGg= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=VmS4kfoBOiXIY5a4r7nD/xwPfQqn3YbOvww1r0cZgS+C//ZAr0LCc0fCXWom3IjxePRxQGz6ZX1y27KdK+XLzh0crkpWwAui7d828SXoNI2b6y8KfFgKXckPN47Kq6hXydJ9wi/EYAnklL41+5RgGVrotRkoJ6vOWvCzzpPLgBc= Received: by 10.114.148.1 with SMTP id v1mr3974235wad.21.1205192241793; Mon, 10 Mar 2008 16:37:21 -0700 (PDT) Received: by 10.114.88.8 with HTTP; Mon, 10 Mar 2008 16:37:21 -0700 (PDT) Message-ID: Date: Mon, 10 Mar 2008 20:37:21 -0300 From: MauZ To: obm-l@mat.puc-rio.br Subject: [SPAM] =?ISO-8859-1?Q?Re:_[obm-l]_soma_de_s=E9rie?= In-Reply-To: <90300.34643.qm@web32208.mail.mud.yahoo.com> MIME-Version: 1.0 Content-Type: text/plain References: <90300.34643.qm@web32208.mail.mud.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: MauZ X-Spam-Status: Yes, hits=5.6 required=5.0 tests=AWL,IN_REP_TO,JAVASCRIPT_UNSAFE,MAILTO_LINK, QUOTED_EMAIL_TEXT,RCVD_IN_MULTIHOP_DSBL,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, SPAM_REDIRECTOR,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ***** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_Part_8416_20770195.1205192241780" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (5.60 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: REFERENCES (-0.5 points) Has a valid-looking References header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: QUOTED_EMAIL_TEXT (-0.8 points) BODY: Contains what looks like a quoted email text SPAM: JAVASCRIPT_UNSAFE (0.3 points) BODY: Easily-executed JavaScript code SPAM: MAILTO_LINK (0.2 points) BODY: Includes a URL link to send an email SPAM: SPAM_REDIRECTOR (0.4 points) URI: Uses open redirection service SPAM: RCVD_IN_MULTIHOP_DSBL (0.8 points) RBL: Received via a relay in multihop.dsbl.org SPAM: [RBL check: found 225.184.233.64.multihop.dsbl.org] SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 225.184.233.64.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 225.184.233.64.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (0.2 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- ------=_Part_8416_20770195.1205192241780 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline eu acabei de ver que =E9 a serie harmonica... mas como fa=E7o pra demonstrar que nunca =E9 inteiro? pq vai pro infinito, beleza... mas pode passar por algum inteiro, oque tem q provar q nunca acontece... se eu usar uma desigualdade como voc=EA msotrou e como achei outras aqui em livros eu saio um pouco do foco que =E9 provar q n=E3o =E9 inteiro... ou to= u errado? se eu tiver falando besteira por favor me corrija! Obrigado Claudio, []s Maurizio Em 10/03/08, Claudio Gustavo escreveu: > > Essa =E9, na verdade, a s=E9rie harm=F4nica, que diverge. Vc pode demon= strar > usando integrais ou usando a desigualdade "1+1/2+...+1/(2^n-1)>n/2". Vc > encontra essas demonstra=E7=F5es no livro de An=E1lise do Elon. > > Abra=E7o. > > *MauZ * escreveu: > > mostrar que 1+1/2+1/3+...+1/n n=E3o =E9 inteiro pra qquer N>1. > > Obrigado! > > > ------------------------------ > Abra sua conta no Yahoo! Mail, > o =FAnico sem limite de espa=E7o para armazenamento! > > ------=_Part_8416_20770195.1205192241780 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline eu acabei de ver que =E9 a serie harmonica...
mas como fa=E7o pra demons= trar que nunca =E9 inteiro?
pq vai pro infinito, beleza...
 mas = pode passar por algum inteiro, oque tem q provar q nunca acontece...
se eu usar uma desigualdade como voc=EA msotrou e como achei outras aqui e= m livros eu saio um pouco do foco que =E9 provar q n=E3o =E9 inteiro... ou = tou errado?

se eu tiver falando besteira por favor me corrija!

Obrigado Clau= dio,
[]s
Maurizio

Em 10/03/08= , Claudio Gustavo <claudioggll@yahoo.com.br> escreveu:<= blockquote class=3D"gmail_quote" style=3D"border-left: 1px solid rgb(204, 2= 04, 204); margin: 0pt 0pt 0pt 0.8ex; padding-left: 1ex;">
  Essa =E9, na verdade, a s=E9rie harm=F4nica, que diverge. Vc po= de demonstrar usando integrais ou usando a desigualdade "1+1/2+...+1/(= 2^n-1)>n/2". Vc encontra essas demonstra=E7=F5es no livro de An=E1l= ise do Elon.
 
  Abra=E7o.

MauZ <mauz.matematica@gmail.com> escreveu:
mostrar que 1+1/2+1/3+...+1/n n=E3o =E9 inteiro pra qquer N>1.
Obrigado!

=20

Abra sua conta no Yahoo! Mail, o =FAnic= o sem limite de espa=E7o para armazenamento!=20


------=_Part_8416_20770195.1205192241780-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Tue Mar 11 10:52:38 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2BDnSsG027657 for ; Tue, 11 Mar 2008 10:49:28 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2BDnSeX027655 for obm-l-MllGbsmmN; Tue, 11 Mar 2008 10:49:28 -0300 Received: from gv-out-0910.google.com (gv-out-0910.google.com [216.239.58.187]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2BDnPsG027651 for ; Tue, 11 Mar 2008 10:49:25 -0300 Received: by gv-out-0910.google.com with SMTP id u5so603991gve.25 for ; Tue, 11 Mar 2008 06:49:52 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:mime-version:content-type; bh=6V12O72WdpRLs/AUkSmPxEJeceHwT86iemDWu5ppVak=; b=IRyYA55RY96DwNeZ8IOU+cGe4n4zpWeTwqmg4b9Z8R9IRhOQS3ySx1BI01eaYWMeTSi9SgTVTyF78+hMtsKJzi16fHiY9lWdBJyzdoJ2HwPTH1r/ypnu1eIHmH6ydFqWZyCO7g+98AxaXPs1F8ueYJnMjJmKPsS8vxSxwQnYlJc= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:mime-version:content-type; b=KASuyaFO2cLpDs/meT7vxTd0VQBLk6wDfj/nb58eQU/+dAB4kDPgrJevNP4H0Fcz/grMcgl5+ZE9Sf92TBJgMN60M056gINdgKukVmSs7VNb6ZTdusv508kT0sLxECQnUEQ7/dsQy48IrsiVaS3ZbTpTGPSWH14SicrlLjqu2Sc= Received: by 10.150.138.8 with SMTP id l8mr3666181ybd.72.1205243390763; Tue, 11 Mar 2008 06:49:50 -0700 (PDT) Received: by 10.150.227.10 with HTTP; Tue, 11 Mar 2008 06:49:49 -0700 (PDT) Message-ID: Date: Tue, 11 Mar 2008 10:49:49 -0300 From: "Ney Falcao" To: obm-l@mat.puc-rio.br Subject: [SPAM] [obm-l] Comerciante desonesto MIME-Version: 1.0 Content-Type: text/plain Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Ney Falcao" X-Spam-Status: Yes, hits=6.4 required=5.0 tests=AWL,HTML_70_90,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, SPAM_PHRASE_00_01,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ****** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_Part_1000_2876572.1205243390751" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (6.40 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: HTML_70_90 (0.9 points) BODY: Message is 70-90% HTML tags SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 187.58.239.216.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 187.58.239.216.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-0.3 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- ------=_Part_1000_2876572.1205243390751 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Ol=E1 amigos, gostaria de uma ajuda com a quest=E3o abaixo. agrade=E7o a colabora=E7=E3o Ney Falc=E3o Um comerciante desonesto decidiu diminuir em 5% o peso de uma mercadoria, mantendo inalterados tanto o pre=E7o quanto a indica=E7=E3o do = peso exibido na embalagem. Com a adultera=E7=E3o, o lucro percentual obtido por unidade de peso vendida foi de: a. (XXX) 5%, exatamente b. (XXX) 4%, exatamente c. (XXX) 4,17%, aproximadamente d. (X X) 5,26%, aproximadamente e. (XXX) 6%, exatamente ------=_Part_1000_2876572.1205243390751 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline
Ol=E1 amigos,
 
gostaria de uma ajuda com a quest=E3o abaixo.
 
agrade=E7o a colabora=E7=E3o
 
Ney Falc=E3o
 

  = ;      Um comerciante desonesto decidiu diminuir em 5% o peso de = uma mercadoria, mantendo inalterados tanto o pre=E7o quanto a indica=E7=E3o= do peso exibido na embalagem. Com a adultera=E7=E3o, o lucro percentual ob= tido por unidade de peso vendida foi de:

 

<= span style=3D"FONT-SIZE: 11pt">a.     &n= bsp;             

(= XXX)

5%, exatamente

 

 

 

 

 

 

 

<= span style=3D"FONT-SIZE: 11pt">b.     &n= bsp;             

(= XXX)

4%, exatamente

<= span style=3D"FONT-SIZE: 11pt">c.     &n= bsp;             

(= XXX)

4,17%, aproximadamente

<= span style=3D"FONT-SIZE: 11pt">d.     &n= bsp;             

(= X X)

5,26%, aproximadamente

<= span style=3D"FONT-SIZE: 11pt">e.     &n= bsp;             

(= XXX)

6%, exatamente

 

 
------=_Part_1000_2876572.1205243390751-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Tue Mar 11 10:52:38 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2BDpQsG027700 for ; Tue, 11 Mar 2008 10:51:26 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2BDpQ1F027698 for obm-l-MllGbsmmN; Tue, 11 Mar 2008 10:51:26 -0300 Received: from doodle.dr.ufu.br (doodle.dr.ufu.br [200.19.146.202]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2BDpOsG027694 for ; Tue, 11 Mar 2008 10:51:24 -0300 Received: (qmail 15756 invoked from network); 11 Mar 2008 13:21:45 -0000 Received: from unknown (HELO 1F102SALOMAO) (salomao@ufu.br@[10.6.0.188]) (envelope-sender ) by doodle.dr.ufu.br (qmail-ldap-1.03) with SMTP for ; 11 Mar 2008 13:21:45 -0000 Message-ID: <001501c8837a$db084460$bc00060a@1F102SALOMAO> From: =?iso-8859-1?Q?Luiz_Alberto_Duran_Salom=E3o?= To: References: Subject: [SPAM] [obm-l] =?iso-8859-1?Q?Re:_=5Bobm-l=5D_soma_de_s=E9rie?= Date: Tue, 11 Mar 2008 10:21:45 -0300 MIME-Version: 1.0 Content-Type: text/plain X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2900.3138 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.3198 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: =?iso-8859-1?Q?Luiz_Alberto_Duran_Salom=E3o?= X-Spam-Status: Yes, hits=5.0 required=5.0 tests=AWL,MAILTO_LINK,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, REFERENCES,SPAM_PHRASE_00_01,USER_AGENT_OE,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ***** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_NextPart_000_0012_01C88361.B54AE570" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (5.00 hits, 5 required) SPAM: REFERENCES (-0.5 points) Has a valid-looking References header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: USER_AGENT_OE (0.2 points) X-Mailer header indicates a non-spam MUA (Outlook Express) SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: MAILTO_LINK (0.2 points) BODY: Includes a URL link to send an email SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 202.146.19.200.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 202.146.19.200.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-0.7 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- This is a multi-part message in MIME format. ------=_NextPart_000_0012_01C88361.B54AE570 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Caros amigos, Seja n um inteiro, com n>1. O que se quer provar =E9 que 1+1/2+1/3+ . . . +1/n n=E3o =E9 inteiro. Seja 2^a a maior pot=EAncia de 2 tal que 2^a =E9 menor do que ou igual a = n. Assim, 1/2^a aparece no somat=F3rio acima mas 1/2^(a+1) n=E3o = aparece. Observe que o m=EDnimo m=FAltiplo comum dos denominadores dos=20 termos do somat=F3rio tem a pot=EAncia 2^a como fator. Agora, no=20 numerador de cada fra=E7=E3o, j=E1 com denominador igual ao m=EDnimo m=FAltiplo comum, temos sempre um n=FAmero par, com exce=E7=E3o do=20 termo correspondente a 1/2^a. Logo, a soma dos numeradores=20 =E9 =EDmpar o que nos leva a concluir que o somat=F3rio n=E3o =E9 um=20 n=FAmero inteiro. Abra=E7os, Luiz Alberto ----- Original Message -----=20 From: MauZ=20 To: obm-l@mat.puc-rio.br=20 Sent: Monday, March 10, 2008 6:13 PM Subject: [obm-l] soma de s=E9rie mostrar que 1+1/2+1/3+...+1/n n=E3o =E9 inteiro pra qquer N>1. Obrigado! -------------------------------------------------------------------------= ----- No virus found in this incoming message. Checked by AVG.=20 Version: 7.5.518 / Virus Database: 269.21.7/1324 - Release Date: = 10/3/2008 19:27 ------=_NextPart_000_0012_01C88361.B54AE570 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable
Caros amigos,
Seja n um inteiro, com n>1. O que se = quer provar=20 =E9 que
1+1/2+1/3+ . . . +1/n   n=E3o = =E9=20 inteiro.
Seja 2^a a maior pot=EAncia de 2 tal = que 2^a =E9 menor=20 do que ou igual a n.
Assim, 1/2^a   aparece no = somat=F3rio acima=20 mas 1/2^(a+1)  n=E3o aparece.
Observe que o m=EDnimo m=FAltiplo comum = dos=20 denominadores dos
termos do somat=F3rio tem a pot=EAncia = 2^a como fator.=20 Agora, no
numerador de cada  fra=E7=E3o, = j=E1 com denominador=20 igual ao m=EDnimo
m=FAltiplo comum, temos sempre um = n=FAmero par, com=20 exce=E7=E3o do
termo correspondente a 1/2^a. Logo, a = soma dos=20 numeradores
=E9 =EDmpar o que nos leva a concluir = que o somat=F3rio=20 n=E3o =E9  um
n=FAmero inteiro.
Abra=E7os,
Luiz Alberto
----- Original Message -----
From:=20 MauZ
Sent: Monday, March 10, 2008 = 6:13=20 PM
Subject: [obm-l] soma de = s=E9rie

mostrar que 1+1/2+1/3+...+1/n n=E3o =E9 inteiro pra = qquer=20 N>1.

Obrigado!

No virus found in this incoming message.
Checked by AVG.=20
Version: 7.5.518 / Virus Database: 269.21.7/1324 - Release Date: = 10/3/2008=20 19:27
------=_NextPart_000_0012_01C88361.B54AE570-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Tue Mar 11 11:35:14 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2BEXpsG030339 for ; Tue, 11 Mar 2008 11:33:51 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2BEXpie030337 for obm-l-MllGbsmmN; Tue, 11 Mar 2008 11:33:51 -0300 Received: from web32202.mail.mud.yahoo.com (web32202.mail.mud.yahoo.com [68.142.207.133]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id m2BEXlsG030330 for ; Tue, 11 Mar 2008 11:33:49 -0300 Received: (qmail 86037 invoked by uid 60001); 11 Mar 2008 14:34:13 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:Date:From:Subject:To:In-Reply-To:MIME-Version:Content-Type:Content-Transfer-Encoding:Message-ID; b=VvhWxzB+UVvHfq+uJPnV8Xt4xeDtfNaheLZt7gC0AmsufM8ygI4MYs3iPIMkm5WrCl6LHulSMFe2wSDt587WV1JHWXWZ+C/bPfj36ClSAc2L50jTd1saSFWuu3b70Zo7Qw8S/X0tGd1ch8C9LRipqINsQ1+xVPfSKn9D8Kn4QFQ=; X-YMail-OSG: SlvJdwAVM1kAiUk51b56yp81cjihOx3TOema8f_Yja_xVjJIA_o9s7acdxENNUzQ6w-- Received: from [189.25.189.18] by web32202.mail.mud.yahoo.com via HTTP; Tue, 11 Mar 2008 12:34:12 ARST Date: Tue, 11 Mar 2008 12:34:12 -0200 (ARST) From: Claudio Gustavo Subject: [SPAM] =?iso-8859-1?q?Re:=20[obm-l]=20soma=20de=20s=E9rie?= To: obm-l@mat.puc-rio.br In-Reply-To: MIME-Version: 1.0 Content-Type: text/plain Content-Transfer-Encoding: 7bit Message-ID: <926569.85338.qm@web32202.mail.mud.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Claudio Gustavo X-Spam-Status: Yes, hits=8.2 required=5.0 tests=AWL,FORGED_YAHOO_RCVD,IN_REP_TO,JAVASCRIPT_UNSAFE, MAILTO_LINK,MIME_BOUND_DIGITS_5,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01,SPAM_REDIRECTOR, SUPERLONG_LINE,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="0-247801001-1205246052=:85338" X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (8.20 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: MIME_BOUND_DIGITS_5 (1.7 points) Spam tool pattern in MIME boundary SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: JAVASCRIPT_UNSAFE (0.3 points) BODY: Easily-executed JavaScript code SPAM: MAILTO_LINK (0.2 points) BODY: Includes a URL link to send an email SPAM: SUPERLONG_LINE (0.0 points) BODY: Contains a line >=199 characters long SPAM: SPAM_REDIRECTOR (0.4 points) URI: Uses open redirection service SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 133.207.142.68.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 133.207.142.68.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-0.8 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- --0-247801001-1205246052=:85338 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 8bit Entendi sua pergunta. Cara, no meu ponto de vista, qdo demonstramos que diverge, ou seja, tende ao infinito, automaticamente demonstramos q não pode ser inteiro. Tender ao infinito é uma forma de indeterminação. Não sei se existe uma outra interpretação/demonstração... Abraço. MauZ escreveu: eu acabei de ver que é a serie harmonica... mas como faço pra demonstrar que nunca é inteiro? pq vai pro infinito, beleza... mas pode passar por algum inteiro, oque tem q provar q nunca acontece... se eu usar uma desigualdade como você msotrou e como achei outras aqui em livros eu saio um pouco do foco que é provar q não é inteiro... ou tou errado? se eu tiver falando besteira por favor me corrija! Obrigado Claudio, []s Maurizio Em 10/03/08, Claudio Gustavo escreveu: Essa é, na verdade, a série harmônica, que diverge. Vc pode demonstrar usando integrais ou usando a desigualdade "1+1/2+...+1/(2^n-1)>n/2". Vc encontra essas demonstrações no livro de Análise do Elon. Abraço. MauZ escreveu: mostrar que 1+1/2+1/3+...+1/n não é inteiro pra qquer N>1. Obrigado! --------------------------------- Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --------------------------------- Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-247801001-1205246052=:85338 Content-Type: text/html; charset=iso-8859-1 Content-Transfer-Encoding: 8bit
  Entendi sua pergunta. Cara, no meu ponto de vista, qdo demonstramos que diverge, ou seja, tende ao infinito, automaticamente demonstramos q não pode ser inteiro. Tender ao infinito é uma forma de indeterminação.
  Não sei se existe uma outra interpretação/demonstração...
 
  Abraço.

MauZ <mauz.matematica@gmail.com> escreveu:
eu acabei de ver que é a serie harmonica...
mas como faço pra demonstrar que nunca é inteiro?
pq vai pro infinito, beleza...
 mas pode passar por algum inteiro, oque tem q provar q nunca acontece...

se eu usar uma desigualdade como você msotrou e como achei outras aqui em livros eu saio um pouco do foco que é provar q não é inteiro... ou tou errado?

se eu tiver falando besteira por favor me corrija!

Obrigado Claudio,
[]s
Maurizio

Em 10/03/08, Claudio Gustavo <claudioggll@yahoo.com.br> escreveu:
  Essa é, na verdade, a série harmônica, que diverge. Vc pode demonstrar usando integrais ou usando a desigualdade "1+1/2+...+1/(2^n-1)>n/2". Vc encontra essas demonstrações no livro de Análise do Elon.
 
  Abraço.

MauZ <mauz.matematica@gmail.com> escreveu:
mostrar que 1+1/2+1/3+...+1/n não é inteiro pra qquer N>1.

Obrigado!

Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento!


Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-247801001-1205246052=:85338-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Tue Mar 11 11:44:28 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2BEhCsG030902 for ; Tue, 11 Mar 2008 11:43:12 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2BEhCwm030900 for obm-l-MllGbsmmN; Tue, 11 Mar 2008 11:43:12 -0300 Received: from zeus.hotlink.com.br (zeus.hotlink.com.br [189.1.1.250]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2BEh9sG030894 for ; Tue, 11 Mar 2008 11:43:09 -0300 Received: by zeus.hotlink.com.br (Postfix, from userid 1002) id A0996488AAF; Tue, 11 Mar 2008 11:46:00 -0300 (BRT) Received: from windows5095252 (veloz-1-2-22.hotlink.com.br [189.1.2.22]) by zeus.hotlink.com.br (Postfix) with SMTP id CFB04488A37 for ; Tue, 11 Mar 2008 11:45:59 -0300 (BRT) Message-ID: <001001c88386$4badb230$5700a8c0@windows5095252> From: "Gustavo Duarte" To: References: Subject: [SPAM] Re: [obm-l] Comerciante desonesto Date: Tue, 11 Mar 2008 11:43:39 -0300 MIME-Version: 1.0 Content-Type: text/plain X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2900.3138 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.3198 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Gustavo Duarte" X-Spam-Status: Yes, hits=6.2 required=5.0 tests=AWL,HTML_70_90,MAILTO_LINK,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, SUPERLONG_LINE,USER_AGENT_OE,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ****** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_NextPart_000_000D_01C8836D.26418080" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (6.20 hits, 5 required) SPAM: REFERENCES (-0.5 points) Has a valid-looking References header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: USER_AGENT_OE (0.2 points) X-Mailer header indicates a non-spam MUA (Outlook Express) SPAM: HTML_70_90 (0.9 points) BODY: Message is 70-90% HTML tags SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: MAILTO_LINK (0.2 points) BODY: Includes a URL link to send an email SPAM: SUPERLONG_LINE (0.0 points) BODY: Contains a line >=199 characters long SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 250.1.1.189.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 250.1.1.189.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-0.4 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- This is a multi-part message in MIME format. ------=_NextPart_000_000D_01C8836D.26418080 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Vamos l=E1 NEY, uma id=E9ia seria : admita que combrasse R$ 100,00 por = 100g, e agora pelos mesmos R$ 100,00 n=E3o fosse mas 100g e sim 95g ( = ou seja 5% a menos no peso ) , no in=EDcio o pre=E7o unit=E1rio do grama = era R$100/100g =3D R$ 1,00 e depois passou a ser calculado deste modo = R$100/ 95g =3D 1,0526, ou seja um aumento de 5,26%.( LETRA D ) Um = abra=E7o e espero ter ajudado!! se tiver algum erro desculpem. ----- Original Message -----=20 From: Ney Falcao=20 To: obm-l@mat.puc-rio.br=20 Sent: Tuesday, March 11, 2008 10:49 AM Subject: [obm-l] Comerciante desonesto Ol=E1 amigos,=20 gostaria de uma ajuda com a quest=E3o abaixo. agrade=E7o a colabora=E7=E3o Ney Falc=E3o Um comerciante desonesto decidiu diminuir em 5% o peso = de uma mercadoria, mantendo inalterados tanto o pre=E7o quanto a = indica=E7=E3o do peso exibido na embalagem. Com a adultera=E7=E3o, o = lucro percentual obtido por unidade de peso vendida foi de: =20 a. =20 (XXX) 5%, exatamente =20 =20 b. =20 (XXX) 4%, exatamente =20 c. =20 (XXX) 4,17%, aproximadamente =20 d. =20 (X X) 5,26%, aproximadamente =20 e. =20 (XXX) 6%, exatamente =20 =20 =20 ------=_NextPart_000_000D_01C8836D.26418080 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable
Vamos l=E1 NEY, uma id=E9ia seria : = admita que=20 combrasse R$ 100,00 por 100g, e agora  pelos mesmos R$ 100,00 n=E3o = fosse mas=20 100g e sim 95g ( ou seja 5% a menos no peso ) , no in=EDcio o pre=E7o = unit=E1rio do=20 grama era R$100/100g =3D R$ 1,00 e depois passou a ser = calculado deste=20 modo R$100/ 95g =3D 1,0526, ou seja um aumento de 5,26%.( LETRA = D=20 ) Um abra=E7o e espero ter ajudado!! se tiver algum erro=20 desculpem.
----- Original Message -----
From:=20 Ney = Falcao=20
Sent: Tuesday, March 11, 2008 = 10:49=20 AM
Subject: [obm-l] Comerciante=20 desonesto

Ol=E1 amigos,
 
gostaria de uma ajuda com a quest=E3o abaixo.
 
agrade=E7o a colabora=E7=E3o
 
Ney Falc=E3o
 

   =20     Um comerciante desonesto decidiu = diminuir em 5%=20 o peso de uma mercadoria, mantendo inalterados tanto o pre=E7o = quanto a=20 indica=E7=E3o do peso exibido na embalagem. Com a = adultera=E7=E3o, o lucro=20 percentual obtido por unidade de peso vendida foi=20 de:

 

a.           = ;      =20  

(XXX)

5%,=20 exatamente

 

 

 

 

 

 

 

b.           = ;      =20  

(XXX)

4%,=20 exatamente

c.           = ;      =20  

(XXX)

4,17%,=20 aproximadamente

d.           = ;      =20  

(X X)

5,26%,=20 aproximadamente

e.           = ;      =20  

(XXX)

6%,=20 exatamente

 

 

------=_NextPart_000_000D_01C8836D.26418080-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Tue Mar 11 12:38:41 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2BFaRsG002397 for ; Tue, 11 Mar 2008 12:36:27 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2BFaRp3002395 for obm-l-MllGbsmmN; Tue, 11 Mar 2008 12:36:27 -0300 Received: from rn-out-0910.google.com (rn-out-0910.google.com [64.233.170.185]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2BFaOsG002390 for ; Tue, 11 Mar 2008 12:36:25 -0300 Received: by rn-out-0910.google.com with SMTP id e11so1653845rng.7 for ; Tue, 11 Mar 2008 08:36:52 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=EVzqpsDbBh3a6ifN3bZ2LuGzwjL02mPq4OcKW4RGjIw=; b=RGbk89m8PqqtcaZFl9WFNmD0LMGqIxAe40K+I6eMAp8Podq8m/R4SSfVAyW+Vw6GkvO6ZVjblyaTkeIi0EUcn8ir21mi5kTLL5FLkXuU0p4c17QChXvDgNyfDevKDla+tx87UD8v4xf7v4gjmzaIaMaZOZ8ZlKU4rCvMPCZsUY8= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=RxsD3aLwL8dPwdI/zImkDfFzfdMVopZBQrwrTP7eRUnygEYupNZK1fTekoKiKrX0LT18a7+gLN1agFqdoHuXD9LK90DOkIZoGVwu7ksh/lx9IVZ5hF3YP/qvsKOooz1neb+4OW+zHCEBJQiXMRTucMLD2zWcVil9PJzWb+vPofg= Received: by 10.114.183.1 with SMTP id g1mr5064750waf.3.1205249811187; Tue, 11 Mar 2008 08:36:51 -0700 (PDT) Received: by 10.114.88.8 with HTTP; Tue, 11 Mar 2008 08:36:48 -0700 (PDT) Message-ID: Date: Tue, 11 Mar 2008 12:36:48 -0300 From: MauZ To: obm-l@mat.puc-rio.br Subject: [SPAM] =?ISO-8859-1?Q?Re:_[obm-l]_soma_de_s=E9rie?= In-Reply-To: <926569.85338.qm@web32202.mail.mud.yahoo.com> MIME-Version: 1.0 Content-Type: text/plain References: <926569.85338.qm@web32202.mail.mud.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: MauZ X-Spam-Status: Yes, hits=5.0 required=5.0 tests=AWL,IN_REP_TO,JAVASCRIPT_UNSAFE,MAILTO_LINK, QUOTED_EMAIL_TEXT,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, REFERENCES,SPAM_PHRASE_01_02,SPAM_REDIRECTOR, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ***** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_Part_6826_7977384.1205249811175" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (5.00 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: REFERENCES (-0.5 points) Has a valid-looking References header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_01_02 (0.5 points) BODY: Spam phrases score is 01 to 02 (low) SPAM: [score: 1] SPAM: QUOTED_EMAIL_TEXT (-0.8 points) BODY: Contains what looks like a quoted email text SPAM: JAVASCRIPT_UNSAFE (0.3 points) BODY: Easily-executed JavaScript code SPAM: MAILTO_LINK (0.2 points) BODY: Includes a URL link to send an email SPAM: SPAM_REDIRECTOR (0.4 points) URI: Uses open redirection service SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 185.170.233.64.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 185.170.233.64.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (0.7 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- ------=_Part_6826_7977384.1205249811175 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Claudio, acontece que 1+1+1+1 tamb=E9m tende ao infinito e s=E3o todos numeros inteiros... Agora a demonstra=E7=E3o do Luiz eu achei genial! Parab=E9ns e mto obrigado= ! Maurizio Em 11/03/08, Claudio Gustavo escreveu: > > Entendi sua pergunta. Cara, no meu ponto de vista, qdo demonstramos que > diverge, ou seja, tende ao infinito, automaticamente demonstramos q n=E3o= pode > ser inteiro. Tender ao infinito =E9 uma forma de indetermina=E7=E3o. > N=E3o sei se existe uma outra interpreta=E7=E3o/demonstra=E7=E3o... > > Abra=E7o. > > *MauZ * escreveu: > > eu acabei de ver que =E9 a serie harmonica... > mas como fa=E7o pra demonstrar que nunca =E9 inteiro? > pq vai pro infinito, beleza... > mas pode passar por algum inteiro, oque tem q provar q nunca acontece... > > se eu usar uma desigualdade como voc=EA msotrou e como achei outras aqui = em > livros eu saio um pouco do foco que =E9 provar q n=E3o =E9 inteiro... ou = tou > errado? > > se eu tiver falando besteira por favor me corrija! > > Obrigado Claudio, > []s > Maurizio > > Em 10/03/08, Claudio Gustavo escreveu: > > > > Essa =E9, na verdade, a s=E9rie harm=F4nica, que diverge. Vc pode dem= onstrar > > usando integrais ou usando a desigualdade "1+1/2+...+1/(2^n-1)>n/2". Vc > > encontra essas demonstra=E7=F5es no livro de An=E1lise do Elon. > > > > Abra=E7o. > > > > *MauZ * escreveu: > > > > mostrar que 1+1/2+1/3+...+1/n n=E3o =E9 inteiro pra qquer N>1. > > > > Obrigado! > > > > > > ------------------------------ > > Abra sua conta no Yahoo! Mail, > > o =FAnico sem limite de espa=E7o para armazenamento! > > > > > ------------------------------ > Abra sua conta no Yahoo! Mail, > o =FAnico sem limite de espa=E7o para armazenamento! > > ------=_Part_6826_7977384.1205249811175 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Claudio,

acontece que 1+1+1+1 tamb=E9m tende ao infinito e s=E3o tod= os numeros inteiros...
Agora a demonstra=E7=E3o do Luiz eu achei genial!= Parab=E9ns e mto obrigado!

Maurizio

Em 11/03/08, Claudio Gustavo <= ;claudioggll@yahoo.com.br&g= t; escreveu:
&nb= sp;
  Abra=E7o.

MauZ <mauz.matematica@gmail.com> escreveu= :
eu acabei de ver que =E9 a serie harmonica...mas como fa=E7o pra demonstrar que nunca =E9 inteiro?
pq vai pro infini= to, beleza...
 mas pode passar por algum inteiro, oque tem q provar q nunca acontece= ...

se eu usar uma desigualdade como voc=EA msotrou e como achei out= ras aqui em livros eu saio um pouco do foco que =E9 provar q n=E3o =E9 inte= iro... ou tou errado?

se eu tiver falando besteira por favor me corrija!

Obrigado Claudio,
[]s
Maurizio

Em 1= 0/03/08, Claudio Gustavo <claudioggll@yahoo.com.br> escreveu:<= /span>
  Essa =E9, na verdade, a s=E9rie harm=F4nica, que diverge. Vc = pode demonstrar usando integrais ou usando a desigualdade "1+1/2+...+1= /(2^n-1)>n/2". Vc encontra essas demonstra=E7=F5es no livro de An= =E1lise do Elon.
 
  Abra=E7o.

MauZ <mauz.matematica@gmail.com> escreveu:
mostrar que 1+1/2+1/3+...+1/n n=E3o= =E9 inteiro pra qquer N>1.

Obrigado!

=
Abra sua conta no Yahoo! Mail, o = =FAnico sem limite de espa=E7o para armazenamento!


=20

Abra sua conta no Yahoo! Mail, o =FAnic= o sem limite de espa=E7o para armazenamento!=20


------=_Part_6826_7977384.1205249811175-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Tue Mar 11 14:29:27 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2BHQjsG009845 for ; Tue, 11 Mar 2008 14:26:45 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2BHQj2K009842 for obm-l-MllGbsmmN; Tue, 11 Mar 2008 14:26:45 -0300 Received: from doodle.dr.ufu.br (doodle.dr.ufu.br [200.19.146.202]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2BHQgsG009825 for ; Tue, 11 Mar 2008 14:26:43 -0300 Received: (qmail 3062 invoked from network); 11 Mar 2008 17:27:11 -0000 Received: from unknown (HELO 1F102SALOMAO) (salomao@ufu.br@[10.6.0.188]) (envelope-sender ) by doodle.dr.ufu.br (qmail-ldap-1.03) with SMTP for ; 11 Mar 2008 17:27:11 -0000 Message-ID: <001d01c8839d$247a2d30$bc00060a@1F102SALOMAO> From: =?iso-8859-1?Q?Luiz_Alberto_Duran_Salom=E3o?= To: Subject: [SPAM] [obm-l] =?iso-8859-1?Q?Fw:_=5Bobm-l=5D_soma_de_s=E9rie?= Date: Tue, 11 Mar 2008 14:27:11 -0300 MIME-Version: 1.0 Content-Type: text/plain X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2900.3138 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.3198 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: =?iso-8859-1?Q?Luiz_Alberto_Duran_Salom=E3o?= X-Spam-Status: Yes, hits=5.6 required=5.0 tests=AWL,MAILTO_LINK,OUTLOOK_FW_MSG,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01,USER_AGENT_OE, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ***** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_NextPart_000_001A_01C88383.FEB5C960" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (5.60 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: OUTLOOK_FW_MSG (-0.1 points) Forwarded email (Outlook style) SPAM: USER_AGENT_OE (0.2 points) X-Mailer header indicates a non-spam MUA (Outlook Express) SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: MAILTO_LINK (0.2 points) BODY: Includes a URL link to send an email SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 202.146.19.200.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 202.146.19.200.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-0.5 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- This is a multi-part message in MIME format. ------=_NextPart_000_001A_01C88383.FEB5C960 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable ----- Original Message -----=20 From: Luiz Alberto Duran Salom=E3o=20 To: obm-l@mat.puc-rio.br=20 Sent: Tuesday, March 11, 2008 10:21 AM Subject: Re: [obm-l] soma de s=E9rie Caros amigos, Seja n um inteiro, com n>1. O que se quer provar =E9 que 1+1/2+1/3+ . . . +1/n n=E3o =E9 inteiro. Seja 2^a a maior pot=EAncia de 2 tal que 2^a =E9 menor do que ou igual a = n. Assim, 1/2^a aparece no somat=F3rio acima mas 1/2^(a+1) n=E3o = aparece. Observe que o m=EDnimo m=FAltiplo comum dos denominadores dos=20 termos do somat=F3rio tem a pot=EAncia 2^a como fator. Agora, no=20 numerador de cada fra=E7=E3o, j=E1 com denominador igual ao m=EDnimo m=FAltiplo comum, temos sempre um n=FAmero par, com exce=E7=E3o do=20 termo correspondente a 1/2^a. Logo, a soma dos numeradores=20 =E9 =EDmpar o que nos leva a concluir que o somat=F3rio n=E3o =E9 um=20 n=FAmero inteiro. Abra=E7os, Luiz Alberto ----- Original Message -----=20 From: MauZ=20 To: obm-l@mat.puc-rio.br=20 Sent: Monday, March 10, 2008 6:13 PM Subject: [obm-l] soma de s=E9rie mostrar que 1+1/2+1/3+...+1/n n=E3o =E9 inteiro pra qquer N>1. Obrigado! -------------------------------------------------------------------------= ----- No virus found in this incoming message. Checked by AVG.=20 Version: 7.5.518 / Virus Database: 269.21.7/1324 - Release Date: = 10/3/2008 19:27 ------=_NextPart_000_001A_01C88383.FEB5C960 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable
 
----- Original Message -----=20
From: Luiz Alberto Duran = Salom=E3o=20
Sent: Tuesday, March 11, 2008 10:21 AM
Subject: Re: [obm-l] soma de s=E9rie

Caros amigos,
Seja n um inteiro, com n>1. O que se = quer provar=20 =E9 que
1+1/2+1/3+ . . . +1/n   n=E3o = =E9=20 inteiro.
Seja 2^a a maior pot=EAncia de 2 tal = que 2^a =E9 menor=20 do que ou igual a n.
Assim, 1/2^a   aparece no = somat=F3rio acima=20 mas 1/2^(a+1)  n=E3o aparece.
Observe que o m=EDnimo m=FAltiplo comum = dos=20 denominadores dos
termos do somat=F3rio tem a pot=EAncia = 2^a como fator.=20 Agora, no
numerador de cada  fra=E7=E3o, = j=E1 com denominador=20 igual ao m=EDnimo
m=FAltiplo comum, temos sempre um = n=FAmero par, com=20 exce=E7=E3o do
termo correspondente a 1/2^a. Logo, a = soma dos=20 numeradores
=E9 =EDmpar o que nos leva a concluir = que o somat=F3rio=20 n=E3o =E9  um
n=FAmero inteiro.
Abra=E7os,
Luiz Alberto
----- Original Message -----
From:=20 MauZ
Sent: Monday, March 10, 2008 = 6:13=20 PM
Subject: [obm-l] soma de = s=E9rie

mostrar que 1+1/2+1/3+...+1/n n=E3o =E9 inteiro pra = qquer=20 N>1.

Obrigado!

No virus found in this incoming message.
Checked by AVG.=20
Version: 7.5.518 / Virus Database: 269.21.7/1324 - Release Date: = 10/3/2008=20 19:27
------=_NextPart_000_001A_01C88383.FEB5C960-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Tue Mar 11 15:17:04 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2BIFOsG013472 for ; Tue, 11 Mar 2008 15:15:24 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2BIFO9e013470 for obm-l-MllGbsmmN; Tue, 11 Mar 2008 15:15:24 -0300 Received: from fg-out-1718.google.com (fg-out-1718.google.com [72.14.220.159]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2BIFKsG013466 for ; Tue, 11 Mar 2008 15:15:21 -0300 Received: by fg-out-1718.google.com with SMTP id e12so8631770fga.3 for ; Tue, 11 Mar 2008 11:15:48 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=w0TW45sRwMqKhhWXPk+e30/XMwBAXr0wLwLQLMs8QK0=; b=oprgQqXpy/U0A3EdVv64mm1A/RoGqTw5+z40EXhOSVPKfnsF3aB1sP5TbHAXU5N5rs44f7ixczGJ0ssdohMvVGv7jc4vBp5OaCvx4Qh6z1A6Xx7utNYwVT1xU7ivFQH0B261UAA+aC6CaiZQ2IsbCdwP/4pZCfLWVzis5/GsBQM= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=Bdc2HkYDejaSFR07E8wEVXRHLxMIHc54vqWBl9OtaRsI0VuOIJrMZbteQxwLNoNJwtZKLvSliGfNpZ83cRr1ckbtUjba9fIPOs7UyfdiK5TBWhLHV2jJSb1i9glQjCgIa8uBEzSN7hFLcfuvgXpBeGM97P0vwiJRpRPwc9oB0U0= Received: by 10.82.145.7 with SMTP id s7mr17121353bud.24.1205259347974; Tue, 11 Mar 2008 11:15:47 -0700 (PDT) Received: by 10.82.127.13 with HTTP; Tue, 11 Mar 2008 11:15:47 -0700 (PDT) Message-ID: Date: Tue, 11 Mar 2008 15:15:47 -0300 From: "Johann Peter Gustav Lejeune Dirichlet" To: obm-l@mat.puc-rio.br Subject: =?ISO-8859-1?Q?Re:_[obm-l]_an=E1lise_em_1949?= In-Reply-To: <000c01c88252$fa804aa0$6701a8c0@pai> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_2263_32844362.1205259347956" References: <000c01c88252$fa804aa0$6701a8c0@pai> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Johann Peter Gustav Lejeune Dirichlet" X-Spam-Status: No, hits=1.1 required=5.0 tests=AWL,FROM_ENDS_IN_NUMS,IN_REP_TO,MAILTO_LINK, MIME_EXCESSIVE_QP,QUOTED_EMAIL_TEXT,REFERENCES, SPAM_PHRASE_00_01,X_MAILING_LIST version=2.44 X-Spam-Level: * ------=_Part_2263_32844362.1205259347956 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Do jeito que est=E1 escrito, eu acho que ele define um n=FAmero real como "= todos os racionais que o precedem, junto com todos os racionais que o sucedem". E= , de uma maneira um pouco rebuscada, define-se um sistema baseado em aproxima=E7=F5es. E n=E3o sei bem o que se quer dizer com "linguagem atual". A defini=E7=E3o = de n=FAmero real n=E3o =E9 a coisa mais f=E1cil de se estudar e/ou imaginar. E= dizer que "Linguagem se perde no tempo" =E9 meio, como poderia dizer?, antiquado. 2008/3/9, Tio Cabri st : > > Boa noite, > estou lendo um livro de an=E1lise real escrito em 1952. > onde ele, o autor, define n=FAmeros reais como um par de classes > classe minorante e calsse majorante. > Algu=E9m saberia me explicar qual seria a linguagem atual. > Obrigado > Cabri > > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > Instru=E7=F5es para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > ------=_Part_2263_32844362.1205259347956 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Do jeito que est=E1 escrito, eu acho que ele define um n=FAmero real como &= quot;todos os racionais que o precedem, junto com todos os racionais que o = sucedem". E, de uma maneira um pouco rebuscada, define-se um sistema b= aseado em aproxima=E7=F5es.

E n=E3o sei bem o que se quer dizer com "linguagem atual". A = defini=E7=E3o de n=FAmero real n=E3o =E9 a coisa mais f=E1cil de se estudar= e/ou imaginar. E dizer que "Linguagem se perde no tempo" =E9 mei= o, como poderia dizer?, antiquado.


2008/3/9, Tio Cabri st <ilhadepaqueta@bol.com.br>:
Boa noite,
estou lendo um livro de an=E1lise real escrito em 1952.
= onde ele, o autor,  define n=FAmeros reais como um par de classes=
classe minorante e calsse majorante.
Algu=E9m saberia me explicar = qual seria a linguagem atual.
Obrigado
Cabri

=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D
Instru=E7=F5es para entrar na lista, sair da l= ista e usar a lista em
http://www.mat.puc-rio.br/~obmlistas/obm-l.html
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D


------=_Part_2263_32844362.1205259347956-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Tue Mar 11 15:33:59 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2BIWMsG014409 for ; Tue, 11 Mar 2008 15:32:22 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2BIWJla014406 for obm-l-MllGbsmmN; Tue, 11 Mar 2008 15:32:19 -0300 Received: from fg-out-1718.google.com (fg-out-1718.google.com [72.14.220.154]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2BIVmsG014376 for ; Tue, 11 Mar 2008 15:31:50 -0300 Received: by fg-out-1718.google.com with SMTP id e12so8636615fga.3 for ; Tue, 11 Mar 2008 11:32:16 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=uxA+12mP+CZjx5PyZxKRKMh/jLK1wcObRFrLZ6l+/84=; b=jfko7hWBFe0GIWLKXcwujB7l2UsD/qMrQSGL9aXBc+vq9KlYXG/m4lL1KIkzpDRht+++H9EmiHOYxzivY0WA6nwOAc7smhX/6JqcGI0S9QlZS4Jfs9Fjw6ZKl3/aHzhYem9H+VlMAQS+lgsISM8jVs5Pjn0io1ITaEKoG6rP4HA= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=YFXOa4Zk1TOdHr5P3PvSCdu4vMzOP1SusmsmeXWxvdVj35PwVFnMO0tSmIQnn4Yi7DMyJbn8qdqNhotPG1Xyw+X626WvYVekVmQW751Dh/xWyA2CrQQARTMXWKBM5D6MTPJzT1WUuDg529m4H8rvqNSpMjC9NVdHrzQ5VBXsgxU= Received: by 10.86.3.4 with SMTP id 4mr8470165fgc.55.1205260336641; Tue, 11 Mar 2008 11:32:16 -0700 (PDT) Received: by 10.86.74.8 with HTTP; Tue, 11 Mar 2008 11:32:13 -0700 (PDT) Message-ID: Date: Tue, 11 Mar 2008 15:32:13 -0300 From: "saulo nilson" To: obm-l@mat.puc-rio.br Subject: =?ISO-8859-1?Q?Re:_[obm-l]_Fw:_[obm-l]_soma_de_s=E9rie?= In-Reply-To: <001d01c8839d$247a2d30$bc00060a@1F102SALOMAO> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_1017_5601599.1205260336636" References: <001d01c8839d$247a2d30$bc00060a@1F102SALOMAO> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "saulo nilson" X-Spam-Status: No, hits=-0.9 required=5.0 tests=AWL,IN_REP_TO,MAILTO_LINK,OUTLOOK_FW_MSG,QUOTED_EMAIL_TEXT, REFERENCES,SPAM_PHRASE_00_01,X_MAILING_LIST version=2.44 X-Spam-Level: ------=_Part_1017_5601599.1205260336636 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline 1+1/2+1/3+1/4=3D(24+12+8+6)/24=3Dpar /par 2008/3/11 Luiz Alberto Duran Salom=E3o : > > ----- Original Message ----- *From:* Luiz Alberto Duran Salom=E3o > *To:* obm-l@mat.puc-rio.br > *Sent:* Tuesday, March 11, 2008 10:21 AM > *Subject:* Re: [obm-l] soma de s=E9rie > > Caros amigos, > Seja n um inteiro, com n>1. O que se quer provar =E9 que > 1+1/2+1/3+ . . . +1/n n=E3o =E9 inteiro. > Seja 2^a a maior pot=EAncia de 2 tal que 2^a =E9 menor do que ou igual a = n. > Assim, 1/2^a aparece no somat=F3rio acima mas 1/2^(a+1) n=E3o aparece. > Observe que o m=EDnimo m=FAltiplo comum dos denominadores dos > termos do somat=F3rio tem a pot=EAncia 2^a como fator. Agora, no > numerador de cada fra=E7=E3o, j=E1 com denominador igual ao m=EDnimo > m=FAltiplo comum, temos sempre um n=FAmero par, com exce=E7=E3o do > termo correspondente a 1/2^a. Logo, a soma dos numeradores > =E9 =EDmpar o que nos leva a concluir que o somat=F3rio n=E3o =E9 um > n=FAmero inteiro. > Abra=E7os, > Luiz Alberto > > ----- Original Message ----- > *From:* MauZ > *To:* obm-l@mat.puc-rio.br > *Sent:* Monday, March 10, 2008 6:13 PM > *Subject:* [obm-l] soma de s=E9rie > > mostrar que 1+1/2+1/3+...+1/n n=E3o =E9 inteiro pra qquer N>1. > > Obrigado! > > ------------------------------ > > No virus found in this incoming message. > Checked by AVG. > Version: 7.5.518 / Virus Database: 269.21.7/1324 - Release Date: 10/3/200= 8 > 19:27 > > ------=_Part_1017_5601599.1205260336636 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline 1+1/2+1/3+1/4=3D(24+12+8+6)/24=3Dpar /par

2008/3/11 Luiz Alberto Duran Salom=E3o <salomao@ufu.br>:
 
----- Original Message -----=20
Sent: Tuesday, March 11, 2008 10:21 AM
Subject: Re: [obm-l] soma de s=E9rie

Caros amigos,
Seja n um inteiro, com n>1. O que s= e quer provar =E9 que
1+1/2+1/3+ . . . +1/n   n=E3= o =E9 inteiro.
Seja 2^a a maior pot=EAncia de 2 tal q= ue 2^a =E9 menor do que ou igual a n.
Assim, 1/2^a   aparece no so= mat=F3rio acima mas 1/2^(a+1)  n=E3o aparece.
Observe que o m=EDnimo m=FAltiplo comu= m dos denominadores dos
termos do somat=F3rio tem a pot=EAncia= 2^a como fator. Agora, no
numerador de cada  fra=E7=E3o, j= =E1 com denominador igual ao m=EDnimo
m=FAltiplo comum, temos sempre um n=FA= mero par, com exce=E7=E3o do
termo correspondente a 1/2^a. Logo, a = soma dos numeradores
=E9 =EDmpar o que nos leva a concluir = que o somat=F3rio n=E3o =E9  um
n=FAmero inteiro.
Abra=E7os,
Luiz Alberto
----- Original Message -----
From: MauZ
Sent: Monday, March 10, 2008 6:13 PM=
Subject: [obm-l] soma de s=E9rie

mostrar que 1+1/2+1/3+...+1/n n=E3o =E9 inteiro pra qquer N&= gt;1.

Obrigado!

No virus found in this incoming message.
Checked by AVG.
Vers= ion: 7.5.518 / Virus Database: 269.21.7/1324 - Release Date: 10/3/2008 19:2= 7


------=_Part_1017_5601599.1205260336636-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Tue Mar 11 16:11:13 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2BJ9GsG016269 for ; Tue, 11 Mar 2008 16:09:16 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2BJ9D38016262 for obm-l-MllGbsmmN; Tue, 11 Mar 2008 16:09:13 -0300 Received: from rn-out-0910.google.com (rn-out-0910.google.com [64.233.170.184]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2BJ8hsG016245 for ; Tue, 11 Mar 2008 16:08:43 -0300 Received: by rn-out-0910.google.com with SMTP id e11so1781714rng.7 for ; Tue, 11 Mar 2008 12:09:10 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; bh=+VFcgwYcTROxnZ0rR7AulDAI6L6B8hE+tosI2NhiRSs=; b=xO6Cggh6Ni0Jo6cADSu5+Ni5SCJaH/fOkQhsBHDak7GUH3rdpkvQZU3ccr+LJnPsXIt6oTasvD1YYc1tr/MnWFXYX2560dh+MaqVeL7i3jGrLGfXuOyNmsYfl04uNG9yhsFgAfonshOVRB8plccUOkgZ8HhHgKFodTQ+Ucw08+M= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; b=iYt0k/SEAqVk3j80Ny83pX3r+KnsQ5OSxfYfJnegifGvkEcT9xTOqbTVfRzxeQ5+HZmFXLItDBedOjxY6buA2xUjam/VFI0kL1EXoJyx85P7bUyncZQ58bZvlevYxeGzMyxn7F8rUYEOanv1J1OCM7jNAVoX6u5TMgYhzzIfZxY= Received: by 10.143.166.18 with SMTP id t18mr3019456wfo.175.1205262550284; Tue, 11 Mar 2008 12:09:10 -0700 (PDT) Received: by 10.70.60.1 with HTTP; Tue, 11 Mar 2008 12:09:09 -0700 (PDT) Message-ID: <7e31215a0803111209s32b1b2dbma68c77e224375f19@mail.gmail.com> Date: Tue, 11 Mar 2008 16:09:09 -0300 From: "Rodrigo Renji" To: obm-l@mat.puc-rio.br Subject: =?ISO-8859-1?Q?Re:_[obm-l]_Fw:_[obm-l]_soma_de_s=E9rie?= In-Reply-To: MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline References: <001d01c8839d$247a2d30$bc00060a@1F102SALOMAO> Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m2BJ90sG016252 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Rodrigo Renji" X-Spam-Status: No, hits=3.8 required=5.0 tests=AWL,IN_REP_TO,OUTLOOK_FW_MSG,QUOTED_EMAIL_TEXT, RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,REFERENCES, SPAM_PHRASE_00_01,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: *** mostrar que 1+1/2+1/3+...+1/n não é inteiro pra qquer N>1. a questão original é uma soma finita e não uma série a série sabemos que diverge, o que se queria na demonstração e que a soma finita acima nunca é inteira soma [k=1, n] 1/k Em 11/03/08, saulo nilson escreveu: > 1+1/2+1/3+1/4=(24+12+8+6)/24=par /par > > > 2008/3/11 Luiz Alberto Duran Salomão : > > > > > > > > > > > > ----- Original Message ----- > > From: Luiz Alberto Duran Salomão > > To: obm-l@mat.puc-rio.br > > Sent: Tuesday, March 11, 2008 10:21 AM > > Subject: Re: [obm-l] soma de série > > > > > > Caros amigos, > > Seja n um inteiro, com n>1. O que se quer provar é que > > 1+1/2+1/3+ . . . +1/n não é inteiro. > > Seja 2^a a maior potência de 2 tal que 2^a é menor do que ou igual a n. > > Assim, 1/2^a aparece no somatório acima mas 1/2^(a+1) não aparece. > > Observe que o mínimo múltiplo comum dos denominadores dos > > termos do somatório tem a potência 2^a como fator. Agora, no > > numerador de cada fração, já com denominador igual ao mínimo > > múltiplo comum, temos sempre um número par, com exceção do > > termo correspondente a 1/2^a. Logo, a soma dos numeradores > > é ímpar o que nos leva a concluir que o somatório não é um > > número inteiro. > > Abraços, > > Luiz Alberto > > > > > > ----- Original Message ----- > > From: MauZ > > To: obm-l@mat.puc-rio.br > > Sent: Monday, March 10, 2008 6:13 PM > > > > Subject: [obm-l] soma de série > > > > mostrar que 1+1/2+1/3+...+1/n não é inteiro pra qquer N>1. > > > > Obrigado! > > > > > > > > ________________________________ > > > > > No virus found in this incoming message. > > Checked by AVG. > > Version: 7.5.518 / Virus Database: 269.21.7/1324 - Release Date: 10/3/2008 > 19:27 > > > > > > > > > > > > ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Tue Mar 11 16:27:40 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2BJPfsG018274 for ; Tue, 11 Mar 2008 16:25:41 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2BJPeSS018270 for obm-l-MllGbsmmN; Tue, 11 Mar 2008 16:25:40 -0300 Received: from fg-out-1718.google.com (fg-out-1718.google.com [72.14.220.159]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2BJPZsG018211 for ; Tue, 11 Mar 2008 16:25:36 -0300 Received: by fg-out-1718.google.com with SMTP id e12so8652139fga.3 for ; Tue, 11 Mar 2008 12:26:02 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=jRQcb0ofvG/cfEl0hLFISBUQ2D+meZb/YsjBrylU7KE=; b=Wf16AdLM0e9HyXtHXW4axHvJFX8+E7O8erlDDAk7p5Qu567Sd6rSzUo033K2ZsM7hKMmM+sIzOsxqy9nknoVA7dHtMYx5R+nRQjJ4SpfzkZbfDthuRPAfXrt/pGDhwxxIVreFMKpsi0SHketkwcL3TO1qKv4KdDBs8Zv8TgekCg= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=xB+nGnl4j6+axmmG9jhXag+uc67zIpz4MWlin0CAnVJHIUmhpw3P5WNP9PI4es19iJ/uLE6BVhRcm//vfwicRdIAR9iVMRSJREOINjVqMsJiAxYPt/xs3MY6bdLux7GUJfQY4c9fZFaWrYTCduQKIWFL4LjpZas1X9d9fGQCqWo= Received: by 10.86.70.8 with SMTP id s8mr8529071fga.29.1205263562725; Tue, 11 Mar 2008 12:26:02 -0700 (PDT) Received: by 10.86.74.8 with HTTP; Tue, 11 Mar 2008 12:26:02 -0700 (PDT) Message-ID: Date: Tue, 11 Mar 2008 16:26:02 -0300 From: "saulo nilson" To: obm-l@mat.puc-rio.br Subject: =?ISO-8859-1?Q?Re:_[obm-l]_Fw:_[obm-l]_soma_de_s=E9rie?= In-Reply-To: MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_1123_19896485.1205263562733" References: <001d01c8839d$247a2d30$bc00060a@1F102SALOMAO> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "saulo nilson" X-Spam-Status: No, hits=-1.0 required=5.0 tests=AWL,IN_REP_TO,MAILTO_LINK,OUTLOOK_FW_MSG,QUOTED_EMAIL_TEXT, REFERENCES,SPAM_PHRASE_00_01,X_MAILING_LIST version=2.44 X-Spam-Level: ------=_Part_1123_19896485.1205263562733 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline apos reduzir temos o caso, perdao. 2008/3/11 saulo nilson : > 1+1/2+1/3+1/4=3D(24+12+8+6)/24=3Dpar /par > > 2008/3/11 Luiz Alberto Duran Salom=E3o : > > > > ----- Original Message ----- *From:* Luiz Alberto Duran Salom=E3o > > *To:* obm-l@mat.puc-rio.br > > *Sent:* Tuesday, March 11, 2008 10:21 AM > > *Subject:* Re: [obm-l] soma de s=E9rie > > > > Caros amigos, > > Seja n um inteiro, com n>1. O que se quer provar =E9 que > > 1+1/2+1/3+ . . . +1/n n=E3o =E9 inteiro. > > Seja 2^a a maior pot=EAncia de 2 tal que 2^a =E9 menor do que ou igual = a n. > > Assim, 1/2^a aparece no somat=F3rio acima mas 1/2^(a+1) n=E3o aparec= e. > > Observe que o m=EDnimo m=FAltiplo comum dos denominadores dos > > termos do somat=F3rio tem a pot=EAncia 2^a como fator. Agora, no > > numerador de cada fra=E7=E3o, j=E1 com denominador igual ao m=EDnimo > > m=FAltiplo comum, temos sempre um n=FAmero par, com exce=E7=E3o do > > termo correspondente a 1/2^a. Logo, a soma dos numeradores > > =E9 =EDmpar o que nos leva a concluir que o somat=F3rio n=E3o =E9 um > > n=FAmero inteiro. > > Abra=E7os, > > Luiz Alberto > > > > ----- Original Message ----- > > *From:* MauZ > > *To:* obm-l@mat.puc-rio.br > > *Sent:* Monday, March 10, 2008 6:13 PM > > *Subject:* [obm-l] soma de s=E9rie > > > > mostrar que 1+1/2+1/3+...+1/n n=E3o =E9 inteiro pra qquer N>1. > > > > Obrigado! > > > > ------------------------------ > > > > No virus found in this incoming message. > > Checked by AVG. > > Version: 7.5.518 / Virus Database: 269.21.7/1324 - Release Date: > > 10/3/2008 19:27 > > > > > ------=_Part_1123_19896485.1205263562733 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline apos reduzir temos o caso, perdao.

2008/3/11 saulo nilson <saulo.nilson@gmail.com>:
1+1/2+1/3+1/4=3D(24+12+8+6)/24= =3Dpar /par

2008/3/11 Luiz Alberto Duran Salom=E3o <salomao@ufu.br>:=20

 
----- Original Message -----=20
Sent: Tuesday, March 11, 2008 10:21 AM
Subject: Re: [obm-l] soma de s=E9rie

Caros amigos,
Seja n um inteiro, com n>1. O que s= e quer provar =E9 que
1+1/2+1/3+ . . . +1/n   n=E3= o =E9 inteiro.
Seja 2^a a maior pot=EAncia de 2 tal q= ue 2^a =E9 menor do que ou igual a n.
Assim, 1/2^a   aparece no so= mat=F3rio acima mas 1/2^(a+1)  n=E3o aparece.
Observe que o m=EDnimo m=FAltiplo comu= m dos denominadores dos
termos do somat=F3rio tem a pot=EAncia= 2^a como fator. Agora, no
numerador de cada  fra=E7=E3o, j= =E1 com denominador igual ao m=EDnimo
m=FAltiplo comum, temos sempre um n=FA= mero par, com exce=E7=E3o do
termo correspondente a 1/2^a. Logo, a = soma dos numeradores
=E9 =EDmpar o que nos leva a concluir = que o somat=F3rio n=E3o =E9  um
n=FAmero inteiro.
Abra=E7os,
Luiz Alberto
----- Original Message -----
From: MauZ
Sent: Monday, March 10, 2008 6:13 PM=
Subject: [obm-l] soma de s=E9rie

mostrar que 1+1/2+1/3+...+1/n n=E3o =E9 inteiro pra qquer N&= gt;1.

Obrigado!

No virus found in this incoming message.
Checked by AVG.
Vers= ion: 7.5.518 / Virus Database: 269.21.7/1324 - Release Date: 10/3/2008 19:2= 7



------=_Part_1123_19896485.1205263562733-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Tue Mar 11 17:16:49 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2BKFQsG026493 for ; Tue, 11 Mar 2008 17:15:26 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2BKFQRt026491 for obm-l-MllGbsmmN; Tue, 11 Mar 2008 17:15:26 -0300 Received: from web32208.mail.mud.yahoo.com (web32208.mail.mud.yahoo.com [68.142.207.139]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id m2BKFNsG026483 for ; Tue, 11 Mar 2008 17:15:24 -0300 Received: (qmail 19075 invoked by uid 60001); 11 Mar 2008 20:15:48 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:Date:From:Subject:To:In-Reply-To:MIME-Version:Content-Type:Content-Transfer-Encoding:Message-ID; b=o9AY8GyleGRjbkdIC12XZs45tcE0CQ59WOTRYhismj7aCdD4BPzJZRG4uaNTJpcMooidhwwHOiv/ZQ4Bt2GDDaiaPB4Jgy6nlzNmjR5c7WZ8Ykj+PCTXK0DtISwyolenT2iwvjANoyYfiaPyYb6m//5A4v8GBX8wOsxBU7kyPPM=; X-YMail-OSG: 1U_WXm0VM1mNIMn3iRomMBIjNTH2jIrdWiGusuTJ Received: from [189.25.189.18] by web32208.mail.mud.yahoo.com via HTTP; Tue, 11 Mar 2008 18:15:47 ARST Date: Tue, 11 Mar 2008 18:15:47 -0200 (ARST) From: Claudio Gustavo Subject: [SPAM] =?iso-8859-1?q?Re:=20[obm-l]=20soma=20de=20s=E9rie?= To: obm-l@mat.puc-rio.br In-Reply-To: <926569.85338.qm@web32202.mail.mud.yahoo.com> MIME-Version: 1.0 Content-Type: text/plain Content-Transfer-Encoding: 7bit Message-ID: <170429.17217.qm@web32208.mail.mud.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Claudio Gustavo X-Spam-Status: Yes, hits=7.4 required=5.0 tests=AWL,FORGED_YAHOO_RCVD,IN_REP_TO,JAVASCRIPT_UNSAFE, MAILTO_LINK,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, SPAM_PHRASE_01_02,SPAM_REDIRECTOR,SUPERLONG_LINE, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******* X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="0-1995923737-1205266547=:17217" X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (7.40 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_01_02 (0.5 points) BODY: Spam phrases score is 01 to 02 (low) SPAM: [score: 1] SPAM: JAVASCRIPT_UNSAFE (0.3 points) BODY: Easily-executed JavaScript code SPAM: MAILTO_LINK (0.2 points) BODY: Includes a URL link to send an email SPAM: SUPERLONG_LINE (0.0 points) BODY: Contains a line >=199 characters long SPAM: SPAM_REDIRECTOR (0.4 points) URI: Uses open redirection service SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 139.207.142.68.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 139.207.142.68.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (0.4 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- --0-1995923737-1205266547=:17217 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 8bit O meu erro foi supor que n tende ao infinito, mas isso não ocorre. Logo o argumento não é válido. Desculpe. Claudio Gustavo escreveu: Entendi sua pergunta. Cara, no meu ponto de vista, qdo demonstramos que diverge, ou seja, tende ao infinito, automaticamente demonstramos q não pode ser inteiro. Tender ao infinito é uma forma de indeterminação. Não sei se existe uma outra interpretação/demonstração... Abraço. MauZ escreveu: eu acabei de ver que é a serie harmonica... mas como faço pra demonstrar que nunca é inteiro? pq vai pro infinito, beleza... mas pode passar por algum inteiro, oque tem q provar q nunca acontece... se eu usar uma desigualdade como você msotrou e como achei outras aqui em livros eu saio um pouco do foco que é provar q não é inteiro... ou tou errado? se eu tiver falando besteira por favor me corrija! Obrigado Claudio, []s Maurizio Em 10/03/08, Claudio Gustavo escreveu: Essa é, na verdade, a série harmônica, que diverge. Vc pode demonstrar usando integrais ou usando a desigualdade "1+1/2+...+1/(2^n-1)>n/2". Vc encontra essas demonstrações no livro de Análise do Elon. Abraço. MauZ escreveu: mostrar que 1+1/2+1/3+...+1/n não é inteiro pra qquer N>1. Obrigado! --------------------------------- Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --------------------------------- Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --------------------------------- Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-1995923737-1205266547=:17217 Content-Type: text/html; charset=iso-8859-1 Content-Transfer-Encoding: 8bit
  O meu erro foi supor que n tende ao infinito, mas isso não ocorre. Logo o argumento não é válido. Desculpe.


Claudio Gustavo <claudioggll@yahoo.com.br> escreveu:
  Entendi sua pergunta. Cara, no meu ponto de vista, qdo demonstramos que diverge, ou seja, tende ao infinito, automaticamente demonstramos q não pode ser inteiro. Tender ao infinito é uma forma de indeterminação.
  Não sei se existe uma outra interpretação/demonstração...
 
  Abraço.

MauZ <mauz.matematica@gmail.com> escreveu:
eu acabei de ver que é a serie harmonica...
mas como faço pra demonstrar que nunca é inteiro?
pq vai pro infinito, beleza...
 mas pode passar por algum inteiro, oque tem q provar q nunca acontece...

se eu usar uma desigualdade como você msotrou e como achei outras aqui em livros eu saio um pouco do foco que é provar q não é inteiro... ou tou errado?

se eu tiver falando besteira por favor me corrija!

Obrigado Claudio,
[]s
Maurizio

Em 10/03/08, Claudio Gustavo <claudioggll@yahoo.com.br> escreveu:
  Essa é, na verdade, a série harmônica, que diverge. Vc pode demonstrar usando integrais ou usando a desigualdade "1+1/2+...+1/(2^n-1)>n/2". Vc encontra essas demonstrações no livro de Análise do Elon.
 
  Abraço.

MauZ <mauz.matematica@gmail.com> escreveu:
mostrar que 1+1/2+1/3+...+1/n não é inteiro pra qquer N>1.

Obrigado!

Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento!


Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento!

Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-1995923737-1205266547=:17217-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Tue Mar 11 18:02:47 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2BL0jsG029278 for ; Tue, 11 Mar 2008 18:00:45 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2BL0jOx029274 for obm-l-MllGbsmmN; Tue, 11 Mar 2008 18:00:45 -0300 Received: from doodle.dr.ufu.br (doodle.dr.ufu.br [200.19.146.202]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2BL0hsG029270 for ; Tue, 11 Mar 2008 18:00:43 -0300 Received: (qmail 20075 invoked from network); 11 Mar 2008 21:01:11 -0000 Received: from unknown (HELO 1F102SALOMAO) (salomao@ufu.br@[10.6.0.188]) (envelope-sender ) by doodle.dr.ufu.br (qmail-ldap-1.03) with SMTP for ; 11 Mar 2008 21:01:11 -0000 Message-ID: <001901c883bb$0a1aca30$bc00060a@1F102SALOMAO> From: =?iso-8859-1?Q?Luiz_Alberto_Duran_Salom=E3o?= To: Subject: [SPAM] [obm-l] =?iso-8859-1?Q?Fw:_=5Bobm-l=5D_Fw:_=5Bobm-l=5D_soma_de_s=E9rie?= Date: Tue, 11 Mar 2008 18:01:12 -0300 MIME-Version: 1.0 Content-Type: text/plain X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2900.3138 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.3198 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: =?iso-8859-1?Q?Luiz_Alberto_Duran_Salom=E3o?= X-Spam-Status: Yes, hits=5.7 required=5.0 tests=AWL,MAILTO_LINK,OUTLOOK_FW_MSG,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01,USER_AGENT_OE, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ***** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_NextPart_000_0016_01C883A1.E4731620" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (5.70 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: OUTLOOK_FW_MSG (-0.1 points) Forwarded email (Outlook style) SPAM: USER_AGENT_OE (0.2 points) X-Mailer header indicates a non-spam MUA (Outlook Express) SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: MAILTO_LINK (0.2 points) BODY: Includes a URL link to send an email SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 202.146.19.200.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 202.146.19.200.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-0.4 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- This is a multi-part message in MIME format. ------=_NextPart_000_0016_01C883A1.E4731620 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Caro Saulo, No seu exemplo, o mmc de 2, 3 e 4 =E9 12 (e n=E3o 24). Portanto, o que temos =E9 1+1/2+1/3+1/4 =3D (12+6+4+3)/12 =3D 25/12, ou seja, =EDmpar/par. Abra=E7os, Luiz Alberto ----- Original Message -----=20 From: saulo nilson=20 To: obm-l@mat.puc-rio.br=20 Sent: Tuesday, March 11, 2008 3:32 PM Subject: Re: [obm-l] Fw: [obm-l] soma de s=E9rie 1+1/2+1/3+1/4=3D(24+12+8+6)/24=3Dpar /par 2008/3/11 Luiz Alberto Duran Salom=E3o : ----- Original Message -----=20 From: Luiz Alberto Duran Salom=E3o=20 To: obm-l@mat.puc-rio.br=20 Sent: Tuesday, March 11, 2008 10:21 AM Subject: Re: [obm-l] soma de s=E9rie Caros amigos, Seja n um inteiro, com n>1. O que se quer provar =E9 que 1+1/2+1/3+ . . . +1/n n=E3o =E9 inteiro. Seja 2^a a maior pot=EAncia de 2 tal que 2^a =E9 menor do que ou igual = a n. Assim, 1/2^a aparece no somat=F3rio acima mas 1/2^(a+1) n=E3o = aparece. Observe que o m=EDnimo m=FAltiplo comum dos denominadores dos=20 termos do somat=F3rio tem a pot=EAncia 2^a como fator. Agora, no=20 numerador de cada fra=E7=E3o, j=E1 com denominador igual ao m=EDnimo m=FAltiplo comum, temos sempre um n=FAmero par, com exce=E7=E3o do=20 termo correspondente a 1/2^a. Logo, a soma dos numeradores=20 =E9 =EDmpar o que nos leva a concluir que o somat=F3rio n=E3o =E9 um=20 n=FAmero inteiro. Abra=E7os, Luiz Alberto ----- Original Message -----=20 From: MauZ=20 To: obm-l@mat.puc-rio.br=20 Sent: Monday, March 10, 2008 6:13 PM Subject: [obm-l] soma de s=E9rie mostrar que 1+1/2+1/3+...+1/n n=E3o =E9 inteiro pra qquer N>1. Obrigado! -------------------------------------------------------------------------= --- No virus found in this incoming message. Checked by AVG.=20 Version: 7.5.518 / Virus Database: 269.21.7/1324 - Release Date: = 10/3/2008 19:27 -------------------------------------------------------------------------= ------- No virus found in this incoming message. Checked by AVG.=20 Version: 7.5.518 / Virus Database: 269.21.7/1324 - Release Date: = 10/3/2008 19:27 ------=_NextPart_000_0016_01C883A1.E4731620 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable
Caro Saulo,
No seu exemplo, o mmc de 2, 3 e 4 =E9 = 12 (e n=E3o=20 24).
Portanto, o que temos =E9
1+1/2+1/3+1/4 =3D (12+6+4+3)/12 = =3D 25/12, ou=20 seja, =EDmpar/par.
Abra=E7os,
Luiz Alberto
----- Original Message -----=20
From: saulo=20 nilson
Sent: Tuesday, March 11, 2008 3:32 PM
Subject: Re: [obm-l] Fw: [obm-l] soma de s=E9rie

1+1/2+1/3+1/4=3D(24+12+8+6)/24=3Dpar /par

2008/3/11 Luiz Alberto Duran Salom=E3o <salomao@ufu.br>:
 
----- Original Message -----=20
Sent: Tuesday, March 11, 2008 10:21 AM
Subject: Re: [obm-l] soma de s=E9rie

Caros amigos,
Seja n um inteiro, com n>1. O que = se quer=20 provar =E9 que
1+1/2+1/3+ . . . +1/n   = n=E3o =E9=20 inteiro.
Seja 2^a a maior pot=EAncia de 2 tal = que 2^a =E9=20 menor do que ou igual a n.
Assim, 1/2^a   aparece no = somat=F3rio=20 acima mas 1/2^(a+1)  n=E3o aparece.
Observe que o m=EDnimo m=FAltiplo = comum dos=20 denominadores dos
termos do somat=F3rio tem a = pot=EAncia 2^a como=20 fator. Agora, no
numerador de cada  fra=E7=E3o, = j=E1 com=20 denominador igual ao m=EDnimo
m=FAltiplo comum, temos sempre um = n=FAmero par, com=20 exce=E7=E3o do
termo correspondente a 1/2^a. Logo, a = soma dos=20 numeradores
=E9 =EDmpar o que nos leva a concluir = que o somat=F3rio=20 n=E3o =E9  um
n=FAmero inteiro.
Abra=E7os,
Luiz Alberto
----- Original Message -----
From: MauZ
Sent: Monday, March 10, 2008 = 6:13=20 PM
Subject: [obm-l] soma de = s=E9rie

mostrar que 1+1/2+1/3+...+1/n n=E3o =E9 inteiro pra = qquer=20 N>1.

Obrigado!

No virus found in this incoming message.
Checked by AVG.=20
Version: 7.5.518 / Virus Database: 269.21.7/1324 - Release Date: = 10/3/2008 19:27


No virus found in this incoming message.
Checked by AVG. =
Version:=20 7.5.518 / Virus Database: 269.21.7/1324 - Release Date: 10/3/2008=20 19:27
------=_NextPart_000_0016_01C883A1.E4731620-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Tue Mar 11 22:19:32 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2C1HQsG019143 for ; Tue, 11 Mar 2008 22:17:26 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2C1HQ3B019141 for obm-l-MllGbsmmN; Tue, 11 Mar 2008 22:17:26 -0300 Received: from wx-out-0506.google.com (wx-out-0506.google.com [66.249.82.236]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2C1HMsG019124 for ; Tue, 11 Mar 2008 22:17:23 -0300 Received: by wx-out-0506.google.com with SMTP id t4so3353471wxc.18 for ; Tue, 11 Mar 2008 18:17:50 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:mime-version:content-type; bh=yQFYignoKm3MeMxSV0UKgHqSJKfJ1L84V5X13EuFjy4=; b=PSj/5vybcd8ttMWjm2B24jZMm2NHYZ+Y7k7YyxzzSR4esr/6L3VPJH43s9e8/IGUbX90TOZyzYbFmJ2qqR5YjQv4R5ASg+Oqx2XiAz4Q1lc88CTv6Y3p9REk9iEQ7gb2gI+CO7siuR1vVJ+HaUG6PRhHCeorSWPL2na8Ptvk1vA= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:mime-version:content-type; b=Bq2sxr8dJ1BUQ2N7P22m3cujYEmOl2rmUpookTfOiL0Qm9WFaRZsjQVgrtNZWRJEt2d55HpgWxXVEWVpPZWRePBpeGVfcs0MTkDrkhAQ1xW6mkMXKcRoKzbNQX2oFnjaO7RVJo627Unbxusn5uKOajoQcC3UcjOb8RgxkGYnd4c= Received: by 10.114.106.1 with SMTP id e1mr6234131wac.95.1205284669409; Tue, 11 Mar 2008 18:17:49 -0700 (PDT) Received: by 10.114.88.8 with HTTP; Tue, 11 Mar 2008 18:17:44 -0700 (PDT) Message-ID: Date: Tue, 11 Mar 2008 22:17:44 -0300 From: MauZ To: obm-l@mat.puc-rio.br Subject: [SPAM] [obm-l] =?ISO-8859-1?Q?N=FAmeros_de_0_a_100_(series)_+_Fila_Indiana?= MIME-Version: 1.0 Content-Type: text/plain Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: MauZ X-Spam-Status: Yes, hits=5.6 required=5.0 tests=AWL,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ***** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_Part_10822_23063390.1205284664394" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (5.60 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 236.82.249.66.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 236.82.249.66.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-0.2 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- ------=_Part_10822_23063390.1205284664394 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline 1)Os n=FAmeros de 0 a 100 est=E3o listados em uma ordem qualquer. Mostre qu= e =E9 poss=EDvel riscar 90 deles de tal forma que os demais fiquem em ordem crescente ou decrescente. Consegui um m=E9todo dessa forma: Pego o primeiro numero > 90 que eu encontrar, depois procuro o proximo tal q a dif seja <=3D 10, isso deve tra= zer uma sequencia decrescente. Caso esse m=E9todo n=E3o funcione, o mesmo m=E9t= odo invertido (come=E7ando do final) trar=E1 uma sequencia crescente. Mas n=E3o= sei se =E9 de fato verdade muito menos consegui provar. 2)Em uma fila indiana as pessoas v=EAem as cores pintadas nas nucas =E0 sua frente. H=E1 quatro cores poss=EDveis e cada pessoa deve tentar acertar sua pr=F3pria cor. Qual deve ser a estrat=E9gia (combinada entre eles a priori, antes mesmo de serem pintados) para que todos, menos eventualmente um, acertem? Esse segundo parece estranho o enunciado... mas pelo que entendi eles n=E3o podem falar um monte de coisa, devem apenas tnetar acertar a propria cor. E nada de jogos mortais e arrancar um peda=E7o da nuca! Agrade=E7o qualquer ajuda, Maurizio ------=_Part_10822_23063390.1205284664394 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline 1)Os n=FAmeros de 0 a 100 est=E3o listados em uma ordem qualquer. Mostre qu= e =E9 poss=EDvel riscar 90 deles de tal forma que os demais fiquem em ordem= crescente ou decrescente.

Consegui um m=E9todo dessa forma: Pego o = primeiro numero > 90 que eu encontrar, depois procuro o proximo tal q a = dif seja <=3D 10, isso deve trazer uma sequencia decrescente. Caso esse = m=E9todo n=E3o funcione, o mesmo m=E9todo invertido (come=E7ando do final) = trar=E1 uma sequencia crescente. Mas n=E3o sei se =E9 de fato verdade muito= menos consegui provar.

2)Em uma fila indiana as pessoas v=EAem as cores pintadas nas nucas =E0= sua frente. H=E1 quatro cores poss=EDveis e cada pessoa deve tentar acerta= r sua pr=F3pria cor. Qual deve ser a estrat=E9gia (combinada entre eles a p= riori, antes mesmo de serem pintados) para que todos, menos eventualmente u= m, acertem?

Esse segundo parece estranho o enunciado... mas pelo que entendi eles n= =E3o podem falar um monte de coisa, devem apenas tnetar acertar a propria c= or. E nada de jogos mortais e arrancar um peda=E7o da nuca!


Agra= de=E7o qualquer ajuda,
Maurizio
------=_Part_10822_23063390.1205284664394-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Tue Mar 11 22:24:48 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2C1NgsG019615 for ; Tue, 11 Mar 2008 22:23:42 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2C1NgCQ019613 for obm-l-MllGbsmmN; Tue, 11 Mar 2008 22:23:42 -0300 Received: from smtpi03s.infolink.com.br (smtpi03s.infolink.com.br [200.187.64.122]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2C1NfsG019599 for ; Tue, 11 Mar 2008 22:23:41 -0300 Received: from smtpi03s.infolink.com.br (localhost [127.0.0.1]) by smtpi03s.infolink.com.br (Postfix) with ESMTP id 0B035712296 for ; Tue, 11 Mar 2008 22:24:10 -0300 (EST) Received: from [127.0.0.1] (unknown [189.60.112.176]) by smtpi03s.infolink.com.br (Postfix) with ESMTP id D170F701AC0 for ; Tue, 11 Mar 2008 22:24:09 -0300 (EST) Message-ID: <47D73078.3030300@infolink.com.br> Date: Tue, 11 Mar 2008 22:23:04 -0300 From: Carlos Nehab User-Agent: Thunderbird 2.0.0.12 (Windows/20080213) MIME-Version: 1.0 To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] =?ISO-8859-1?Q?an=E1lise_em_1949?= References: <000c01c88252$fa804aa0$6701a8c0@pai> In-Reply-To: <000c01c88252$fa804aa0$6701a8c0@pai> Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: 7bit X-Antivirus: avast! (VPS 080311-0, 11/03/2008), Outbound message X-Antivirus-Status: Clean Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Carlos Nehab X-Spam-Status: No, hits=4.7 required=5.0 tests=AWL,CTYPE_JUST_HTML,IN_REP_TO,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, USER_AGENT,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** Oi, Cabri,

Apenas o caminho das pedras: dê uma olhada em "Corte de Dedekind".  Por exemplo em
http://pt.wikipedia.org/wiki/Cortes_de_Dedekind

Desculpe  se não tenho tempo para maiores explicações.

Abraços,
Nehab

Tio Cabri st escreveu: 
Boa noite,
estou lendo um livro de análise real escrito em 1952.
onde ele, o autor,  define números reais como um par de classes
classe minorante e calsse majorante.
Alguém saberia me explicar qual seria a linguagem atual.
Obrigado
Cabri

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========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Mar 12 00:41:12 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2C3dNsG003672 for ; Wed, 12 Mar 2008 00:39:23 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2C3dNZR003670 for obm-l-MllGbsmmN; Wed, 12 Mar 2008 00:39:23 -0300 Received: from web37014.mail.mud.yahoo.com (web37014.mail.mud.yahoo.com [209.191.85.99]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id m2C3dLsG003666 for ; Wed, 12 Mar 2008 00:39:22 -0300 Received: (qmail 92277 invoked by uid 60001); 12 Mar 2008 03:39:48 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:Date:From:Subject:To:MIME-Version:Content-Type:Content-Transfer-Encoding:Message-ID; b=Gj4xXj1cl4QTCAhSdJQf0mNBknoxyUsJSN97CpK0UOZBppaTQig4CNOgeOfgxmUmgSjdDd+7Fo5/3D4HLX3tOwdOio5+Beqti5WNoM+ruKZRIBd+tcgzMT5sIVBpBXBwfzUTJOXyCIRQfakdAg1+CxlXyH8xqQpzeR3MCuhHDvQ=; X-YMail-OSG: StWtWvkVM1mxLqE2BGsamkpgkGCont6HbLqKgH5eKxjGbe1kaZ2V5Yo9U8Ytn1Vxmg-- Received: from [201.19.230.89] by web37014.mail.mud.yahoo.com via HTTP; Wed, 12 Mar 2008 00:39:48 ART Date: Wed, 12 Mar 2008 00:39:48 -0300 (ART) From: Bruno Carvalho Subject: [SPAM] [obm-l] Matrizes To: obm-l@mat.puc-rio.br MIME-Version: 1.0 Content-Type: text/plain Content-Transfer-Encoding: 7bit Message-ID: <777121.90323.qm@web37014.mail.mud.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Bruno Carvalho X-Spam-Status: Yes, hits=7.9 required=5.0 tests=AWL,FORGED_YAHOO_RCVD,MIME_BOUND_DIGITS_5,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01,SPAM_REDIRECTOR, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******* X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="0-376584965-1205293188=:90323" X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (7.90 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: MIME_BOUND_DIGITS_5 (1.7 points) Spam tool pattern in MIME boundary SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: SPAM_REDIRECTOR (0.4 points) URI: Uses open redirection service SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 99.85.191.209.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 99.85.191.209.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-1.4 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- --0-376584965-1205293188=:90323 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 8bit Oi Pessoal, Peço ajuda ( orientação) na demonstração da seguinte afirmação sobre matrizes. Sejam T matriz nxn ; J matriz n x1 e M matriz nx1. Prove que se T possui uma inversa então TJ tem uma única solução. Obrigado Bruno --------------------------------- Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-376584965-1205293188=:90323 Content-Type: text/html; charset=iso-8859-1 Content-Transfer-Encoding: 8bit
Oi Pessoal,
 
Peço ajuda ( orientação) na demonstração  da seguinte afirmação sobre matrizes.
Sejam T matriz nxn ; J matriz n x1  e M matriz nx1. Prove que se T possui uma inversa então TJ tem uma única solução.
 
Obrigado
 
Bruno

Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-376584965-1205293188=:90323-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Mar 12 11:25:20 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2CEMisG002796 for ; Wed, 12 Mar 2008 11:22:44 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2CEMiKM002794 for obm-l-MllGbsmmN; Wed, 12 Mar 2008 11:22:44 -0300 Received: from relay2.bol.com.br (relay2.bol.com.br [200.221.4.106]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2CEMhsG002791 for ; Wed, 12 Mar 2008 11:22:43 -0300 Received: from localhost (localhost [127.0.0.1]) by salsa2.bol.com.br (Postfix) with ESMTP id 857CFE00705D for ; Wed, 12 Mar 2008 11:23:12 -0300 (BRT) Received: from bol.com.br (whisper10.mail.sys.intranet [172.26.5.91]) by salsa2.bol.com.br (Postfix) with ESMTP id 660B3E006F22 for ; Wed, 12 Mar 2008 11:23:12 -0300 (BRT) Date: Wed, 12 Mar 2008 11:23:12 -0300 Message-Id: Subject: [obm-l] SOMA DOS QUADRADOS MIME-Version: 1.0 X-Sensitivity: 3 Content-Type: multipart/alternative; boundary="_=__=_XaM3_.1205331792.2A.272669.42.30120.52.42.007.1809978730" From: "arkon" To: "obm-l" X-XaM3-API-Version: 4.3(R1) (B10) X-SenderIP: 200.140.133.74 X-SIG5: 41157a017a1ee4eed42e440fcd677df3 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "arkon" X-Spam-Status: No, hits=1.3 required=5.0 tests=AWL,BIG_FONT,HTML_50_70,LINES_OF_YELLING, LINES_OF_YELLING_2,SPAM_PHRASE_00_01,TO_LOCALPART_EQ_REAL, X_MAILING_LIST version=2.44 X-Spam-Level: * --_=__=_XaM3_.1205331792.2A.272669.42.30120.52.42.007.1809978730 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable Pessoal algu=E9m poderia me enviar, por favor, a resolu=E7=E3o dessa ques= t=E3o (UFPB =96 77) A soma dos quadrados das ra=EDzes da equa=E7=E3o x^5 =96 5x= ^3 + 6x =3D 0 =E9: a) 0. b) 10. c) 12. d) 8. e) 6= . DESDE J=C1 MUITO OBRIGADO --_=__=_XaM3_.1205331792.2A.272669.42.30120.52.42.007.1809978730 Content-Type: text/html; charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable

<= B style=3D"mso-bidi-font-weight: normal">Pessoal algu=E9m poderia me enviar, por favor, a resolu=E7=E3= o dessa quest=E3o

<= B style=3D"mso-bidi-font-weight: normal"> 

<= B style=3D"mso-bidi-font-weight: normal">(UFPB =96 77) A soma dos quadrados das ra=EDzes da equa=E7=E3= o x^5 =96 5x^3 + 6x =3D 0 =E9:

<= B style=3D"mso-bidi-font-weight: normal"> 

<= B style=3D"mso-bidi-font-weight: normal">a) 0.   &n= bsp;       b) 10.         &nbs= p; c) 12.    = ;        d) 8.         &n= bsp;   e) 6.

<= B style=3D"mso-bidi-font-weight: normal"> 

<= B style=3D"mso-bidi-font-weight: normal">DESDE J=C1 MUITO OBRIGADO

<= /DIV>
--_=__=_XaM3_.1205331792.2A.272669.42.30120.52.42.007.1809978730-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Mar 12 13:05:48 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2CG4EsG007469 for ; Wed, 12 Mar 2008 13:04:14 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2CG4EUo007467 for obm-l-MllGbsmmN; Wed, 12 Mar 2008 13:04:14 -0300 Received: from c300a-2.friendster.com (c300a-2.friendster.com [209.11.169.51]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2CG49sH007448 for ; Wed, 12 Mar 2008 13:04:12 -0300 Date: Wed, 12 Mar 2008 13:04:12 -0300 Received: from unknown (HELO mailmerge1) ([10.16.72.3]) by c300a-2.friendster.com with ESMTP; 12 Mar 2008 09:04:37 -0700 Message-Id: <6libi9$aqhju8@c300a.gbxsc.friendster.com> From: Jamil Silva Subject: [SPAM] [obm-l] Reminder: Jamil Silva has invited you to join Friendster To: obm-l@mat.puc-rio.br X-Campaign-ID: 10290 X-Campaign-Type: 5 X-Message-Ref: NDG5wK9OMYDACRPoK6vG0v_-hkMNQZ84wt6mMlteLlQ* Content-Type: text/plain MIME-Version: 1.0 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Jamil Silva X-Spam-Status: Yes, hits=9.0 required=5.0 tests=BIG_FONT,CLICK_BELOW,EXCUSE_14,HTML_FONT_COLOR_CYAN, HTML_FONT_COLOR_GRAY,HTML_FONT_COLOR_UNSAFE, MSG_ID_ADDED_BY_MTA_3,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, SPAM_PHRASE_03_05,WEB_BUGS,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ********* X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----_=_FSter_001_3251205337872466" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (9.00 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: CLICK_BELOW (0.3 points) BODY: Asks you to click below SPAM: EXCUSE_14 (0.2 points) BODY: Tells you how to stop further spam SPAM: SPAM_PHRASE_03_05 (1.1 points) BODY: Spam phrases score is 03 to 05 (medium) SPAM: [score: 4] SPAM: HTML_FONT_COLOR_CYAN (0.4 points) BODY: HTML font color is cyan SPAM: BIG_FONT (0.3 points) BODY: FONT Size +2 and up or 3 and up SPAM: HTML_FONT_COLOR_GRAY (0.3 points) BODY: HTML font color is gray SPAM: HTML_FONT_COLOR_UNSAFE (0.3 points) BODY: HTML font color not within safe 6x6x6 palette SPAM: WEB_BUGS (0.2 points) BODY: Image tag with an ID code to identify you SPAM: MSG_ID_ADDED_BY_MTA_3 (0.9 points) 'Message-Id' was added by a relay (3) SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 51.169.11.209.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 51.169.11.209.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- This is a MIME email, the first part is the text message. ------_=_FSter_001_3251205337872466 Content-Type: text/plain; charset="UTF-8" Content-Transfer-Encoding: 7bit You're invited to join Jamil Silva's network of friends. In addition to seeing what Jamil is up to, you can reconnect with old friends, meet new friends, start a blog, build a custom profile, keep track of birthdays, and so much more! Click below to join Jamil's network. http://www.friendster.com/join.php?inviteref=34280739&invite=bwi4XTAfuME9LV-4-BHCKxDvM_Ib03PueIDaNQlEeS0* ***************************************************************** If you do not wish to receive notification emails from Friendster, please click below: http://www.friendster.com/blockemails.php?invite=b2JtLWxAbWF0LnB1Yy1yaW8uYnI* ------_=_FSter_001_3251205337872466 Content-Type: text/html; charset="UTF-8" Content-Transfer-Encoding: 7bit Friendster Friend Alert
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------_=_FSter_001_3251205337872466-- Date: Wed, 12 Mar 2008 09:04:37 -0700 Message-Id: <1205337877.30117@mailmerge1> ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Mar 12 15:23:38 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2CILCsG017964 for ; Wed, 12 Mar 2008 15:21:12 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2CILC20017962 for obm-l-MllGbsmmN; Wed, 12 Mar 2008 15:21:12 -0300 Received: from fk-out-0910.google.com (fk-out-0910.google.com [209.85.128.187]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2CIL9sG017957 for ; Wed, 12 Mar 2008 15:21:10 -0300 Received: by fk-out-0910.google.com with SMTP id 22so14748687fkq.13 for ; Wed, 12 Mar 2008 11:21:38 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=hk8sM9z0usncirrzj2CqAOmWvJsV2NGq1S4mIZ5n4n4=; b=WYpeFyuN4l5cQNzsLeobwJYOim6uU2Y3lr7fHkHPsKFYQYidFVZabb3gOH0YSt21b5u/0T4FT42T5WXwI2TvL5uYLBI+vwS4C6fkff+l+AIF/3sZHSchEbgopkawaZbApwcWEWGIAt+jPlZndikGrSRYf0Sz8qfIPxr07Bvf4yo= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=ceWqMr74cMLzdQ5pOaCLFKU/px7jwLupuvW6N7/HM1Y4YVo4++xH69nQUsdg7cgew88qI7xO9xW18Ra4LpDjfU7nNYa/tE9joDhYNbrI5nW/4trSWPOj0Qf7sWT/+C642uykSSkISOqvt9HQ4Z47n2rYvhPAHp2lhGtTqKYr4vE= Received: by 10.82.118.2 with SMTP id q2mr20485190buc.27.1205346097234; Wed, 12 Mar 2008 11:21:37 -0700 (PDT) Received: by 10.86.72.6 with HTTP; Wed, 12 Mar 2008 11:21:37 -0700 (PDT) Message-ID: <3bd00efc0803121121pfb6fd86g4ef280fd45131aea@mail.gmail.com> Date: Wed, 12 Mar 2008 15:21:37 -0300 From: "Marcelo Salhab Brogliato" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] SOMA DOS QUADRADOS In-Reply-To: MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_21497_17706175.1205346097232" References: Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Marcelo Salhab Brogliato" X-Spam-Status: No, hits=1.7 required=5.0 tests=AWL,BIG_FONT,IN_REP_TO,LINES_OF_YELLING,MAILTO_LINK, QUOTED_EMAIL_TEXT,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, REFERENCES,SPAM_PHRASE_00_01,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: * ------=_Part_21497_17706175.1205346097232 Content-Type: text/plain; charset=WINDOWS-1252 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Ol=E1 Arkon, x^5 - 5x^3 + 6x =3D 0 x(x^4 - 5x^2 + 6) =3D 0 x(x^2 - 2)(x^2 - 3) =3D 0 raizes: 0, +-sqrt(2) e +-sqrt(3) assim, a soma dos quadrados =E9: 2 + 2 + 3 + 3 =3D 10 abra=E7os, Salhab 2008/3/12 arkon : > *Pessoal algu=E9m poderia me enviar, por favor, a resolu=E7=E3o dessa qu= est=E3o * > > * * > > *(UFPB =96 77) A soma dos quadrados das ra=EDzes da equa=E7=E3o x^5 =96 5= x^3 + 6x =3D > 0 =E9:* > > * * > > *a) 0. b) 10. c) 12. d) 8. e) > 6.* > > * * > > *DESDE J=C1 MUITO OBRIGADO* > ------=_Part_21497_17706175.1205346097232 Content-Type: text/html; charset=WINDOWS-1252 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Ol=E1 Arkon,

x^5 - 5x^3 + 6x =3D 0
x(x^4 - 5x^2 + 6) =3D 0
x(x= ^2 - 2)(x^2 - 3) =3D 0

raizes: 0, +-sqrt(2) e +-sqrt(3)
assim, a = soma dos quadrados =E9: 2 + 2 + 3 + 3 =3D 10

abra=E7os,
Salhab

2008/3/12 arkon <arkon@bol.com.br>:

= Pessoal algu=E9m poderia me enviar, por favo= r, a resolu=E7=E3o dessa quest=E3o

 

= (UFPB =96 77) A soma dos quadrados das ra=ED= zes da equa=E7=E3o x^5 =96 5x^3 + 6x =3D 0 =E9:

 

= a) 0.     &nb= sp;     b) 10.    &nbs= p;      c) 12.    = ;        d) 8.  &= nbsp;          e) 6.

 

= DESDE J=C1 MUITO OBRIGADO<= /p>


------=_Part_21497_17706175.1205346097232-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Mar 12 15:56:31 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2CItCsG020366 for ; Wed, 12 Mar 2008 15:55:12 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2CItBMJ020364 for obm-l-MllGbsmmN; Wed, 12 Mar 2008 15:55:11 -0300 Received: from fg-out-1718.google.com (fg-out-1718.google.com [72.14.220.152]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2CIt7sG020355 for ; Wed, 12 Mar 2008 15:55:10 -0300 Received: by fg-out-1718.google.com with SMTP id e12so9090153fga.3 for ; Wed, 12 Mar 2008 11:55:36 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; bh=pw9pT88dmnWxZVNNR4yUIXuTMsEVW4I68ansugJUHlA=; b=s0COvrssBd8D3uoEgo12veYHkLQi0mwtP2T8A3ybAurWWmAb159QOlY8iavvUqvfzP8pegBTyt4618gzvi2GEKdgCE8EL1SAgUtQhpcGM7MHe5DWeciCJqvu+0eI6+T5wQCVI59FDLNXL5L1ONuRoo4HDvkn3HnHZffSsDmQr1I= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; b=tBQbf+yn9OPAf2LH0YL9yi9WAr8/aSYqHX5anCOaBLAZMdqmsKlju4A0Rtv06kk/0JNPTW/KQcNyLAmfq7jElJGWWCkWbDOhfVxq3oeaKDAtIx/ig0aiXgDbS5ZyCfwBRbJvsKCE1f/SvP3NabytQVBvg4X3MTEvnfqHIwe+Kuc= Received: by 10.82.158.12 with SMTP id g12mr20545308bue.0.1205348135731; Wed, 12 Mar 2008 11:55:35 -0700 (PDT) Received: by 10.82.127.13 with HTTP; Wed, 12 Mar 2008 11:55:35 -0700 (PDT) Message-ID: Date: Wed, 12 Mar 2008 15:55:35 -0300 From: "Johann Peter Gustav Lejeune Dirichlet" To: obm-l@mat.puc-rio.br Subject: =?ISO-8859-1?Q?Re:_[obm-l]_N=FAmeros_de_0_a_100_(series)_+_Fila_Indiana?= In-Reply-To: MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline References: Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m2CItBsG020362 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Johann Peter Gustav Lejeune Dirichlet" X-Spam-Status: No, hits=0.7 required=5.0 tests=AWL,FROM_ENDS_IN_NUMS,IN_REP_TO,REFERENCES, SPAM_PHRASE_00_01,SUPERLONG_LINE,X_MAILING_LIST version=2.44 X-Spam-Level: Em 11/03/08, MauZ escreveu: > 1)Os números de 0 a 100 estão listados em uma ordem qualquer. Mostre que é possível riscar 90 deles de tal forma que os demais fiquem em ordem crescente ou decrescente. > > Consegui um método dessa forma: Pego o primeiro numero > 90 que eu encontrar, depois procuro o proximo tal q a dif seja <= 10, isso deve trazer uma sequencia decrescente. Caso esse método não funcione, o mesmo método invertido (começando do final) trará uma sequencia crescente. Mas não sei se é de fato verdade muito menos consegui provar. > Bem, parece que isto é o mesmo que dizer "Temos uma seqüência de 100 naturais (podemos supor isto sem perda de generalidade). Prove que existem 10 elementos nela que formam uma seqüência crescente ou decrescente." Em vez de apagar 90, escolhe 10! Imagine a seqüência (a_1,a_2,a_3,...,a_100). Para cada a_i, associe a maior seqüência crescente começando por a_i. Se alguma destas seqüências for grande (10 ou mais caras), acabou. Caso contrário, cada seqüência dessas tem tamanho no máximo 9. i ==> (b_i_1,b_i_2,b_i_3,...,b_i_9) A partir daqui, acho que dá pra apliucar um PCP (casa dos pombos) esperto. > 2)Em uma fila indiana as pessoas vêem as cores pintadas nas nucas à sua frente. Há quatro cores possíveis e cada pessoa deve tentar acertar sua própria cor. Qual deve ser a estratégia (combinada entre eles a priori, antes mesmo de serem pintados) para que todos, menos eventualmente um, acertem? > > Esse segundo parece estranho o enunciado... mas pelo que entendi eles não podem falar um monte de coisa, devem apenas tnetar acertar a propria cor. E nada de jogos mortais e arrancar um pedaço da nuca! > > > Agradeço qualquer ajuda, > Maurizio > ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Mar 12 16:02:50 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2CJ1isG020758 for ; Wed, 12 Mar 2008 16:01:44 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2CJ1hmA020756 for obm-l-MllGbsmmN; Wed, 12 Mar 2008 16:01:43 -0300 Received: from fg-out-1718.google.com (fg-out-1718.google.com [72.14.220.157]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2CJ1fsG020724 for ; Wed, 12 Mar 2008 16:01:42 -0300 Received: by fg-out-1718.google.com with SMTP id e12so9092145fga.3 for ; Wed, 12 Mar 2008 12:02:10 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; bh=zwZW+ct1Ecf/TZdcqx/9fhIqzPOmQah6IfJkhcHVc5M=; b=O8WQRJz5qP8u80W54nvWagLAZik4i5HhPUvvOYsGxomDhZDZ7PiGhYO6zagLDSVhCk7jQ7R5E4l7gyTIGGsXnoCjD4rGITqIDHn98fJQUzkxk6fkeRrIQzKgWMrmT+XJs3LJkLyVA45+BkOR02jCK7thtEjzC2QBENtEjZqX5mM= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; b=MINlCZ3ZzYkfjSUfFMoSrwRI40Zh31eGqSk7mvonjHNbxDkJVYRaiFbmHDfnIgyK2JdNAbAyIUjUmy46shU5fI55rxKzoFMIOSl4kxneeFl9sA32eZ+0tXyZ9ZjbWkQNxIsjfOY/7HduZual59Lvv8amm0/ff9096Wqo0ZaXGBY= Received: by 10.82.138.6 with SMTP id l6mr20564575bud.35.1205348530182; Wed, 12 Mar 2008 12:02:10 -0700 (PDT) Received: by 10.82.127.13 with HTTP; Wed, 12 Mar 2008 12:02:10 -0700 (PDT) Message-ID: Date: Wed, 12 Mar 2008 16:02:10 -0300 From: "Johann Peter Gustav Lejeune Dirichlet" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] SOMA DOS QUADRADOS In-Reply-To: <3bd00efc0803121121pfb6fd86g4ef280fd45131aea@mail.gmail.com> MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline References: <3bd00efc0803121121pfb6fd86g4ef280fd45131aea@mail.gmail.com> Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m2CJ1hsG020754 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Johann Peter Gustav Lejeune Dirichlet" X-Spam-Status: No, hits=0.6 required=5.0 tests=AWL,FROM_ENDS_IN_NUMS,IN_REP_TO,REFERENCES, SPAM_PHRASE_00_01,X_MAILING_LIST version=2.44 X-Spam-Level: Em 12/03/08, Marcelo Salhab Brogliato escreveu: > Olá Arkon, > > x^5 - 5x^3 + 6x = 0 Podemos excluir a raiz nula. Ela não altera o resultado. x^4-5x^2+6=0 Se as raizes sao a,b,c,d, temos a+b+c+d=0 ab+ac+ad+bc+bd+cd=-5 abc+abd+acd+bcd=0 abcd=6 Temos a^2+b^2+c^2+d^2=(a+b)^2-2ab+(c+d)^2-2cd=((a+b)^2+(c+d)^2)-2(ab+cd)= ((a+b+c+d)^2-2(a+b)(c+d))-2(ab+cd)=(a+b+c+d)^2-2(ab+ac+ad+bc+bd+cd)=0-2*(-5)=10 ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Mar 12 16:04:59 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2CJ43sG021017 for ; Wed, 12 Mar 2008 16:04:03 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2CJ4329021015 for obm-l-MllGbsmmN; Wed, 12 Mar 2008 16:04:03 -0300 Received: from fk-out-0910.google.com (fk-out-0910.google.com [209.85.128.186]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2CJ40sG020998 for ; Wed, 12 Mar 2008 16:04:01 -0300 Received: by fk-out-0910.google.com with SMTP id 22so14765739fkq.13 for ; Wed, 12 Mar 2008 12:04:29 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; bh=2CiWlhBWJOUDRMaB9SLbSUqGkkK48hz9CG3yh4hj0WU=; b=Bi/jtRHqRDfX/pAum9wpBXv1b+zL+YHYm0+ZOxLC4olHDsIsTpFsEDzOpyAyOLSx9Fs9quWSzG0ARhDlHab/H+V6A4uruqt/JY0crhJkct4yJNdDwJtwxuKEH3gg8PaZ2OXoEaHknn+AIZWGs+kVRvgULtcH6PAYJ4PoONiYoFM= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; b=VyYwvE3NhxzQwFX6l0DG0Vv9ZexvjWfgdSshPucDGaUQZv6gAX8L6ew10anVz+cYUYxj6zqjXUj+Z5ofs/nCBd0ZlmXSaOooOwZGmjjKFzTqP6OMhjsd1AmKTA0FVk5bHHPmgdOOIaJX4h/YRGBowLxTE+sfUUyz5R5+hVwDc/w= Received: by 10.82.149.8 with SMTP id w8mr20552507bud.29.1205348668841; Wed, 12 Mar 2008 12:04:28 -0700 (PDT) Received: by 10.82.127.13 with HTTP; Wed, 12 Mar 2008 12:04:28 -0700 (PDT) Message-ID: Date: Wed, 12 Mar 2008 16:04:28 -0300 From: "Johann Peter Gustav Lejeune Dirichlet" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Matrizes In-Reply-To: <777121.90323.qm@web37014.mail.mud.yahoo.com> MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline References: <777121.90323.qm@web37014.mail.mud.yahoo.com> Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m2CJ42sG021005 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Johann Peter Gustav Lejeune Dirichlet" X-Spam-Status: No, hits=2.6 required=5.0 tests=AWL,FROM_ENDS_IN_NUMS,IN_REP_TO,QUOTED_EMAIL_TEXT, RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,REFERENCES, SIGNATURE_LONG_SPARSE,SPAM_PHRASE_00_01,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: ** Em 12/03/08, Bruno Carvalho escreveu: > Oi Pessoal, > > Peço ajuda ( orientação) na demonstração da seguinte afirmação sobre > matrizes. > Sejam T matriz nxn ; J matriz n x1 e M matriz nx1. Prove que se T possui > uma inversa então TJ tem uma única solução. > TJ é alguma equação? Bem, se for algo como TX=J, podemos pensar assim: TX=J se e só se T^-1*TX=T^-1J se e só se X=T^-1J. E fim! > Obrigado > > Bruno > > ________________________________ > Abra sua conta no Yahoo! Mail, o único sem limite de espaço para > armazenamento! > > -- Ideas are bulletproof. V ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Mar 12 16:16:56 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2CIx2sG020541 for ; Wed, 12 Mar 2008 15:59:03 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2CIwnla020512 for obm-l-MllGbsmmN; Wed, 12 Mar 2008 15:58:49 -0300 Received: from colorado.uspnet.usp.br (colorado.uspnet.usp.br [143.107.254.72]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2CIw1sG020467 for ; Wed, 12 Mar 2008 15:58:07 -0300 Received: (qmail 24815 invoked from network); 12 Mar 2008 18:58:30 -0000 X-Mail-Scanner: Scanned by qSheff-II-2.1-r1 (http://www.enderunix.org/qsheff/) Received: from negev.uspnet.usp.br (HELO localhost) ([143.107.254.65]) (envelope-sender ) by colorado.uspnet.usp.br (qmail-ldap-1.03) with SMTP for ; 12 Mar 2008 18:58:30 -0000 Received: from 192.168.240.1 (192.168.240.1 [192.168.240.1]) by webmail.usp.br (Horde MIME library) with HTTP; Wed, 12 Mar 2008 15:58:30 -0300 Message-ID: <20080312155830.qhihy7jio0wkwgcg@webmail.usp.br> Date: Wed, 12 Mar 2008 15:58:30 -0300 From: Arlane Manoel S Silva To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] SOMA DOS QUADRADOS References: In-Reply-To: MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1; DelSp="Yes"; format="flowed" Content-Disposition: inline User-Agent: Internet Messaging Program (IMP) H3 (4.1.5-cvs) Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m2CIwRsG020492 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Arlane Manoel S Silva X-Spam-Status: No, hits=2.3 required=5.0 tests=AWL,IN_REP_TO,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SIGNATURE_LONG_SPARSE, SPAM_PHRASE_00_01,USER_AGENT,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: ** Uma das raízes é 0. Logo basta olhar para x^4-5x^2+6=(x^2-2)(x^2-3)=0. Citando arkon : > Pessoal alguém poderia me enviar, por favor, a resolução dessa questão > > (UFPB – 77) A soma dos quadrados das raízes da equação x^5 – 5x^3 + 6x = 0 é: > > a) 0. b) 10. c) 12. d) 8. e) 6. > > DESDE JÁ MUITO OBRIGADO > -- Arlane Manoel S Silva MAT-IME-USP ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Mar 12 19:58:48 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2CMvDsG004669 for ; Wed, 12 Mar 2008 19:57:13 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2CMvDmW004666 for obm-l-MllGbsmmN; Wed, 12 Mar 2008 19:57:13 -0300 Received: from wr-out-0506.google.com (wr-out-0506.google.com [64.233.184.235]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2CMvAsG004656 for ; Wed, 12 Mar 2008 19:57:11 -0300 Received: by wr-out-0506.google.com with SMTP id c30so2217048wra.21 for ; Wed, 12 Mar 2008 15:57:39 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=VE7QxM5rV3u4gx6paPEhlO4xJtjGheV4zq5IgimrQ3s=; b=vj2/hR+iANeXhmKYqxdQDnKoTbZiPgQCWkNuAZZSQ4p1GCmv1cbJbavdgx23cwY6DwJspvVYeCD8ZWZLQZz9wl3nThwg0d8Gs97FjZMNhtC3vnuxNFJ8V1kGDaz1yKbsa8XLnlggnn6cMrLmurBK48Lp4dHWPs65iNT/BnS1550= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=tZDTVQYvlj0dnEGUmG2JL1yHFYqX40n1J1wZ4RbHQ5t4hKqASqCG8BUNOvfrG7Ag9fTjE1KA+dkqwFr+fNTwUPz3Zkyj7z3/g3UUccW2WnVywrb8bWzQK+yBzrCmRieCMlqFpw9KcDIDCr2WFA73r5E0d8RrKE7u6UWZGZTvZ1k= Received: by 10.114.132.5 with SMTP id f5mr8078129wad.50.1205362658791; Wed, 12 Mar 2008 15:57:38 -0700 (PDT) Received: by 10.114.88.8 with HTTP; Wed, 12 Mar 2008 15:57:38 -0700 (PDT) Message-ID: Date: Wed, 12 Mar 2008 19:57:38 -0300 From: MauZ To: obm-l@mat.puc-rio.br Subject: [SPAM] =?ISO-8859-1?Q?Re:_[obm-l]_N=FAmeros_de_0_a_100_(series)_+_Fila_Indiana?= In-Reply-To: MIME-Version: 1.0 Content-Type: text/plain References: Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: MauZ X-Spam-Status: Yes, hits=5.5 required=5.0 tests=AWL,IN_REP_TO,MAILTO_LINK,MAILTO_TO_SPAM_ADDR, MIME_EXCESSIVE_QP,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ***** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_Part_19109_22601804.1205362658783" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (5.50 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: REFERENCES (-0.5 points) Has a valid-looking References header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: QUOTED_EMAIL_TEXT (-0.8 points) BODY: Contains what looks like a quoted email text SPAM: MAILTO_LINK (0.2 points) BODY: Includes a URL link to send an email SPAM: MIME_EXCESSIVE_QP (1.0 points) RAW: Excessive quoted-printable encoding in body SPAM: MAILTO_TO_SPAM_ADDR (0.7 points) URI: Includes a link to a likely spammer email address SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 235.184.233.64.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 235.184.233.64.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-0.1 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- ------=_Part_19109_22601804.1205362658783 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Em 12/03/08, Johann Peter Gustav Lejeune Dirichlet < peterdirichlet2003@gmail.com> escreveu: > > Em 11/03/08, MauZ escreveu: > > > 1)Os n=FAmeros de 0 a 100 est=E3o listados em uma ordem qualquer. Mostr= e que > =E9 poss=EDvel riscar 90 deles de tal forma que os demais fiquem em ordem > crescente ou decrescente. > > > > Consegui um m=E9todo dessa forma: Pego o primeiro numero > 90 que eu > encontrar, depois procuro o proximo tal q a dif seja <=3D 10, isso deve t= razer > uma sequencia decrescente. Caso esse m=E9todo n=E3o funcione, o mesmo m= =E9todo > invertido (come=E7ando do final) trar=E1 uma sequencia crescente. Mas n= =E3o sei se > =E9 de fato verdade muito menos consegui provar. > > > > > Bem, parece que isto =E9 o mesmo que dizer > > "Temos uma seq=FC=EAncia de 100 naturais (podemos supor isto sem perda de > generalidade). > Prove que existem 10 elementos nela que formam uma seq=FC=EAncia crescent= e > ou decrescente." Em vez de apagar 90, escolhe 10! > > Imagine a seq=FC=EAncia (a_1,a_2,a_3,...,a_100). Para cada a_i, associe a > maior seq=FC=EAncia crescente come=E7ando por a_i. Se alguma destas > seq=FC=EAncias for grande (10 ou mais caras), acabou. Caso contr=E1rio, c= ada > seq=FC=EAncia dessas tem tamanho no m=E1ximo 9. > > i =3D=3D> (b_i_1,b_i_2,b_i_3,...,b_i_9) > > A partir daqui, acho que d=E1 pra apliucar um PCP (casa dos pombos) esper= to. Cara, Sinceramente eu achei sua ideia muito interessante. Mas como eu formalizo essa ideia? eu tenho muita dificildade em formalizar = a matem=E1tica! Eu to pensando pelo PCP e to quase entendendo pq funciona. mas se vc puder dar mais um empurr=E3ozinho eu agrade=E7o Abra=E7os, Maurizio > 2)Em uma fila indiana as pessoas v=EAem as cores pintadas nas nucas =E0 s= ua > frente. H=E1 quatro cores poss=EDveis e cada pessoa deve tentar acertar s= ua > pr=F3pria cor. Qual deve ser a estrat=E9gia (combinada entre eles a prior= i, > antes mesmo de serem pintados) para que todos, menos eventualmente um, > acertem? > > > > Esse segundo parece estranho o enunciado... mas pelo que entendi eles > n=E3o podem falar um monte de coisa, devem apenas tnetar acertar a propri= a > cor. E nada de jogos mortais e arrancar um peda=E7o da nuca! > > > > > > Agrade=E7o qualquer ajuda, > > Maurizio > > > > > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > Instru=E7=F5es para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > ------=_Part_19109_22601804.1205362658783 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline


------=_Part_19109_22601804.1205362658783-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Mar 13 00:05:38 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2D340sG027029 for ; Thu, 13 Mar 2008 00:04:00 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2D340vg027026 for obm-l-MllGbsmmN; Thu, 13 Mar 2008 00:04:00 -0300 Received: from wa-out-1112.google.com (wa-out-1112.google.com [209.85.146.176]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2D33vsG027008 for ; Thu, 13 Mar 2008 00:03:58 -0300 Received: by wa-out-1112.google.com with SMTP id m28so3895332wag.13 for ; Wed, 12 Mar 2008 20:04:26 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:mime-version:content-type:content-transfer-encoding:content-disposition; bh=kAizrhKVeOLPaX2xEZyOquTiUlJVHPijkY+XVifdtfo=; b=Wv5APgPuBCBYVZYNO8g2du2rF2soT/kBiY+8L+SPfqA8QLCBnCSaUMV0nGxkaWbn15uRk1aakMRiWtJ4XLhuPtw9U6FSQblrfRF+kf0d0QMZLtLOgwi1hYf/HuQNgHTgun+0yvDN9+1RMeD8ihoPmh4+XZgZdx6htXvcvgSbxtw= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:mime-version:content-type:content-transfer-encoding:content-disposition; b=LI1/hXeqpUYaB+gha4A0A6jy9SI43s2jKYO+38X1asNdhUr1ZM0a5BDMKpYJJdsugE52ry3sCvpq+4xkaUrmM7zQUV4h9ae6pmvYLAi+UQL4IxZQ9qqWQyYOq59hyn3mfpYko4ehdQDZglBXBMGkQn4m05SSOAYqSSBGPgtT7so= Received: by 10.115.88.1 with SMTP id q1mr8431870wal.64.1205377465855; Wed, 12 Mar 2008 20:04:25 -0700 (PDT) Received: by 10.114.146.4 with HTTP; Wed, 12 Mar 2008 20:04:25 -0700 (PDT) Message-ID: <1f424590803122004y72984a15i322dfbc3a2cedc5d@mail.gmail.com> Date: Thu, 13 Mar 2008 00:04:25 -0300 From: "Luiz Rodrigues" To: obm-l@mat.puc-rio.br Subject: [SPAM] [obm-l] =?ISO-8859-1?Q?Olimp=EDadas?= MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline Content-Transfer-Encoding: 7bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m2D33xsG027020 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Luiz Rodrigues" X-Spam-Status: Yes, hits=5.3 required=5.0 tests=AWL,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ***** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (5.30 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 176.146.85.209.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 176.146.85.209.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-0.5 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- Olá pessoal!!! Tudo bem??? Vou preparar alguns alunos do Ensino Fundamental II (antigo Ensino Fundamental) para as Olimpíadas Brasileiras. Meu problema é: que livros utilizar? Alguém poderia me indicar alguns? Abraço para todos!!! Luiz. ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Mar 13 11:55:25 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2DErZsG031607 for ; Thu, 13 Mar 2008 11:53:35 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2DErZ3w031605 for obm-l-MllGbsmmN; Thu, 13 Mar 2008 11:53:35 -0300 Received: from wa-out-1112.google.com (wa-out-1112.google.com [209.85.146.182]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2DErXsG031600 for ; Thu, 13 Mar 2008 11:53:33 -0300 Received: by wa-out-1112.google.com with SMTP id m28so4184772wag.13 for ; Thu, 13 Mar 2008 07:54:02 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:mime-version:content-type; bh=KpJq185XcjpJSbQR38SYmEDFKu/IkXmdghKtDmZMhMs=; b=ivzm90RZvc3F73zqTmm/RWyDZzXswTGrlkcRSY5amV/qTHOcqKKudG1XKmHGMmWhjSws5v+t2Aj7bu9LXl+KKSbGa5WdPupAZWMVO3nZSpKOnW9/2XaWgaohh5sTqm84sRYqK4+haZ9jrGj4o1ghOUBzPSqZylwUnzbPEeIt+PA= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:mime-version:content-type; b=a9kAsOzHa5u5LPSldzzBldk9JblFRuZSwvCefPJrpR5Jgh6553p36/MLoCBJFhweRkofwADGHlnw7N/dT3uc49sg1fDDGKF9Eh0ioWe08vSOhadOQpQRiCciiHnzTROmnbPfFfdsH2kI84S6++FHTLFqGuNtCXLrTLEW0jh4rv0= Received: by 10.114.81.1 with SMTP id e1mr9505532wab.11.1205420042308; Thu, 13 Mar 2008 07:54:02 -0700 (PDT) Received: by 10.114.178.9 with HTTP; Thu, 13 Mar 2008 07:54:00 -0700 (PDT) Message-ID: Date: Thu, 13 Mar 2008 11:54:00 -0300 From: "Thelio Gama" To: obm-l@mat.puc-rio.br Subject: [obm-l] combinatoria dificil MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_17066_15547514.1205420042314" Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Thelio Gama" X-Spam-Status: No, hits=3.1 required=5.0 tests=AWL,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: *** ------=_Part_17066_15547514.1205420042314 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline =C9 pessoal... Achei muito dif=EDcil esta quest=E3o. Agrade=E7o se algu=E9m puder explic= =E1-la. Thelio uma turma tem aulas =E0s 2=AA, 4=AA e 6=AA feiras, de 8-9 horas e de 11-12 = horas. As mat=E9rias s=E3o portugues, matem=E1tica e ingles, cada uma com duas aulas semanais, em dias diferentes. De quantos modos pode ser feito o hor=E1rio dessa turma? a)96 ; b) 144 ; c)192 ; d) 6! ; e) 120 ------=_Part_17066_15547514.1205420042314 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline
=C9 pessoal...
 
Achei muito dif=EDcil esta quest=E3o. Agrade=E7o se algu=E9m puder exp= lic=E1-la.
 
Thelio
 
uma turma tem aulas =E0s 2=AA, 4=AA e 6=AA feiras, de 8-9 horas e de 1= 1-12 horas. As mat=E9rias s=E3o portugues, matem=E1tica e ingles, cada uma = com duas aulas semanais, em dias diferentes. De quantos modos pode ser feit= o o hor=E1rio dessa turma?
a)96  ; b) 144   ; c)192   ; d) 6!  = ;  ; e) 120
------=_Part_17066_15547514.1205420042314-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Mar 13 16:35:05 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2DJX6sG021246 for ; Thu, 13 Mar 2008 16:33:07 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2DJX6Ml021243 for obm-l-MllGbsmmN; Thu, 13 Mar 2008 16:33:06 -0300 Received: from gama-rt.urisan.tche.br (smtp.san.uri.br [200.203.104.150]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2DJX1sG021178 for ; Thu, 13 Mar 2008 16:33:04 -0300 Received: from www.urisan.tche.br (localhost [127.0.0.1]) by gama-rt.urisan.tche.br (Postfix) with ESMTP id 10D08174403 for ; Thu, 13 Mar 2008 16:33:39 -0300 (BRT) Received: from 10.1.1.189 by www.urisan.tche.br with HTTP; Thu, 13 Mar 2008 16:33:39 -0300 (BRT) Message-ID: <1114.10.1.1.189.1205436819.squirrel@www.urisan.tche.br> In-Reply-To: <1f424590803122004y72984a15i322dfbc3a2cedc5d@mail.gmail.com> References: <1f424590803122004y72984a15i322dfbc3a2cedc5d@mail.gmail.com> Date: Thu, 13 Mar 2008 16:33:39 -0300 (BRT) Subject: [SPAM] Re: [obm-l] =?iso-8859-1?Q?Olimp=EDadas?= From: rbdantas@urisan.tche.br To: obm-l@mat.puc-rio.br User-Agent: SquirrelMail/1.4.6 MIME-Version: 1.0 Content-Type: text/plain;charset=iso-8859-1 Content-Transfer-Encoding: 7bit X-Priority: 3 (Normal) Importance: Normal Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: rbdantas@urisan.tche.br X-Spam-Status: Yes, hits=5.5 required=5.0 tests=IN_REP_TO,NO_REAL_NAME,PRIORITY_NO_NAME,QUOTED_EMAIL_TEXT, RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,REFERENCES, SPAM_PHRASE_00_01,USER_AGENT,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ***** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (5.50 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: REFERENCES (-0.5 points) Has a valid-looking References header SPAM: USER_AGENT (-0.5 points) Found a User-Agent header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: NO_REAL_NAME (1.3 points) From: does not include a real name SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: QUOTED_EMAIL_TEXT (-0.8 points) BODY: Contains what looks like a quoted email text SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 150.104.203.200.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 150.104.203.200.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: PRIORITY_NO_NAME (1.0 points) Message has priority setting, but no X-Mailer SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- > Ola Luiz, Um bom inicio seria pela coleção de revistas Eureka editados pela SBM que tem a vantagem de poder baixar de graça pela net. Se vc tiver sorte de encontrar algum livro publicado pela editora MIR sobre esse assunto em algum sebo seria muito bom. Abs. Rivaldo Olá pessoal!!! > Tudo bem??? > Vou preparar alguns alunos do Ensino Fundamental II (antigo Ensino > Fundamental) para as Olimpíadas Brasileiras. > Meu problema é: que livros utilizar? > Alguém poderia me indicar alguns? > Abraço para todos!!! > Luiz. > > ========================================================================= > Instruções para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > ========================================================================= > ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Mar 13 16:49:32 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2DJmJsG025315 for ; Thu, 13 Mar 2008 16:48:20 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2DJmHJ5025313 for obm-l-MllGbsmmN; Thu, 13 Mar 2008 16:48:17 -0300 Received: from el-out-1112.google.com (el-out-1112.google.com [209.85.162.183]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2DJlwsG025256 for ; Thu, 13 Mar 2008 16:48:01 -0300 Received: by el-out-1112.google.com with SMTP id o28so2319255ele.3 for ; Thu, 13 Mar 2008 12:48:27 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=15wD41IY3e1lokp4JNusp6OEu5CRYSuQ5ICJMCnowak=; b=jGrvfJ/iRL1bM92ateacYnmuCyanv4xDrgyY0/8eW7WRhyiTp8oiUehFGqzpeZTe+NQ/C6W4maTz6FS1inkgQRwPWjEHTFN4nsL3sCSDBQeGPZAkSmz1jSbmT2CzDYMhFSMZo6yOvkOaxGJcyBVNbUJ9g/EGQ7wFkBVKJhCbb1Q= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=my6i72Iz/lDbmMv6XtMqFY5I65obKF0zl4OQS6jqI85bDcMV6Uqd5O/VlhvdiZgipJ9Q1TdSruxu8SCe1hucQCENYjF/ETDGO5eRr99oJvxv3ddxqC/w1VJFZeCtB6qfODFPGi5ONAP15S4CXhcwee8glMEXXLKY97rznRd5WtY= Received: by 10.114.254.1 with SMTP id b1mr10226332wai.132.1205437704256; Thu, 13 Mar 2008 12:48:24 -0700 (PDT) Received: by 10.114.158.9 with HTTP; Thu, 13 Mar 2008 12:48:24 -0700 (PDT) Message-ID: <3bd00efc0803131248q46972f7y69079b676edd6341@mail.gmail.com> Date: Thu, 13 Mar 2008 16:48:24 -0300 From: "Marcelo Salhab Brogliato" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] combinatoria dificil In-Reply-To: MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_18964_4768995.1205437704252" References: Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Marcelo Salhab Brogliato" X-Spam-Status: No, hits=3.6 required=5.0 tests=AWL,IN_REP_TO,MAILTO_LINK,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: *** ------=_Part_18964_4768995.1205437704252 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Ol=E1 Thelio, Temos 3 mat=E9rias, cada uma com 2 aulas semanais em dias diferentes, e 3 dias. Para o primeiro dia, vamos escolher 2 das 3 mat=E9rias: 3*2 =3D 6 modos Para o segundo dia, s=F3 podemos repetir uma mat=E9ria, portanto temos: 2(d= evido a ordem)*2*1 =3D 4 modos Para o terceiro dia, as mat=E9rias j=E1 est=E3o determinadas, temos apenas = a ordem, portanto: 2 modos assim, temos: 6*4*2 =3D 48 modos mas n=E3o tem alternativa.. ent=E3o devo ter errado. Vamos aguardar algu=E9m me corrigir ;) abra=E7os, Salhab 2008/3/13 Thelio Gama : > =C9 pessoal... > > Achei muito dif=EDcil esta quest=E3o. Agrade=E7o se algu=E9m puder explic= =E1-la. > > Thelio > > uma turma tem aulas =E0s 2=AA, 4=AA e 6=AA feiras, de 8-9 horas e de 11-1= 2 horas. > As mat=E9rias s=E3o portugues, matem=E1tica e ingles, cada uma com duas a= ulas > semanais, em dias diferentes. De quantos modos pode ser feito o hor=E1rio > dessa turma? > a)96 ; b) 144 ; c)192 ; d) 6! ; e) 120 > ------=_Part_18964_4768995.1205437704252 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Ol=E1 Thelio,

Temos 3 mat=E9rias, cada uma com 2 aulas semanais em d= ias diferentes, e 3 dias.
Para o primeiro dia, vamos escolher 2 das 3 ma= t=E9rias: 3*2 =3D 6 modos
Para o segundo dia, s=F3 podemos repetir uma m= at=E9ria, portanto temos: 2(devido a ordem)*2*1 =3D 4 modos
Para o terceiro dia, as mat=E9rias j=E1 est=E3o determinadas, temos apenas = a ordem, portanto: 2 modos

assim, temos: 6*4*2 =3D 48 modos
mas n= =E3o tem alternativa.. ent=E3o devo ter errado.
Vamos aguardar algu=E9m = me corrigir ;)

abra=E7os,
Salhab


2008/3/13 Th= elio Gama <teliogama@gmail.com>:
=C9 pessoal...
 
Achei muito dif=EDcil esta quest=E3o. Agrade=E7o se algu=E9m puder exp= lic=E1-la.
 
Thelio
 
uma turma tem aulas =E0s 2=AA, 4=AA e 6=AA feiras, de 8-9 horas e de 1= 1-12 horas. As mat=E9rias s=E3o portugues, matem=E1tica e ingles, cada uma = com duas aulas semanais, em dias diferentes. De quantos modos pode ser feit= o o hor=E1rio dessa turma?
a)96  ; b) 144   ; c)192   ; d) 6!  = ;  ; e) 120

------=_Part_18964_4768995.1205437704252-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Mar 13 18:42:08 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2DLejsG003668 for ; Thu, 13 Mar 2008 18:40:45 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2DLejxC003666 for obm-l-MllGbsmmN; Thu, 13 Mar 2008 18:40:45 -0300 Received: from mx1.dglnet.com.br (mx1.dglnet.com.br [201.76.39.219]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2DLeisG003663 for ; Thu, 13 Mar 2008 18:40:44 -0300 Received: from Rafael (unknown [201.82.46.164]) (Authenticated sender: rafaelcano@dglnet.com.br) by mx1.dglnet.com.br (Postfix) with ESMTP id 10A491EBC527 for ; Thu, 13 Mar 2008 18:41:15 -0300 (BRT) Message-ID: <002b01c88553$d9e7b540$e600a8c0@Rafael> From: "Rafael Cano" To: References: <3bd00efc0803131248q46972f7y69079b676edd6341@mail.gmail.com> Subject: [SPAM] Re: [obm-l] combinatoria dificil Date: Thu, 13 Mar 2008 18:47:36 -0300 MIME-Version: 1.0 Content-Type: text/plain X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2900.3138 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.3198 X-Antivirus: avast! (VPS 080313-0, 13/03/2008), Outbound message X-Antivirus-Status: Clean Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Rafael Cano" X-Spam-Status: Yes, hits=5.9 required=5.0 tests=AWL,MAILTO_LINK,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, REFERENCES,SPAM_PHRASE_00_01,SUPERLONG_LINE,USER_AGENT_OE, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ***** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_NextPart_000_0028_01C8853A.B4555DF0" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (5.90 hits, 5 required) SPAM: REFERENCES (-0.5 points) Has a valid-looking References header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: USER_AGENT_OE (0.2 points) X-Mailer header indicates a non-spam MUA (Outlook Express) SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: MAILTO_LINK (0.2 points) BODY: Includes a URL link to send an email SPAM: SUPERLONG_LINE (0.0 points) BODY: Contains a line >=199 characters long SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 219.39.76.201.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 219.39.76.201.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (0.2 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- This is a multi-part message in MIME format. ------=_NextPart_000_0028_01C8853A.B4555DF0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Ol=E1, Salhab, eu n=E3o consegui encontrar nenhum erro na sua solu=E7=E3o. Na = verdade eu consegui resolver de outra forma e cheguei no mesmo = resultado. Como nenhuma mat=E9ria pode repetir no mesmo dia ent=E3o = obrigatoriamente nos 3 dias os tr=EAs pares t=EAm que aparecer (vou = chamar de A, B, C pra ficar mais f=E1cil): (A,B), (B,C) e (C,A). Veja = que h=E1 3!=3D6 formas de escolher os pares para cada dia e em cada dia = podemos inverter a ordem das mat=E9rias, ou seja, h=E1 6 formas de = escolher em qual dia fica cada par e 2 formas de organizar as mat=E9rias = por dia. Logo: 6*2*2*2=3D48. Abra=E7os ----- Original Message -----=20 From: Marcelo Salhab Brogliato=20 To: obm-l@mat.puc-rio.br=20 Sent: Thursday, March 13, 2008 4:48 PM Subject: Re: [obm-l] combinatoria dificil Ol=E1 Thelio, Temos 3 mat=E9rias, cada uma com 2 aulas semanais em dias diferentes, = e 3 dias. Para o primeiro dia, vamos escolher 2 das 3 mat=E9rias: 3*2 =3D 6 = modos Para o segundo dia, s=F3 podemos repetir uma mat=E9ria, portanto = temos: 2(devido a ordem)*2*1 =3D 4 modos Para o terceiro dia, as mat=E9rias j=E1 est=E3o determinadas, temos = apenas a ordem, portanto: 2 modos assim, temos: 6*4*2 =3D 48 modos mas n=E3o tem alternativa.. ent=E3o devo ter errado. Vamos aguardar algu=E9m me corrigir ;) abra=E7os, Salhab 2008/3/13 Thelio Gama : =C9 pessoal... Achei muito dif=EDcil esta quest=E3o. Agrade=E7o se algu=E9m puder = explic=E1-la. Thelio uma turma tem aulas =E0s 2=AA, 4=AA e 6=AA feiras, de 8-9 horas e de = 11-12 horas. As mat=E9rias s=E3o portugues, matem=E1tica e ingles, cada = uma com duas aulas semanais, em dias diferentes. De quantos modos pode = ser feito o hor=E1rio dessa turma?=20 a)96 ; b) 144 ; c)192 ; d) 6! ; e) 120 ------=_NextPart_000_0028_01C8853A.B4555DF0 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable
Ol=E1,
Salhab, eu n=E3o consegui encontrar = nenhum erro na=20 sua solu=E7=E3o. Na verdade eu consegui resolver de outra forma e = cheguei no mesmo=20 resultado.
Como nenhuma mat=E9ria pode repetir no = mesmo dia=20 ent=E3o obrigatoriamente nos 3 dias os tr=EAs pares t=EAm que aparecer = (vou chamar de=20 A, B, C pra ficar mais f=E1cil): (A,B), (B,C) e (C,A). Veja que h=E1 = 3!=3D6 formas de=20 escolher os pares para cada dia e em cada dia podemos inverter a = ordem das=20 mat=E9rias, ou seja, h=E1 6 formas de escolher em qual dia fica = cada par e 2=20 formas de organizar as mat=E9rias por dia. Logo: = 6*2*2*2=3D48.
 
Abra=E7os
 
----- Original Message -----
From:=20 Marcelo Salhab=20 Brogliato
Em 12/03/08, Johann Peter Gustav Lejeune Dirichlet <peterdirichlet2003@gmail.com> escreveu:<= /span>
Em 11/03/08, MauZ <mauz.mat= ematica@gmail.com> escreveu:

> 1)Os n=FAmeros de 0 a 100 = est=E3o listados em uma ordem qualquer. Mostre que =E9 poss=EDvel riscar 90= deles de tal forma que os demais fiquem em ordem crescente ou decrescente.=
>
> Consegui um m=E9todo dessa forma: Pego o primeiro numero >= ; 90 que eu encontrar, depois procuro o proximo tal q a dif seja <=3D 10= , isso deve trazer uma sequencia decrescente. Caso esse m=E9todo n=E3o func= ione, o mesmo m=E9todo invertido (come=E7ando do final) trar=E1 uma sequenc= ia crescente. Mas n=E3o sei se =E9 de fato verdade muito menos consegui pro= var.
>


Bem, parece que isto =E9 o mesmo que dizer

&quo= t;Temos uma seq=FC=EAncia de 100 naturais (podemos supor isto sem perda de<= br> generalidade).
Prove que existem 10 elementos nela que formam uma s= eq=FC=EAncia crescente
ou decrescente." Em vez de apagar 90, escolhe 10!

Imagine a = seq=FC=EAncia (a_1,a_2,a_3,...,a_100). Para cada a_i, associe a
maior s= eq=FC=EAncia crescente come=E7ando por a_i. Se alguma destas
seq=FC=EAn= cias for grande (10 ou mais caras), acabou. Caso contr=E1rio, cada
seq=FC=EAncia dessas tem tamanho no m=E1ximo 9.

i =3D=3D> (b_i= _1,b_i_2,b_i_3,...,b_i_9)

A partir daqui, acho que d=E1 pra apliuc= ar um PCP (casa dos pombos) esperto.

Cara,

Sinc= eramente eu achei sua ideia muito interessante.
Mas como eu formalizo essa ideia? eu tenho muita dificildade em formalizar = a matem=E1tica!

Eu to pensando pelo PCP e to quase entendendo pq fun= ciona. mas se vc puder dar mais um empurr=E3ozinho eu agrade=E7o

Abr= a=E7os,
Maurizio

> 2)Em uma fila indiana as pessoas v=EAem as cores pintadas nas nu= cas =E0 sua frente. H=E1 quatro cores poss=EDveis e cada pessoa deve tentar= acertar sua pr=F3pria cor. Qual deve ser a estrat=E9gia (combinada entre e= les a priori, antes mesmo de serem pintados) para que todos, menos eventual= mente um, acertem?
>
> Esse segundo parece estranho o enunciado... mas pelo que ent= endi eles n=E3o podem falar um monte de coisa, devem apenas tnetar acertar = a propria cor. E nada de jogos mortais e arrancar um peda=E7o da nuca!
= >
>
> Agrade=E7o qualquer ajuda,
>  Maurizio
= >


=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D
Instru=E7=F5es para entrar na lista, sair da lista e usar = a lista em
http://www.mat= .puc-rio.br/~obmlistas/obm-l.html
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D
Sent: Thursday, March 13, 2008 = 4:48=20 PM
Subject: Re: [obm-l] = combinatoria=20 dificil

Ol=E1 Thelio,

Temos 3 mat=E9rias, cada uma com 2 = aulas=20 semanais em dias diferentes, e 3 dias.
Para o primeiro dia, vamos = escolher=20 2 das 3 mat=E9rias: 3*2 =3D 6 modos
Para o segundo dia, s=F3 = podemos repetir uma=20 mat=E9ria, portanto temos: 2(devido a ordem)*2*1 =3D 4 modos
Para o = terceiro=20 dia, as mat=E9rias j=E1 est=E3o determinadas, temos apenas a ordem, = portanto: 2=20 modos

assim, temos: 6*4*2 =3D 48 modos
mas n=E3o tem = alternativa.. ent=E3o=20 devo ter errado.
Vamos aguardar algu=E9m me corrigir=20 ;)

abra=E7os,
Salhab


2008/3/13 Thelio Gama <teliogama@gmail.com>:
=C9 pessoal...
 
Achei muito dif=EDcil esta quest=E3o. Agrade=E7o se algu=E9m = puder=20 explic=E1-la.
 
Thelio
 
uma turma tem aulas =E0s 2=AA, 4=AA e 6=AA feiras, de 8-9 horas = e de 11-12=20 horas. As mat=E9rias s=E3o portugues, matem=E1tica e ingles, cada = uma com duas=20 aulas semanais, em dias diferentes. De quantos modos pode ser feito = o=20 hor=E1rio dessa turma?
a)96  ; b) 144   ; c)192   ; d)=20 6!    ; e)=20 120

------=_NextPart_000_0028_01C8853A.B4555DF0-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Mar 13 23:16:01 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2E2EKsG031375 for ; Thu, 13 Mar 2008 23:14:20 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2E2EK7F031373 for obm-l-MllGbsmmN; Thu, 13 Mar 2008 23:14:20 -0300 Received: from rv-out-0910.google.com (rv-out-0910.google.com [209.85.198.186]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2E2EHsG031369 for ; Thu, 13 Mar 2008 23:14:18 -0300 Received: by rv-out-0910.google.com with SMTP id c27so2308610rvf.9 for ; Thu, 13 Mar 2008 19:14:47 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=3BMTS7rYfPz1ZyA3ai40nH7dy8PnkLbNZaEgn3XlJl4=; b=PtKM24WzSMjeatzmXcbOU2wAg4Ud9lbkVYbZHwfmVE3Z1SzQeajX5ajl6GkkonXMDS36VWU2Z6l96KNnmfraawZhPmakOEzzalynayWz9RY5IMzGtdMsbebOGZ5DVltmvD2WnN5QYHMon5VkvO7nm9ne8KnPfttInjd18DsexAQ= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=LZgo23GMBIqErEHRyy+0rhsKaUAaPv6RnUKL1oW6j8huarkGMNu4fWbl0t8a0XIiMcQKcPD7EYpEo9gFUALhKFzvQPgOYSSLRzEGNjWQOZzO+JWdZiZopq+dCrQx1TB4aIXYM4sQGhdveqsfbQTZaGr4qwkXniB8Re/S5Q40Pmg= Received: by 10.140.252.16 with SMTP id z16mr6226823rvh.196.1205460887480; Thu, 13 Mar 2008 19:14:47 -0700 (PDT) Received: by 10.141.122.1 with HTTP; Thu, 13 Mar 2008 19:14:47 -0700 (PDT) Message-ID: <4de96b200803131914h3f9a1688i3fd9bb6730e57da@mail.gmail.com> Date: Thu, 13 Mar 2008 23:14:47 -0300 From: "Antonio Manuel Castro del Rio" To: obm-l@mat.puc-rio.br Subject: =?ISO-8859-1?Q?Re:_[obm-l]_Olimp=EDadas?= In-Reply-To: <1f424590803122004y72984a15i322dfbc3a2cedc5d@mail.gmail.com> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_10337_13853794.1205460887448" References: <1f424590803122004y72984a15i322dfbc3a2cedc5d@mail.gmail.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Antonio Manuel Castro del Rio" X-Spam-Status: No, hits=3.4 required=5.0 tests=AWL,IN_REP_TO,MAILTO_LINK,MIME_EXCESSIVE_QP, QUOTED_EMAIL_TEXT,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, REFERENCES,SPAM_PHRASE_00_01,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: *** ------=_Part_10337_13853794.1205460887448 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Ola Luiz, Como o Rivaldo lhe indicou procurar em algum sebo, entre nesse endere=E7o: www.estantevirtual.com.br, s=E3o 734 sebos em todo o Brasil, com 15.198.537livros. Espero que voc=EA tenha sorte. Um abra=E7o, Antonio del Rio Em 13/03/08, Luiz Rodrigues escreveu: > > Ol=E1 pessoal!!! > Tudo bem??? > Vou preparar alguns alunos do Ensino Fundamental II (antigo Ensino > Fundamental) para as Olimp=EDadas Brasileiras. > Meu problema =E9: que livros utilizar? > Algu=E9m poderia me indicar alguns? > Abra=E7o para todos!!! > Luiz. > > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > Instru=E7=F5es para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > ------=_Part_10337_13853794.1205460887448 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Ola Luiz, Como o Rivaldo lhe indicou procurar em algum sebo, entre nesse en= dere=E7o:
www.estantevirtua= l.com.br, s=E3o 734 sebos em todo o Brasil, com 15.198.537 livros. Espe= ro que voc=EA tenha sorte.
Um abra=E7o, Antonio del Rio

Em 13= /03/08, Luiz Rodrigues <rodrigueslz@gmail.com> escreveu: Ol=E1 pessoal!!!
Tudo bem???
Vou preparar alguns alunos do Ensino F= undamental II (antigo Ensino
Fundamental) para as Olimp=EDadas Brasilei= ras.
Meu problema =E9: que livros utilizar?
Algu=E9m poderia me ind= icar alguns?
Abra=E7o para todos!!!
Luiz.

=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D
Instru=E7=F5es para entrar na l= ista, sair da lista e usar a lista em
http://www.mat.puc-rio.br/~obmlistas/obm-l.html<= /a>
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D

------=_Part_10337_13853794.1205460887448-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Fri Mar 14 00:23:53 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2DLFKsG002762 for ; Thu, 13 Mar 2008 18:15:25 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2DLFFkx002757 for obm-l-MllGbsmmN; Thu, 13 Mar 2008 18:15:15 -0300 Received: from web55206.mail.re4.yahoo.com (web55206.mail.re4.yahoo.com [206.190.58.170]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id m2DLEtsG002691 for ; Thu, 13 Mar 2008 18:14:56 -0300 Received: (qmail 34564 invoked by uid 60001); 13 Mar 2008 21:15:24 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:Date:From:Subject:To:MIME-Version:Content-Type:Content-Transfer-Encoding:Message-ID; b=bUBh/Jol71wI6Vo72gbLu+PcXS4kV3uv/mpxuVCoeffKZTEmfUPA89W/3T+Xfx1ce5gnfunR74n32H7o/TjluiK/qDiD4CzBpFPJ2w8PTm74wsBh08voqwzVaDFKLnuC/+7/QTbehDQIYWBdbFrdfsjfEi9oYnNbpOjUHpyOPXY=; X-YMail-OSG: mF7dhysVM1lrsZY_x_JX11E0uaynJcQ7Lk.mG33njME5g1JkHy9_K6PuxwpQHs66yNqw.DWN4IUNkGLj3KbYcDvav11WN6fOwquG3fKM9.tZlflvikGZQtEO7VmciQ-- Received: from [200.147.66.56] by web55206.mail.re4.yahoo.com via HTTP; Thu, 13 Mar 2008 18:15:24 ART Date: Thu, 13 Mar 2008 18:15:24 -0300 (ART) From: =?iso-8859-1?q?C=E9sar=20Santos?= Subject: [SPAM] [obm-l] =?iso-8859-1?q?Teorema=20de=20Green=20(quest=E3o)?= To: obm-l@mat.puc-rio.br MIME-Version: 1.0 Content-Type: text/plain Content-Transfer-Encoding: 7bit Message-ID: <235671.34421.qm@web55206.mail.re4.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: =?iso-8859-1?q?C=E9sar=20Santos?= X-Spam-Status: Yes, hits=8.9 required=5.0 tests=AWL,FORGED_YAHOO_RCVD,MIME_BOUND_DIGITS_5,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01,SPAM_REDIRECTOR, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="0-503592340-1205442924=:34421" X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (8.90 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: MIME_BOUND_DIGITS_5 (1.7 points) Spam tool pattern in MIME boundary SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: SPAM_REDIRECTOR (0.4 points) URI: Uses open redirection service SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 170.58.190.206.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 170.58.190.206.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-0.4 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- --0-503592340-1205442924=:34421 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 8bit A questão pede para calcular a integral de linha C de F.dr onde F(x,y) = e^yi + xe^yj E o caminho C é o contorno da região: 0<= x <= 1 (onde <= indica menor ou igual) arcsen(x) <=y<= pi/2. Eu já resolvi várias vezes a questão e encontrei a resposta 1, mas de acordo com o livro a resposta é 0. Alguém, por favor, poderia resolver a questão e indicar meu erro? --------------------------------- Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-503592340-1205442924=:34421 Content-Type: text/html; charset=iso-8859-1 Content-Transfer-Encoding: 8bit
A questão pede para calcular a integral de linha C de F.dr onde F(x,y) = e^yi + xe^yj
E o caminho C é o contorno da região:
0<= x <= 1 (onde <= indica menor ou igual)
arcsen(x) <=y<= pi/2.
 
Eu já resolvi várias vezes a questão e encontrei a resposta 1, mas de acordo com o livro a resposta é 0. Alguém, por favor, poderia resolver a questão e indicar meu erro?

Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-503592340-1205442924=:34421-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Fri Mar 14 12:33:31 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2EFV1sG000595 for ; Fri, 14 Mar 2008 12:31:01 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2EFV14B000593 for obm-l-MllGbsmmN; Fri, 14 Mar 2008 12:31:01 -0300 Received: from relay1.bol.com.br (relay1.bol.com.br [200.221.4.105]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2EFUxsG000590 for ; Fri, 14 Mar 2008 12:30:59 -0300 Received: from localhost (localhost [127.0.0.1]) by salsa1.bol.com.br (Postfix) with ESMTP id B5A3018DA8 for ; Fri, 14 Mar 2008 12:12:35 -0300 (BRT) Received: from bol.com.br (whisper4.mail.sys.intranet [172.26.5.139]) by salsa1.bol.com.br (Postfix) with ESMTP id 800C54A9D9 for ; Fri, 14 Mar 2008 12:12:35 -0300 (BRT) Date: Fri, 14 Mar 2008 12:12:35 -0300 Message-Id: Subject: [obm-l] AFA 03/04 MIME-Version: 1.0 X-Sensitivity: 3 Content-Type: multipart/alternative; boundary="_=__=_XaM3_.1205507555.2A.429342.42.1855.52.42.007.1483364001" From: "arkon" To: "obm-l" X-XaM3-API-Version: 4.3(R1) (B10) X-SenderIP: 200.140.133.74 X-SIG5: 5d4855a4e6682204ca80a0ba5e82c79a Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "arkon" X-Spam-Status: No, hits=1.4 required=5.0 tests=AWL,BIG_FONT,HTML_50_70,LINES_OF_YELLING, LINES_OF_YELLING_2,MAILTO_LINK,SPAM_PHRASE_00_01, SUPERLONG_LINE,TO_LOCALPART_EQ_REAL,X_MAILING_LIST version=2.44 X-Spam-Level: * --_=__=_XaM3_.1205507555.2A.429342.42.1855.52.42.007.1483364001 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable Pessoal algu=E9m pode me enviar, por favor, a resolu=E7=E3o dessa quest=E3= o (AFA 03/04) A equa=E7=E3o x^3 + mx^2 + 2x + n =3D 0, onde m e n s=E3o n=FA= meros reais e i^2 =3D - 1, admite 1 + i como raiz. Ent=E3o m + n =E9 igual a: a) =96 2. b) 0. c) 1. d) 2. E aproveitando a oportunidade algu=E9m pode me enviar, por favor, no meu = e-mail, arkon@bol.com.br, a resolu=E7=E3o dessa outra (AFA 03/04) Um foguete cuja massa vale 6 toneladas =E9 colocado em posi=E7= =E3o vertical para lan=E7amento. Se a velocidade de escape dos gases vale= 1 km/s, a quantidade de gases expelida por segundo, a fim de proporciona= r o empuxo necess=E1rio para dar ao foguete uma acelera=E7=E3o para cima = igual a 20 m/s^2 =E9: a) 120 kg. b) 180 kg. c) 100 kg. d) 80 kg. DESDE J=C1 MUITO OBRIGADO --_=__=_XaM3_.1205507555.2A.429342.42.1855.52.42.007.1483364001 Content-Type: text/html; charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable

<= B style=3D"mso-bidi-font-weight: normal">Pessoal algu=E9m pode me enviar, por favor, a resolu=E7=E3o= dessa quest=E3o

<= B style=3D"mso-bidi-font-weight: normal"> 

(AFA 03/04) A equa=E7=E3o x^3 + mx^2 + 2x + n =3D 0,= onde m e n s=E3o n=FAmeros reais e

i^2 =3D - 1, admite 1 +  i como raiz. Ent=E3o m + n =E9 igual a:

 

a) =96 2. &nb= sp;       b) 0.       c) 1.        = d) 2.  

 

E aproveitando a oportunidade algu=E9m pode me envia= r, por favor, no meu

e-mail, arkon@bol.com.br, a resolu=E7=E3o dessa outra=

 

(AFA 03/04) Um foguete cuja massa vale 6 toneladas =E9= colocado em posi=E7=E3o vertical para lan=E7amento. Se a velocidade de e= scape dos gases vale 1 km/s, a quantidade de gases expelida por segundo, = a fim de proporcionar o empuxo necess=E1rio para dar ao foguete uma acele= ra=E7=E3o para cima igual a 20 m/s^2 =E9:

 

= a) 120 = kg.  &n= bsp;   b) 180 kg.&n= bsp;  c)  &n= bsp;  d) 80 kg.

&= nbsp;

DESDE J=C1 MUITO OBRIGADO

 

--_=__=_XaM3_.1205507555.2A.429342.42.1855.52.42.007.1483364001-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Fri Mar 14 14:44:38 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2EHh2sG021126 for ; Fri, 14 Mar 2008 14:43:02 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2EHh1c7021124 for obm-l-MllGbsmmN; Fri, 14 Mar 2008 14:43:01 -0300 Received: from smtp.uol.com.br (smtps.uol.com.br [200.221.4.131]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2EHh0sG021121 for ; Fri, 14 Mar 2008 14:43:00 -0300 Received: from localhost (localhost [127.0.0.1]) by socom2.uol.com.br (Postfix) with ESMTP id C5ACC1789 for ; Fri, 14 Mar 2008 14:43:31 -0300 (BRT) Received: from MARTE (unknown [200.128.35.137]) by socom2.uol.com.br (Postfix) with ESMTP id 44342539 for ; Fri, 14 Mar 2008 14:43:31 -0300 (BRT) Message-ID: <2E2AD4A5B842401BB9820078CDDD50F0@MARTE> From: "Ojesed Mirror" To: References: In-Reply-To: Subject: [SPAM] [obm-l] SigmaDelta Date: Fri, 14 Mar 2008 14:43:29 -0300 MIME-Version: 1.0 Content-Type: text/plain X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Windows Mail 6.0.6000.16480 X-MimeOLE: Produced By Microsoft MimeOLE V6.0.6000.16545 X-SIG5: acb4a3a7cdc4b211c00bc7b10f490ce9 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Ojesed Mirror" X-Spam-Status: Yes, hits=5.6 required=5.0 tests=IN_REP_TO,MISSING_OUTLOOK_NAME,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ***** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_NextPart_000_0066_01C885E1.C50082E0" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (5.60 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: REFERENCES (-0.5 points) Has a valid-looking References header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 137.35.128.200.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 137.35.128.200.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: MISSING_OUTLOOK_NAME (1.1 points) Message looks like Outlook, but isn't SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- This is a multi-part message in MIME format. ------=_NextPart_000_0066_01C885E1.C50082E0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Ol=E1 lista, pe=E7o ajuda, n=E3o achei uma sa=EDda anal=EDtica. A(n) =3D A(n-1) + ( D(n) - A(n-1) )/n onde: D(n) =3D sinal( I(n) )*R=20 e I(n) =3D I(n-1) + V - D(n-1) Mostrar que A(n) converge para V quando |V| < R Considerar:=20 A(0) =3D D(0) =3D I(0) =3D 0. n inteiro, R constante real positiva, V constante real. sinal() retorna 1 para argumento positivo, -1 para argumento negativo e = 0 para argumento nulo. Obrigado, Ojesed. ------=_NextPart_000_0066_01C885E1.C50082E0 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable
Ol=E1 lista, pe=E7o ajuda, n=E3o achei = uma sa=EDda=20 anal=EDtica.
 
A(n) =3D A(n-1) + ( D(n) - A(n-1) = )/n
 
onde:
 
D(n) =3D sinal( I(n) )*R
e
I(n) =3D I(n-1) + V - = D(n-1)
 
Mostrar que A(n) converge para V = quando |V|=20 < R
 
Considerar:
A(0) =3D D(0) =3D I(0) =3D = 0.
n inteiro, R constante real positiva, V = constante=20 real.
sinal() retorna 1 para argumento = positivo, -1 para=20 argumento negativo e 0 para argumento nulo.
 
 
Obrigado, = Ojesed.
------=_NextPart_000_0066_01C885E1.C50082E0-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Fri Mar 14 16:06:50 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2EJ5DsG026489 for ; Fri, 14 Mar 2008 16:05:13 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2EJ5DCi026487 for obm-l-MllGbsmmN; Fri, 14 Mar 2008 16:05:13 -0300 Received: from rv-out-0910.google.com (rv-out-0910.google.com [209.85.198.191]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2EJ5AsG026481 for ; Fri, 14 Mar 2008 16:05:11 -0300 Received: by rv-out-0910.google.com with SMTP id c27so2523911rvf.9 for ; Fri, 14 Mar 2008 12:05:40 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:user-agent:mime-version:to:subject:content-type:content-transfer-encoding:from; bh=92AK6/vApFr4ZE2sV9UOYHHPA+0e6FspeDsKmyDlKpM=; b=A0wCMPzPLpgPmkPV4fYCotQLFCGTMVYBuD5DHuaS0VQ2wxjpLWpXiQ1eiMaLR2HSfmOVFUgtmmAyrYm8KAwNspxoZFQsby6h7xpI7Z/pjhbF4zZIbVwvFIPqt1IwJqJIleFkFaXpEaguii3VZgTI/jkJVPlxFoAFX217piTmiD0= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:user-agent:mime-version:to:subject:content-type:content-transfer-encoding:from; b=kziLhdJir0QHGVkZGcNad5T+11fuev2dqh6ikyUR9yLGnmOe9TTwxVzJbGnK7pHftYUDBTm51c9SMGi6Viu88vqpY3WMmKWbbYDhBDWbJzg41F5BDzIW+o9vj3iynpbq8XPGGg4ve1DYU0EKP2ekK35Jxukuh/XHYeLF/xxMnB4= Received: by 10.140.207.3 with SMTP id e3mr6745619rvg.194.1205521540885; Fri, 14 Mar 2008 12:05:40 -0700 (PDT) Received: from ?192.168.99.198? ( [201.87.26.27]) by mx.google.com with ESMTPS id e19sm15323871qbe.6.2008.03.14.12.05.38 (version=TLSv1/SSLv3 cipher=RC4-MD5); Fri, 14 Mar 2008 12:05:39 -0700 (PDT) Message-ID: <47DACC7F.10404@usp.br> Date: Fri, 14 Mar 2008 16:05:35 -0300 User-Agent: Thunderbird 2.0.0.9 (X11/20071031) MIME-Version: 1.0 To: obm-l@mat.puc-rio.br Subject: [SPAM] [obm-l] Enquete epistemologica Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit From: albert richerd carnier guedes Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: albert richerd carnier guedes X-Spam-Status: Yes, hits=5.3 required=5.0 tests=RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01, USER_AGENT,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ***** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (5.30 hits, 5 required) SPAM: USER_AGENT (-0.5 points) Found a User-Agent header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 191.198.85.209.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 191.198.85.209.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- Eu tava lendo por aí que alguns matemáticos são meio que cabreros com o método indutivo por causa da idéia de que alguma hora o método pode falhar, sendo assim, o método dedutivo é o verdadeiro modo de se chegar a uma resposta segura e real dos problemas matemáticos. Um tanto Popperiano, mas vá lá. Alguém também sente esta desconfiança em relação ao método indutivo ? ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Fri Mar 14 21:58:26 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2F0uesG014798 for ; Fri, 14 Mar 2008 21:56:40 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2F0uZnn014788 for obm-l-MllGbsmmN; Fri, 14 Mar 2008 21:56:35 -0300 Received: from sc2.he.tucows.com (smtpout2004.sc2.he.tucows.com [64.97.155.4]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2F0uFsG014780 for ; Fri, 14 Mar 2008 21:56:16 -0300 Received: from sc2-out06.emaildefenseservice.com (64.97.201.176) by sc2.he.tucows.com (7.3.127) id 47C42A4A01386D5A for obm-l@mat.puc-rio.br; Sat, 15 Mar 2008 00:56:46 +0000 X-SpamScore: 2 X-Spamcatcher-Summary: 2,0,0,ea5e8a0005f76a64,7e4a50e6bb652784,marcusaurelio80@globo.com,-,RULES_HIT:10:355:379:541:542:960:962:967:973:980:988:989:1021:1029:1155:1160:1189:1221:1260:1308:1309:1313:1314:1345:1436:1437:1515:1516:1517:1521:1535:1542:1567:1575:1588:1589:1592:1594:1691:1711:1714:1730:1749:1777:1792:2525:2528:2559:2564:2682:2685:2857:2859:2902:2917:2933:2937:2939:2942:2945:2947:2951:2954:3022:3586:3869:3876:3877:3934:3936:3938:3941:3944:4321:4379:4605:5007:6114:6117: 6261:7679:7688:7904,0,RBL:none,CacheIP:none,Bayesian:0.5,0.5,0.5,Netcheck:none,DomainCache:0,MSF:not bulk,SPF:,MSBL:none,DNSBL:none X-Spamcatcher-Explanation: Received: from esquadrao (unknown [201.29.28.214]) (Authenticated sender: marcusaurelio80@globo.com) by sc2-out06.emaildefenseservice.com (Postfix) with ESMTP for ; Sat, 15 Mar 2008 00:56:44 +0000 (UTC) From: =?iso-8859-1?Q?Marcus_Aur=E9lio?= To: Subject: [SPAM] [obm-l] Divisibilidade por 13 Date: Fri, 14 Mar 2008 21:56:27 -0300 Message-ID: <001c01c88637$6fc9ab70$4f5d0250$@com> MIME-Version: 1.0 Content-Type: text/plain X-Mailer: Microsoft Office Outlook 12.0 thread-index: AciGN2XSQjmNTKffTLmuDqgjidb/Lg== Content-Language: pt-br Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: =?iso-8859-1?Q?Marcus_Aur=E9lio?= X-Spam-Status: Yes, hits=7.0 required=5.0 tests=FROM_ENDS_IN_NUMS,HTML_50_70,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******* X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_NextPart_000_001D_01C8861E.4A7C7370" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. 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Logo q + n vale: =20 a) 10739 b) 10026 c) 13052 d) 10582 e) 10126 =20 ------=_NextPart_000_001D_01C8861E.4A7C7370 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable

Algu=E9m me ajude nessa quest=E3o, qual o = crit=E9rio de divisibilidade por 13?

 

O n=FAmero natural N =3D( 10^5 + =A03.10^4 + 7.10^2 = + 440 + n) =E9 divis=EDvel por 13, n =E9 um numero natural menor que 10, e q =E9 o quociente da = divis=E3o de N por 13. Logo q + n vale:

 

a)      10739=A0=A0=A0 b) = 10026=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0 c) = 13052=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0 d) 10582=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0 e) 10126

=A0

------=_NextPart_000_001D_01C8861E.4A7C7370-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Fri Mar 14 22:15:22 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2F1EDsG016399 for ; Fri, 14 Mar 2008 22:14:13 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2F1EC7J016397 for obm-l-MllGbsmmN; Fri, 14 Mar 2008 22:14:12 -0300 Received: from fg-out-1718.google.com (fg-out-1718.google.com [72.14.220.154]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2F1E9sG016348 for ; Fri, 14 Mar 2008 22:14:10 -0300 Received: by fg-out-1718.google.com with SMTP id e12so10057211fga.3 for ; Fri, 14 Mar 2008 18:14:40 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; bh=Z/bIQ7XD4Fye//0+1NP6qBoE20zLFnNf91lR6UIWiQ0=; b=Std5NjmKzQcf3Siw94HcbGp5rF2Zr246I32Jx/NctyZK1/8/EeOO68vW3717cuG+Kp8U6T9KrgcufeqX3XwK0BU87m+AlPIUHRsZ5xSfrgUPwxE58raQDxC1/FRUXIjJBpeVPty18q02fD04N4z2whrwOvSSN6Qn4P8uxOSI+i0= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; b=RWe4ivOKWAocITM7y7QQKCedWl1qnB2lKg4VEUKLZRYzENGnPN86J06f/xAD0sI4yufS6b7XfrcrcfVpz+M/h375GUW+r/9KU6efVZbRHqzVM9Ub8pXlZ/f+C2nziyk+x/fsTeb1A1fjCsfzWRVNOqyLxzdFz81gtIYhs6VMhIE= Received: by 10.78.155.4 with SMTP id c4mr32679301hue.21.1205543679671; Fri, 14 Mar 2008 18:14:39 -0700 (PDT) Received: by 10.78.42.5 with HTTP; Fri, 14 Mar 2008 18:14:37 -0700 (PDT) Message-ID: <8994b830803141814l12410e89xe92e804a6478b5fb@mail.gmail.com> Date: Fri, 14 Mar 2008 22:14:37 -0300 From: "=?ISO-8859-1?Q?Maur=EDcio_Collares?=" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Enquete epistemologica In-Reply-To: <47DACC7F.10404@usp.br> MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline References: <47DACC7F.10404@usp.br> Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m2F1EBsG016393 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "=?ISO-8859-1?Q?Maur=EDcio_Collares?=" X-Spam-Status: No, hits=1.2 required=5.0 tests=AWL,IN_REP_TO,QUOTED_EMAIL_TEXT,REFERENCES, SPAM_PHRASE_00_01,X_MAILING_LIST version=2.44 X-Spam-Level: * Provas matemáticas que usam o método indutivo não são consideradas formais, eu acho. Tal fato é inclusive, motivo de diversas piadas que matemáticos contam sobre engenheiros (do tipo "vale para n = 1, vale para n = 2, então vale sempre"). Vale lembrar, só pra constar, que a indução matemática não é, em si, uma manifestação do "método indutivo". A indução matemática tem esse nome porque serve para provar *dedutivamente* coisas conjecturadas a partir do "método indutivo" (i.e., supor que uma idéia vale para o caso geral porque ela vale para alguns casos particulares). Isso se reflete no fato de que, ao construir uma prova por indução matemática, você tem que conhecer de antemão o resultado final que deseja provar. -- Abraços, Maurício PS: Eu estou estudando para ser engenheiro. Nada contra tal profissão :) On 3/14/08, albert richerd carnier guedes wrote: > Eu tava lendo por aí que alguns matemáticos são meio que cabreros com o > método indutivo por causa da idéia de que alguma hora o método pode > falhar, sendo assim, o método dedutivo é o verdadeiro modo de se chegar > a uma resposta segura e real dos problemas matemáticos. > Um tanto Popperiano, mas vá lá. > Alguém também sente esta desconfiança em relação ao método indutivo ? ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sat Mar 15 07:54:27 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2FAqlsG021360 for ; Sat, 15 Mar 2008 07:52:47 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2FAqloP021358 for obm-l-MllGbsmmN; Sat, 15 Mar 2008 07:52:47 -0300 Received: from wa-out-1112.google.com (wa-out-1112.google.com [209.85.146.182]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2FAqjsG021354 for ; Sat, 15 Mar 2008 07:52:45 -0300 Received: by wa-out-1112.google.com with SMTP id m28so5207777wag.13 for ; Sat, 15 Mar 2008 03:53:15 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; bh=GTSSDDTd+PqKji2skyLHVc82NYLMyeBJpBo06ff6FTw=; b=OqYSBgoSc5fsLuC1RaY06REzg4IwVtgNwB8cOWN2QOKNPKLWP5Ds3BvuC3PXOTr3sS/hqTRzPYnlqy9M0RFOGlsYSV8cs1ubxH3zz0JH/8rIgnltIY7QjfEq+fkRnervIMkJZ2hjfC5ekltmf4u2TmGWL34AP19Qxq+2XKTJP0U= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; b=FK7xyiYHXUCJOX8YDp9iluPh2SQLGsdTMJZVK+RmITEoFjL6rh/v0qnoqdAfcrjTcv40ZzmM4pT9sLyq6cAs1PuE2n+5uHSjAygJxbx5YFjaEFuMZxTCrvRFXnOfg/IrHuuYrQTp7/Ctz26qy4fMlTA1hGlFAvf1SCtz88Me3lQ= Received: by 10.114.166.1 with SMTP id o1mr13914922wae.5.1205578395347; Sat, 15 Mar 2008 03:53:15 -0700 (PDT) Received: by 10.114.146.4 with HTTP; Sat, 15 Mar 2008 03:53:15 -0700 (PDT) Message-ID: <1f424590803150353m4edeca71qe6917ba8657bea44@mail.gmail.com> Date: Sat, 15 Mar 2008 07:53:15 -0300 From: "Luiz Rodrigues" To: obm-l@mat.puc-rio.br Subject: =?ISO-8859-1?Q?Re:_[obm-l]_Olimp=EDadas?= In-Reply-To: <4de96b200803131914h3f9a1688i3fd9bb6730e57da@mail.gmail.com> MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline References: <1f424590803122004y72984a15i322dfbc3a2cedc5d@mail.gmail.com> <4de96b200803131914h3f9a1688i3fd9bb6730e57da@mail.gmail.com> Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m2FAqksG021356 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Luiz Rodrigues" X-Spam-Status: No, hits=4.4 required=5.0 tests=AWL,IN_REP_TO,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** Olá Antonio, olá Rivaldo!!! Tudo bem??? Muito obrigado pelas dicas. Abração!!! Luiz. 2008/3/13 Antonio Manuel Castro del Rio : > Ola Luiz, Como o Rivaldo lhe indicou procurar em algum sebo, entre nesse > endereço: > www.estantevirtual.com.br, são 734 sebos em todo o Brasil, com 15.198.537 > livros. Espero que você tenha sorte. > Um abraço, Antonio del Rio > > Em 13/03/08, Luiz Rodrigues escreveu: > > > > > > > > Olá pessoal!!! > > Tudo bem??? > > Vou preparar alguns alunos do Ensino Fundamental II (antigo Ensino > > Fundamental) para as Olimpíadas Brasileiras. > > Meu problema é: que livros utilizar? > > Alguém poderia me indicar alguns? > > Abraço para todos!!! > > Luiz. > > > > > > ========================================================================= > > Instruções para entrar na lista, sair da lista e usar a lista em > > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > > ========================================================================= > > > > ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sat Mar 15 12:03:41 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2FF0psG031987 for ; Sat, 15 Mar 2008 12:00:51 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2FF0p4k031985 for obm-l-MllGbsmmN; Sat, 15 Mar 2008 12:00:51 -0300 Received: from web52904.mail.re2.yahoo.com (web52904.mail.re2.yahoo.com [206.190.49.14]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id m2FF0msG031981 for ; Sat, 15 Mar 2008 12:00:49 -0300 Received: (qmail 58078 invoked by uid 60001); 15 Mar 2008 15:01:19 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:Date:From:Subject:To:In-Reply-To:MIME-Version:Content-Type:Content-Transfer-Encoding:Message-ID; b=nXWeFNP2NDTzM5Bx1IIq/K9MfoGp6aC+dOJfCbeurB2czp+FzJAy57x1J2yW1TD1p+D8tYuT+kDLiK/Oe7U6kZ2LNsYBdUFexmkCtxSnXdGlXn2h6qSTW2K+1rCz5NiCDCBMjXW8IpRfo6ItNAbmFR0YT9FoqxueKgZ0222MVdM=; X-YMail-OSG: hKfXyxIVM1mvMJTOYpj4g_1HUC_e8xFcCciFonlRtyltXI6HQ9wbEtS5EorVRxsZ6Hindn6XwwEV5GMUJmUD6ifq2sVPxkymOMavZtnF7aYpv0gc0gFBry1nneNnrwWuXerjWDbeFuOcmBTbL9lAZIdI Received: from [201.67.229.217] by web52904.mail.re2.yahoo.com via HTTP; Sat, 15 Mar 2008 12:01:18 ART Date: Sat, 15 Mar 2008 12:01:18 -0300 (ART) From: Antonio Giansante Subject: [SPAM] Re: [obm-l] Divisibilidade por 13 To: obm-l@mat.puc-rio.br In-Reply-To: <001c01c88637$6fc9ab70$4f5d0250$@com> MIME-Version: 1.0 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 7bit Message-ID: <42506.56828.qm@web52904.mail.re2.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Antonio Giansante X-Spam-Status: Yes, hits=7.1 required=5.0 tests=FORGED_YAHOO_RCVD,IN_REP_TO,MAILTO_TO_SPAM_ADDR, RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******* X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (7.10 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: MAILTO_TO_SPAM_ADDR (0.7 points) URI: Includes a link to a likely spammer email address SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 14.49.190.206.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 14.49.190.206.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- Um número é divisível por 13 se o quádruplo (4 vezes) do último algarismo, somado ao número sem o último algarismo, resultar um número divisível por 13. EX: 25672 --> 2567+8 = 2575--> 257+20 = 277-->27+21=48 Porém, creio que nesse caso seja mais rápido você fazer a divisão do número e ver como vai ficar o resto. Ficará um número do tipo 2n ou 3n. Assim, você descobrirá qual o valor do n e, ao mesmo tempo, obteráo valor de q. --- Marcus Aurélio escreveu: > Alguém me ajude nessa questão, qual o critério de > divisibilidade por 13? > > > > O número natural N =( 10^5 + 3.10^4 + 7.10^2 + 440 > + n) é divisível por 13, > n é um numero natural menor que 10, e q é o > quociente da divisão de N por > 13. Logo q + n vale: > > > > a) 10739 b) 10026 c) 13052 > d) 10582 > e) 10126 > > > > Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! http://br.mail.yahoo.com/ ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sat Mar 15 12:05:41 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2FF3nsG032094 for ; Sat, 15 Mar 2008 12:03:49 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2FF3nHP032092 for obm-l-MllGbsmmN; Sat, 15 Mar 2008 12:03:49 -0300 Received: from web52906.mail.re2.yahoo.com (web52906.mail.re2.yahoo.com [206.190.49.16]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id m2FF3lsG032080 for ; Sat, 15 Mar 2008 12:03:47 -0300 Received: (qmail 80358 invoked by uid 60001); 15 Mar 2008 15:04:17 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:Date:From:Subject:To:In-Reply-To:MIME-Version:Content-Type:Content-Transfer-Encoding:Message-ID; b=wrfqZWDzeBFgKUpehGylux02hoFo8FhT6mP4bRyGjr72w38JfR1t0n4ZWw+0AjndmXIp2e/Ez9ImgI9fM+drHoSQA2XPOz6GcngSJVJR79eX6Ih4GS1MUMhx+SZosXW+PUXRNq+LdsR7yAqpmGrdbGvox4FJDVr8uxbVwJT8nUg=; X-YMail-OSG: 3VTO1L0VM1nHEHbUcVmGPoN6SSNIlk6f7DnA3iS.6KbbdrVYZjkJhCyhQAVqD_Mo9mEKthtl0AtD_pZ3arWdaw7WzmjofQuinAnfbtQYaHG_jiwSsMLMKOQ58m85FzBaf4aMaYtjIlk3XTkiTEMIUpjjFQ-- Received: from [201.67.229.217] by web52906.mail.re2.yahoo.com via HTTP; Sat, 15 Mar 2008 12:04:17 ART Date: Sat, 15 Mar 2008 12:04:17 -0300 (ART) From: Antonio Giansante Subject: [SPAM] Re: [obm-l] Divisibilidade por 13 To: obm-l@mat.puc-rio.br In-Reply-To: <001c01c88637$6fc9ab70$4f5d0250$@com> MIME-Version: 1.0 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 7bit Message-ID: <371082.78999.qm@web52906.mail.re2.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Antonio Giansante X-Spam-Status: Yes, hits=7.1 required=5.0 tests=AWL,FORGED_YAHOO_RCVD,IN_REP_TO,MAILTO_TO_SPAM_ADDR, RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******* X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (7.10 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: MAILTO_TO_SPAM_ADDR (0.7 points) URI: Includes a link to a likely spammer email address SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 16.49.190.206.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 16.49.190.206.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-0.0 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- Um número é divisível por 13 se o quádruplo (4 vezes) do último algarismo, somado ao número sem o último algarismo, resultar um número divisível por 13. EX: 25672 --> 2567+8 = 2575--> 257+20 = 277-->27+21=48 que não é divisível or 13 Porém, creio que nesse caso seja mais rápido você fazer a divisão do número e ver como vai ficar o resto. Ficará um número do tipo 2n ou 3n. Assim, você descobrirá qual o valor do n (6 para 2n e 9 para 3n, por exemplo) e, ao mesmo tempo, obteráo valor de q. é isso. --- Marcus Aurélio escreveu: > Alguém me ajude nessa questão, qual o critério de > divisibilidade por 13? > > > > O número natural N =( 10^5 + 3.10^4 + 7.10^2 + 440 > + n) é divisível por 13, > n é um numero natural menor que 10, e q é o > quociente da divisão de N por > 13. Logo q + n vale: > > > > a) 10739 b) 10026 c) 13052 > d) 10582 > e) 10126 > > > > Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! http://br.mail.yahoo.com/ ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sat Mar 15 12:33:49 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2FFWdsG002142 for ; Sat, 15 Mar 2008 12:32:39 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2FFWctE002140 for obm-l-MllGbsmmN; Sat, 15 Mar 2008 12:32:38 -0300 Received: from wx-out-0506.google.com (wx-out-0506.google.com [66.249.82.224]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2FFWZsG002137 for ; Sat, 15 Mar 2008 12:32:37 -0300 Received: by wx-out-0506.google.com with SMTP id t4so5508849wxc.18 for ; Sat, 15 Mar 2008 08:33:06 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=2DzRb0kAfoq1EhZCTuAnRL+hht+dzr1e1ZqnNXgU1WI=; b=nqxXkyWGMKvKHRFGfMUNv3hdkSm004ti/fz79iZzmyZLpeLXyUjL9g8xpHuUDPvIytFxO1hRoN+jiLYRt7XCXKVycoKR4rXat0Hg/iyYk6vZb5jlHoVl360AxkKC99D4Dz6cSXK5Zd6u7e34WLMyIMSflllAFKz23I+X0ZimVDQ= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=Ulw5zA7t2PZjwUcJkNtFM9bM5/s9sUp+oU1l9mvZbh5+q6EH1IS8zxF13ofyPn+GXwhB0qiEnvgv0kqq6cPVNl2Pk8SCtSlYvNWRw0G3FNdgshKObiHOsfY8IHGl2SQymjWKsLsjEn6Gm0eJJCRodTSLswQhoLhHg7hzBqNK7ek= Received: by 10.150.200.8 with SMTP id x8mr7084621ybf.80.1205595186260; Sat, 15 Mar 2008 08:33:06 -0700 (PDT) Received: by 10.150.57.9 with HTTP; Sat, 15 Mar 2008 08:33:06 -0700 (PDT) Message-ID: <5bb472220803150833l62a0652cr733205809c23af05@mail.gmail.com> Date: Sat, 15 Mar 2008 12:33:06 -0300 From: "Joao Victor Brasil" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] AFA 03/04 In-Reply-To: MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_4646_23296368.1205595186264" References: Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Joao Victor Brasil" X-Spam-Status: No, hits=4.5 required=5.0 tests=AWL,BIG_FONT,HTML_50_70,IN_REP_TO,JAVASCRIPT_UNSAFE, LINES_OF_YELLING,MAILTO_LINK,QUOTED_EMAIL_TEXT, RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,REFERENCES, SPAM_PHRASE_00_01,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** ------=_Part_4646_23296368.1205595186264 Content-Type: text/plain; charset=WINDOWS-1252 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Da um pulo em www.sassabetudo.com.br. Se n=E3o for com.br =E9 outra termina= =E7=E3o e procura no google. Joao Victor On 3/14/08, arkon wrote: > > *Pessoal algu=E9m pode me enviar, por favor, a resolu=E7=E3o dessa quest= =E3o * > > * * > > *(AFA 03/04) A equa=E7=E3o x^3 + mx^2 + 2x + n =3D 0, onde m e n s=E3o n= =FAmeros > reais e * > > *i^2 =3D - 1, admite 1 + i como raiz. Ent=E3o m + n =E9 igual a:* > > * * > > *a) =96 2. b) 0. c) 1. d) 2. * > > * * > > *E aproveitando a oportunidade algu=E9m pode me enviar, por favor, no meu= * > > *e-mail, arkon@bol.com.br, a resolu=E7=E3o dessa outra* > > * * > > *(AFA 03/04) Um foguete cuja massa vale 6 toneladas =E9 colocado em posi= =E7=E3o > vertical para lan=E7amento. Se a velocidade de escape dos gases vale 1 km= /s, a > quantidade de gases expelida por segundo, a fim de proporcionar o empuxo > necess=E1rio para dar ao foguete uma acelera=E7=E3o para cima igual a 20 = m/s^2 =E9: > * > > * * > > *a) 120 kg. b) 180 kg. c) 100 kg. d) 80 kg.* > > * * > > *DESDE J=C1 MUITO OBRIGADO* > > * * > ------=_Part_4646_23296368.1205595186264 Content-Type: text/html; charset=WINDOWS-1252 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline
Da um pulo em www.sassabetud= o.com.br. Se n=E3o for com.br =E9 outra t= ermina=E7=E3o e procura no google.
 
Joao Victor

 

------=_Part_4646_23296368.1205595186264-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sat Mar 15 16:54:59 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2FJrFsG004717 for ; Sat, 15 Mar 2008 16:53:15 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2FJrFkP004715 for obm-l-MllGbsmmN; Sat, 15 Mar 2008 16:53:15 -0300 Received: from wa-out-1112.google.com (wa-out-1112.google.com [209.85.146.178]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2FJrDsG004710 for ; Sat, 15 Mar 2008 16:53:14 -0300 Received: by wa-out-1112.google.com with SMTP id m28so5432461wag.13 for ; Sat, 15 Mar 2008 12:53:44 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; bh=6Tz9xt92j5UqIL5BHVqQ5ZPj6U63CMxxuKlqY3Xb5Yc=; b=Vlt5dWQ3UamA21rZ0os04d6CsPNcGo1XBCcOG2T90rHKEtC0dDS4uv5gybjA70sQRIPvpMUvpbXOR034+lQHV86MqOmdODKhjPTv8WIHpww52NNPSX6QG/7bg+/7SLboU4QWPWua0QFQ4YosXzLKEoWSfMKJxCNsVayR4rljcqQ= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; b=vYOjNakgkdwkyaHANDBKuDnYf9OYKN09592NaDKqZBoIE7SZXuse7Osg/rxmgrfTR23UYPwxaUPyXQDOViTvkZiMDT8vRw5tPVFNstgjWb7EyXiC6I1yQOzsWlULY53hO66C5wkShctx2b4lfRlqLCxrcwex0RgQ58Y1JTHERbw= Received: by 10.114.171.1 with SMTP id t1mr14840154wae.83.1205610824566; Sat, 15 Mar 2008 12:53:44 -0700 (PDT) Received: by 10.115.48.11 with HTTP; Sat, 15 Mar 2008 12:53:43 -0700 (PDT) Message-ID: <686b6ed50803151253o51f84389yfdb7c3e1324b8ca0@mail.gmail.com> Date: Sat, 15 Mar 2008 16:53:43 -0300 From: "Daniel Kiss" To: obm-l@mat.puc-rio.br Subject: =?ISO-8859-1?Q?Re:_[obm-l]_Teorema_de_Green_(quest=E3o)?= In-Reply-To: <235671.34421.qm@web55206.mail.re4.yahoo.com> MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline References: <235671.34421.qm@web55206.mail.re4.yahoo.com> Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m2FJrEsG004713 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Daniel Kiss" X-Spam-Status: No, hits=3.7 required=5.0 tests=IN_REP_TO,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: *** A região é fechada... vale o Teorema de Green, então: integral de linha ao longo de C de F.dr = integral dupla na região delimitada por C de dQ/dx - dP/dy lembre-se que nesse caso, P(x,y)= exp(y) e Q(x,y)=x*exp(y) Assim, dQ/dx - dP/dy = d(x*exp(y))/dx - d(exp(y))/dy = exp(y) - exp(y) = 0 A integral dupla em uma região da função constante zero é zero... Portanto a integral de linha de Fdr ao longo de C é zero. Em 13/03/08, César Santos escreveu: > A questão pede para calcular a integral de linha C de F.dr onde F(x,y) = > e^yi + xe^yj > E o caminho C é o contorno da região: > 0<= x <= 1 (onde <= indica menor ou igual) > arcsen(x) <=y<= pi/2. > > Eu já resolvi várias vezes a questão e encontrei a resposta 1, mas de > acordo com o livro a resposta é 0. Alguém, por favor, poderia resolver a > questão e indicar meu erro? > > > --------------------------------- > Abra sua conta no Yahoo! Mail, o único sem limite de espaço para > armazenamento! ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sat Mar 15 22:11:01 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2G19EsG020301 for ; Sat, 15 Mar 2008 22:09:14 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2G19Efg020299 for obm-l-MllGbsmmN; Sat, 15 Mar 2008 22:09:14 -0300 Received: from py-out-1112.google.com (py-out-1112.google.com [64.233.166.180]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2G19CsG020295 for ; Sat, 15 Mar 2008 22:09:12 -0300 Received: by py-out-1112.google.com with SMTP id f47so4984670pye.14 for ; Sat, 15 Mar 2008 18:09:43 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:user-agent:mime-version:to:subject:references:in-reply-to:content-type:content-transfer-encoding; bh=2UFmWkv7ZmzBpzqRR/5f0OAp2xJUiQh1/Bt337iCXKQ=; b=LKPB9GNK+5DLvagkCwGQxS90LNWzD73FTEgL56CkcoSlNOLt8O8kws+LHVzrB8wc3X732ln+lmFV3qt+6ZQvUAhuy2v+wo4gCjCQUuI5d4QReWPRFlKTG9f4LPFi1fHqjHCID1Cv3mr3utRNszbaGqySSDZfo1y3sO8Wh6ekr8k= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:user-agent:mime-version:to:subject:references:in-reply-to:content-type:content-transfer-encoding; b=hIbECyu78eRbIqrZvlgQ2cNlbAqqa4Mn/72Ad0p/R0CWwMjk4F+grg6S5gONB/C3PdTxtieNLa78uZymIme6n0Qe3HEvPlhHZSiJFKUlDqEBPZzsSp35V69LvxidBnQWV4ZPijfE8B1PW91NLYgb89DrZTdtTaZ0rCsRA1EwLg0= Received: by 10.65.135.19 with SMTP id m19mr27697544qbn.18.1205629782657; Sat, 15 Mar 2008 18:09:42 -0700 (PDT) Received: from ?192.168.99.198? ( [201.20.249.53]) by mx.google.com with ESMTPS id f17sm17279584qba.35.2008.03.15.18.09.40 (version=TLSv1/SSLv3 cipher=RC4-MD5); Sat, 15 Mar 2008 18:09:41 -0700 (PDT) Message-ID: <47DC7351.2020201@gmail.com> Date: Sat, 15 Mar 2008 22:09:37 -0300 From: albert richerd carnier guedes User-Agent: Thunderbird 2.0.0.9 (X11/20071031) MIME-Version: 1.0 To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Divisibilidade por 13 References: <371082.78999.qm@web52906.mail.re2.yahoo.com> In-Reply-To: <371082.78999.qm@web52906.mail.re2.yahoo.com> Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 8bit Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: albert richerd carnier guedes X-Spam-Status: No, hits=4.0 required=5.0 tests=IN_REP_TO,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,REFERENCES, SPAM_PHRASE_00_01,USER_AGENT,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** Caramba Antônio, e como se chega a este método para divisão por 13, pois não é nadinha trivial. Antonio Giansante escreveu: > Um número é divisível por 13 se o quádruplo (4 vezes) > do último algarismo, somado ao número sem o último > algarismo, resultar um número divisível por 13. EX: > 25672 --> 2567+8 = 2575--> 257+20 = 277-->27+21=48 que > não é divisível or 13 Porém, creio que nesse caso seja > mais rápido você fazer a divisão do número e ver como > vai ficar o resto. Ficará um número do tipo 2n ou 3n. > Assim, você descobrirá qual o valor do n (6 para 2n e > 9 para 3n, por exemplo) e, ao mesmo tempo, obteráo > valor de q. é isso. ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sat Mar 15 22:43:13 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2G1gCsG022015 for ; Sat, 15 Mar 2008 22:42:12 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2G1gCWr022013 for obm-l-MllGbsmmN; Sat, 15 Mar 2008 22:42:12 -0300 Received: from py-out-1112.google.com (py-out-1112.google.com [64.233.166.177]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2G1gAsG022010 for ; Sat, 15 Mar 2008 22:42:10 -0300 Received: by py-out-1112.google.com with SMTP id f47so5000110pye.14 for ; Sat, 15 Mar 2008 18:42:41 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:user-agent:mime-version:to:subject:references:in-reply-to:content-type; bh=XRx8E/aJc2KILhBiwJeqMenI83TOsXm5qO+23KHYww4=; b=wuEQLECYSmvxqOd6+zWoezO4nifxYZMeiOGGu3RXv8ndtYQtkVoDnXdjYcBKbq/NNrpLLkns4BavYDlHNk3HrIR3bdxPPV3weZmHBhhXUx9MHEP6ZeTnmkrTyKqk9UDRSueradHaueD4OI50psaiC0w7kQdjtqs/qDn0hbbTrxE= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:user-agent:mime-version:to:subject:references:in-reply-to:content-type; b=HIU3TSTAz0dnr2HYQUo761qx+dkR6GhMz8R4Xx0cp9Z9Jym69oxOqE4QVifPooNnkKapAAlKImon0ifv4+I+o8WOAdVNPcrz+uLNfp+Ov0uc01Mx1V6AVBquULLZOaODoiejCCgfyz6NkgYHEswCxQKyzAC3W3XXa13/E75gEzM= Received: by 10.64.91.15 with SMTP id o15mr12071283qbb.28.1205631761681; Sat, 15 Mar 2008 18:42:41 -0700 (PDT) Received: from ?192.168.99.198? ( [201.20.249.53]) by mx.google.com with ESMTPS id e18sm17241361qba.27.2008.03.15.18.42.40 (version=SSLv3 cipher=RC4-MD5); Sat, 15 Mar 2008 18:42:40 -0700 (PDT) Message-ID: <47DC7B0E.9010802@gmail.com> Date: Sat, 15 Mar 2008 22:42:38 -0300 From: "arcguede@gmail.com" User-Agent: Thunderbird 2.0.0.12 (Windows/20080213) MIME-Version: 1.0 To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Enquete epistemologica References: <47DACC7F.10404@usp.br> <8994b830803141814l12410e89xe92e804a6478b5fb@mail.gmail.com> In-Reply-To: <8994b830803141814l12410e89xe92e804a6478b5fb@mail.gmail.com> Content-Type: multipart/alternative; boundary="------------070201000400050608040607" Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "arcguede@gmail.com" X-Spam-Status: No, hits=3.3 required=5.0 tests=AWL,EMAIL_ATTRIBUTION,IN_REP_TO,MAILTO_LINK, QUOTED_EMAIL_TEXT,RCVD_IN_MULTIHOP_DSBL,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, USER_AGENT,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: *** This is a multi-part message in MIME format. --------------070201000400050608040607 Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 8bit É por aí, eu vi esta desconfiança do método indutivo da matemática vinda de um matemático russo (que me escapa a memória quem era), mas ele afirmava que deveria ser feito mais esforços para se provar teoremas por meios dedutivos. O assunto envolvia segurança de criptografia, acho que tá bem relacionado. Mas concordo que o método indutivo matemático é diferente do científico em geral. Mas que um tem o germe do outro, isso tem. Maurício Collares escreveu: > Provas matemáticas que usam o método indutivo não são consideradas > formais, eu acho. Tal fato é inclusive, motivo de diversas piadas que > matemáticos contam sobre engenheiros (do tipo "vale para n = 1, vale > para n = 2, então vale sempre"). > > Vale lembrar, só pra constar, que a indução matemática não é, em si, > uma manifestação do "método indutivo". A indução matemática tem esse > nome porque serve para provar *dedutivamente* coisas conjecturadas a > partir do "método indutivo" (i.e., supor que uma idéia vale para o > caso geral porque ela vale para alguns casos particulares). Isso se > reflete no fato de que, ao construir uma prova por indução matemática, > você tem que conhecer de antemão o resultado final que deseja provar. > > -- > Abraços, > Maurício > > PS: Eu estou estudando para ser engenheiro. Nada contra tal profissão :) > > On 3/14/08, albert richerd carnier guedes wrote: > >> Eu tava lendo por aí que alguns matemáticos são meio que cabreros com o >> método indutivo por causa da idéia de que alguma hora o método pode >> falhar, sendo assim, o método dedutivo é o verdadeiro modo de se chegar >> a uma resposta segura e real dos problemas matemáticos. >> Um tanto Popperiano, mas vá lá. >> Alguém também sente esta desconfiança em relação ao método indutivo ? >> > > ========================================================================= > Instruções para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > ========================================================================= > > --------------070201000400050608040607 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: 7bit É por aí, eu vi esta desconfiança do método indutivo da matemática vinda de um matemático russo (que me escapa a memória quem era), mas ele afirmava que deveria ser feito mais esforços para se provar teoremas por meios dedutivos. O assunto envolvia segurança de criptografia, acho que tá bem relacionado.
Mas concordo que o método indutivo matemático é diferente do científico em geral.
Mas que um tem o germe do outro, isso tem.

Maurício Collares escreveu:
--------------070201000400050608040607-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sun Mar 16 09:55:16 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2GCrnsG013736 for ; Sun, 16 Mar 2008 09:53:49 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2GCrmVv013734 for obm-l-MllGbsmmN; Sun, 16 Mar 2008 09:53:48 -0300 Received: from py-out-1112.google.com (py-out-1112.google.com [64.233.166.182]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2GCrlsG013730 for ; Sun, 16 Mar 2008 09:53:47 -0300 Received: by py-out-1112.google.com with SMTP id f47so5248065pye.14 for ; Sun, 16 Mar 2008 05:54:19 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:mime-version:content-type; bh=KfDNNnLy7LsNgkFHqlG7+OqcXBC5Tl9jbSG9pIr922c=; b=QygQeZaOgA8eXHot2cfayPqCt4zPe7DhpgC+gRmLFh8b+8GmaudZFic3qrl8dfIlUBpX7Yqpwwwt34bmMx05PtrGF5zdd5/Cv8lKY03oijrmDMYCst8tDpn8ndiOurnWs1xxZqrq6M2qg11dl2IVYF7/r/CERpbIrRZLf0bwLEQ= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:mime-version:content-type; b=L/MqaCa9rZe3XzWPhWdU+5izjBfcRB/g7WqxMr6wqN9IVbDIr2UpKrKxXIk1y/B93QsN9n8OgTudNIlbHWt5YDosEMzonEculuWbF0dK9FaLPhU6WNoOvT+fHL7vHzCyV+mpbc7wHqzpOA9+x9QoY4KN+JHR95L9wbFfhFQJyc8= Received: by 10.65.196.2 with SMTP id y2mr28560141qbp.36.1205672058710; Sun, 16 Mar 2008 05:54:18 -0700 (PDT) Received: by 10.65.206.20 with HTTP; Sun, 16 Mar 2008 05:54:18 -0700 (PDT) Message-ID: Date: Sun, 16 Mar 2008 09:54:18 -0300 From: "=?ISO-8859-1?Q?Pedro_J=FAnior?=" To: obm-l Subject: [SPAM] [obm-l] =?ISO-8859-1?Q?Material_de_Congru=EAncia?= MIME-Version: 1.0 Content-Type: text/plain Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "=?ISO-8859-1?Q?Pedro_J=FAnior?=" X-Spam-Status: Yes, hits=5.7 required=5.0 tests=AWL,FROM_ENDS_IN_NUMS,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, SPAM_PHRASE_00_01,TO_LOCALPART_EQ_REAL,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ***** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_Part_5074_828998.1205672058698" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (5.70 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: TO_LOCALPART_EQ_REAL (-0.3 points) To: repeats local-part as real name SPAM: FROM_ENDS_IN_NUMS (0.9 points) From: ends in numbers SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 182.166.233.64.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 182.166.233.64.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-0.7 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- ------=_Part_5074_828998.1205672058698 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline O=E1 pessoal, estou preparando algumas crian=E7as para OBM na escola em que trabalho, e queria saber de voc=EAs se algu=E9m tem um bom material (did=E1= tico) sobre congru=EAncias. Se algu=E9m tiver, por favor se puder me enviar, desde j=E1 agrade=E7o! Pedro J=FAnior Jo=E3o Pessoa - PB ------=_Part_5074_828998.1205672058698 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline O=E1 pessoal, estou preparando algumas crian=E7as para OBM na escola em que= trabalho, e queria saber de voc=EAs se algu=E9m tem um bom material (did= =E1tico) sobre congru=EAncias.
Se algu=E9m tiver, por favor se puder me = enviar, desde j=E1 agrade=E7o!
Pedro J=FAnior
Jo=E3o Pessoa - PB
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Seja a integral dupla na região R(x,y): e^[(y-x)(y+x)]dxdy, onde R(x,y) está no plano xy e é limitada pelo trapezóide de vértices em (0,1), (0,2), (2,0), (1,0), calcular essa integral.
'e' está elevado ao produto (y-x)(y+x) e é o número de euller.

Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-747499893-1205677704=:88547-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sun Mar 16 12:32:16 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2GFV6sG023994 for ; Sun, 16 Mar 2008 12:31:06 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2GFV6NP023992 for obm-l-MllGbsmmN; Sun, 16 Mar 2008 12:31:06 -0300 Received: from web52909.mail.re2.yahoo.com (web52909.mail.re2.yahoo.com [206.190.49.19]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id m2GFV3sG023968 for ; Sun, 16 Mar 2008 12:31:04 -0300 Received: (qmail 75619 invoked by uid 60001); 16 Mar 2008 15:31:34 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:Date:From:Subject:To:In-Reply-To:MIME-Version:Content-Type:Content-Transfer-Encoding:Message-ID; b=qNYcE7WvseLOQ9kUAkVN8ExQPU9grAhiC8axtWzz9x/zJ16sz791cVb2FU3cl6QNjWke4bCaJotspcazYm7ZQuP9d4mJ0h+xRl/vGwyV1MIIqaCr4u8fR0lUsNqmQrzZakxL5zES5iD+Vt8NnGl2KTP8FKnk37CstI3+r8K4hc8=; X-YMail-OSG: NzoI94MVM1mg.mFRucRqSIBtVH__T734spRwM9vADdQRah3HNd9WsQjsjF8JrXoCV8a.Y3i9ZQ45UNKXg2A452SzltIt70uyO0exAFgF3u5A69P_dQmgv4U9jMi1di2mRr6IBudmX1JYoo0- Received: from [189.31.103.180] by web52909.mail.re2.yahoo.com via HTTP; Sun, 16 Mar 2008 12:31:34 ART Date: Sun, 16 Mar 2008 12:31:34 -0300 (ART) From: Antonio Giansante Subject: [SPAM] Re: [obm-l] Divisibilidade por 13 To: obm-l@mat.puc-rio.br In-Reply-To: <47DC7351.2020201@gmail.com> MIME-Version: 1.0 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 7bit Message-ID: <856952.75333.qm@web52909.mail.re2.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Antonio Giansante X-Spam-Status: Yes, hits=6.4 required=5.0 tests=FORGED_YAHOO_RCVD,IN_REP_TO,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ****** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (6.40 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 19.49.190.206.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 19.49.190.206.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- Então Albert...esse critério para o 13 e para vários outros primos já foi postado aqui há algum tempo. Dê uma olhada em http://www.mat.puc-rio.br/~obmlistas/obm-l.200701/msg00208.html que lá está tudo bem explicado e resumido. Boa diversão!! --- albert richerd carnier guedes escreveu: > Caramba Antônio, e como se chega a este método para > divisão por 13, pois > não é nadinha trivial. > > > Antonio Giansante escreveu: > > Um número é divisível por 13 se o quádruplo (4 > vezes) > > do último algarismo, somado ao número sem o último > > algarismo, resultar um número divisível por 13. > EX: > > 25672 --> 2567+8 = 2575--> 257+20 = 277-->27+21=48 > que > > não é divisível or 13 Porém, creio que nesse caso > seja > > mais rápido você fazer a divisão do número e ver > como > > vai ficar o resto. Ficará um número do tipo 2n ou > 3n. > > Assim, você descobrirá qual o valor do n (6 para > 2n e > > 9 para 3n, por exemplo) e, ao mesmo tempo, obteráo > > valor de q. é isso. > ========================================================================= > Instruções para entrar na lista, sair da lista e > usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > ========================================================================= > Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! http://br.mail.yahoo.com/ ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sun Mar 16 12:41:05 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2GFe6sG024304 for ; Sun, 16 Mar 2008 12:40:06 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2GFe5pp024300 for obm-l-MllGbsmmN; Sun, 16 Mar 2008 12:40:05 -0300 Received: from web52907.mail.re2.yahoo.com (web52907.mail.re2.yahoo.com [206.190.49.17]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id m2GFe3sG024291 for ; Sun, 16 Mar 2008 12:40:04 -0300 Received: (qmail 70194 invoked by uid 60001); 16 Mar 2008 15:40:34 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:Date:From:Subject:To:In-Reply-To:MIME-Version:Content-Type:Content-Transfer-Encoding:Message-ID; b=1scK0kyxyzGP5SgrX24hIMXytfpG4/jEYKjlr1/Uc88PffXyDQGHWN1qhOw6v0yERmtxWe1WZ0wMy0+MxLvU/gHH/PbgAfMSKUQg5+kaT7AeNFJXy+ONYUuXpUucd0r0CrGbcVc2XxvHN2vW5FSt4lxLOkPtXUJXTSVQAarlH8Q=; X-YMail-OSG: Z3n..gQVM1moI8Tc0BibSUQHCN2Ina5zV3umsGLpd7XZlC50E3j23ESdxfffxDr3dPgOpQs1Lxh1j8Dyu3QEd_p4LEIxs8mzN.AXm9smhWTzxkG_ng0J5SPYOvTOR7qnnsXC5m_HypS.Kgc- Received: from [189.31.103.180] by web52907.mail.re2.yahoo.com via HTTP; Sun, 16 Mar 2008 12:40:34 ART Date: Sun, 16 Mar 2008 12:40:34 -0300 (ART) From: Antonio Giansante Subject: [SPAM] Re: [obm-l] Divisibilidade por 13 To: obm-l@mat.puc-rio.br In-Reply-To: <47DC7351.2020201@gmail.com> MIME-Version: 1.0 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 7bit Message-ID: <728643.68779.qm@web52907.mail.re2.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Antonio Giansante X-Spam-Status: Yes, hits=6.4 required=5.0 tests=FORGED_YAHOO_RCVD,IN_REP_TO,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ****** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (6.40 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 17.49.190.206.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 17.49.190.206.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- Quase esqueci de comentar: achei também um outro critério de divisibilidade por 13 na revista do professor de matemática. Dê uma olhada em http://www.rpm.org.br/novo/conheca/58/divisibilidade.pdf. Também é interessante. Não há a demonstração para o 13 (só para o 7), mas fica claro que fazer -9k ou + 4r dá no mesmo, uma vez que 9 + 4 = 13 e em um dos métodos faz-se a diferença pra chegar ao múltyiplo anterior, enquanto no segundo soma-se para chegar ao próximo. VAleu? Espero te ajudado. Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! http://br.mail.yahoo.com/ ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sun Mar 16 21:17:40 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2H0F2sG003283 for ; Sun, 16 Mar 2008 21:15:03 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2H0EwkS003277 for obm-l-MllGbsmmN; Sun, 16 Mar 2008 21:14:58 -0300 Received: from rv-out-0910.google.com (rv-out-0910.google.com [209.85.198.188]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2H0EjsG003271 for ; Sun, 16 Mar 2008 21:14:46 -0300 Received: by rv-out-0910.google.com with SMTP id c27so3068510rvf.9 for ; Sun, 16 Mar 2008 17:15:18 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; bh=JximJRpRhzMUBmwh3mdkU/vGN92LfA8dLs8SSJ0J9Eo=; b=xVxxu8ginwVbQVQjThL+9sHItvmSoVPAatFAENL4Ji5nfV38hmviUS3cR7/9OpgZD7wSZL+LFIZce0PF7K7j5vJtFHYzaNlTNat527ToprzHQcz3EDKCdFzarrslhbOrLbtZDQEpa8fLOAfhguQVcmx6Bgqimv7ndV6k2DbiTNE= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; b=lN0+kNqqXkq6BW9VGJuvnQ6k7bf7YofdiUSxs9ntq/p66beeKiANautfWOc5+jeo1vHNBgk4TjZloHLX3WPaC/CEOz/G/U1mcYXabkEvavMAdc35W07FGwWSnsqxevURei1n+LqoC5SEKUHVfb5u0ZkhCUnFWYEGI8RO9syO+mI= Received: by 10.140.252.16 with SMTP id z16mr7298180rvh.196.1205712918018; Sun, 16 Mar 2008 17:15:18 -0700 (PDT) Received: by 10.141.193.2 with HTTP; Sun, 16 Mar 2008 17:15:18 -0700 (PDT) Message-ID: Date: Sun, 16 Mar 2008 21:15:18 -0300 From: "Murilo Giacometti" To: obm-l@mat.puc-rio.br Subject: =?ISO-8859-1?Q?Re:_[obm-l]_Material_de_Congru=EAncia?= In-Reply-To: MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline References: Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m2H0EpsG003274 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Murilo Giacometti" X-Spam-Status: No, hits=4.4 required=5.0 tests=IN_REP_TO,MAILTO_TO_SPAM_ADDR,QUOTED_EMAIL_TEXT, RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,REFERENCES, SPAM_PHRASE_00_01,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** Congruência módulo ou congruência de figuras geométricas? On 16/03/2008, Pedro Júnior wrote: > Oá pessoal, estou preparando algumas crianças para OBM na escola em que > trabalho, e queria saber de vocês se alguém tem um bom material (didático) > sobre congruências. > Se alguém tiver, por favor se puder me enviar, desde já agradeço! > Pedro Júnior > João Pessoa - PB > ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sun Mar 16 21:56:53 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2H0sRsG005134 for ; Sun, 16 Mar 2008 21:54:27 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2H0sNmf005128 for obm-l-MllGbsmmN; Sun, 16 Mar 2008 21:54:23 -0300 Received: from n23b.bullet.mail.sp1.yahoo.com (n23b.bullet.mail.sp1.yahoo.com [69.147.64.243]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id m2H0s2sG005113 for ; Sun, 16 Mar 2008 21:54:03 -0300 Received: from [216.252.122.216] by n23.bullet.sp1.yahoo.com with NNFMP; 17 Mar 2008 00:54:34 -0000 Received: from [69.147.65.174] by t1.bullet.sp1.yahoo.com with NNFMP; 17 Mar 2008 00:54:34 -0000 Received: from [127.0.0.1] by omp509.mail.sp1.yahoo.com with NNFMP; 17 Mar 2008 00:54:34 -0000 X-Yahoo-Newman-Property: ymail-5 X-Yahoo-Newman-Id: 887357.34867.bm@omp509.mail.sp1.yahoo.com Received: (qmail 57449 invoked by uid 60001); 17 Mar 2008 00:54:34 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=Received:Date:From:Subject:To:MIME-Version:Content-Type:Content-Transfer-Encoding:Message-ID; b=5H0IgJtFxzNo0M9WHXq+52mcBfmRmkB7lDwLvhNDREZH2v0JqKvslMFpeoNh3Ok1yN49Pp/Mpx0baYX/AF5UBnQga+WUYz3SiHm6DDs9qzBhVwNfJvjOIhCU1ZJuZOEO5CSSbPeCrO/HI7J6wLZdPVoQygH7xrMmXzdfrkb5Pbo=; Received: from [201.5.131.128] by web45705.mail.sp1.yahoo.com via HTTP; Sun, 16 Mar 2008 21:54:34 ART Date: Sun, 16 Mar 2008 21:54:34 -0300 (ART) From: =?iso-8859-1?q?Jos=E9=20de=20Jesus=20Rosa?= Subject: [SPAM] [obm-l] duvida To: obm-l@mat.puc-rio.br MIME-Version: 1.0 Content-Type: text/plain Content-Transfer-Encoding: 7bit Message-ID: <271113.55179.qm@web45705.mail.sp1.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: =?iso-8859-1?q?Jos=E9=20de=20Jesus=20Rosa?= X-Spam-Status: Yes, hits=9.0 required=5.0 tests=FORGED_YAHOO_RCVD,MIME_BOUND_DIGITS_5,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_01_02,SPAM_REDIRECTOR, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ********* X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="0-105856608-1205715274=:55179" X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (9.00 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: MIME_BOUND_DIGITS_5 (1.7 points) Spam tool pattern in MIME boundary SPAM: SPAM_PHRASE_01_02 (0.5 points) BODY: Spam phrases score is 01 to 02 (low) SPAM: [score: 1] SPAM: SPAM_REDIRECTOR (0.4 points) URI: Uses open redirection service SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 128.131.5.201.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 128.131.5.201.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- --0-105856608-1205715274=:55179 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 8bit Por favor, me ajudem nessa questão: Seja X um conjunto finito de cardinalidade n. Use a indução para mostrar que o conjunto das bijeções f: X---X tem cadnalidade n! --------------------------------- Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --------------------------------- Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-105856608-1205715274=:55179 Content-Type: text/html; charset=iso-8859-1 Content-Transfer-Encoding: 8bit
Por favor, me ajudem nessa questão:
 
Seja X um conjunto finito de cardinalidade n. Use a indução para mostrar que o conjunto das bijeções f: X---X tem cadnalidade n!
 
 

Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento!

Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-105856608-1205715274=:55179-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Mon Mar 17 10:20:19 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2HDGvsG010625 for ; Mon, 17 Mar 2008 10:16:57 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2HDGvsE010623 for obm-l-MllGbsmmN; Mon, 17 Mar 2008 10:16:57 -0300 Received: from mobius.impa.br (mobius.impa.br [147.65.1.81]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2HDGusG010619; Mon, 17 Mar 2008 10:16:56 -0300 Received: from [147.65.2.170] (obm-01.impa.br [147.65.2.170]) (authenticated bits=0) by mobius.impa.br (8.13.8/8.13.8) with ESMTP id m2HDHTt9008108 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=NO); Mon, 17 Mar 2008 10:17:29 -0300 Message-ID: <47DE6FA2.6040408@impa.br> Date: Mon, 17 Mar 2008 10:18:26 -0300 From: Olimpiada Brasileira de Matematica User-Agent: Thunderbird 1.5.0.14 (Windows/20071210) MIME-Version: 1.0 To: aobm-l@mat.puc-rio.br, Lista de discussao Subject: [obm-l] Cadastramento OBM-2008 Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 8bit X-Greylist: Sender succeeded SMTP AUTH authentication, not delayed by milter-greylist-3.0 (mobius.impa.br [147.65.1.27]); Mon, 17 Mar 2008 10:17:29 -0300 (BRT) Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Olimpiada Brasileira de Matematica X-Spam-Status: No, hits=4.8 required=5.0 tests=AWL,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01, USER_AGENT,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** Caros sócios e amigos da OBM, Estão abertas as inscrições para participar da OBM-2008. Todas as escolas das redes pública e privada podem participar. Período de cadastramento: 15 de março até 5 de maio de 2008 apenas no site da OBM www.obm.org.br Importante: Nosso sistema de cadastramento mudou, por favor, se a sua escola já participou da competição em anos anteriores, também deve realizar o novo cadastramento em 2008. Cordialmente, Secretaria da OBM ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Mon Mar 17 10:31:19 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2HDSGsG011267 for ; Mon, 17 Mar 2008 10:28:16 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2HDSGHY011265 for obm-l-MllGbsmmN; Mon, 17 Mar 2008 10:28:16 -0300 Received: from relay2.bol.com.br (relay2.bol.com.br [200.221.4.106]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2HDSEsG011261 for ; Mon, 17 Mar 2008 10:28:14 -0300 Received: from localhost (localhost [127.0.0.1]) by salsa2.bol.com.br (Postfix) with ESMTP id 3D879E0066AF for ; Mon, 17 Mar 2008 10:28:48 -0300 (BRT) Received: from bol.com.br (whisper7.mail.sys.intranet [172.26.5.82]) by salsa2.bol.com.br (Postfix) with ESMTP id D36DAE0067AB for ; Mon, 17 Mar 2008 10:28:47 -0300 (BRT) Date: Mon, 17 Mar 2008 10:28:47 -0300 Message-Id: Subject: Re: [obm-l] AFA 03/04 MIME-Version: 1.0 X-Sensitivity: 3 Content-Type: multipart/alternative; boundary="_=__=_XaM3_.1205760527.2A.573808.42.23337.52.42.007.2089288427" From: "arkon" To: "obm-l" X-XaM3-API-Version: 4.3(R1) (B10) X-SenderIP: 200.140.133.73 X-SIG5: eb5bc2f1cdf1cbf31611d73ab551c8dc Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "arkon" X-Spam-Status: No, hits=1.3 required=5.0 tests=AWL,BIG_FONT,LINES_OF_YELLING,LINES_OF_YELLING_2, MAILTO_LINK,SPAM_PHRASE_00_01,SUPERLONG_LINE, TO_LOCALPART_EQ_REAL,X_MAILING_LIST version=2.44 X-Spam-Level: * --_=__=_XaM3_.1205760527.2A.573808.42.23337.52.42.007.2089288427 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable Obrigado pela informa=E7=E3o Jo=E3o Victor, por=E9m nesse site n=E3o tem = resolu=E7=F5es e sim apenas as provas. Abra=E7os > Da um pulo em www.sassabetudo.com.br. Se n=E3o for com.br =E9 outra ter= mina=E7=E3o e procura no google. > > Joao Victor > On 3/14/08, arkon wrote: > Pessoal algu=E9m pode me enviar, por favor, a resolu=E7=E3o dessa quest=E3= o (AFA 03/04) A equa=E7=E3o x^3 + mx^2 + 2x + n =3D 0, onde m e n s=E3o n=FA= meros reais e i^2 =3D - 1, admite 1 + i como raiz. Ent=E3o m + n =E9 igual a: a) - 2. b) 0. c) 1. d) 2. E aproveitando a oportunidade algu=E9m pode me enviar, por favor, no meu = e-mail, arkon@bol.com.br, a resolu=E7=E3o dessa outra (AFA 03/04) Um foguete cuja massa vale 6 toneladas =E9 colocado em posi=E7= =E3o vertical para lan=E7amento. Se a velocidade de escape dos gases vale= 1 km/s, a quantidade de gases expelida por segundo, a fim de proporciona= r o empuxo necess=E1rio para dar ao foguete uma acelera=E7=E3o para cima = igual a 20 m/s^2 =E9: a) 120 kg. b) 180 kg. c) 100 kg. d) 80 kg. DESDE J=C1 MUITO OBRIGADO --_=__=_XaM3_.1205760527.2A.573808.42.23337.52.42.007.2089288427 Content-Type: text/html; charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable
Obrigado pela informa=E7=E3o Jo=E3o Victor, por=E9m nesse site n=E3o= tem resolu=E7=F5es e sim apenas as provas.
 
Abra=E7os
 
> Da um pulo em www.sa= ssabetudo.com.br. Se n=E3o for com.br = =E9 outra termina=E7=E3o e procura no google.
>  
> Joao Victor

 
> On 3/14/08, arkon <arkon@bol.com.br= > wrote:
>

Pessoal algu=E9m pode= me enviar, por favor, a resolu=E7=E3o dessa quest=E3o =

 

(AFA 03/04) A equa=E7= =E3o x^3 + mx^2 + 2x + n =3D 0, onde m e n s=E3o n=FAmeros reais e

i^2 =3D - 1, admite 1= +  i como raiz. Ent=E3o m + n =E9 igual a:

 

a) - 2. &n= bsp;       b) 0.  &n= bsp;    c) 1.     &n= bsp;  d) 2.  

 

E aproveitando a opor= tunidade algu=E9m pode me enviar, por favor, no meu

e-mail, arkon@bol.com.br, a resolu=E7=E3o dessa outra

 

(AFA 03/04) Um foguet= e cuja massa vale 6 toneladas =E9 colocado em posi=E7=E3o vertical para l= an=E7amento. Se a velocidade de escape dos gases vale 1 km/s, a quantidad= e de gases expelida por segundo, a fim de proporcionar o empuxo necess=E1= rio para dar ao foguete uma acelera=E7=E3o para cima igual a 20 m/s^2 =E9= :

 

a)= 120 kg.      b) 180 kg. = ;  c) 100 kg.    d) 80 kg.=

<= /SPAN> 

DESDE J=C1 MUITO OBRI= GADO

 

=

--_=__=_XaM3_.1205760527.2A.573808.42.23337.52.42.007.2089288427-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Mon Mar 17 11:11:07 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2HE7psG014165 for ; Mon, 17 Mar 2008 11:07:52 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2HE7phv014163 for obm-l-MllGbsmmN; Mon, 17 Mar 2008 11:07:51 -0300 Received: from ug-out-1314.google.com (ug-out-1314.google.com [66.249.92.170]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2HE7msG014155 for ; Mon, 17 Mar 2008 11:07:50 -0300 Received: by ug-out-1314.google.com with SMTP id q7so551698uge.0 for ; Mon, 17 Mar 2008 07:08:21 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; bh=09GvXhp9xEZ7kLhkwOUf74SZwJ5E1SzaqoHchfQVGXo=; b=Yf/tXYCUFSB75jQ7gvcvHkJLgag+9+iom4219+Pe3ngCya/MHv3m+YHgHSZHH16oHy3h0Xqk/fDGV2Bla/lBWhT1NbTOcpZU677hJ/pFYWNWnAdWksTW5NYiw1vmy6nhbAbmS6rUHqwa9kwTaZbwd4MnnbQcZwXY510Ky1uI/so= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; b=qyo3OWi9sUIsxMUlSnzKdiQPd1wKIpKHmqwhLaA1d4KpnS/Y+b3Q3xLY0hb/j+8PFoPGuJiLcib4RuPYg4NH60DMnn5lhqyUYh/gbNNGVvFKppuDFXDl3FXDCs33xQoo8fIShpausik+09rzA3vVYYat4waDJZ/6hWpqpU8h+pg= Received: by 10.67.15.15 with SMTP id s15mr2920473ugi.27.1205762901190; Mon, 17 Mar 2008 07:08:21 -0700 (PDT) Received: by 10.66.219.5 with HTTP; Mon, 17 Mar 2008 07:08:21 -0700 (PDT) Message-ID: <2d483c770803170708s6f3486a0i9b1a76a7c5c99c8b@mail.gmail.com> Date: Mon, 17 Mar 2008 11:08:21 -0300 From: "Ralph Teixeira" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Solido In-Reply-To: <700771.18342.qm@web33803.mail.mud.yahoo.com> MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline References: <700771.18342.qm@web33803.mail.mud.yahoo.com> Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m2HE7psG014161 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Ralph Teixeira" X-Spam-Status: No, hits=4.1 required=5.0 tests=AWL,IN_REP_TO,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** Nos limites para a integral em x, aquele x=9-y^2 está "misterioso", acho que é ali o problema... Bom, vamos lá. Se a gente realmente quer "dx dy", temos que encontrar a projeção do sólido no plano xy. Eu fiz um desenho aqui com um certo cuidado, e me parece que esta projeção é a região entre x=1+y^2 (pois a curva de interseção entre o cilindro parabólico z=1-y^2 e o plano z=2-x se projeta em xOy sobre 2-x=1-y^2, isto é, x=1+y^2) e x=2. O resto, eu concordo contigo. Então a integral correta seria: Int (y=-1 a y=1) Int (x=1+y^2 a x=2) (1-y^2)-(2-x) dx dy Vejamos... conta... conta.... deu 8/15, confere com o gabarito que você tem. Abraço, Ralph P.S.: Eu acho que eu prefiro fazer esta aí usando dy dz... Deixa eu ver... Ficaria Int (y=-1 a y=1) Int (z=0 a z=1-y^2) 2-(2-z) dz dy. A vantagem disto é que a gente não precisa "dissecar" aquela interseção entre x+z=2 e z=1-y^2, mas eu concordo que não está MUITO mais fácil não. 2008/3/15 Klaus Ferraz : > > Determine o volume do solido limitado pelas superficies z=1-y^2 , x+z=2 e > x=2 e para z>=0. > v=8/15. > Eu só queria que montasse a integral dupla. Porque a que estou achando tah > dando errado. > Estou achando $_(-1,1)$(-y^2+9,y^2+1)[1-y^2 - (2-x)]dxdy. Não sei qual meu > erro. > > Grato. > > ________________________________ > Abra sua conta no Yahoo! Mail, o único sem limite de espaço para > armazenamento! ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Mon Mar 17 12:36:47 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2HFZRsG020861 for ; Mon, 17 Mar 2008 12:35:27 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2HFZRXU020859 for obm-l-MllGbsmmN; Mon, 17 Mar 2008 12:35:27 -0300 Received: from relay1.bol.com.br (relay1.bol.com.br [200.221.4.105]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2HFZMsG020843 for ; Mon, 17 Mar 2008 12:35:22 -0300 Received: from localhost (localhost [127.0.0.1]) by salsa1.bol.com.br (Postfix) with ESMTP id F15554AA3E for ; Mon, 17 Mar 2008 12:35:55 -0300 (BRT) Received: from bol.com.br (whisper4.mail.sys.intranet [172.26.5.139]) by salsa1.bol.com.br (Postfix) with ESMTP id B56A84A804; Mon, 17 Mar 2008 12:35:54 -0300 (BRT) Date: Mon, 17 Mar 2008 12:35:54 -0300 Message-Id: Subject: [obm-l] Perplexidade MIME-Version: 1.0 X-Sensitivity: 3 Content-Type: text/plain; charset=iso-8859-1 From: eric.guedes@bol.com.br To: "obm-l" Cc: "obm-l" X-XaM3-API-Version: 4.3(R1) (B10) X-SenderIP: 201.36.164.55 X-SIG5: 4554a05e333698aab2898aa39d8f996d Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m2HFZPsG020847 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: eric.guedes@bol.com.br X-Spam-Status: No, hits=1.5 required=5.0 tests=NO_REAL_NAME,SPAM_PHRASE_00_01,TO_LOCALPART_EQ_REAL, X_MAILING_LIST version=2.44 X-Spam-Level: * Estou perplexo com a indiferenca de voces. Estou a meses tentando denunciar um crime (homicidio) ocorrido numa clinica psiquiatrica. A Abin - Agencia Brasileira de Informacoes - estah envolvida. As denuncias simplesmente sao ignoradas ou nem aceitas sequer. Agora estao tentando me matar, se eu bobear me pegam. As autoridades e a midia SABEM e fazem questao de IGNORAR. Ja fui a policia, varias vezes, mandei a denuncia para o ministerio publico, procurei a Policia Federal, a Civil, a Militar... nada, nenhum sinal. [ ]'s Aguardo resposta. ============================================== Eric Campos Bastos Guedes - matematico, poeta e filosofo Sacerdote da V.I.D.A. - Verdadeira Igreja da Divindade Axiomatica http://www.orkut.com/Community.aspx?cmm=10960949 http://br.geocities.com/mathfire2001/ e-mail: mathfire@gmail.com / eric.guedes@bol.com.br MSN: fator-n@hotmail.com / Y!M: mathfire2001 Cel. 0xx-21-8131-7542 / Skype: eric.campos.bastos.guedes ICARAI - NITEROI - RJ - BRASIL ============================================== ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Mon Mar 17 12:36:47 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2HFZRsG020861 for ; Mon, 17 Mar 2008 12:35:27 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2HFZRXU020859 for obm-l-MllGbsmmN; Mon, 17 Mar 2008 12:35:27 -0300 Received: from relay1.bol.com.br (relay1.bol.com.br [200.221.4.105]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2HFZMsG020843 for ; Mon, 17 Mar 2008 12:35:22 -0300 Received: from localhost (localhost [127.0.0.1]) by salsa1.bol.com.br (Postfix) with ESMTP id F15554AA3E for ; Mon, 17 Mar 2008 12:35:55 -0300 (BRT) Received: from bol.com.br (whisper4.mail.sys.intranet [172.26.5.139]) by salsa1.bol.com.br (Postfix) with ESMTP id B56A84A804; Mon, 17 Mar 2008 12:35:54 -0300 (BRT) Date: Mon, 17 Mar 2008 12:35:54 -0300 Message-Id: Subject: [obm-l] Perplexidade MIME-Version: 1.0 X-Sensitivity: 3 Content-Type: text/plain; charset=iso-8859-1 From: eric.guedes@bol.com.br To: "obm-l" Cc: "obm-l" X-XaM3-API-Version: 4.3(R1) (B10) X-SenderIP: 201.36.164.55 X-SIG5: 4554a05e333698aab2898aa39d8f996d Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m2HFZPsG020847 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: eric.guedes@bol.com.br X-Spam-Status: No, hits=1.5 required=5.0 tests=NO_REAL_NAME,SPAM_PHRASE_00_01,TO_LOCALPART_EQ_REAL, X_MAILING_LIST version=2.44 X-Spam-Level: * Estou perplexo com a indiferenca de voces. Estou a meses tentando denunciar um crime (homicidio) ocorrido numa clinica psiquiatrica. A Abin - Agencia Brasileira de Informacoes - estah envolvida. As denuncias simplesmente sao ignoradas ou nem aceitas sequer. Agora estao tentando me matar, se eu bobear me pegam. As autoridades e a midia SABEM e fazem questao de IGNORAR. Ja fui a policia, varias vezes, mandei a denuncia para o ministerio publico, procurei a Policia Federal, a Civil, a Militar... nada, nenhum sinal. [ ]'s Aguardo resposta. ============================================== Eric Campos Bastos Guedes - matematico, poeta e filosofo Sacerdote da V.I.D.A. - Verdadeira Igreja da Divindade Axiomatica http://www.orkut.com/Community.aspx?cmm=10960949 http://br.geocities.com/mathfire2001/ e-mail: mathfire@gmail.com / eric.guedes@bol.com.br MSN: fator-n@hotmail.com / Y!M: mathfire2001 Cel. 0xx-21-8131-7542 / Skype: eric.campos.bastos.guedes ICARAI - NITEROI - RJ - BRASIL ============================================== ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Mon Mar 17 12:50:28 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2HFn9sG021532 for ; Mon, 17 Mar 2008 12:49:09 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2HFn9mi021530 for obm-l-MllGbsmmN; Mon, 17 Mar 2008 12:49:09 -0300 Received: from fg-out-1718.google.com (fg-out-1718.google.com [72.14.220.159]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2HFn6sG021525 for ; Mon, 17 Mar 2008 12:49:07 -0300 Received: by fg-out-1718.google.com with SMTP id e12so11137434fga.3 for ; Mon, 17 Mar 2008 08:49:39 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; bh=bl3BTXZCbW2HM8xnNryrdZyh3k4WKY6Xux8II2/osFY=; b=jtEgWdnaN98ZswbydmdUevS91SWxgl+sMBDZymDbQTJLkuc4BCw/swLt7+6voj1mGJyNPS8wmuKPjgHJrDULLqTBDKk7DMWPa51L1Z1wIJEEUO/uznod2ZJMSfLomF9LDzOOazY5Qr5ahz4RlBUXboDbYQBvGpcE9OtGjb9G2p0= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; b=WF6c5e70p/D4gE9t4Rkq0z8rsKdS+a8aNEvmJ+zhWfsBl9biOGDVpkNsaXya8nVh/pBAQgI7t6Yjrq7ra0arMg5rDTWEh0O5HvOPzIHpKc3jMMKybam4SU2r6Q+iZeuyLVki2Whz3kH8CZnaHuYgQZN/fMiO05Z7kefZvHmzvwc= Received: by 10.82.116.15 with SMTP id o15mr16101841buc.11.1205768539922; Mon, 17 Mar 2008 08:42:19 -0700 (PDT) Received: by 10.82.127.13 with HTTP; Mon, 17 Mar 2008 08:42:19 -0700 (PDT) Message-ID: Date: Mon, 17 Mar 2008 12:42:19 -0300 From: "Johann Peter Gustav Lejeune Dirichlet" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Enquete epistemologica In-Reply-To: <47DC7B0E.9010802@gmail.com> MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline References: <47DACC7F.10404@usp.br> <8994b830803141814l12410e89xe92e804a6478b5fb@mail.gmail.com> <47DC7B0E.9010802@gmail.com> Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m2HFn8sG021528 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Johann Peter Gustav Lejeune Dirichlet" X-Spam-Status: No, hits=0.2 required=5.0 tests=AWL,FROM_ENDS_IN_NUMS,IN_REP_TO,QUOTED_EMAIL_TEXT, REFERENCES,SIGNATURE_LONG_SPARSE,SPAM_PHRASE_00_01, X_MAILING_LIST version=2.44 X-Spam-Level: Não sei bem qual é o problema com o modo de resolver problemas assim. Desde muito tempo pessoas não confiam no método de demonstração via contradição. E também tem pessoas que não apostam uma ficha no Axioma da Escolha. Por ora estes são os únicos casos de `dúvida epistemológica' que lembro. Em 15/03/08, arcguede@gmail.com escreveu: > > É por aí, eu vi esta desconfiança do método indutivo da matemática vinda de > um matemático russo (que me escapa a memória quem era), mas ele afirmava que > deveria ser feito mais esforços para se provar teoremas por meios dedutivos. > O assunto envolvia segurança de criptografia, acho que tá bem relacionado. > Mas concordo que o método indutivo matemático é diferente do científico em > geral. > Mas que um tem o germe do outro, isso tem. > > Maurício Collares escreveu: > Provas matemáticas que usam o método indutivo não são consideradas > formais, eu acho. Tal fato é inclusive, motivo de diversas piadas que > matemáticos contam sobre engenheiros (do tipo "vale para n = 1, vale > para n = 2, então vale sempre"). > > Vale lembrar, só pra constar, que a indução matemática não é, em si, > uma manifestação do "método indutivo". A indução matemática tem esse > nome porque serve para provar *dedutivamente* coisas conjecturadas a > partir do "método indutivo" (i.e., supor que uma idéia vale para o > caso geral porque ela vale para alguns casos particulares). Isso se > reflete no fato de que, ao construir uma prova por indução matemática, > você tem que conhecer de antemão o resultado final que deseja provar. > > -- > Abraços, > Maurício > > PS: Eu estou estudando para ser engenheiro. Nada contra tal profissão :) > > On 3/14/08, albert richerd carnier guedes wrote: > > > Eu tava lendo por aí que alguns matemáticos são meio que cabreros com o > método indutivo por causa da idéia de que alguma hora o método pode > falhar, sendo assim, o método dedutivo é o verdadeiro modo de se chegar > a uma resposta segura e real dos problemas matemáticos. > Um tanto Popperiano, mas vá lá. > Alguém também sente esta desconfiança em relação ao método indutivo ? > > ========================================================================= > Instruções para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > ========================================================================= > > > > -- Ideas are bulletproof. V ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Mon Mar 17 12:51:14 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2HFoGsG021590 for ; Mon, 17 Mar 2008 12:50:16 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2HFoFrf021588 for obm-l-MllGbsmmN; Mon, 17 Mar 2008 12:50:15 -0300 Received: from fg-out-1718.google.com (fg-out-1718.google.com [72.14.220.156]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2HFoDsG021584 for ; Mon, 17 Mar 2008 12:50:14 -0300 Received: by fg-out-1718.google.com with SMTP id e12so11137806fga.3 for ; Mon, 17 Mar 2008 08:50:46 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; bh=mc5wfAWyvRiyN+X/2LvlsktKSRVIOZx8Y1EgsAzlGvw=; b=QC4CTmJAfRXABR0IXjIkTIBJKf8MUjxSHY5+7uJkS8r17Vv4G9vLvL99gTf7TBWREDZC8PA+jklRUMx749Re4MCQjL2dEFgx7KkEGX1ijcrchPwovfZ5QkS47UisNYY53z2muFTWifmPDLdq1HZ8dT9rXuwfOMfubyI+IurmO64= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; b=sIFC+Tjvouo2ZwdwQX+rkqVknIXd9qkrbxDECB4DIFSaRu6Q8nx4Unq/ig7dZXEP8ajEleUt00SAVpDQ3MBu3AMry3MT0aMfvZkMsLDsFXWstEk2nC4AeRLpGVKGwbjF0Y0KoS/Iw5b2Y7IlrAz715Kgy4sri5lVmlUj4t2cR3k= Received: by 10.82.167.9 with SMTP id p9mr9038516bue.7.1205769045622; Mon, 17 Mar 2008 08:50:45 -0700 (PDT) Received: by 10.82.127.13 with HTTP; Mon, 17 Mar 2008 08:50:45 -0700 (PDT) Message-ID: Date: Mon, 17 Mar 2008 12:50:45 -0300 From: "Johann Peter Gustav Lejeune Dirichlet" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] AFA 03/04 In-Reply-To: <5bb472220803150833l62a0652cr733205809c23af05@mail.gmail.com> MIME-Version: 1.0 Content-Type: text/plain; charset=WINDOWS-1252 Content-Disposition: inline References: <5bb472220803150833l62a0652cr733205809c23af05@mail.gmail.com> Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m2HFoFsG021586 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Johann Peter Gustav Lejeune Dirichlet" X-Spam-Status: No, hits=0.1 required=5.0 tests=AWL,FROM_ENDS_IN_NUMS,IN_REP_TO,QUOTED_EMAIL_TEXT, REFERENCES,SIGNATURE_LONG_SPARSE,SPAM_PHRASE_00_01, X_MAILING_LIST version=2.44 X-Spam-Level: Em 15/03/08, Joao Victor Brasil escreveu: > Da um pulo em www.sassabetudo.com.br. Se não for com.br é outra terminação e > procura no google. > > Joao Victor > > > On 3/14/08, arkon wrote: > > > > > > > > > > Pessoal alguém pode me enviar, por favor, a resolução dessa questão > > > > > > > > (AFA 03/04) A equação x^3 + mx^2 + 2x + n = 0, onde m e n são números > reais e > > > > i^2 = - 1, admite 1 + i como raiz. Então m + n é igual a: > > > > > > > > a) – 2. b) 0. c) 1. d) 2. Bem, levando em conta que se (1+i) é raiz então (1-i) também é, o polinômio acima é divisível por x^2-2x+2. x^2-2x+2=0 x^2=2x-2 x^3=2x^2-2x x^3=2(2x-2)-2x x^3=4x-4-2x=2x-4 Assim, x^3 + mx^2 + 2x + n =(2x-4)+m(2x-2)+2x+n=(2+2m+2)x+(-4-2m+n)=0 acarreta 2m+4=0 e n-2m=4 >> >> >> >> E aproveitando a oportunidade alguém pode me enviar, por favor, no meu >> >> e-mail, arkon@bol.com.br, a resolução dessa outra > > > > > > > > (AFA 03/04) Um foguete cuja massa vale 6 toneladas é colocado em posição > vertical para lançamento. Se a velocidade de escape dos gases vale 1 km/s, a > quantidade de gases expelida por segundo, a fim de proporcionar o empuxo > necessário para dar ao foguete uma aceleração para cima igual a 20 m/s^2 é: > > > > > > > > a) 120 kg. b) 180 kg. c) 100 kg. d) 80 kg. > > > > > > > > DESDE JÁ MUITO OBRIGADO > > > > > > -- Ideas are bulletproof. V ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Mon Mar 17 17:27:50 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2HKPvsG008714 for ; Mon, 17 Mar 2008 17:25:57 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2HKPv3E008712 for obm-l-MllGbsmmN; Mon, 17 Mar 2008 17:25:57 -0300 Received: from web37011.mail.mud.yahoo.com (web37011.mail.mud.yahoo.com [209.191.85.96]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id m2HKPssG008697 for ; Mon, 17 Mar 2008 17:25:55 -0300 Received: (qmail 48185 invoked by uid 60001); 17 Mar 2008 20:26:23 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:Date:From:Subject:To:In-Reply-To:MIME-Version:Content-Type:Content-Transfer-Encoding:Message-ID; b=a1F6u7x09PBntj+HWKUWoefk7IMZVYQaP4EPn0B2ez0HdsoQOiVYdXhQMbuAqg5JWVY2cpo9ASyW9nd1hWdz3FppDlVZ2LtSh1PYaEFMP4j5e1TARPmJNOVaKrYY82wTxxSZvblMIKOqJRkbZnQOtru12ESWWET5Stl3mHGkcyM=; X-YMail-OSG: SqYRI8sVM1nhacjcMru6KiBayvAmNbn8vGnqlVPuPRDzWgeDwKvpQREz4W7wd1HObJlybG2nXP..ULCuTt5CJDvysAPP2lzMhBrXV54j.RBSxF9iMcE- Received: from [161.148.38.248] by web37011.mail.mud.yahoo.com via HTTP; Mon, 17 Mar 2008 17:26:23 ART Date: Mon, 17 Mar 2008 17:26:23 -0300 (ART) From: Bruno Carvalho Subject: [SPAM] Re: [obm-l] Matrizes To: obm-l@mat.puc-rio.br In-Reply-To: MIME-Version: 1.0 Content-Type: text/plain Content-Transfer-Encoding: 7bit Message-ID: <691945.47797.qm@web37011.mail.mud.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Bruno Carvalho X-Spam-Status: Yes, hits=8.5 required=5.0 tests=ASCII_FORM_ENTRY,AWL,FORGED_YAHOO_RCVD,IN_REP_TO, MAILTO_TO_SPAM_ADDR,MIME_BOUND_DIGITS_5,QUOTED_EMAIL_TEXT, RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01, SPAM_REDIRECTOR,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="0-151423587-1205785583=:47797" X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (8.50 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: MIME_BOUND_DIGITS_5 (1.7 points) Spam tool pattern in MIME boundary SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: QUOTED_EMAIL_TEXT (-0.8 points) BODY: Contains what looks like a quoted email text SPAM: ASCII_FORM_ENTRY (0.1 points) BODY: Contains an ASCII-formatted form SPAM: MAILTO_TO_SPAM_ADDR (0.7 points) URI: Includes a link to a likely spammer email address SPAM: SPAM_REDIRECTOR (0.4 points) URI: Uses open redirection service SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 96.85.191.209.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 96.85.191.209.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-0.0 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- --0-151423587-1205785583=:47797 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 8bit Johann , desculpe faltou completar.." TJ=M tem uma única solução". tomo a liberdade de perguntar : a)Se eu quizesse fazer por absurdo, ou seja suponho que T é invertível e afirmar que a solução não é única, como ficaria ? tem saída? confesso que tenho muita dificuldade para fazer demonsntrações Mais uma vez agradeço a sua atenção. Um abraço. bruno ========================================================= Johann Peter Gustav Lejeune Dirichlet escreveu: Em 12/03/08, Bruno Carvalho escreveu: > Oi Pessoal, > > Peço ajuda ( orientação) na demonstração da seguinte afirmação sobre > matrizes. > Sejam T matriz nxn ; J matriz n x1 e M matriz nx1. Prove que se T possui > uma inversa então TJ tem uma única solução. > TJ é alguma equação? Bem, se for algo como TX=J, podemos pensar assim: TX=J se e só se T^-1*TX=T^-1J se e só se X=T^-1J. E fim! > Obrigado > > Bruno > > ________________________________ > Abra sua conta no Yahoo! Mail, o único sem limite de espaço para > armazenamento! > > -- Ideas are bulletproof. V ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= --------------------------------- Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-151423587-1205785583=:47797 Content-Type: text/html; charset=iso-8859-1 Content-Transfer-Encoding: 8bit
Johann , desculpe faltou completar.." TJ=M tem uma única solução".
tomo a liberdade de perguntar :
 
a)Se eu quizesse fazer por absurdo, ou seja suponho que T é invertível e afirmar que a solução não é única, como ficaria ? tem saída?
 
confesso que tenho muita dificuldade  para fazer demonsntrações
 
Mais uma vez agradeço a sua atenção.
 
Um abraço.
 
bruno
=========================================================
Johann Peter Gustav Lejeune Dirichlet <peterdirichlet2003@gmail.com> escreveu:
Em 12/03/08, Bruno Carvalho escreveu:
> Oi Pessoal,
>
> Peço ajuda ( orientação) na demonstração da seguinte afirmação sobre
> matrizes.
> Sejam T matriz nxn ; J matriz n x1 e M matriz nx1. Prove que se T possui
> uma inversa então TJ tem uma única solução.
>

TJ é alguma equação?

Bem, se for algo como TX=J, podemos pensar assim:
TX=J se e só se T^-1*TX=T^-1J se e só se X=T^-1J. E fim!


> Obrigado
>
> Bruno
>
> ________________________________
> Abra sua conta no Yahoo! Mail, o único sem limite de espaço para
> armazenamento!
>
>


--
Ideas are bulletproof.

V

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Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-151423587-1205785583=:47797-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Mon Mar 17 18:56:17 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2HLsUsG015069 for ; Mon, 17 Mar 2008 18:54:30 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2HLsUvh015067 for obm-l-MllGbsmmN; Mon, 17 Mar 2008 18:54:30 -0300 Received: from fg-out-1718.google.com (fg-out-1718.google.com [72.14.220.153]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2HLsRsG015063 for ; Mon, 17 Mar 2008 18:54:28 -0300 Received: by fg-out-1718.google.com with SMTP id e12so11250663fga.3 for ; Mon, 17 Mar 2008 14:55:00 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=pm5Y+Y8C8g3Og3d8L86RE9w6g/GSee2oF3H/3+McMq4=; b=I6COUtbCrV/EjFiQNyn9+6Qkb1iiLY7iJ0Ejn5fPZHS0PBsvm71vk+CSGnJNVwThXty85xqlEKX6e8ZHSdxFtx2JGCjWCAH3r4fST363LWQRugJoQ7HUwx68K5CQioO0/GwFbrQsIT25FHdV/ob+SFiiAinGIrKbY4p6VTLyuUM= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=on7jgtQeorj45oHgO+MpOhjbOdKKFFj0z4ATJlH4wDKXHNxp8fojod4ed9HhXHrUZwOWAup9mpCbwMIzPw2iGPPY6KCyJT3pnXfCbyoqmXjmG6O6F8FAa9FCoZ/cyFImZAimNejMZhqivobKOaCwDLheKrjmzVGSAbG96sa5P5U= Received: by 10.86.90.2 with SMTP id n2mr13907639fgb.43.1205790899799; Mon, 17 Mar 2008 14:54:59 -0700 (PDT) Received: by 10.86.74.8 with HTTP; Mon, 17 Mar 2008 14:54:59 -0700 (PDT) Message-ID: Date: Mon, 17 Mar 2008 18:54:59 -0300 From: "saulo nilson" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] AFA 03/04 In-Reply-To: <5bb472220803150833l62a0652cr733205809c23af05@mail.gmail.com> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_4698_15520295.1205790899781" References: <5bb472220803150833l62a0652cr733205809c23af05@mail.gmail.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "saulo nilson" X-Spam-Status: No, hits=-0.6 required=5.0 tests=AWL,BIG_FONT,HTML_50_70,IN_REP_TO,LINES_OF_YELLING, MAILTO_LINK,QUOTED_EMAIL_TEXT,REFERENCES,SPAM_PHRASE_00_01, X_MAILING_LIST version=2.44 X-Spam-Level: ------=_Part_4698_15520295.1205790899781 Content-Type: text/plain; charset=WINDOWS-1252 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline 6000*20=3DE-6000*10=3D E=3D6000*30 dm/dt*1000=3D180000 dm/dt=3D180kg/s 2008/3/15 Joao Victor Brasil : > Da um pulo em www.sassabetudo.com.br. Se n=E3o for com.br =E9 outra termi= na=E7=E3o > e procura no google. > > Joao Victor > > > On 3/14/08, arkon wrote: > > > > *Pessoal algu=E9m pode me enviar, por favor, a resolu=E7=E3o dessa que= st=E3o * > > > > * * > > > > *(AFA 03/04) A equa=E7=E3o x^3 + mx^2 + 2x + n =3D 0, onde m e n s=E3o = n=FAmeros > > reais e * > > > > *i^2 =3D - 1, admite 1 + i como raiz. Ent=E3o m + n =E9 igual a:* > > > > * * > > > > *a) =96 2. b) 0. c) 1. d) 2. * > > > > * * > > > > *E aproveitando a oportunidade algu=E9m pode me enviar, por favor, no m= eu > > * > > > > *e-mail, arkon@bol.com.br, a resolu=E7=E3o dessa outra* > > > > * * > > > > *(AFA 03/04) Um foguete cuja massa vale 6 toneladas =E9 colocado em > > posi=E7=E3o vertical para lan=E7amento. Se a velocidade de escape dos g= ases vale 1 > > km/s, a quantidade de gases expelida por segundo, a fim de proporcionar= o > > empuxo necess=E1rio para dar ao foguete uma acelera=E7=E3o para cima ig= ual a 20 > > m/s^2 =E9:* > > > > * * > > > > *a) 120 kg. b) 180 kg. c) 100 kg. d) 80 kg.* > > > > * * > > > > *DESDE J=C1 MUITO OBRIGADO* > > > > * * > > > > ------=_Part_4698_15520295.1205790899781 Content-Type: text/html; charset=WINDOWS-1252 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline
6000*20=3DE-6000*10=3D
E=3D6000*30
dm/dt*1000=3D180000
dm/dt=3D180kg/s
2008/3/15 Joao Victor Brasil <jvbrasil@gmail.com>:
Da um pulo em www.sassabetudo.com.br. Se n=E3o for com.br =E9 outra termina=E7=E3o e procura no google.
 
Joao Victor

 
On 3/14/08, = arkon <arkon@b= ol.com.br> wrote:=20

<= font face=3D"Times New Roman">Pessoal algu=E9m pode me enviar, por favor, a= resolu=E7=E3o dessa quest=E3o

 

(AFA 03/04) A equa=E7=E3o x^3 + mx^2 = + 2x + n =3D 0, onde m e n s=E3o n=FAmeros reais e

i^2 =3D - 1, admite 1 +  <= /span>i como raiz. Ent=E3o m + n =E9 igual a:

 

a) =96 2.   &nbs= p;     b) 0.     =   c) 1.        = d) 2.  

 

E aproveitando a oportunidade algu=E9= m pode me enviar, por favor, no meu

e-mail, arkon@b= ol.com.br, a res= olu=E7=E3o dessa outra

 

(AFA 03/04) Um foguete cuja massa val= e 6 toneladas =E9 colocado em posi=E7=E3o vertical para lan=E7amento. Se a = velocidade de escape dos gases vale 1 km/s, a quantidade de gases expelida = por segundo, a fim de proporcionar o empuxo necess=E1rio para dar ao foguet= e uma acelera=E7=E3o para cima igual a 20 m/s^2 =E9:

 

a) 120 kg.=       b) 180 kg.   c= ) 100 kg.    d) 80 kg.=

 

DESDE J=C1 MUITO OBRIGADO

 



------=_Part_4698_15520295.1205790899781-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Mon Mar 17 19:24:16 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2HMMusG019886 for ; Mon, 17 Mar 2008 19:22:56 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2HMMtWf019879 for obm-l-MllGbsmmN; Mon, 17 Mar 2008 19:22:55 -0300 Received: from smtpi03s.infolink.com.br (smtpi03s.infolink.com.br [200.187.64.122]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2HMMpsG019829 for ; Mon, 17 Mar 2008 19:22:52 -0300 Received: from smtpi03s.infolink.com.br (localhost [127.0.0.1]) by smtpi03s.infolink.com.br (Postfix) with ESMTP id 9B376714066 for ; Mon, 17 Mar 2008 19:23:25 -0300 (EST) Received: from [127.0.0.1] (unknown [189.60.112.176]) by smtpi03s.infolink.com.br (Postfix) with ESMTP id 7BC4270AC2A for ; Mon, 17 Mar 2008 19:23:25 -0300 (EST) Message-ID: <47DEEF18.4080108@infolink.com.br> Date: Mon, 17 Mar 2008 19:22:16 -0300 From: Carlos Nehab User-Agent: Thunderbird 2.0.0.12 (Windows/20080213) MIME-Version: 1.0 To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Perplexidade References: In-Reply-To: Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: 7bit X-Antivirus: avast! (VPS 080317-0, 17/03/2008), Outbound message X-Antivirus-Status: Clean Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Carlos Nehab X-Spam-Status: No, hits=4.7 required=5.0 tests=AWL,CTYPE_JUST_HTML,IN_REP_TO,MAILTO_LINK,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, USER_AGENT,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** Caro Eric,

Aqui não é o Forum adequado para este tipo de denúncia, mas sim as instituições que você mencionou. 
Portanto, não acho nem oportuno nem produtivo insistir.

Abraços,
Carlos Nehab

eric.guedes@bol.com.br escreveu: 
Estou perplexo com a indiferenca de voces.

Estou a meses tentando denunciar um crime (homicidio) ocorrido numa clinica psiquiatrica. A Abin - Agencia Brasileira de Informacoes - estah envolvida.

As denuncias simplesmente sao ignoradas ou nem aceitas sequer.

Agora estao tentando me matar, se eu bobear me pegam.

As autoridades e a midia SABEM e fazem questao de IGNORAR.

Ja fui a policia, varias vezes, mandei a denuncia para o ministerio publico, procurei a Policia Federal, a Civil, a Militar... nada, nenhum sinal.

[ ]'s

Aguardo resposta.

==============================================
Eric Campos Bastos Guedes - matematico, poeta e filosofo
Sacerdote da V.I.D.A. - Verdadeira Igreja da Divindade Axiomatica
http://www.orkut.com/Community.aspx?cmm=10960949
http://br.geocities.com/mathfire2001/
e-mail: mathfire@gmail.com   /  eric.guedes@bol.com.br
MSN: fator-n@hotmail.com  /  Y!M: mathfire2001
Cel. 0xx-21-8131-7542       /   Skype: eric.campos.bastos.guedes
ICARAI - NITEROI - RJ - BRASIL
==============================================



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========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Mon Mar 17 20:04:38 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2HN2ksG026053 for ; Mon, 17 Mar 2008 20:02:50 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2HN2ejM026049 for obm-l-MllGbsmmN; Mon, 17 Mar 2008 20:02:40 -0300 Received: from fg-out-1718.google.com (fg-out-1718.google.com [72.14.220.154]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2HN2OsG026035 for ; Mon, 17 Mar 2008 20:02:25 -0300 Received: by fg-out-1718.google.com with SMTP id e12so11270268fga.3 for ; Mon, 17 Mar 2008 16:02:57 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=9THmevpnB1E1p8+c9xhcnorIQUqifEJV+OQjrZfyJPU=; b=Y5CwWqUlOb16JKaRt2luJ3lTRlVTUjT5NgoA5CunQ+TUasvnK/UAxyCADVjIU/wOr2m4qs2enXftCpbHxWAUG7m+tQ238ITJqG1ObcBiZuj3i9jnSpp4YMvU21auRGv93M3ncZpXMZ1AJvvQ2Ggd+GjhBxUcOmPNAHjKhJbXYjc= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=F4kOtxIchifF8kPwisZ+u4bibd3reIgjGzhRA2Kg68BxIyq2NdO/Qipo3MbRZVFSvq++KzDsoKATyRp6cjN/SII7TH5AjUyktzGgdERuM6BpmO874UoxO5MqZymCNUtGgrDqKynj8VpmMx8QeM4GEg6nG/7jSb+FBtvIS/voVRM= Received: by 10.86.50.8 with SMTP id x8mr7382591fgx.25.1205794977849; Mon, 17 Mar 2008 16:02:57 -0700 (PDT) Received: by 10.86.74.8 with HTTP; Mon, 17 Mar 2008 16:02:57 -0700 (PDT) Message-ID: Date: Mon, 17 Mar 2008 20:02:57 -0300 From: "saulo nilson" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Solido In-Reply-To: <700771.18342.qm@web33803.mail.mud.yahoo.com> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_4852_14160704.1205794977843" References: <700771.18342.qm@web33803.mail.mud.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "saulo nilson" X-Spam-Status: No, hits=-0.5 required=5.0 tests=AWL,IN_REP_TO,MAILTO_LINK,REFERENCES,SPAM_PHRASE_01_02, SPAM_REDIRECTOR,X_MAILING_LIST version=2.44 X-Spam-Level: ------=_Part_4852_14160704.1205794977843 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline modulo I(2,0)I(2-x,0)I(rq(1-z),-rq(1-z))dydzdx=3D =3DI(2,0)I(2-x,0) 2rq(1-z)dzdx=3D =3D-2I(2,0)2/3*(1-z)^3/2dx=3D =3D4/3**2/5 *(1-z)^5/2 (2,0)=3D8/15 2008/3/15 Klaus Ferraz : > Determine o volume do solido limitado pelas superficies z=3D1-y^2 , x+z= =3D2 e > x=3D2 e para z>=3D0. > v=3D8/15. > Eu s=F3 queria que montasse a integral dupla. Porque a que estou achando = tah > dando errado. > Estou achando $_(-1,1)$(-y^2+9,y^2+1)[1-y^2 - (2-x)]dxdy. N=E3o sei qual = meu > erro. > > Grato. > > ------------------------------ > Abra sua conta no Yahoo! Mail, > o =FAnico sem limite de espa=E7o para armazenamento! > ------=_Part_4852_14160704.1205794977843 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline
modulo I(2,0)I(2-x,0)I(rq(1-z),-rq(1-z))dydzdx=3D
=3DI(2,0)I(2-x,0) 2rq(1-z)dzdx=3D
=3D-2I(2,0)2/3*(1-z)^3/2dx=3D
=3D4/3**2/5 *(1-z)^5/2 (2,0)=3D8/15

2008/3/15 Klaus Ferraz <klausferraz@yahoo.com.br>:
Determine o volume do solido limitado pelas superficies z=3D1-y^2 , x+= z=3D2 e x=3D2 e para z>=3D0.
v=3D8/15.
Eu s=F3 queria que montasse a integral dupla. Porque a que estou achan= do tah dando errado.
Estou achando $_(-1,1)$(-y^2+9,y^2+1)[1-y^2 - (2-x)]dxdy. N=E3o sei qu= al meu erro.
 
Grato.

Abra sua conta no Yahoo! Mail, o =FAnico sem li= mite de espa=E7o para armazenamento!

------=_Part_4852_14160704.1205794977843-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Mon Mar 17 20:06:13 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2HN52sG026181 for ; Mon, 17 Mar 2008 20:05:04 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2HN4tdM026172 for obm-l-MllGbsmmN; Mon, 17 Mar 2008 20:04:55 -0300 Received: from fg-out-1718.google.com (fg-out-1718.google.com [72.14.220.154]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2HN4QsG026141 for ; Mon, 17 Mar 2008 20:04:26 -0300 Received: by fg-out-1718.google.com with SMTP id e12so11270804fga.3 for ; Mon, 17 Mar 2008 16:04:59 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=p35AqP3t6HNMSgNTu5tBYIvNLG9lUFYWnYS66GqwrhM=; b=mfHu8zJc2CwGiZgHPomaZ4uD7bEB/pGRw8GK9sLsl5osNwzp0RzVMdkt6wI+Wc+nuhqbaY/QGHTIqtjNcmGoniV54UbjqgoON1wIGXnVXcTfWuMwg+E8bv+ebfizBs1Bqum2Gtra/Qkcmte5CWQnQ71kOXjRzfOY+gjfkY1CcMg= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=XvpQDfgD/VVh/esLvpf/WyK0NQBCzoTXmREiPSqM7CVebBXR6PN8F5jyp+y+jTj9aQjnLWWOqj/v6ROS15OimKe3EtP3C7EtBKg+Gd2Ax7P+Pl7DRqr2l9NA37sDE0B0u+6geUZQTUrrRPmg10t8Wqz8f8zPeCXAwMafxVFR7I4= Received: by 10.86.79.19 with SMTP id c19mr14021154fgb.16.1205795099261; Mon, 17 Mar 2008 16:04:59 -0700 (PDT) Received: by 10.86.74.8 with HTTP; Mon, 17 Mar 2008 16:04:59 -0700 (PDT) Message-ID: Date: Mon, 17 Mar 2008 20:04:59 -0300 From: "saulo nilson" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Solido In-Reply-To: MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_4868_7470008.1205795099247" References: <700771.18342.qm@web33803.mail.mud.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "saulo nilson" X-Spam-Status: No, hits=-1.7 required=5.0 tests=AWL,EMAIL_ATTRIBUTION,IN_REP_TO,MAILTO_LINK, QUOTED_EMAIL_TEXT,REFERENCES,SPAM_PHRASE_01_02, SPAM_REDIRECTOR,X_MAILING_LIST version=2.44 X-Spam-Level: ------=_Part_4868_7470008.1205795099247 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline A regiao e um paraboloide cortado pelo plano x+z=3D2 On Mon, Mar 17, 2008 at 8:02 PM, saulo nilson wrote: > modulo I(2,0)I(2-x,0)I(rq(1-z),-rq(1-z))dydzdx=3D > =3DI(2,0)I(2-x,0) 2rq(1-z)dzdx=3D > =3D-2I(2,0)2/3*(1-z)^3/2dx=3D > =3D4/3**2/5 *(1-z)^5/2 (2,0)=3D8/15 > > 2008/3/15 Klaus Ferraz : > > > Determine o volume do solido limitado pelas superficies z=3D1-y^2 , x+= z=3D2 > > e x=3D2 e para z>=3D0. > > v=3D8/15. > > Eu s=F3 queria que montasse a integral dupla. Porque a que estou achand= o > > tah dando errado. > > Estou achando $_(-1,1)$(-y^2+9,y^2+1)[1-y^2 - (2-x)]dxdy. N=E3o sei qua= l > > meu erro. > > > > Grato. > > > > ------------------------------ > > Abra sua conta no Yahoo! Mail, > > o =FAnico sem limite de espa=E7o para armazenamento! > > > > ------=_Part_4868_7470008.1205795099247 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline A regiao e um paraboloide cortado pelo plano x+z=3D2

On Mon, Mar 17, 2008 at 8:02 PM, saulo nilson &l= t;saulo.nilson@gmail.com> = wrote:
modulo I(2,0)I(2-x,0)I(rq(1-z),-rq(1-z))dydzdx=3D
=3DI(2,0)I(2-x,0) 2rq(1-z)dzdx=3D
=3D-2I(2,0)2/3*(1-z)^3/2dx=3D
=3D4/3**2/5 *(1-z)^5/2 (2,0)=3D8/15

2008/3/15 Klaus Ferraz <klausferraz@yahoo.com.br>:
Determine o volume do solido limitado pelas superficies z=3D1-y^2 , x+= z=3D2 e x=3D2 e para z>=3D0.
v=3D8/15.
Eu s=F3 queria que montasse a integral dupla. Porque a que estou achan= do tah dando errado.
Estou achando $_(-1,1)$(-y^2+9,y^2+1)[1-y^2 - (2-x)]dxdy. N=E3o sei qu= al meu erro.
 
Grato.

Abra sua conta no Yahoo! Mail, o =FAnico sem li= mite de espa=E7o para armazenamento!
<= /div>

------=_Part_4868_7470008.1205795099247-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Mon Mar 17 22:43:56 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2I1frsG006130 for ; Mon, 17 Mar 2008 22:41:53 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2I1frd3006128 for obm-l-MllGbsmmN; Mon, 17 Mar 2008 22:41:53 -0300 Received: from sc2.he.tucows.com (mail06.sc2.he.tucows.com [64.97.154.80]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2I1fpsG006125 for ; Mon, 17 Mar 2008 22:41:52 -0300 Received: from sc2-out04.emaildefenseservice.com (64.97.201.174) by sc2.he.tucows.com (7.3.127) id 47D894BD004AC880 for obm-l@mat.puc-rio.br; Tue, 18 Mar 2008 01:42:24 +0000 X-SpamScore: 10 X-Spamcatcher-Summary: 10,1,0,52b9f38e7b77f391,8824a359d297a841,cauchy@globo.com,-,RULES_HIT:355:379:541:582:988:989:1152:1260:1277:1311:1313:1314:1345:1437:1513:1515:1516:1518:1521:1534:1536:1559:1593:1594:1711:1714:1730:1747:1766:1792:1825:2184:2393:2559:2562:2828:3869:3876:3877:5007:6114:6312:7652:7904,0,RBL:none,CacheIP:none,Bayesian:0.5,0.5,0.5,Netcheck:none,DomainCache:0,MSF:not bulk,SPF:,MSBL:none,DNSBL:none X-Spamcatcher-Explanation: (100%) BODY: unobfuscated drug words: 1; Received: from sc2.he.tucows.com (mail11.sc2.he.tucows.com [64.97.154.89]) by sc2-out04.emaildefenseservice.com (Postfix) with ESMTP for ; Tue, 18 Mar 2008 01:42:24 +0000 (UTC) Received: from [189.12.61.21] by sc2.he.tucows.com with HTTP; Tue, 18 Mar 2008 01:42:24 +0000 Date: Mon, 17 Mar 2008 22:42:24 -0300 Message-ID: <47C429A700061464@mail11.sc2.he.tucows.com> From: cauchy@globo.com Subject: [SPAM] [obm-l] trigonometria To: obm-l@mat.puc-rio.br MIME-Version: 1.0 Content-Type: text/plain; charset="ISO-8859-15" X-Mailer: GloboMail X-Originating-IP: 189.12.61.21 Content-Transfer-Encoding: 7bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m2I1fqsG006126 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: cauchy@globo.com X-Spam-Status: Yes, hits=7.1 required=5.0 tests=NO_REAL_NAME,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, SPAM_PHRASE_00_01,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******* X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (7.10 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: NO_REAL_NAME (1.3 points) From: does not include a real name SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 89.154.97.64.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 89.154.97.64.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- Seja f(x)=cos(nx).sen(5x/n), onde n é um inteiro positivo. Determine a soma dos valores de n para os quais f tem período igual a 3pi. ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Mon Mar 17 23:21:09 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2I2JnsG008524 for ; Mon, 17 Mar 2008 23:19:49 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2I2Jn0s008522 for obm-l-MllGbsmmN; Mon, 17 Mar 2008 23:19:49 -0300 Received: from sc2.he.tucows.com (mail06.sc2.he.tucows.com [64.97.154.80]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2I2JlsG008519 for ; Mon, 17 Mar 2008 23:19:48 -0300 Received: from sc2-out07.emaildefenseservice.com (64.97.201.177) by sc2.he.tucows.com (7.3.127) id 47D894BD004B0B54 for obm-l@mat.puc-rio.br; Tue, 18 Mar 2008 02:16:21 +0000 X-SpamScore: 10 X-Spamcatcher-Summary: 10,1,0,6bb7c1f2435eea31,b46511d128768760,marcusaurelio80@globo.com,-,RULES_HIT:10:355:379:541:542:960:962:967:973:980:988:989:1021:1029:1155:1160:1189:1221:1260:1308:1309:1313:1314:1345:1436:1437:1515:1516:1517:1521:1534:1542:1560:1575:1588:1589:1592:1594:1691:1711:1714:1730:1749:1777:1792:1825:2184:2525:2526:2528:2559:2564:2682:2685:2857:2859:2902:2917:2933:2937:2939:2942:2945:2947:2951:2954:3022:3869:3876:3877:3934:3936:3938:3941:3944:4321:4379:4699:5007: 6114:6117:6261:7679:7688:7904,0,RBL:none,CacheIP:none,Bayesian:0.5,0.5,0.5,Netcheck:none,DomainCache:0,MSF:not bulk,SPF:,MSBL:none,DNSBL:none X-Spamcatcher-Explanation: (100%) BODY: unobfuscated drug words: 1; Received: from esquadrao (unknown [201.29.80.234]) (Authenticated sender: marcusaurelio80@globo.com) by sc2-out07.emaildefenseservice.com (Postfix) with ESMTP for ; Tue, 18 Mar 2008 02:16:20 +0000 (UTC) From: =?iso-8859-1?Q?Marcus_Aur=E9lio?= To: Subject: [SPAM] [obm-l] Ajuda em PA Date: Mon, 17 Mar 2008 23:16:15 -0300 Message-ID: <000001c8889e$0ce0f9a0$26a2ece0$@com> MIME-Version: 1.0 Content-Type: text/plain X-Mailer: Microsoft Office Outlook 12.0 Thread-Index: AciIngs2G/TX5q1+TdCpam+/XTy6kQ== Content-Language: pt-br Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: =?iso-8859-1?Q?Marcus_Aur=E9lio?= X-Spam-Status: Yes, hits=7.0 required=5.0 tests=AWL,FROM_ENDS_IN_NUMS,HTML_50_70,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******* X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_NextPart_000_0001_01C88884.E793C1A0" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (7.00 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: FROM_ENDS_IN_NUMS (0.9 points) From: ends in numbers SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: HTML_50_70 (0.3 points) BODY: Message is 50-70% HTML tags SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 177.201.97.64.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 177.201.97.64.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-0.0 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- Esta é uma mensagem em várias partes no formato MIME. ------=_NextPart_000_0001_01C88884.E793C1A0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Algu=E9m sabe como resolver esse exerc=EDcio da AFA? Os n=FAmeros inteiros positivos s=E3o agrupados em partes disjuntas, da = seguinte maneira: {1}; {2,3}; {4,5,6}; {7,8,9,10}; {11,12,13,14,15};...Seja S a = soma dos elementos que comp=F5e o 24=BA conjunto desta seq=FC=EAncia. Calcule = S. =20 ------=_NextPart_000_0001_01C88884.E793C1A0 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable

Algu=E9m sabe como resolver esse exerc=EDcio da AFA?

Os n=FAmeros inteiros positivos s=E3o agrupados em partes disjuntas, da = seguinte maneira: {1}; {2,3}; {4,5,6}; {7,8,9,10}; {11,12,13,14,15};...Seja S a = soma dos elementos que comp=F5e o 24=BA conjunto desta seq=FC=EAncia. Calcule = S.

 =

------=_NextPart_000_0001_01C88884.E793C1A0-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Mon Mar 17 23:56:35 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2I2tOsG009563 for ; Mon, 17 Mar 2008 23:55:24 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2I2tN3X009561 for obm-l-MllGbsmmN; Mon, 17 Mar 2008 23:55:23 -0300 Received: from wf-out-1314.google.com (wf-out-1314.google.com [209.85.200.172]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2I2tLsG009556 for ; Mon, 17 Mar 2008 23:55:22 -0300 Received: by wf-out-1314.google.com with SMTP id 27so6316220wfd.18 for ; Mon, 17 Mar 2008 19:55:54 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=5d/FsY21Grquqa9fIyw+VwC19FnGfvSaqAa6H7M/0Vg=; b=mdoG9e0xEHoqzt+HqDnA8RDKKF/mMTYpVPhEpVOR8oZ98xN6DFfYuyAhFNgWW1jCUoYYDtEZJTu6OsY1X+XJ9nD+xsZScHCiIV0baLT8YXIIIyziLsy9LlsHUyCYpyP7eDHJao4dhDdJ0rq57vbIH4/NmnQBuJ0lXhhhGvZtnHw= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=WxQAPk/ms4tyBN+uVxIV74ukCiW8+9asbnOT7chKuGAYHvBHuKfhSGo9pgrC7Jpln1a9h+puzcEpWjHxfQ2XSG6MiqKZmExXfWLlOFDMyhwmb3bVRZqf5BbG0KxKrVqIh2Gkdag/yb84fznGK3JTgVAtwe0qRpU8T+NGtTaulYA= Received: by 10.142.141.21 with SMTP id o21mr769552wfd.84.1205808954704; Mon, 17 Mar 2008 19:55:54 -0700 (PDT) Received: by 10.142.13.2 with HTTP; Mon, 17 Mar 2008 19:55:54 -0700 (PDT) Message-ID: Date: Mon, 17 Mar 2008 23:55:54 -0300 From: Denisson To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Ajuda em PA In-Reply-To: <000001c8889e$0ce0f9a0$26a2ece0$@com> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_15309_12607193.1205808954698" References: <000001c8889e$0ce0f9a0$26a2ece0$@com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Denisson X-Spam-Status: No, hits=4.6 required=5.0 tests=IN_REP_TO,MAILTO_LINK,MAILTO_TO_SPAM_ADDR, QUOTED_EMAIL_TEXT,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, REFERENCES,SPAM_PHRASE_00_01,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** ------=_Part_15309_12607193.1205808954698 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Se voc=EA fizer Soma =3D ((1+23)*23)/2 =3D 276 vai obter o =FAltimo element= o da 23=AA parte. (Note que o =FAltimo termo que uma parte =E9 igual ao n=FAmero de el= ementos dela + o =FAltimo inteiro positivo da parte anterior). Logo a 24=AA parte inicia-se no n=FAmero 277 e tem 24 elementos, formando a seguinte soma de P= A de raz=E3o 1: S =3D ((277+ 301)*24)/2 =3D 6936 Em 17/03/08, Marcus Aur=E9lio escreveu: > > Algu=E9m sabe como resolver esse exerc=EDcio da AFA? > > Os n=FAmeros inteiros positivos s=E3o agrupados em partes disjuntas, da > seguinte maneira: {1}; {2,3}; {4,5,6}; {7,8,9,10}; {11,12,13,14,15};...Se= ja > S a soma dos elementos que comp=F5e o 24=BA conjunto desta seq=FC=EAncia.= Calcule S. > > > " ------=_Part_15309_12607193.1205808954698 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Se voc=EA fizer Soma =3D ((1+23)*23)/2 =3D 276 vai obter o =FAltimo element= o da 23=AA parte. (Note que o =FAltimo termo que uma parte =E9 igual ao n= =FAmero de elementos dela + o =FAltimo inteiro positivo da parte anterior).= Logo a 24=AA parte inicia-se no n=FAmero 277 e tem 24 elementos, formando = a seguinte soma de PA de raz=E3o 1:

S =3D ((277+ 301)*24)/2 =3D 6936

Em 17/03/08, Marcus Aur=E9lio <marcusaurelio80@globo.com> e= screveu:

Algu=E9m sabe como resolver esse exerc=EDcio da AFA?

Os n=FAmeros inteiros positivos s=E3o agrupados em partes disjuntas, da seguin= te maneira: {1}; {2,3}; {4,5,6}; {7,8,9,10}; {11,12,13,14,15};...Seja S a soma= dos elementos que comp=F5e o 24=BA conjunto desta seq=FC=EAncia. Calcule S.

 


" ------=_Part_15309_12607193.1205808954698-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Tue Mar 18 09:07:35 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2IC4usG005645 for ; Tue, 18 Mar 2008 09:04:56 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2IC4uQS005641 for obm-l-MllGbsmmN; Tue, 18 Mar 2008 09:04:56 -0300 Received: from aacpdlotus.net.ms.gov.br (aacpdlotus.net.ms.gov.br [200.181.116.8]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2IC4ssG005601 for ; Tue, 18 Mar 2008 09:04:55 -0300 Importance: Normal X-Priority: 3 (Normal) Subject: [SPAM] Res:[obm-l] Cadastramento OBM-2008 MIME-Version: 1.0 From: JoaoCarlos_Junior@net.ms.gov.br To: obm-l@mat.puc-rio.br Date: Tue, 18 Mar 2008 08:05:29 -0400 Message-ID: X-Mailer: Lotus Domino Web Server Release 6.5.5 November 30, 2005 X-MIMETrack: Serialize by Notes Server on aacpdlotus/NETMS(Release 6.5.5|November 30, 2005) at 18/03/2008 08:05:29, Serialize complete at 18/03/2008 08:05:29, Itemize by Notes Server on aacpdlotus/NETMS(Release 6.5.5|November 30, 2005) at 18/03/2008 08:05:29, Serialize by Router on aacpdlotus/NETMS(Release 6.5.5|November 30, 2005) at 18/03/2008 08:05:34, Serialize complete at 18/03/2008 08:05:34 Content-Transfer-Encoding: 7bit MIME-Version: 1.0 Content-Type: text/plain Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: JoaoCarlos_Junior@net.ms.gov.br X-Spam-Status: Yes, hits=8.1 required=5.0 tests=AWL,CTYPE_JUST_HTML,HTML_FONT_COLOR_MAGENTA, HTML_FONT_FACE_BAD,HTML_FONT_FACE_ODD,MIME_EXCESSIVE_QP, NO_REAL_NAME,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, SPAM_PHRASE_00_01,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: text/html; charset=ISO-8859-1 X-Spam-Prev-Content-Transfer-Encoding: quoted-printable SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (8.10 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: NO_REAL_NAME (1.3 points) From: does not include a real name SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: HTML_FONT_COLOR_MAGENTA (0.4 points) BODY: HTML font color is magenta SPAM: HTML_FONT_FACE_ODD (0.3 points) BODY: HTML font face is not a commonly used face SPAM: HTML_FONT_FACE_BAD (0.2 points) BODY: HTML font face is not a word SPAM: MIME_EXCESSIVE_QP (1.0 points) RAW: Excessive quoted-printable encoding in body SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 8.116.181.200.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 8.116.181.200.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: CTYPE_JUST_HTML (0.4 points) HTML-only mail, with no text version SPAM: AWL (-1.3 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results ---------------------
Prezada Secret=E1ria da OBM,
Demais competentes a= me respoder:
 
Caso a escola de meu filho n= =E3o se cadastre, existe alguma forma poss=EDvel pela qual ele possa partic= ipar?
 
Fraternalmente, Jo=E3o.
-----owner-obm-l@mat.puc-rio.br escreveu: -----

=
Para: aobm-l@mat.puc-= rio.br, Lista de discussao <obm-l@mat.puc-rio.br>
De: Olimpiada Br= asileira de Matematica <obm@impa.br>
Enviado por: owner-obm-l@mat.= puc-rio.br
Data: 17/03/2008 9:18
Assunto: [obm-l] Cadastramento OBM-2= 008

Caros s=F3cios e amigos da OBM,<= BR>
Est=E3o abertas as inscri=E7=F5es para participar da OBM-2008.
To= das as escolas das redes p=FAblica e privada podem participar.

Per= =EDodo de cadastramento:
15 de mar=E7o at=E9  5 de maio de 2008
= apenas no site da OBM www.obm.org.br

Importante:  Nosso sistema= de cadastramento mudou, por favor, se a sua
escola
j=E1 participou = da competi=E7=E3o em anos anteriores, tamb=E9m deve realizar o novo
cada= stramento em 2008.

Cordialmente,

Secretaria da OBM







=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D
Instru=E7=F5es para entrar na lista, sair da lista= e usar a lista em
http://www.mat.puc-rio.br/~obmlistas/obm-l.html=
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=

= ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Tue Mar 18 13:08:23 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2IG64sG003177 for ; Tue, 18 Mar 2008 13:06:04 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2IG64Xs003172 for obm-l-MllGbsmmN; Tue, 18 Mar 2008 13:06:04 -0300 Received: from web90502.mail.mud.yahoo.com (web90502.mail.mud.yahoo.com [216.252.100.169]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id m2IG5tsG003086 for ; Tue, 18 Mar 2008 13:05:56 -0300 Received: (qmail 75575 invoked by uid 60001); 18 Mar 2008 16:06:25 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:X-Mailer:Date:From:Subject:To:MIME-Version:Content-Type:Content-Transfer-Encoding:Message-ID; b=nIFCxt6odg/IC5zgQoR1pNXfD054k9epsEszm2eYmr8y7rGDbEdUSIk0IGD0MmWUa9bwV8xCsnzWIfdV3KtKCb1idA4gCMAoezQzLpSA1HibW43hRrBIaXqZLv+l70AJEmvxB9+5cpa2W7thqHzEGQ0unD5l28Pqlfa4TO7O5x0=; X-YMail-OSG: g.AzJM0VM1m.wAz.XlzIaFrLnztQHIfVSgNra8YeypsBseOXBVqqyYssUgOKKZSSt4UbBnlzG7_pidjL4lgo4sbAKsNp6mqSgxVUiLcoQ5OH99lo0QoI2H1a85b9D978gbmCHTM0OmVscnzL3tBQMezpqEz2ag-- Received: from [201.36.164.55] by web90502.mail.mud.yahoo.com via HTTP; Tue, 18 Mar 2008 09:06:25 PDT X-Mailer: YahooMailRC/902.38 YahooMailWebService/0.7.162 Date: Tue, 18 Mar 2008 09:06:25 -0700 (PDT) From: Eric Campos Bastos Guedes Subject: [SPAM] Res: [obm-l] Probabilidade Surreal To: obm-l@mat.puc-rio.br, mathfire@gmail.com, Atendimento - SBM , Brasil melhor RJ , BrasilMelhor_RJ , Claudio Buffara , Daniele Akemi , Delirio Coletivo lista , =?iso-8859-1?Q?Educac=E3o_Matem=E1tica_em_Revista?= , Heraldo Borges , Humberto Bortolossi , Joice Nascimento , =?iso-8859-1?Q?Jorge_Petr=FAcio_Viana?= , Lizandra Nascimento SBM , Marcos Mota Murtha , =?iso-8859-1?Q?Maur=EDcio_Emanuel?= , Priscilla Bosco , Revista Matematica Universitaria , RPM MIME-Version: 1.0 Content-Type: text/plain; charset=iso-8859-1 Message-ID: <894033.75489.qm@web90502.mail.mud.yahoo.com> Content-Transfer-Encoding: 7bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m2IG5wsG003131 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Eric Campos Bastos Guedes X-Spam-Status: Yes, hits=8.8 required=5.0 tests=AWL,FORGED_YAHOO_RCVD,FROM_ENDS_IN_NUMS, MAILTO_TO_SPAM_ADDR,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, SPAM_PHRASE_00_01,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (8.80 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: FROM_ENDS_IN_NUMS (0.9 points) From: ends in numbers SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: MAILTO_TO_SPAM_ADDR (0.7 points) URI: Includes a link to a likely spammer email address SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 169.100.252.216.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 169.100.252.216.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-0.0 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- Sou matematico membro da SBM e tenho denuncias graves a fazer... Sei que este estah longe de ser o lugar certo para fazer estas denuncias, mas ja fui a todas as policias (federal, civil, militar) ja mandei a denuncia ao ministerio publico (com todos os meus dados - eu existo, nao sou uma ficcao), liguei pro disque denuncia, liguei para a corregedoria da policia (127)... ate agora nada... lhufas... se eu que sou um matematico com trabalhos publicados, premiacoes, etc nao consigo fazer uma denuncia da mais alta gravidade, que dira o resto da populacao. Por favor, gostaria de dicas onde eu possa postar minha denuncia. A situacao estah feia. Sei que vou morrer... mas antes vou mostrar que eles mexeram com o cara errado... falow... meus dados para contato: ============================================== Eric Campos Bastos Guedes - matematico, poeta e filosofo http://br.geocities.com/mathfire2001/ e-mail: mathfire@gmail.com / eric.guedes@bol.com.br MSN: fator-n@hotmail.com / Y!M: mathfire2001 Cel. 0xx-21-8131-7542 / Skype: eric.campos.bastos.guedes RUA DOMINGUES DE SÁ, 422 - CASA ICARAI - NITEROI - RJ - BRASIL CEP: 24220-091 ============================================== Os dados da vitima: NOME: ROBERTO PROFISSAO: ANALISTA DE SISTEMAS COR DA PELE: BRANCA ALTURA: ENTRE 1,74m E 1,84m PESO: EM TORNO DE 80Kg NOME DA FILHA: ALINE ANO DE NASCIMENTO DA FILHA: 1998 ONDE FOI MORTO: NUMA CLINICA PSIQUIATRICA EM SÃO GONÇALO QUANDO MORREU: EM ABRIL DE 2007 QUANDO ROBERTO FOI INTERNADO NA CLÍNICA: EM MARÇO DE 2007 ELE FOI MORTO AO COMPLETAR 30 DIAS DE INTERNADO, JUSTAMENTE O PRAZO COBERTO PELO PLANO DE SAUDE. poderia ter sido eu ou voce... =============================================== ----- Mensagem original ---- De: Eric Campos Bastos Guedes Para: obm-l@mat.puc-rio.br Enviadas: Quinta-feira, 6 de Março de 2008 23:09:22 Assunto: [obm-l] Probabilidade Surreal QUESTAO DESCONCERTANTE: Qual a probabilidade de um analista de sistemas ter sido morto numa clinica psiquiatrica em Sao Goncalo / RJ no ano de 2007 e alguem, de nome "Eric Campos Bastos Guedes" estar tentando a meses denunciar o fato as autoridades e a midia, sem exito? MINHA RESPOSTA: Essa probabilidade estah bastante proxima de 1. Por favor, ENTREM EM CONTATO. Como matematico e membro da SBM PECO A AJUDA DE VOCES. A midia SABE e IGNORA. ============================================= Eric Campos Bastos Guedes Formulas para primos http://geocities.yahoo.com.br/mathfire2001 http://br.geocities.com/mathfire2001/ Projeto Matematica para Todos mathfire2001@yahoo.com.br MSN: fator-n@hotmail.com Celular: 0xx-21-8131-7542 ============================================= Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! http://br.mail.yahoo.com/ ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! http://br.mail.yahoo.com/ ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Tue Mar 18 14:20:52 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2IHJNsG008905 for ; Tue, 18 Mar 2008 14:19:23 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2IHJMHa008903 for obm-l-MllGbsmmN; Tue, 18 Mar 2008 14:19:22 -0300 Received: from fg-out-1718.google.com (fg-out-1718.google.com [72.14.220.154]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2IHJKsG008898 for ; Tue, 18 Mar 2008 14:19:21 -0300 Received: by fg-out-1718.google.com with SMTP id e12so619fga.3 for ; Tue, 18 Mar 2008 10:19:49 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=P01/jOje8RHut5NfZ1qLjiBLJSQ7VN8h3HRqyfqwfdQ=; b=NkmhhpUwspj1MKAMGZYmXUY/BFaAEr3xpCrNYgvu8Y3VU4OQW6DC1YixYEj+oVZjfLKgwVkh2ErC7/BZxo9T61o4iPrHHSH2LxTijEuSsFxTif9AZzpeCyRnlgGSILzIShk2N8zAiiC5YcZl2Py0uYSHHvFk0eDl601Og+JBggA= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=GgImRcEl1lYgpNWZ0b6sxEj4SkvE4ykNDeDk+jaE74qcLTqfEzCG3AM9SxjWRzx+2vZBeR1e5CSezj+KBgM8JpRqvsuIOlDAX9GhbpnJPKE2Esp14dSb2UQagm2gOpx9AJq3XnmdcSWt2HT5jGEAAjPThSX9Xeux2kOLtxV3sCU= Received: by 10.86.73.17 with SMTP id v17mr6307276fga.37.1205860789836; Tue, 18 Mar 2008 10:19:49 -0700 (PDT) Received: by 10.86.74.8 with HTTP; Tue, 18 Mar 2008 10:19:49 -0700 (PDT) Message-ID: Date: Tue, 18 Mar 2008 14:19:49 -0300 From: "saulo nilson" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] trigonometria In-Reply-To: <47C429A700061464@mail11.sc2.he.tucows.com> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_366_4435031.1205860789857" References: <47C429A700061464@mail11.sc2.he.tucows.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "saulo nilson" X-Spam-Status: No, hits=-1.3 required=5.0 tests=AWL,EMAIL_ATTRIBUTION,IN_REP_TO,MAILTO_LINK, MIME_EXCESSIVE_QP,QUOTED_EMAIL_TEXT,REFERENCES, SPAM_PHRASE_00_01,X_MAILING_LIST version=2.44 X-Spam-Level: ------=_Part_366_4435031.1205860789857 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Ja resolveram esse exercicio nesta lista. On Mon, Mar 17, 2008 at 10:42 PM, wrote: > Seja f(x)=3Dcos(nx).sen(5x/n), onde n =E9 um inteiro positivo. Determine = a > soma > dos valores de n para os quais f tem per=EDodo igual a 3pi. > > > > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > Instru=E7=F5es para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > ------=_Part_366_4435031.1205860789857 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Ja resolveram esse exercicio nesta lista.

On Mon, Mar 17, 2008 at 10:42 PM, <cauchy@globo.com> wrote:
Seja f(x)=3Dcos(nx).sen(5x/n), o= nde n =E9 um inteiro positivo. Determine a soma
dos valores de n para os= quais f tem per=EDodo igual a 3pi.



=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D
Instru=E7=F5es para entrar na lista, sair da lista e usar a lista= em
http://www.mat.puc-rio.br/~obmlistas/obm-l.html
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D

------=_Part_366_4435031.1205860789857-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Tue Mar 18 16:54:26 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2IJq7sG019578 for ; Tue, 18 Mar 2008 16:52:10 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2IJpxZ7019569 for obm-l-MllGbsmmN; Tue, 18 Mar 2008 16:52:00 -0300 Received: from relay3.bol.com.br (relay3.bol.com.br [200.221.4.107]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2IJpgsG019552 for ; Tue, 18 Mar 2008 16:51:43 -0300 Received: from localhost (localhost [127.0.0.1]) by salsa3.bol.com.br (Postfix) with ESMTP id 9308EE00806F for ; Tue, 18 Mar 2008 07:26:13 -0300 (BRT) Received: from bol.com.br (whisper8.mail.sys.intranet [172.26.5.83]) by salsa3.bol.com.br (Postfix) with ESMTP id 67405E008725 for ; Tue, 18 Mar 2008 07:24:11 -0300 (BRT) Date: Tue, 18 Mar 2008 16:50:06 -0300 Message-Id: Subject: [obm-l] =?iso-8859-1?b?UVVFU1TDTyBBTlRJR0E=?= MIME-Version: 1.0 X-Sensitivity: 3 Content-Type: multipart/alternative; boundary="_=__=_XaM3_.1205869806.2A.901002.42.11628.52.42.007.580640451" From: "gugolplexj" To: "obm-l" X-XaM3-API-Version: 4.3(R1) (B10) X-SenderIP: 189.28.222.122 X-SIG5: 7db7ab88e38f1ecc75ef9c6b8c03909e Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "gugolplexj" X-Spam-Status: No, hits=0.2 required=5.0 tests=AWL,SPAM_PHRASE_00_01,TO_LOCALPART_EQ_REAL,X_MAILING_LIST version=2.44 X-Spam-Level: --_=__=_XaM3_.1205869806.2A.901002.42.11628.52.42.007.580640451 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable Ol=E1, Creio q esse problema j=E1 transitou por aqui h=E1 algum tempo. "Quais os n=FAmeros naturais a, b, c diferentes entre s=ED, tais que 1/a +1/b + 1/c =3D 1?" Grato, Jorge. --_=__=_XaM3_.1205869806.2A.901002.42.11628.52.42.007.580640451 Content-Type: text/html; charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable 
Provas matemáticas que usam o método indutivo não são consideradas
formais, eu acho. Tal fato é inclusive, motivo de diversas piadas que
matemáticos contam sobre engenheiros (do tipo "vale para n = 1, vale
para n = 2, então vale sempre").

Vale lembrar, só pra constar, que a indução matemática não é, em si,
uma manifestação do "método indutivo". A indução matemática tem esse
nome porque serve para provar *dedutivamente* coisas conjecturadas a
partir do "método indutivo" (i.e., supor que uma idéia vale para o
caso geral porque ela vale para alguns casos particulares). Isso se
reflete no fato de que, ao construir uma prova por indução matemática,
você tem que conhecer de antemão o resultado final que deseja provar.

--
Abraços,
Maurício

PS: Eu estou estudando para ser engenheiro. Nada contra tal profissão :)

On 3/14/08, albert richerd carnier guedes <arcguede@gmail.com> wrote:
  
Eu tava lendo por aí que alguns matemáticos são meio que cabreros com o
 método indutivo por causa da idéia de que alguma hora o método pode
 falhar, sendo assim, o método dedutivo é o verdadeiro modo de se chegar
 a uma resposta segura e real dos problemas matemáticos.
 Um tanto Popperiano, mas vá lá.
 Alguém também sente esta desconfiança em relação ao método indutivo ?
    

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On 3/14/08, = arkon <arkon@bol.com.br> = wrote:

<= font face=3D"Times New Roman">Pessoal algu=E9m pode me enviar, por favor, a= resolu=E7=E3o dessa quest=E3o

 

(AFA 03/04) A equa=E7=E3o x^3 + mx^2 = + 2x + n =3D 0, onde m e n s=E3o n=FAmeros reais e

i^2 =3D - 1, admite 1 +  <= /span>i como raiz. Ent=E3o m + n =E9 igual a:

 

a) =96 2.   &nbs= p;     b) 0.     =   c) 1.        = d) 2.  

 

E aproveitando a oportunidade algu=E9= m pode me enviar, por favor, no meu

e-mail, arkon@bol.com.br, a resolu=E7=E3o dessa o= utra

 

(AFA 03/04) Um foguete cuja massa val= e 6 toneladas =E9 colocado em posi=E7=E3o vertical para lan=E7amento. Se a = velocidade de escape dos gases vale 1 km/s, a quantidade de gases expelida = por segundo, a fim de proporcionar o empuxo necess=E1rio para dar ao foguet= e uma acelera=E7=E3o para cima igual a 20 m/s^2 =E9:

 

a) 120 kg.=       b) 180 kg.   c= ) 100 kg.    d) 80 kg.=

 

DESDE J=C1 MUITO OBRIGADO

 

Ol=E1,
 
Creio q esse problema j=E1 transitou por aqui h=E1 algum tempo.
 
"Quais os n=FAmeros naturais a, b, c diferentes entre s=ED, tai= s que 
1/a +1/b + 1/c =3D 1?"
 
Grato,
Jorge.
--_=__=_XaM3_.1205869806.2A.901002.42.11628.52.42.007.580640451-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Tue Mar 18 19:45:02 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2IMhUsG012595 for ; Tue, 18 Mar 2008 19:43:30 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2IMhTtX012593 for obm-l-MllGbsmmN; Tue, 18 Mar 2008 19:43:29 -0300 Received: from rn-out-0910.google.com (rn-out-0910.google.com [64.233.170.185]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2IMhPsG012587 for ; Tue, 18 Mar 2008 19:43:27 -0300 Received: by rn-out-0910.google.com with SMTP id e11so151856rng.7 for ; Tue, 18 Mar 2008 15:44:00 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; bh=AbRSJ8BIlKAZqWe733k1pk7yaKzKIdg6ii2eocT49pc=; b=HDhpCvCH35Z0BVwkgyIZzDFLTxt2pJ9yVfsSHcstOintDkyMpnrIkjxiE7zICgWoaSZnte6HK/CmwALL5qRZKsFRoppYzCIB6nNN04NHYCjbOeGIKcdnvIdYha5S4WAXXgQTUVH1NWjLE2AqfEvkPwgweTm4N9lmBX205vx6C14= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; b=r/OfP96CWGun57WzuB8aMbEEzTuhX3TM/fM5f+rfZ8t7hkv6pRH+uSCkBCwRJ6lObDvFMACSBvYTH+U4cJ4bh6dKehLnfUebY7c/OtzKiAWiOVbTxhpjEo3yYaH+wnAsRmFGMFEKLZiSuEhWItcdwu/uRYrMtm1SNmZIunYlyb4= Received: by 10.150.189.9 with SMTP id m9mr1327905ybf.142.1205880239828; Tue, 18 Mar 2008 15:43:59 -0700 (PDT) Received: by 10.150.144.4 with HTTP; Tue, 18 Mar 2008 15:43:59 -0700 (PDT) Message-ID: Date: Tue, 18 Mar 2008 19:43:59 -0300 From: "Paulo Santa Rita" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Probabilidade Surreal In-Reply-To: <894033.75489.qm@web90502.mail.mud.yahoo.com> MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline References: <894033.75489.qm@web90502.mail.mud.yahoo.com> Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m2IMhSsG012590 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Paulo Santa Rita" X-Spam-Status: No, hits=4.2 required=5.0 tests=AWL,IN_REP_TO,MAILTO_TO_SPAM_ADDR,QUOTED_EMAIL_TEXT, RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,REFERENCES, SPAM_PHRASE_00_01,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** Ola Eric, Esta lista não é o local adeguado para você fazer este tipo de denuncia. Eu sou membro do Ministério Publico Federal. Vamos conversar. Escreve pra mim em particular. Com os melhores votos de Paz profunda, sou Paulo Santa Rita 3,1329,120308 Em 18/03/08, Eric Campos Bastos Guedes escreveu: > Sou matematico membro da SBM e tenho denuncias graves a fazer... > > Sei que este estah longe de ser o lugar certo para fazer estas > denuncias, mas ja fui a todas as policias (federal, civil, militar) > ja mandei a denuncia ao ministerio publico (com todos os meus > dados - eu existo, nao sou uma ficcao), liguei pro disque denuncia, > liguei para a corregedoria da policia (127)... ate agora nada... > lhufas... > se eu que sou um matematico com trabalhos publicados, premiacoes, > etc nao consigo fazer uma denuncia da mais alta gravidade, > que dira o resto da populacao. > > Por favor, gostaria de dicas onde eu possa postar minha denuncia. > > A situacao estah feia. > > Sei que vou morrer... > > mas antes vou mostrar que eles mexeram com o cara errado... > > falow... > > meus dados para contato: > > ============================================== > Eric Campos Bastos Guedes - matematico, poeta e filosofo > http://br.geocities.com/mathfire2001/ > e-mail: mathfire@gmail.com / eric.guedes@bol.com.br > MSN: fator-n@hotmail.com / Y!M: mathfire2001 > Cel. 0xx-21-8131-7542 / Skype: eric.campos.bastos.guedes > RUA DOMINGUES DE SÁ, 422 - CASA > ICARAI - NITEROI - RJ - BRASIL > CEP: 24220-091 > ============================================== > > Os dados da vitima: > > NOME: ROBERTO > PROFISSAO: ANALISTA DE SISTEMAS > COR DA PELE: BRANCA > ALTURA: ENTRE 1,74m E 1,84m > PESO: EM TORNO DE 80Kg > NOME DA FILHA: ALINE > ANO DE NASCIMENTO DA FILHA: 1998 > ONDE FOI MORTO: NUMA CLINICA PSIQUIATRICA EM SÃO GONÇALO > QUANDO MORREU: EM ABRIL DE 2007 > QUANDO ROBERTO FOI INTERNADO NA CLÍNICA: EM MARÇO DE 2007 > ELE FOI MORTO AO COMPLETAR 30 DIAS DE INTERNADO, JUSTAMENTE O PRAZO COBERTO PELO PLANO DE SAUDE. > > poderia ter sido eu ou voce... > =============================================== > > ----- Mensagem original ---- > De: Eric Campos Bastos Guedes > Para: obm-l@mat.puc-rio.br > Enviadas: Quinta-feira, 6 de Março de 2008 23:09:22 > Assunto: [obm-l] Probabilidade Surreal > > QUESTAO DESCONCERTANTE: > Qual a probabilidade de um analista de sistemas ter sido morto numa > clinica psiquiatrica em Sao Goncalo / RJ no ano de 2007 e alguem, > de nome "Eric Campos Bastos Guedes" estar tentando a meses > denunciar o fato as autoridades e a midia, sem exito? > > MINHA RESPOSTA: > Essa probabilidade estah bastante proxima de 1. > > Por favor, ENTREM EM CONTATO. > Como matematico e membro da SBM > PECO A AJUDA DE VOCES. > > A midia SABE e IGNORA. > > ============================================= > Eric Campos Bastos Guedes > Formulas para primos > http://geocities.yahoo.com.br/mathfire2001 > http://br.geocities.com/mathfire2001/ > Projeto Matematica para Todos > mathfire2001@yahoo.com.br > MSN: fator-n@hotmail.com > Celular: 0xx-21-8131-7542 > ============================================= > > > > Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! > http://br.mail.yahoo.com/ > > ========================================================================= > Instruções para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > ========================================================================= > > > > > > Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! > http://br.mail.yahoo.com/ > > ========================================================================= > Instruções para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > ========================================================================= > ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Tue Mar 18 23:31:08 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2J2TQsG015864 for ; Tue, 18 Mar 2008 23:29:26 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2J2TQBZ015862 for obm-l-MllGbsmmN; Tue, 18 Mar 2008 23:29:26 -0300 Received: from web32703.mail.mud.yahoo.com (web32703.mail.mud.yahoo.com [68.142.207.247]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id m2J2T9sG015854 for ; Tue, 18 Mar 2008 23:29:09 -0300 Received: (qmail 1788 invoked by uid 60001); 19 Mar 2008 02:29:37 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:Date:From:Subject:To:In-Reply-To:MIME-Version:Content-Type:Content-Transfer-Encoding:Message-ID; b=nzaiauN8gbhx8pZiKmKm25UCQ8ahvOfzrfeNGz+ltlWIVQv8t329CZv6MAs8hxG67xk/zxWEjMxj0nIusnY56Fss8R9lMBlQXd6Mr1I9FJroteCN/dxIeUVKVLa6zQOQGcTVcV8GhPFrD0izWRsVyS/IK/bz9V7JIPrBOOGJ1zU=; X-YMail-OSG: qzgA6HUVM1n6hne.EkWEObzNuo.cAphlO.x9J2G914v7drWJgFy7.x3Ehae72htTuKogSG8E29uDqkaL6a0fTKs5q_yA9ef9BFkGdJqPy5hUzB_Zg3A- Received: from [201.9.19.111] by web32703.mail.mud.yahoo.com via HTTP; Tue, 18 Mar 2008 23:29:37 ART Date: Tue, 18 Mar 2008 23:29:37 -0300 (ART) From: alexmay nunes soares Subject: [SPAM] Re: [obm-l] trigonometria To: obm-l@mat.puc-rio.br In-Reply-To: MIME-Version: 1.0 Content-Type: text/plain Content-Transfer-Encoding: 7bit Message-ID: <222149.274.qm@web32703.mail.mud.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: alexmay nunes soares X-Spam-Status: Yes, hits=6.9 required=5.0 tests=AWL,FORGED_YAHOO_RCVD,IN_REP_TO,MAILTO_LINK,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01,SPAM_REDIRECTOR, SUPERLONG_LINE,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ****** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="0-856220917-1205893777=:274" X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (6.90 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: MAILTO_LINK (0.2 points) BODY: Includes a URL link to send an email SPAM: SUPERLONG_LINE (0.0 points) BODY: Contains a line >=199 characters long SPAM: SPAM_REDIRECTOR (0.4 points) URI: Uses open redirection service SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 247.207.142.68.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 247.207.142.68.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-0.1 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- --0-856220917-1205893777=:274 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 8bit Uma condição necessária (mas, não suficiente) para q f tenha período 3pi é q F(0)=F(3pi) logo, vem q : cos(0).sen(0)=cos(n*3pi).sen(15pi/n) = 0daí temos duas possibilidades: cos (n*3pi)=0 ou sen(15pi/n)=0 1º caso : cos (n*3pi)=0 vem que n*3pi = pi/2 + k*pi logo 3n=1/2 + k que obviamente n admite soluções inteiras. 2º caso: sen(15pi/n)=0 de onde temos que 15pi/n=kpi logo n.k=15 e portanto k e nsão divisores positivos de 15, isto é k e n pertencem ao conj.{1,3,5,15}. Como foi dito isto é uma condição necessária, mas não suficiente é preciso testar as soluções uma a uma: n=1 implica f( x) =cos(x).sen(5x), q notamos não servir pois tem preríodo pi e não 3pi. n=3 implica f( x) =cos(3x).sen(5x/3), que tem período 3pi e portanto é solução n=5 implica f( x) =cos(5x).sen(x), q notamos não servir pois tem preríodo pi e não 3pi. n=15 implica f( x) =cos(15x).sen(x/3), que tem período 3pi e portanto é solução Resposta correta : 3+15=18!!! saulo nilson escreveu: Ja resolveram esse exercicio nesta lista. On Mon, Mar 17, 2008 at 10:42 PM, wrote: Seja f(x)=cos(nx).sen(5x/n), onde n é um inteiro positivo. Determine a soma dos valores de n para os quais f tem período igual a 3pi. ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= --------------------------------- Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-856220917-1205893777=:274 Content-Type: text/html; charset=iso-8859-1 Content-Transfer-Encoding: 8bit
Uma condição necessária (mas, não suficiente) para q f tenha período 3pi é q F(0)=F(3pi) logo, vem q : cos(0).sen(0)=cos(n*3pi).sen(15pi/n)  = 0daí temos duas possibilidades: cos (n*3pi)=0 ou sen(15pi/n)=0
 
1º caso : cos (n*3pi)=0 vem que n*3pi = pi/2 + k*pi logo 3n=1/2 + k que obviamente n admite soluções inteiras.
 
2º caso: sen(15pi/n)=0 de onde temos que 15pi/n=kpi logo n.k=15 e portanto k e nsão divisores positivos de 15, isto é k e n pertencem ao conj.{1,3,5,15}.
 
Como foi dito isto é uma condição necessária, mas não suficiente é preciso testar as soluções uma a uma:
 
n=1 implica f( x) =cos(x).sen(5x), q notamos não servir pois tem preríodo pi e não 3pi.
 
n=3 implica f( x) =cos(3x).sen(5x/3), que tem período 3pi e portanto é solução
 
n=5 implica f( x) =cos(5x).sen(x), q notamos não servir pois tem preríodo pi e não 3pi.
n=15 implica f( x) =cos(15x).sen(x/3), que tem período 3pi e portanto é solução
 
Resposta correta : 3+15=18!!!
 
 
 
 
 


saulo nilson <saulo.nilson@gmail.com> escreveu:
Ja resolveram esse exercicio nesta lista.

On Mon, Mar 17, 2008 at 10:42 PM, <cauchy@globo.com> wrote:
Seja f(x)=cos(nx).sen(5x/n), onde n é um inteiro positivo. Determine a soma
dos valores de n para os quais f tem período igual a 3pi.



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Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-856220917-1205893777=:274-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Mar 19 05:31:29 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2J8TQsG004415 for ; Wed, 19 Mar 2008 05:29:26 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2J8TQ44004413 for obm-l-MllGbsmmN; Wed, 19 Mar 2008 05:29:26 -0300 Received: from fg-out-1718.google.com (fg-out-1718.google.com [72.14.220.156]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2J8TOsG004408 for ; Wed, 19 Mar 2008 05:29:24 -0300 Received: by fg-out-1718.google.com with SMTP id e12so267066fga.3 for ; Wed, 19 Mar 2008 01:29:58 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=N/jVLbU7o/GWz6h53SEsPZ8Q3pLm5PRUog6/GxToueE=; b=IzdfVTjJS3t+zViieU+Kq+xGoFxITpqtGyeXMeLY9zXLYC9oe4zN1OfZpLBO4R2ZoVMCXBVOvN29ss8DFdGNwAc0M4AZCNQLMylfSEiRm4dsN7oW/EiBD97fv+DWddxp7NFvnFcVcwM1vPKGnLkigyYjuxgiHH4wClR6zyVbFdg= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=WCCEtg/lBUC3BqSBGubfXhLzWcoywMCGJylVp2BLMlmlMsuQnWlQVlB8jyFY6iWbrajlO9igPU81y5yEly0YlfQv6ZYXdFlc6KMznZxndsRY6G6ePYY0wQPOv1Rkd7s6AoRgIN8y9yJj+AYhg7F8tLSiRGmNRO2os5Ydk8MlaWM= Received: by 10.86.66.19 with SMTP id o19mr6901963fga.46.1205915398442; Wed, 19 Mar 2008 01:29:58 -0700 (PDT) Received: by 10.86.74.8 with HTTP; Wed, 19 Mar 2008 01:29:58 -0700 (PDT) Message-ID: Date: Wed, 19 Mar 2008 05:29:58 -0300 From: "saulo nilson" To: obm-l@mat.puc-rio.br Subject: =?ISO-8859-1?Q?Re:_[obm-l]_QUEST=C3O_ANTIGA?= In-Reply-To: MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_1597_11037336.1205915398448" References: Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "saulo nilson" X-Spam-Status: No, hits=-1.9 required=5.0 tests=AWL,EMAIL_ATTRIBUTION,IN_REP_TO,MAILTO_LINK, QUOTED_EMAIL_TEXT,REFERENCES,SPAM_PHRASE_00_01, X_MAILING_LIST version=2.44 X-Spam-Level: ------=_Part_1597_11037336.1205915398448 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline abc=3Dab+ac+bc=3Dw x^3+Sx^2+wx-w=3D0 a+b+c=3Dk ab(c-1)=3Dc(a+b) c>1 c=3D2 ab=3D2(a+b) a+b=3Dn ab=3D2n a^2+2ab+b^2=3Dn^2 a^2+4n^2/a^2=3Dn^2-4n a^2=3Dx x^2+x4n^2-x(n^2-4n)=3D0 delta=3D(n^2-4n)^2-16n^2=3D(n^2-8n)n^2 a^2=3Dn(n-4+-rq(n(n-8)))/2 de cara n=3D9 a^2=3D9 a=3D3 b=3D6 1/2+1/3+1/6=3D1 cqd On Tue, Mar 18, 2008 at 4:50 PM, gugolplexj wrote: > Ol=E1, > > Creio q esse problema j=E1 transitou por aqui h=E1 algum tempo. > > "Quais os n=FAmeros naturais a, b, c diferentes entre s=ED, tais que > 1/a +1/b + 1/c =3D 1?" > > Grato, > Jorge. > ------=_Part_1597_11037336.1205915398448 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline
abc=3Dab+ac+bc=3Dw
x^3+Sx^2+wx-w=3D0
a+b+c=3Dk
ab(c-1)=3Dc(a+b)
c>1
c=3D2
ab=3D2(a+b)
a+b=3Dn
ab=3D2n
a^2+2ab+b^2=3Dn^2
a^2+4n^2/a^2=3Dn^2-4n
a^2=3Dx
x^2+x4n^2-x(n^2-4n)=3D0
delta=3D(n^2-4n)^2-16n^2=3D(n^2-8n)n^2
a^2=3Dn(n-4+-rq(n(n-8)))/2
de cara
n=3D9
a^2=3D9
a=3D3
b=3D6
1/2+1/3+1/6=3D1
cqd
 
On Tue, Mar 18, 2008 at 4:50 PM, gugolplexj <= gugolplexj@bol.c= om.br> wrote:
Ol=E1,
 
Creio q esse problema j=E1 transitou por aqui h=E1 algum tempo.
 
"Quais os n=FAmeros naturais a, b, c diferentes entre s=ED, = tais que 
1/a +1/b + 1/c =3D 1?"
 
Grato,
Jorge.

------=_Part_1597_11037336.1205915398448-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Mar 19 09:41:52 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2JCdrsG022704 for ; Wed, 19 Mar 2008 09:39:53 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2JCdrwm022702 for obm-l-MllGbsmmN; Wed, 19 Mar 2008 09:39:53 -0300 Received: from aacpdlotus.net.ms.gov.br (aacpdlotus.net.ms.gov.br [200.181.116.8]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2JCdqsG022699 for ; Wed, 19 Mar 2008 09:39:52 -0300 Importance: Normal X-Priority: 3 (Normal) Subject: [SPAM] Res:[obm-l] =?ISO-8859-1?Q?QUEST=C3O_ANTIGA?= MIME-Version: 1.0 From: JoaoCarlos_Junior@net.ms.gov.br To: obm-l@mat.puc-rio.br Date: Wed, 19 Mar 2008 08:40:27 -0400 Message-ID: X-Mailer: Lotus Domino Web Server Release 6.5.5 November 30, 2005 X-MIMETrack: Serialize by Notes Server on aacpdlotus/NETMS(Release 6.5.5|November 30, 2005) at 19/03/2008 08:40:27, Serialize complete at 19/03/2008 08:40:27, Itemize by Notes Server on aacpdlotus/NETMS(Release 6.5.5|November 30, 2005) at 19/03/2008 08:40:27, Serialize by Router on aacpdlotus/NETMS(Release 6.5.5|November 30, 2005) at 19/03/2008 08:40:33, Serialize complete at 19/03/2008 08:40:33 Content-Transfer-Encoding: 7bit MIME-Version: 1.0 Content-Type: text/plain Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: JoaoCarlos_Junior@net.ms.gov.br X-Spam-Status: Yes, hits=8.1 required=5.0 tests=AWL,BIG_FONT,CTYPE_JUST_HTML,HTML_50_70, HTML_FONT_COLOR_MAGENTA,HTML_FONT_FACE_BAD, HTML_FONT_FACE_ODD,NO_REAL_NAME,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: text/html; charset=ISO-8859-1 X-Spam-Prev-Content-Transfer-Encoding: quoted-printable SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (8.10 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: NO_REAL_NAME (1.3 points) From: does not include a real name SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: HTML_FONT_COLOR_MAGENTA (0.4 points) BODY: HTML font color is magenta SPAM: BIG_FONT (0.3 points) BODY: FONT Size +2 and up or 3 and up SPAM: HTML_FONT_FACE_ODD (0.3 points) BODY: HTML font face is not a commonly used face SPAM: HTML_50_70 (0.3 points) BODY: Message is 50-70% HTML tags SPAM: HTML_FONT_FACE_BAD (0.2 points) BODY: HTML font face is not a word SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 8.116.181.200.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 8.116.181.200.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: CTYPE_JUST_HTML (0.4 points) HTML-only mail, with no text version SPAM: AWL (-0.9 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results ---------------------

1= /a + 1/b + 1/c  =3D 1 =

 

 =

a, b, c s=E3o naturais distintos de zero. Logo, abc =E9= maior que qualquer dos elementos de {ab, ac, bc, a, b, c}.

Pensemos em um ret=E2ngulo, cuja base tem uma unidade de medida. Divid= amo-lo(a) em colunas iguais de largura 1/abc. As bc primeiras colunas s=E3o= o primeiro termo da express=E3o matem=E1tica acima; as ac colunas seguinte= s, o segundo termo, e, por =FAltimo, ter-se-=E1 as ab =FAltimas colunas, o = terceiro termo. Ora, isso =E9 sempre poss=EDvel de ser feito com quaisquer = inteiros distintos entre si, e at=E9 mesmo se s=E3o eles iguais dois a dois= ou os tr=EAs simultaneamente.

 

Fraternalmente, Jo=E3o.


-----owner-obm-l@mat.puc-rio.br escre= veu: -----

Para: "obm-l" <obm-l@mat.puc-rio.br>
De: "gugolplexj" <gugo= lplexj@bol.com.br>
Enviado por: owner-obm-l@mat.puc-rio.br
Data: 1= 8/03/2008 15:50
Assunto: [obm-l] QUEST=C3O ANTIGA

Ol=E1= ,
 
Creio q esse problema j=E1 transitou por aqui= h=E1 algum tempo.
 
"Quais os n=FAmeros naturais= a, b, c diferentes entre s=ED, tais que 
1/a +1/b + 1= /c =3D 1?"
 
Grato,
Jorge.

= ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Mar 19 11:20:17 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2JEJ2sG028859 for ; Wed, 19 Mar 2008 11:19:02 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2JEJ2uq028857 for obm-l-MllGbsmmN; Wed, 19 Mar 2008 11:19:02 -0300 Received: from ug-out-1314.google.com (ug-out-1314.google.com [66.249.92.170]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2JEIxsG028849 for ; Wed, 19 Mar 2008 11:19:00 -0300 Received: by ug-out-1314.google.com with SMTP id q7so1079103uge.0 for ; Wed, 19 Mar 2008 07:19:34 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; bh=pWr6iv02srR5fvUynQcoI+WAX2aIpVN7OZvGhg7ge4Q=; b=eN51ViKm5Eh6eMYPSU3YyfucgEwuBOKvjcMKyCFyU6IA4V1xDgIPvrA7aST4gz/M/QtF79f0tKKE+50UKv+qmqvcacbe7c4DCaqCE1V67UUOV/cJNLoguji2QjC1Kf1k6BJRwWDw7VH+Dig0sMAo0tWKSqFKwrRkc0SxWXPKzHI= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; b=Bu/yD5xcfTVFT7y35M0PPmO/HyUFGVibV/I3yj5ELhijAD3Kfp3KoJnv/QY0RCfRzIqo0js3iSeUkSoJ+r6kw/gZqL9IjNpU+TpC01gI1OE/fhphngeeFnIbpxiuvjPLSWzDyPdj0nYEzZ/cwRvMLisT+vwVe4mpRCe/G8NcFq8= Received: by 10.67.87.18 with SMTP id p18mr656242ugl.32.1205935963044; Wed, 19 Mar 2008 07:12:43 -0700 (PDT) Received: by 10.66.219.5 with HTTP; Wed, 19 Mar 2008 07:12:42 -0700 (PDT) Message-ID: <2d483c770803190712g51635fcdhefaab2aa0dce8d9d@mail.gmail.com> Date: Wed, 19 Mar 2008 11:12:42 -0300 From: "Ralph Teixeira" To: obm-l@mat.puc-rio.br Subject: =?ISO-8859-1?Q?Re:_[obm-l]_QUEST=C3O_ANTIGA?= In-Reply-To: MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline References: Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m2JEJ1sG028853 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Ralph Teixeira" X-Spam-Status: No, hits=4.0 required=5.0 tests=AWL,IN_REP_TO,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** Acho mais acessível resolver esta assim: não há mal algum em supor que a0 não dá). Também não pode ser a>=3, pois então 1/a+1/b+1/c < 1/3+1/3+1/3 =1. Conclusão: a=2. Agora, fica 1/b+1/c=1/2. Por um raciocínio análogo, não pode ser b>=4, pois aí teríamos 1/b+1/c < 1/4+1/4=1/2. Como b>a, só pode ser b=3. Agora jogue a=2 e b=3 na equação, e descubra que c=6. Abraço, Ralph On Tue, Mar 18, 2008 at 4:50 PM, gugolplexj wrote: > > Olá, > > Creio q esse problema já transitou por aqui há algum tempo. > > "Quais os números naturais a, b, c diferentes entre sí, tais que > 1/a +1/b + 1/c = 1?" > > Grato, > Jorge. ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Mar 19 12:25:54 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2JFOasG008850 for ; Wed, 19 Mar 2008 12:24:36 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2JFOZkp008847 for obm-l-MllGbsmmN; Wed, 19 Mar 2008 12:24:35 -0300 Received: from wr-out-0506.google.com (wr-out-0506.google.com [64.233.184.230]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2JFOXsG008818 for ; Wed, 19 Mar 2008 12:24:33 -0300 Received: by wr-out-0506.google.com with SMTP id c46so588191wra.18 for ; Wed, 19 Mar 2008 08:25:08 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; bh=tzAld6Wcvaer7eO4If8JwqdD4+3o+G3LV6ua/2emrj0=; b=XWuC2ogu2/uZcLhIarvYbONlPCDJ5qt5pGNJyc4DN0mc6eUVYdE/SuekYp11o1rQBWRftRCLsGqbFFqePv3m+aHlDINLtptIKPtRFm4zD0cfwCuEmD04eapiCUJAxsZufOnvV32Hh/ky3sqigerpLSB7BedKVNXbQh7UIO0imXw= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; b=mDAnWdhzy1Iq1ZWsxd2z9gJ9zCpqwT1nw14MDyn0Zqivig7JQ8r1zBcYeplBkWgG1c57NRfbUyVgZ4BD2AA3QNpImwKhkUUF3jpZYx1ONaeE8p5/koElTpCQPUcxcs/NlQBV5FjJWJA1/dRpPwoxCio7wKOyWNGhve+RSLszFUY= Received: by 10.141.29.18 with SMTP id g18mr197783rvj.298.1205940307252; Wed, 19 Mar 2008 08:25:07 -0700 (PDT) Received: by 10.141.28.13 with HTTP; Wed, 19 Mar 2008 08:25:06 -0700 (PDT) Message-ID: <2b5739960803190825o1e6ecd2dx857f6977616d1195@mail.gmail.com> Date: Wed, 19 Mar 2008 12:25:06 -0300 From: "Rogerio Ponce" To: obm-l@mat.puc-rio.br Subject: =?ISO-8859-1?Q?Re:_[obm-l]_QUEST=C3O_ANTIGA?= In-Reply-To: <2d483c770803190712g51635fcdhefaab2aa0dce8d9d@mail.gmail.com> MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline References: <2d483c770803190712g51635fcdhefaab2aa0dce8d9d@mail.gmail.com> Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m2JFOZsG008845 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Rogerio Ponce" X-Spam-Status: No, hits=3.7 required=5.0 tests=AWL,IN_REP_TO,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: *** Maravilha, Ralph! A solucao da "derivada errada" tambem foi muito boa! ( http://www.mail-archive.com/obm-l@mat.puc-rio.br/msg41313.html ) []'s Rogerio Ponce. Em 19/03/08, Ralph Teixeira escreveu: > Acho mais acessível resolver esta assim: não há mal algum em supor que > a > Agora, não pode ser a=1 (pois 1/b+1/c=0 com b,c>0 não dá). Também não > pode ser a>=3, pois então 1/a+1/b+1/c < 1/3+1/3+1/3 =1. > > Conclusão: a=2. > > Agora, fica 1/b+1/c=1/2. Por um raciocínio análogo, não pode ser b>=4, > pois aí teríamos 1/b+1/c < 1/4+1/4=1/2. Como b>a, só pode ser b=3. > > Agora jogue a=2 e b=3 na equação, e descubra que c=6. > > Abraço, > > Ralph > > > On Tue, Mar 18, 2008 at 4:50 PM, gugolplexj wrote: > > > > Olá, > > > > Creio q esse problema já transitou por aqui há algum tempo. > > > > "Quais os números naturais a, b, c diferentes entre sí, tais que > > 1/a +1/b + 1/c = 1?" > > > > Grato, > > Jorge. ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Mar 19 15:23:18 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2JILNsG019957 for ; Wed, 19 Mar 2008 15:21:23 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2JILMQm019955 for obm-l-MllGbsmmN; Wed, 19 Mar 2008 15:21:22 -0300 Received: from web52903.mail.re2.yahoo.com (web52903.mail.re2.yahoo.com [206.190.49.13]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id m2JILJsG019918 for ; Wed, 19 Mar 2008 15:21:20 -0300 Received: (qmail 82435 invoked by uid 60001); 19 Mar 2008 18:21:48 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:Date:From:Subject:To:In-Reply-To:MIME-Version:Content-Type:Content-Transfer-Encoding:Message-ID; b=PJGMQPUCzZ0EfP6XuQOzflG1Q0MJewR3fulF4iAcH2DrG/qzBfO1USvvlYEQgk02bPFNeu8d8YoHqCYwqtX9JUgNwrKkUv/P4WpfLL94qdgO9aKwOMwg6DsgLvIoS8OfEXdsKBI/xvRN7FSjtptCPp0JVi7L7EV9gNEcl2MjJDM=; X-YMail-OSG: lVbkFo8VM1kqBk3VoCmRLdKP6GWQimSelObRCWuYHWn8AEia9wBxf8yPGdKsM.yJDYtq66M0GF8g8GG8Hpl6U2aiUSL4CuNxhW3Zb3Ey2KSje8X.Blub1mq8vp_S Received: from [189.31.103.180] by web52903.mail.re2.yahoo.com via HTTP; Wed, 19 Mar 2008 15:21:47 ART Date: Wed, 19 Mar 2008 15:21:47 -0300 (ART) From: Antonio Giansante Subject: [SPAM] Re: [obm-l] combinatoria dificil To: obm-l@mat.puc-rio.br In-Reply-To: <002b01c88553$d9e7b540$e600a8c0@Rafael> MIME-Version: 1.0 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 7bit Message-ID: <953029.80204.qm@web52903.mail.re2.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Antonio Giansante X-Spam-Status: Yes, hits=6.4 required=5.0 tests=FORGED_YAHOO_RCVD,IN_REP_TO,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ****** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (6.40 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 13.49.190.206.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 13.49.190.206.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- Olá. Sempre que eu tenho dificuldades em resolver um problema de combinatória eu "apelo" para a árvore de possibilidades. Ficou assim(Obs: O "tanso" aqui fez como MAT, FIS e QUI, ao invés das disciplinas do enunciado, mas dá na mesma, ok? Desculpe pela viajada): segunda quarta sexta QUI FIS FIS MAT QUI MAT QUI FIS MAT QUI MAT FIS Dessa forma, se a 1a aula do 1o dia for FIS, tb teremos oito opçoes, e o mesmo para QUI, perfazendo um total de 24 possibilidades. Vamos analisar agora o que acontece com uma dessas escolhas. Supondo que tenhamos escolhido a primeira opção da árvore para as primeiras aulas: MAT QUI FIS Então, na segunda aula, só poderemos ter as opções FIS MAT QUI ou QUI FIS MAT. Observe que outras ordens destes não são possíveis devido à condição de nõ poder ser matérias iguais no mesmo dia. Sendo assim, temos duas opções de preenchimento das aulas da semana para cada opção da árvore. Como são 24 opções iniciais, dá um total de: 24x2=48. Entretanto, nós ainda não consideremaos o fato de que a ordem das duas aulas podem ser trocadas no dia. Assim, se começarmos a preencher as opções da segunda aula primeiro, teremos mais 48 possibildades, o que dá um total de 96 possibilidades de horário.....Ou não, como diria Caetano! (posso ter errado também, ehehe). Espero ter ajudado. ABÇS --- Rafael Cano escreveu: > Olá, > Salhab, eu não consegui encontrar nenhum erro na sua > solução. Na verdade eu consegui resolver de outra > forma e cheguei no mesmo resultado. > Como nenhuma matéria pode repetir no mesmo dia então > obrigatoriamente nos 3 dias os três pares têm que > aparecer (vou chamar de A, B, C pra ficar mais > fácil): (A,B), (B,C) e (C,A). Veja que há 3!=6 > formas de escolher os pares para cada dia e em cada > dia podemos inverter a ordem das matérias, ou seja, > há 6 formas de escolher em qual dia fica cada par e > 2 formas de organizar as matérias por dia. Logo: > 6*2*2*2=48. > > Abraços > > ----- Original Message ----- > From: Marcelo Salhab Brogliato > To: obm-l@mat.puc-rio.br > Sent: Thursday, March 13, 2008 4:48 PM > Subject: Re: [obm-l] combinatoria dificil > > > Olá Thelio, > > Temos 3 matérias, cada uma com 2 aulas semanais em > dias diferentes, e 3 dias. > Para o primeiro dia, vamos escolher 2 das 3 > matérias: 3*2 = 6 modos > Para o segundo dia, só podemos repetir uma > matéria, portanto temos: 2(devido a ordem)*2*1 = 4 > modos > Para o terceiro dia, as matérias já estão > determinadas, temos apenas a ordem, portanto: 2 > modos > > assim, temos: 6*4*2 = 48 modos > mas não tem alternativa.. então devo ter errado. > Vamos aguardar alguém me corrigir ;) > > abraços, > Salhab > > > > 2008/3/13 Thelio Gama : > > É pessoal... > > Achei muito difícil esta questão. Agradeço se > alguém puder explicá-la. > > Thelio > > uma turma tem aulas às 2ª, 4ª e 6ª feiras, de > 8-9 horas e de 11-12 horas. As matérias são > portugues, matemática e ingles, cada uma com duas > aulas semanais, em dias diferentes. De quantos modos > pode ser feito o horário dessa turma? > a)96 ; b) 144 ; c)192 ; d) 6! ; e) 120 > > Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! http://br.mail.yahoo.com/ ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Mar 19 16:46:29 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2JJj5sG026162 for ; Wed, 19 Mar 2008 16:45:05 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2JJj4SF026160 for obm-l-MllGbsmmN; Wed, 19 Mar 2008 16:45:04 -0300 Received: from el-out-1112.google.com (el-out-1112.google.com [209.85.162.183]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2JJj2sG026150 for ; Wed, 19 Mar 2008 16:45:02 -0300 Received: by el-out-1112.google.com with SMTP id o28so456454ele.3 for ; Wed, 19 Mar 2008 12:45:36 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; bh=NLtg4lR5XKq9NU/iL4m2/uTpBWtI3z260OfKwXLopNY=; b=DgnPQi5xYv6Aj5qi+njzlFqkfAdAb94jrTa4no3+ns9MS1tv8TS82u9yLxqtxLyPPcZ1yrRjoCV1ptzSRhwQaT1kUpOQnnQXgpVCbdZ8B5g3I3Lwo1xBc9dxJVA6XrlXYZhKNh81D4Zio/YFa8K0oh6SIgedxUrrhCkH7xxfp2w= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; b=umiCBBISBQfSNP2az+bPKUi6vTqi2CWC0JDn4As1xM0WDflrMMfElyDvYGdEH5obaplRkuSBH+OgdqCTGzdcG8iVz9pj9NqfVGyqJlSxRBBxMk3Z1etgAjtjmEAl929wEoAz5rsnF6+DWaIQx+XR/VP5sVXhdjsZ2mSgelOmVfc= Received: by 10.114.37.1 with SMTP id k1mr2094410wak.6.1205955935023; Wed, 19 Mar 2008 12:45:35 -0700 (PDT) Received: by 10.114.58.13 with HTTP; Wed, 19 Mar 2008 12:45:34 -0700 (PDT) Message-ID: <3e7bcb580803191245m31ac75c0sbdff40c27e0e58ac@mail.gmail.com> Date: Wed, 19 Mar 2008 16:45:34 -0300 From: "=?ISO-8859-1?Q?Henrique_Renn=F3?=" To: obm-l@mat.puc-rio.br Subject: =?ISO-8859-1?Q?Re:_[obm-l]_QUEST=C3O_ANTIGA?= In-Reply-To: MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline References: Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m2JJj3sG026158 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "=?ISO-8859-1?Q?Henrique_Renn=F3?=" X-Spam-Status: No, hits=1.1 required=5.0 tests=AWL,IN_REP_TO,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SIGNATURE_SHORT_SPARSE, SPAM_PHRASE_00_01,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: * Olá Saulo, On Wed, Mar 19, 2008 at 5:29 AM, saulo nilson wrote: > abc=ab+ac+bc=w > x^3+Sx^2+wx-w=0 Não seria -S ao invés de S? > a+b+c=k > ab(c-1)=c(a+b) > c>1 > c=2 Por que você considerou c=2? > ab=2(a+b) > a+b=n > ab=2n > a^2+2ab+b^2=n^2 > a^2+4n^2/a^2=n^2-4n De onde surgiu esta última igualdade? > a^2=x > x^2+x4n^2-x(n^2-4n)=0 > delta=(n^2-4n)^2-16n^2=(n^2-8n)n^2 > a^2=n(n-4+-rq(n(n-8)))/2 > de cara > n=9 > a^2=9 > a=3 > b=6 > 1/2+1/3+1/6=1 > cqd > > > > On Tue, Mar 18, 2008 at 4:50 PM, gugolplexj wrote: > > > > > > > Olá, > > > > Creio q esse problema já transitou por aqui há algum tempo. > > > > "Quais os números naturais a, b, c diferentes entre sí, tais que > > 1/a +1/b + 1/c = 1?" > > > > Grato, > > Jorge. > > -- Henrique ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Mar 19 17:28:03 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2JKQtsG029025 for ; Wed, 19 Mar 2008 17:26:55 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2JKQss1029023 for obm-l-MllGbsmmN; Wed, 19 Mar 2008 17:26:54 -0300 Received: from web52909.mail.re2.yahoo.com (web52909.mail.re2.yahoo.com [206.190.49.19]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id m2JKQnsG029016 for ; Wed, 19 Mar 2008 17:26:52 -0300 Received: (qmail 47528 invoked by uid 60001); 19 Mar 2008 20:27:23 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:Date:From:Subject:To:In-Reply-To:MIME-Version:Content-Type:Content-Transfer-Encoding:Message-ID; b=lJSBCqBz107hV72vEww/J02n9CqKalV34pUEf6PdIhAoHVb2ZEQ4h2z7PClf9hJGS2KF9XLgrn+fBdby9RiuQFEebva/KWZk4mFe93lrq2DWHSgNBg0QSh4ZsPQ+s/Wz7KCp5qylkYVTyZpOih/MA99VIdq46vGf3rcA6c5JkaI=; X-YMail-OSG: 3WytmywVM1mgdp4LC1AWlQXZnEO_S8I.J4qJvpxB Received: from [189.31.103.180] by web52909.mail.re2.yahoo.com via HTTP; Wed, 19 Mar 2008 17:27:23 ART Date: Wed, 19 Mar 2008 17:27:23 -0300 (ART) From: Antonio Giansante Subject: [SPAM] Re: [obm-l] combinatoria dificil To: obm-l@mat.puc-rio.br In-Reply-To: <953029.80204.qm@web52903.mail.re2.yahoo.com> MIME-Version: 1.0 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 7bit Message-ID: <328479.47059.qm@web52909.mail.re2.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Antonio Giansante X-Spam-Status: Yes, hits=6.4 required=5.0 tests=AWL,FORGED_YAHOO_RCVD,IN_REP_TO,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ****** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (6.40 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 19.49.190.206.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 19.49.190.206.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-0.0 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- Desculpem..depois que eu percebi: eu falei que foi pego a 1a opção, porém a ordem MAT QUI FIS é a 5a opção. --- Antonio Giansante escreveu: > Olá. Sempre que eu tenho dificuldades em resolver um > problema de combinatória eu "apelo" para a árvore de > possibilidades. Ficou assim(Obs: O "tanso" aqui fez > como MAT, FIS e QUI, ao invés das disciplinas do > enunciado, mas dá na mesma, ok? Desculpe pela > viajada): > > segunda quarta sexta > > QUI > FIS FIS > MAT > > QUI > MAT QUI FIS > MAT > > QUI > MAT FIS > > Dessa forma, se a 1a aula do 1o dia for FIS, tb > teremos oito opçoes, e o mesmo para QUI, perfazendo > um > total de 24 possibilidades. Vamos analisar agora o > que > acontece com uma dessas escolhas. Supondo que > tenhamos > escolhido a primeira opção da árvore para as > primeiras > aulas: > MAT QUI FIS > > Então, na segunda aula, só poderemos ter as opções > > FIS MAT QUI ou QUI FIS MAT. > Observe que outras ordens destes não são possíveis > devido à condição de nõ poder ser matérias iguais no > mesmo dia. Sendo assim, temos duas opções de > preenchimento das aulas da semana para cada opção da > árvore. Como são 24 opções iniciais, dá um total de: > 24x2=48. > Entretanto, nós ainda não consideremaos o fato de > que > a ordem das duas aulas podem ser trocadas no dia. > Assim, se começarmos a preencher as opções da > segunda > aula primeiro, teremos mais 48 possibildades, o que > dá > um total de 96 possibilidades de horário.....Ou não, > como diria Caetano! (posso ter errado também, > ehehe). > Espero ter ajudado. ABÇS > > > > > --- Rafael Cano escreveu: > > > Olá, > > Salhab, eu não consegui encontrar nenhum erro na > sua > > solução. Na verdade eu consegui resolver de outra > > forma e cheguei no mesmo resultado. > > Como nenhuma matéria pode repetir no mesmo dia > então > > obrigatoriamente nos 3 dias os três pares têm que > > aparecer (vou chamar de A, B, C pra ficar mais > > fácil): (A,B), (B,C) e (C,A). Veja que há 3!=6 > > formas de escolher os pares para cada dia e em > cada > > dia podemos inverter a ordem das matérias, ou > seja, > > há 6 formas de escolher em qual dia fica cada par > e > > 2 formas de organizar as matérias por dia. Logo: > > 6*2*2*2=48. > > > > Abraços > > > > ----- Original Message ----- > > From: Marcelo Salhab Brogliato > > To: obm-l@mat.puc-rio.br > > Sent: Thursday, March 13, 2008 4:48 PM > > Subject: Re: [obm-l] combinatoria dificil > > > > > > Olá Thelio, > > > > Temos 3 matérias, cada uma com 2 aulas semanais > em > > dias diferentes, e 3 dias. > > Para o primeiro dia, vamos escolher 2 das 3 > > matérias: 3*2 = 6 modos > > Para o segundo dia, só podemos repetir uma > > matéria, portanto temos: 2(devido a ordem)*2*1 = 4 > > modos > > Para o terceiro dia, as matérias já estão > > determinadas, temos apenas a ordem, portanto: 2 > > modos > > > > assim, temos: 6*4*2 = 48 modos > > mas não tem alternativa.. então devo ter errado. > > Vamos aguardar alguém me corrigir ;) > > > > abraços, > > Salhab > > > > > > > > 2008/3/13 Thelio Gama : > > > > É pessoal... > > > > Achei muito difícil esta questão. Agradeço se > > alguém puder explicá-la. > > > > Thelio > > > > uma turma tem aulas às 2ª, 4ª e 6ª feiras, de > > 8-9 horas e de 11-12 horas. As matérias são > > portugues, matemática e ingles, cada uma com duas > > aulas semanais, em dias diferentes. De quantos > modos > > pode ser feito o horário dessa turma? > > a)96 ; b) 144 ; c)192 ; d) 6! ; e) 120 > > > > > > > > Abra sua conta no Yahoo! Mail, o único sem > limite de espaço para armazenamento! > http://br.mail.yahoo.com/ > ========================================================================= > Instruções para entrar na lista, sair da lista e > usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > ========================================================================= > Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! http://br.mail.yahoo.com/ ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Mar 19 19:24:07 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2JMMRsG005141 for ; Wed, 19 Mar 2008 19:22:27 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2JMMRlf005138 for obm-l-MllGbsmmN; Wed, 19 Mar 2008 19:22:27 -0300 Received: from mx1.dglnet.com.br (mx1.dglnet.com.br [201.76.39.219]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2JMMPsG005131 for ; Wed, 19 Mar 2008 19:22:25 -0300 Received: from Rafael (unknown [201.82.46.164]) (Authenticated sender: rafaelcano@dglnet.com.br) by mx1.dglnet.com.br (Postfix) with ESMTP id 2B7831EBC4F6 for ; Wed, 19 Mar 2008 19:23:00 -0300 (BRT) Message-ID: <002f01c88a10$b9776aa0$e600a8c0@Rafael> From: "Rafael Cano" To: References: <328479.47059.qm@web52909.mail.re2.yahoo.com> Subject: [SPAM] Re: [obm-l] combinatoria dificil Date: Wed, 19 Mar 2008 19:29:34 -0300 MIME-Version: 1.0 Content-Type: text/plain; format=flowed; charset="iso-8859-1"; reply-type=original Content-Transfer-Encoding: 7bit X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2900.3138 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.3198 X-Antivirus: avast! (VPS 080319-0, 19/03/2008), Outbound message X-Antivirus-Status: Clean Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Rafael Cano" X-Spam-Status: Yes, hits=5.4 required=5.0 tests=AWL,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, REFERENCES,SPAM_PHRASE_00_01,USER_AGENT_OE,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ***** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (5.40 hits, 5 required) SPAM: REFERENCES (-0.5 points) Has a valid-looking References header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: USER_AGENT_OE (0.2 points) X-Mailer header indicates a non-spam MUA (Outlook Express) SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: QUOTED_EMAIL_TEXT (-0.8 points) BODY: Contains what looks like a quoted email text SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 219.39.76.201.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 219.39.76.201.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (0.7 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- Olá Antonio. Acho que você contou duas vezes cada horário possível. Da maneira que você fez você já tinha considerado a ordem das aulas em cada dia. A árvore de possibilidades já considera todas as formas de se preencher a primeira aula de cada dia. Por exemplo: suponha que a primeira aula de cada dia é MAT, FIS, QUI, nessa ordem, e que a segunda aula de cada dia é FIS, QUI, MAT. Mas o ramo da árvore que começa com FIS também considera que é possível formar um horário em que a primeira aula de cada dia é FIS, QUI, MAT, e a segunda aula de cada dia é MAT, FIS, QUI, ou seja, exatamente o horário anterior, mas com a ordem das matérias invertidas. Abraços ----- Original Message ----- From: "Antonio Giansante" To: Sent: Wednesday, March 19, 2008 5:27 PM Subject: Re: [obm-l] combinatoria dificil > Desculpem..depois que eu percebi: eu falei que foi > pego a 1a opção, porém a ordem MAT QUI FIS é a 5a > opção. > --- Antonio Giansante > escreveu: > >> Olá. Sempre que eu tenho dificuldades em resolver um >> problema de combinatória eu "apelo" para a árvore de >> possibilidades. Ficou assim(Obs: O "tanso" aqui fez >> como MAT, FIS e QUI, ao invés das disciplinas do >> enunciado, mas dá na mesma, ok? Desculpe pela >> viajada): >> >> segunda quarta sexta >> >> QUI >> FIS FIS >> MAT >> >> QUI >> MAT QUI FIS >> MAT >> >> QUI >> MAT FIS >> >> Dessa forma, se a 1a aula do 1o dia for FIS, tb >> teremos oito opçoes, e o mesmo para QUI, perfazendo >> um >> total de 24 possibilidades. Vamos analisar agora o >> que >> acontece com uma dessas escolhas. Supondo que >> tenhamos >> escolhido a primeira opção da árvore para as >> primeiras >> aulas: >> MAT QUI FIS >> >> Então, na segunda aula, só poderemos ter as opções >> >> FIS MAT QUI ou QUI FIS MAT. >> Observe que outras ordens destes não são possíveis >> devido à condição de nõ poder ser matérias iguais no >> mesmo dia. Sendo assim, temos duas opções de >> preenchimento das aulas da semana para cada opção da >> árvore. Como são 24 opções iniciais, dá um total de: >> 24x2=48. >> Entretanto, nós ainda não consideremaos o fato de >> que >> a ordem das duas aulas podem ser trocadas no dia. >> Assim, se começarmos a preencher as opções da >> segunda >> aula primeiro, teremos mais 48 possibildades, o que >> dá >> um total de 96 possibilidades de horário.....Ou não, >> como diria Caetano! (posso ter errado também, >> ehehe). >> Espero ter ajudado. ABÇS >> > 2008/3/13 Thelio Gama : >> > >> > É pessoal... >> > >> > Achei muito difícil esta questão. Agradeço se >> > alguém puder explicá-la. >> > >> > Thelio >> > >> > uma turma tem aulas às 2ª, 4ª e 6ª feiras, de >> > 8-9 horas e de 11-12 horas. As matérias são >> > portugues, matemática e ingles, cada uma com duas >> > aulas semanais, em dias diferentes. De quantos >> modos >> > pode ser feito o horário dessa turma? >> > a)96 ; b) 144 ; c)192 ; d) 6! ; e) 120 >> > >> > >> >> >> >> Abra sua conta no Yahoo! Mail, o único sem >> limite de espaço para armazenamento! >> http://br.mail.yahoo.com/ >> > ========================================================================= >> Instruções para entrar na lista, sair da lista e >> usar a lista em >> http://www.mat.puc-rio.br/~obmlistas/obm-l.html >> > ========================================================================= >> > > > > Abra sua conta no Yahoo! Mail, o único sem limite de espaço para > armazenamento! > http://br.mail.yahoo.com/ > ========================================================================= > Instruções para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > ========================================================================= ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Mar 19 21:19:56 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2K0IesG012385 for ; Wed, 19 Mar 2008 21:18:40 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2K0Ie0j012383 for obm-l-MllGbsmmN; Wed, 19 Mar 2008 21:18:40 -0300 Received: from fg-out-1718.google.com (fg-out-1718.google.com [72.14.220.157]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2K0IbsG012361 for ; Wed, 19 Mar 2008 21:18:38 -0300 Received: by fg-out-1718.google.com with SMTP id e12so505462fga.3 for ; Wed, 19 Mar 2008 17:19:12 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=qXGE28Hh+sueRhWci9lrdwAVLMEotoovvDtrpJSq40k=; b=a0XIQ3Hkh4xYtkJdJskGY1ThyG3c3oBALdbiKuLUovAnI+dMWUPfFb5O5mBfzDeLDTXVdnSxebQAnNR5HLXtEmZPwORNGf3Q6DtEo4bQlNYequG5e85Yy9PGFDn6IpUiqhHneibSZD5NTkEeFIwtFO+Keu1xMuc+E3CQlnF05+8= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=Y+NCnphW2bzHgDsFbK4ufoOHvgQ3qL4VPLpZ1LzxdPZahLyG51xaHgHtI8rrQXXnJ95A9ATWbd3ebE3rQXWXwWfy3wRbE3gy+XNxXCov3LIqoJ9Hqu/7o4r0vuAfilXsluoBPbCjfDqQT0/mYuHkvuDg5vGrEErslR42UmCxIzM= Received: by 10.86.27.9 with SMTP id a9mr436130fga.62.1205971925113; Wed, 19 Mar 2008 17:12:05 -0700 (PDT) Received: by 10.86.74.8 with HTTP; Wed, 19 Mar 2008 17:12:05 -0700 (PDT) Message-ID: Date: Wed, 19 Mar 2008 21:12:05 -0300 From: "saulo nilson" To: obm-l@mat.puc-rio.br Subject: =?ISO-8859-1?Q?Re:_[obm-l]_QUEST=C3O_ANTIGA?= In-Reply-To: <3e7bcb580803191245m31ac75c0sbdff40c27e0e58ac@mail.gmail.com> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_3314_22790559.1205971925101" References: <3e7bcb580803191245m31ac75c0sbdff40c27e0e58ac@mail.gmail.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "saulo nilson" X-Spam-Status: No, hits=-0.3 required=5.0 tests=AWL,HTML_FONT_COLOR_GRAY,HTML_FONT_COLOR_UNSAFE,IN_REP_TO, MAILTO_LINK,MIME_EXCESSIVE_QP,QUOTED_EMAIL_TEXT,REFERENCES, SPAM_PHRASE_00_01,X_MAILING_LIST version=2.44 X-Spam-Level: ------=_Part_3314_22790559.1205971925101 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline esse polinomio era uma primeira ideia, c=3D2 e so uma solu=E7ao. 2008/3/19 Henrique Renn=F3 : > Ol=E1 Saulo, > > On Wed, Mar 19, 2008 at 5:29 AM, saulo nilson > wrote: > > abc=3Dab+ac+bc=3Dw > > x^3+Sx^2+wx-w=3D0 > > N=E3o seria -S ao inv=E9s de S? > > > a+b+c=3Dk > > ab(c-1)=3Dc(a+b) > > c>1 > > c=3D2 > > Por que voc=EA considerou c=3D2? > > > ab=3D2(a+b) > > a+b=3Dn > > ab=3D2n > > a^2+2ab+b^2=3Dn^2 > > a^2+4n^2/a^2=3Dn^2-4n > > De onde surgiu esta =FAltima igualdade? > > > a^2=3Dx > > x^2+x4n^2-x(n^2-4n)=3D0 > > delta=3D(n^2-4n)^2-16n^2=3D(n^2-8n)n^2 > > a^2=3Dn(n-4+-rq(n(n-8)))/2 > > de cara > > n=3D9 > > a^2=3D9 > > a=3D3 > > b=3D6 > > 1/2+1/3+1/6=3D1 > > cqd > > > > > > > > On Tue, Mar 18, 2008 at 4:50 PM, gugolplexj > wrote: > > > > > > > > > > > Ol=E1, > > > > > > Creio q esse problema j=E1 transitou por aqui h=E1 algum tempo. > > > > > > "Quais os n=FAmeros naturais a, b, c diferentes entre s=ED, tais que > > > 1/a +1/b + 1/c =3D 1?" > > > > > > Grato, > > > Jorge. > > > > > > > > -- > Henrique > > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > Instru=E7=F5es para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > ------=_Part_3314_22790559.1205971925101 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline esse polinomio era uma primeira ideia, c=3D2 e so uma solu=E7ao.

2008/3/19 Henrique Renn=F3 <henrique.renno@gmail.com>:
Ol=E1 Saulo,

On Wed, Mar 19, 2008 at 5:29 AM, saulo nilson <= ;saulo.nilson@gmail.com> w= rote:
> abc=3Dab+ac+bc=3Dw
> x^3+Sx^2+wx-w=3D0

N= =E3o seria -S ao inv=E9s de S?

> a+b+c=3Dk
> ab(c-1)=3Dc(a+b)
> c= >1
> c=3D2

Por que voc=EA considerou c=3D2?

> ab=3D2(a+b)
> a+b=3Dn
> ab=3D2n<= br>> a^2+2ab+b^2=3Dn^2
> a^2+4n^2/a^2=3Dn^2-4n

De ond= e surgiu esta =FAltima igualdade?

> a^2=3Dx
> x^2+x4n^2-x(n^2-4n)=3D0
&= gt; delta=3D(n^2-4n)^2-16n^2=3D(n^2-8n)n^2
> a^2=3Dn(n-4+-rq(n(n-8)))= /2
> de cara
> n=3D9
> a^2=3D9
> a=3D3
> b=3D= 6
> 1/2+1/3+1/6=3D1
> cqd
>
>
>
> On Tue, Mar 18, 2008 at 4:50 PM, g= ugolplexj <gugolplexj@bol.com.b= r> wrote:
>
> >
> >
> > Ol=E1,
&= gt; >
> > Creio q esse problema j=E1 transitou por aqui h=E1 algum tempo.> >
> > "Quais os n=FAmeros naturais a, b, c diferent= es entre s=ED, tais que
> > 1/a +1/b + 1/c =3D 1?"
> &g= t;
> > Grato,
> > Jorge.
>
>



-= -
Henrique

=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D
Instru=E7=F5es para entrar na lista, sair da lista= e usar a lista em
http://www.mat.puc-rio.br/~obmlistas/obm-l.html
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D

------=_Part_3314_22790559.1205971925101-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Mar 19 23:58:13 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2K2uMsG019122 for ; Wed, 19 Mar 2008 23:56:22 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2K2uLea019119 for obm-l-MllGbsmmN; Wed, 19 Mar 2008 23:56:21 -0300 Received: from wr-out-0506.google.com (wr-out-0506.google.com [64.233.184.232]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2K2uIsG019108 for ; Wed, 19 Mar 2008 23:56:19 -0300 Received: by wr-out-0506.google.com with SMTP id c46so1008522wra.18 for ; Wed, 19 Mar 2008 19:56:53 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; bh=igBOhtcvnJJmFOS5q9s7+CCuBCaxWLbpsYS8DA2nFFM=; b=rIpf+AhTpb9YdgqZ7CARkY6NmbeQ/4Doa4pow+q+vUQB2Qnwm2lfDzcjuk0uK7JYNNZUnA5Sjw2hB+0gDj729nYrpdt261+G5Lfmt2jAF/LfttYeKTFA9YPNO3q31VtAT+1DuARPfNS/Gq15z3x5p/Of3phdMQVffxW/mIKcwHA= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; b=AOz+t9J0DzxQEe2A2McLehHe0MwAXHRs4jR9YAIGPNscsPsHRGSBkNkJMrGByvgdI/sydy6a0szS1nXOAPLIlfaIfk8mwI6V1A93+ywwZBDU4oODdXUa9kzBoTwBctkS7SdPfufvRBa8BMWm6dfEzHaogkHIyXIV+cS8JblkG+s= Received: by 10.150.206.1 with SMTP id d1mr626085ybg.4.1205981813496; Wed, 19 Mar 2008 19:56:53 -0700 (PDT) Received: by 10.150.57.9 with HTTP; Wed, 19 Mar 2008 19:56:53 -0700 (PDT) Message-ID: <5bb472220803191956x5985de0cx3e9f90dd4250a71@mail.gmail.com> Date: Wed, 19 Mar 2008 23:56:53 -0300 From: "Joao Victor Brasil" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] combinatoria dificil In-Reply-To: <002f01c88a10$b9776aa0$e600a8c0@Rafael> MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline References: <328479.47059.qm@web52909.mail.re2.yahoo.com> <002f01c88a10$b9776aa0$e600a8c0@Rafael> Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m2K2uKsG019114 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Joao Victor Brasil" X-Spam-Status: No, hits=3.9 required=5.0 tests=AWL,IN_REP_TO,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: *** Estava pensando o seguinte, se D1 é segunda, D2 quarta e D3 sexta, e H1 aula de 8-9 hs e H2 aula de 11-12 hs, quantas possibilidades de matérias podemos ter por aula? D1 H1:3 matérias (MAT, FIS, QUI) H2:2 matérias (a que não foi escolhida antes) D2 H1:3 matérias (MAT, FIS, QUI, pode ser a segunda aula da semana, todas voltam) H2:2 matérias (a que não foi escolhida antes) D3 H1:2 matérias (Uma matéria já usou suas duas aulas semanais) H2:1 matérias Pelo princípio multiplicativo, teremos 3x2x3x2x2x1 = 72. Mas D1H1 pode trocar com D1H2 sem prejuízo, teremos então 72x2x2x2 (uma multiplicação para cada dia)=576. Com esse processo, contamos mais de uma vez os horários, devemos divir por 3! para corrigir nosso erro. Logo teremos 96 horários diferentes. Joao Victor Brasil On 3/19/08, Rafael Cano wrote: > Olá Antonio. > Acho que você contou duas vezes cada horário possível. > Da maneira que você fez você já tinha considerado a ordem das aulas em cada > dia. A árvore de possibilidades já considera todas as formas de se preencher > a primeira aula de cada dia. Por exemplo: suponha que a primeira aula de > cada dia é MAT, FIS, QUI, nessa ordem, e que a segunda aula de cada dia é > FIS, QUI, MAT. Mas o ramo da árvore que começa com FIS também considera que > é possível formar um horário em que a primeira aula de cada dia é FIS, QUI, > MAT, e a segunda aula de cada dia é MAT, FIS, QUI, ou seja, exatamente o > horário anterior, mas com a ordem das matérias invertidas. > Abraços > > ----- Original Message ----- > From: "Antonio Giansante" > To: > Sent: Wednesday, March 19, 2008 5:27 PM > Subject: Re: [obm-l] combinatoria dificil > > > > Desculpem..depois que eu percebi: eu falei que foi > > pego a 1a opção, porém a ordem MAT QUI FIS é a 5a > > opção. > > --- Antonio Giansante > > escreveu: > > > >> Olá. Sempre que eu tenho dificuldades em resolver um > >> problema de combinatória eu "apelo" para a árvore de > >> possibilidades. Ficou assim(Obs: O "tanso" aqui fez > >> como MAT, FIS e QUI, ao invés das disciplinas do > >> enunciado, mas dá na mesma, ok? Desculpe pela > >> viajada): > >> > >> segunda quarta sexta > >> > >> QUI > >> FIS FIS > >> MAT > >> > >> QUI > >> MAT QUI FIS > >> MAT > >> > >> QUI > >> MAT FIS > >> > >> Dessa forma, se a 1a aula do 1o dia for FIS, tb > >> teremos oito opçoes, e o mesmo para QUI, perfazendo > >> um > >> total de 24 possibilidades. Vamos analisar agora o > >> que > >> acontece com uma dessas escolhas. Supondo que > >> tenhamos > >> escolhido a primeira opção da árvore para as > >> primeiras > >> aulas: > >> MAT QUI FIS > >> > >> Então, na segunda aula, só poderemos ter as opções > >> > >> FIS MAT QUI ou QUI FIS MAT. > >> Observe que outras ordens destes não são possíveis > >> devido à condição de nõ poder ser matérias iguais no > >> mesmo dia. Sendo assim, temos duas opções de > >> preenchimento das aulas da semana para cada opção da > >> árvore. Como são 24 opções iniciais, dá um total de: > >> 24x2=48. > >> Entretanto, nós ainda não consideremaos o fato de > >> que > >> a ordem das duas aulas podem ser trocadas no dia. > >> Assim, se começarmos a preencher as opções da > >> segunda > >> aula primeiro, teremos mais 48 possibildades, o que > >> dá > >> um total de 96 possibilidades de horário.....Ou não, > >> como diria Caetano! (posso ter errado também, > >> ehehe). > >> Espero ter ajudado. ABÇS > > >> > 2008/3/13 Thelio Gama : > >> > > >> > É pessoal... > >> > > >> > Achei muito difícil esta questão. Agradeço se > >> > alguém puder explicá-la. > >> > > >> > Thelio > >> > > >> > uma turma tem aulas às 2ª, 4ª e 6ª feiras, de > >> > 8-9 horas e de 11-12 horas. As matérias são > >> > portugues, matemática e ingles, cada uma com duas > >> > aulas semanais, em dias diferentes. De quantos > >> modos > >> > pode ser feito o horário dessa turma? > >> > a)96 ; b) 144 ; c)192 ; d) 6! ; e) 120 > >> > > >> > > >> > >> > >> > >> Abra sua conta no Yahoo! Mail, o único sem > >> limite de espaço para armazenamento! > >> http://br.mail.yahoo.com/ > >> > > ========================================================================= > >> Instruções para entrar na lista, sair da lista e > >> usar a lista em > >> http://www.mat.puc-rio.br/~obmlistas/obm-l.html > >> > > ========================================================================= > >> > > > > > > > > Abra sua conta no Yahoo! Mail, o único sem limite de espaço para > > armazenamento! > > http://br.mail.yahoo.com/ > > ========================================================================= > > Instruções para entrar na lista, sair da lista e usar a lista em > > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > > ========================================================================= > > ========================================================================= > Instruções para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > ========================================================================= > ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Mar 20 12:19:35 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2KFHXsG022696 for ; Thu, 20 Mar 2008 12:17:33 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2KFHXWr022693 for obm-l-MllGbsmmN; Thu, 20 Mar 2008 12:17:33 -0300 Received: from smtp.uol.com.br (smtps.uol.com.br [200.221.4.131]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2KFHSsG022633 for ; Thu, 20 Mar 2008 12:17:29 -0300 Received: from localhost (localhost [127.0.0.1]) by socom11.uol.com.br (Postfix) with ESMTP id D62C81073 for ; Thu, 20 Mar 2008 12:18:04 -0300 (BRT) Received: from PreturlanPC (unknown [201.82.21.15]) by socom11.uol.com.br (Postfix) with ESMTP id 3A051A0B for ; Thu, 20 Mar 2008 12:18:04 -0300 (BRT) From: =?iso-8859-1?Q?Jo=E3o_Gabriel_Preturlan?= To: Subject: [SPAM] [obm-l] Sistema Date: Thu, 20 Mar 2008 12:18:16 -0300 Message-ID: <000001c88a9d$9f38d6a0$ddaa83e0$@com.br> MIME-Version: 1.0 Content-Type: text/plain X-Mailer: Microsoft Office Outlook 12.0 Thread-Index: AciKnZ7cM/sf4TuKQ9aknhfmW4IHXQ== Content-Language: pt-br X-SIG5: 34a127255e9c79859d82ef3105e02421 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: =?iso-8859-1?Q?Jo=E3o_Gabriel_Preturlan?= X-Spam-Status: Yes, hits=6.1 required=5.0 tests=HTML_50_70,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, SPAM_PHRASE_00_01,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ****** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_NextPart_000_0001_01C88A84.79EB9EA0" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (6.10 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: HTML_50_70 (0.3 points) BODY: Message is 50-70% HTML tags SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 15.21.82.201.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 15.21.82.201.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- Esta é uma mensagem em várias partes no formato MIME. ------=_NextPart_000_0001_01C88A84.79EB9EA0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Ol=E1 a todos! =20 Pe=E7o ajuda neste problema: =20 =93Considerando o sistema linear com as duas seguintes equa=E7=F5es: =20 (log a)x + [(sen b)^2]y =3D 1 [log(a+b)x + [(cos b)^2]y =3D 2 =20 Com a > 0 e b > 0. Prove que se ([log(base 9){b/a}]^cos2x) < 1, (Pi/4) < = x < (3Pi/4), ent=E3o o sistema admite uma =FAnica solu=E7=E3o.=94 =20 Obs.: l=EA-se =93([log(base 9){b/a}]^cos2x) < 1=94 como: logaritmo de b = sobre a na base 9, elevado ao co-seno de 2x, menor que um. =20 Desde j=E1 agrade=E7o! =20 JG. No virus found in this outgoing message. Checked by AVG.=20 Version: 7.5.519 / Virus Database: 269.21.7/1335 - Release Date: = 19/03/2008 09:54 =20 ------=_NextPart_000_0001_01C88A84.79EB9EA0 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable

Ol=E1 a todos!

 

Pe=E7o ajuda neste problema:

 

“Considerando o sistema linear com as duas = seguintes equa=E7=F5es:

 

(log a)x + [(sen b)^2]y =3D = 1

[log(a+b)x + [(cos b)^2]y =3D 2

 

Com a > 0 e b > 0. Prove que se ([log(base = 9){b/a}]^cos2x) < 1, (Pi/4) < x < (3Pi/4), ent=E3o o sistema admite uma =FAnica = solu=E7=E3o.”

 

Obs.: l=EA-se =A0“([log(base 9){b/a}]^cos2x) = < 1” como: logaritmo de b sobre a na base 9, elevado ao co-seno de 2x, menor = que um.

 

Desde j=E1 agrade=E7o!

 

JG.


No virus found in this outgoing message.
Checked by AVG.
Version: 7.5.519 / Virus Database: 269.21.7/1335 - Release Date: = 19/03/2008 09:54

------=_NextPart_000_0001_01C88A84.79EB9EA0-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Mar 20 13:40:21 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2KGcIsG030771 for ; Thu, 20 Mar 2008 13:38:18 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2KGcIVK030762 for obm-l-MllGbsmmN; Thu, 20 Mar 2008 13:38:18 -0300 Received: from web52909.mail.re2.yahoo.com (web52909.mail.re2.yahoo.com [206.190.49.19]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id m2KGcEsG030741 for ; Thu, 20 Mar 2008 13:38:15 -0300 Received: (qmail 16183 invoked by uid 60001); 20 Mar 2008 16:38:49 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:Date:From:Subject:To:In-Reply-To:MIME-Version:Content-Type:Content-Transfer-Encoding:Message-ID; b=jW1ci3SI046y2h/Fm78c7Jdq5S7YaOjMBCnhjBPnH2wh1V+dFNPi0CyUlKE4SjTfp5CUBZBUuJDcrVrYAJSOIxc/LgHCm+B3yByznGqbTwHkbI2S31mOmloqxP8tmygc/TXUJB+zzRaBfMfuUBmPnhJEfutlr7VSIRus8Vsdx4s=; X-YMail-OSG: P2DWcRcVM1nVF76XuRrDo40jSxzAXYTYp28af3vf6pCv.yeszQ.Ts0jnk8TGfxF9poLocKpsZTD32RdR85XuY2C.4SCqy6vd7.IVzEweo.H9_ld.d.aCVx8mhQieL0rxulSjzy.qogTS4Ko- Received: from [189.31.103.180] by web52909.mail.re2.yahoo.com via HTTP; Thu, 20 Mar 2008 13:38:49 ART Date: Thu, 20 Mar 2008 13:38:49 -0300 (ART) From: Antonio Giansante Subject: [SPAM] Re: [obm-l] combinatoria dificil To: obm-l@mat.puc-rio.br In-Reply-To: <002f01c88a10$b9776aa0$e600a8c0@Rafael> MIME-Version: 1.0 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 7bit Message-ID: <902341.13893.qm@web52909.mail.re2.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Antonio Giansante X-Spam-Status: Yes, hits=6.4 required=5.0 tests=FORGED_YAHOO_RCVD,IN_REP_TO,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ****** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (6.40 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 19.49.190.206.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 19.49.190.206.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- É verdade...viajei!!! Voltemos à prancheta!!! abçs --- Rafael Cano escreveu: > Olá Antonio. > Acho que você contou duas vezes cada horário > possível. > Da maneira que você fez você já tinha considerado a > ordem das aulas em cada > dia. A árvore de possibilidades já considera todas > as formas de se preencher > a primeira aula de cada dia. Por exemplo: suponha > que a primeira aula de > cada dia é MAT, FIS, QUI, nessa ordem, e que a > segunda aula de cada dia é > FIS, QUI, MAT. Mas o ramo da árvore que começa com > FIS também considera que > é possível formar um horário em que a primeira aula > de cada dia é FIS, QUI, > MAT, e a segunda aula de cada dia é MAT, FIS, QUI, > ou seja, exatamente o > horário anterior, mas com a ordem das matérias > invertidas. > Abraços > > ----- Original Message ----- > From: "Antonio Giansante" > To: > Sent: Wednesday, March 19, 2008 5:27 PM > Subject: Re: [obm-l] combinatoria dificil > > > > Desculpem..depois que eu percebi: eu falei que foi > > pego a 1a opção, porém a ordem MAT QUI FIS é a > 5a > > opção. > > --- Antonio Giansante > > escreveu: > > > >> Olá. Sempre que eu tenho dificuldades em resolver > um > >> problema de combinatória eu "apelo" para a árvore > de > >> possibilidades. Ficou assim(Obs: O "tanso" aqui > fez > >> como MAT, FIS e QUI, ao invés das disciplinas do > >> enunciado, mas dá na mesma, ok? Desculpe pela > >> viajada): > >> > >> segunda quarta sexta > >> > >> QUI > >> FIS FIS > >> MAT > >> > >> QUI > >> MAT QUI FIS > >> MAT > >> > >> QUI > >> MAT FIS > >> > >> Dessa forma, se a 1a aula do 1o dia for FIS, tb > >> teremos oito opçoes, e o mesmo para QUI, > perfazendo > >> um > >> total de 24 possibilidades. Vamos analisar agora > o > >> que > >> acontece com uma dessas escolhas. Supondo que > >> tenhamos > >> escolhido a primeira opção da árvore para as > >> primeiras > >> aulas: > >> MAT QUI FIS > >> > >> Então, na segunda aula, só poderemos ter as > opções > >> > >> FIS MAT QUI ou QUI FIS MAT. > >> Observe que outras ordens destes não são > possíveis > >> devido à condição de nõ poder ser matérias iguais > no > >> mesmo dia. Sendo assim, temos duas opções de > >> preenchimento das aulas da semana para cada opção > da > >> árvore. Como são 24 opções iniciais, dá um total > de: > >> 24x2=48. > >> Entretanto, nós ainda não consideremaos o fato de > >> que > >> a ordem das duas aulas podem ser trocadas no dia. > >> Assim, se começarmos a preencher as opções da > >> segunda > >> aula primeiro, teremos mais 48 possibildades, o > que > >> dá > >> um total de 96 possibilidades de horário.....Ou > não, > >> como diria Caetano! (posso ter errado também, > >> ehehe). > >> Espero ter ajudado. ABÇS > > >> > 2008/3/13 Thelio Gama : > >> > > >> > É pessoal... > >> > > >> > Achei muito difícil esta questão. Agradeço > se > >> > alguém puder explicá-la. > >> > > >> > Thelio > >> > > >> > uma turma tem aulas às 2ª, 4ª e 6ª feiras, > de > >> > 8-9 horas e de 11-12 horas. As matérias são > >> > portugues, matemática e ingles, cada uma com > duas > >> > aulas semanais, em dias diferentes. De quantos > >> modos > >> > pode ser feito o horário dessa turma? > >> > a)96 ; b) 144 ; c)192 ; d) 6! ; e) > 120 > >> > > >> > > >> > >> > >> > >> Abra sua conta no Yahoo! Mail, o único sem > >> limite de espaço para armazenamento! > >> http://br.mail.yahoo.com/ > >> > > > ========================================================================= > >> Instruções para entrar na lista, sair da lista e > >> usar a lista em > >> http://www.mat.puc-rio.br/~obmlistas/obm-l.html > >> > > > ========================================================================= > >> > > > > > > > > Abra sua conta no Yahoo! Mail, o único sem > limite de espaço para > > armazenamento! > > http://br.mail.yahoo.com/ > > > ========================================================================= > > Instruções para entrar na lista, sair da lista e > usar a lista em > > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > > > ========================================================================= > > > ========================================================================= > Instruções para entrar na lista, sair da lista e > usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > ========================================================================= > Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! http://br.mail.yahoo.com/ ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Mar 20 13:46:36 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2KGijsG031277 for ; Thu, 20 Mar 2008 13:44:45 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2KGijs1031275 for obm-l-MllGbsmmN; Thu, 20 Mar 2008 13:44:45 -0300 Received: from wx-out-0506.google.com (wx-out-0506.google.com [66.249.82.233]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2KGidsG031246 for ; Thu, 20 Mar 2008 13:44:40 -0300 Received: by wx-out-0506.google.com with SMTP id t4so1165701wxc.18 for ; Thu, 20 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<99886d920803200945u2e477f6fu6e90547fd91446dc@mail.gmail.com> Date: Thu, 20 Mar 2008 17:45:13 +0100 From: "=?UTF-8?Q?Bruno_Fran=C3=A7a_dos_Reis?=" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Cadastramento OBM-2008 In-Reply-To: MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_31073_18701591.1206031513766" References: Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "=?UTF-8?Q?Bruno_Fran=C3=A7a_dos_Reis?=" X-Spam-Status: No, hits=3.9 required=5.0 tests=AWL,IN_REP_TO,MAILTO_TO_SPAM_ADDR,QUOTED_EMAIL_TEXT, RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,REFERENCES, SPAM_PHRASE_00_01,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: *** ------=_Part_31073_18701591.1206031513766 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: base64 Content-Disposition: inline Sm9hbywgZXUgbsOjbyBzZWkgcmVzcG9uZGVyIMOgIHN1YSBwZXJndW50YSwgbWFzIHBvc3NvIHRl 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(localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2KJDYsG008484 for ; Thu, 20 Mar 2008 16:13:34 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2KJDYGv008482 for obm-l-MllGbsmmN; Thu, 20 Mar 2008 16:13:34 -0300 Received: from fg-out-1718.google.com (fg-out-1718.google.com [72.14.220.157]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2KJDVsG008474 for ; Thu, 20 Mar 2008 16:13:32 -0300 Received: by fg-out-1718.google.com with SMTP id e12so837123fga.3 for ; Thu, 20 Mar 2008 12:14:07 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=X5AAUbIAvAKzCOSl6hwGV6F85P+4yq0dbsywyUA+bcc=; b=bH3q1brpjqVufkxQNO5FyptEIKmOSC5PnFlIhHIMprxa2EFZZCbe2l6lM60Er8imhQt3XPuV/ieUvBzAyR1p6yHml7FVH7l9OfRFTdJykud2/eLGpWvUSLAw9BSMATJPgCpjnFwPu+0ETUT8YEzOMrqcGakz33/EC7VaYJdfWPA= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=AeI8RLKrfNO78dVj9wGBsEZeXB9o9G5BSQRux/YPcjU3pu4tL/EQWkOqwQIoL0MagwwcwqH1PxdQxHzdVq24xnaOzZFGc19foTsGC6dfoe+lKZTSidYA5B8umkE8QcoO2FIqI1aLNYexUoKbVhHaLFmEfc3J3nVKvmcqp/uhfZw= Received: by 10.86.27.9 with SMTP id a9mr1150539fga.62.1206040446791; Thu, 20 Mar 2008 12:14:06 -0700 (PDT) Received: by 10.86.74.8 with HTTP; Thu, 20 Mar 2008 12:14:06 -0700 (PDT) Message-ID: Date: Thu, 20 Mar 2008 16:14:06 -0300 From: "saulo nilson" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Sistema In-Reply-To: <000001c88a9d$9f38d6a0$ddaa83e0$@com.br> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_995_19590535.1206040446781" References: <000001c88a9d$9f38d6a0$ddaa83e0$@com.br> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "saulo nilson" X-Spam-Status: No, hits=-1.1 required=5.0 tests=AWL,IN_REP_TO,MAILTO_LINK,QUOTED_EMAIL_TEXT,REFERENCES, SPAM_PHRASE_00_01,X_MAILING_LIST version=2.44 X-Spam-Level: ------=_Part_995_19590535.1206040446781 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline (log a)x + [(sen b)^2]y =3D 1 [log(a+b)x + [(cos b)^2]y =3D 2 x+(senb)^2/loga *y=3D1/loga x+cosb^2/log(a+b) *y=3D2/log(a+b) y*(senb^2/loga -cosb^2/log(a+b)=3D(log(a+b) -2loga)/(logalog(a+b)) (log(a+b)^senb^2/a^cosb^2)y=3Dlog((a+b)/a^2) tem uma unica solu=E7ao se (a+b)=3D!a^2 (a+b)^senb^2=3D!a^cosb^2 senb^2log(a+b)=3D!cosb^2*loga tgb^2=3D!loga(base(a+b)) 2008/3/20 Jo=E3o Gabriel Preturlan : > Ol=E1 a todos! > > > > Pe=E7o ajuda neste problema: > > > > "Considerando o sistema linear com as duas seguintes equa=E7=F5es: > > > > (log a)x + [(sen b)^2]y =3D 1 > > [log(a+b)x + [(cos b)^2]y =3D 2 > > > > Com a > 0 e b > 0. Prove que se ([log(base 9){b/a}]^cos2x) < 1, (Pi/4) < = x > < (3Pi/4), ent=E3o o sistema admite uma =FAnica solu=E7=E3o." > > > > Obs.: l=EA-se "([log(base 9){b/a}]^cos2x) < 1" como: logaritmo de b sobr= e a > na base 9, elevado ao co-seno de 2x, menor que um. > > > > Desde j=E1 agrade=E7o! > > > > JG. > > No virus found in this outgoing message. > Checked by AVG. > Version: 7.5.519 / Virus Database: 269.21.7/1335 - Release Date: > 19/03/2008 09:54 > ------=_Part_995_19590535.1206040446781 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline
(log a)x + [(sen b)^2]y =3D 1
[log(a+b)x + [(cos b)^2]y =3D 2
x+(senb)^2/loga *y=3D1/loga
x+cosb^2/log(a+b) *y=3D2/log(a+b)
y*(senb^2/loga -cosb^2/log(a+b)=3D(log(a+b) -2loga)/(logalog(a+b))
(log(a+b)^senb^2/a^cosb^2)y=3Dlog((a+b)/a^2)
 tem uma unica solu=E7ao se
(a+b)=3D!a^2
(a+b)^senb^2=3D!a^cosb^2
senb^2log(a+b)=3D!cosb^2*loga
tgb^2=3D!loga(base(a+b))


 
2008/3/20 Jo=E3o Gabriel Preturlan <jgpreturlan@uol.com.br= >:

Ol=E1 a todos!

 

Pe=E7o ajuda neste problema:

 

"Considerando o sistema linear com as duas seguintes equa=E7=F5es:<= /p>

 

(log a)x + [(sen b)^2]y =3D 1

[log(a+b)x + [(cos b)^2]y =3D 2

 

Com a > 0 e b > 0. Prove que se ([log(base 9){b/a}]^cos2x) < 1,= (Pi/4) < x < (3Pi/4), ent=E3o o sistema admite uma =FAnica solu=E7= =E3o."

 

Obs.: l=EA-se  "([log(base 9){b/a}]^cos2x) < 1" como: = logaritmo de b sobre a na base 9, elevado ao co-seno de 2x, menor que um.

 

Desde j=E1 agrade=E7o!

 

JG.


No virus found in this outgoing message.
Checked by = AVG.
Version: 7.5.519 / Virus Database: 269.21.7/1335 - Release Date: 19= /03/2008 09:54


------=_Part_995_19590535.1206040446781-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Mar 20 17:43:46 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2KKf7sG013565 for ; Thu, 20 Mar 2008 17:41:07 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2KKf7ok013563 for obm-l-MllGbsmmN; Thu, 20 Mar 2008 17:41:07 -0300 Received: from web52906.mail.re2.yahoo.com (web52906.mail.re2.yahoo.com [206.190.49.16]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id m2KKf3sG013559 for ; Thu, 20 Mar 2008 17:41:04 -0300 Received: (qmail 56937 invoked by uid 60001); 20 Mar 2008 20:41:38 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:Date:From:Subject:To:In-Reply-To:MIME-Version:Content-Type:Content-Transfer-Encoding:Message-ID; b=He7rtM4g3TDJaiCpdo1SwVVRsa+Y5sUntlIWa6vCUHJMGUlVaUfRA/lHdFN1tWHnvVZFAI4QrOUIYQkscy+310Irynxsx7tRYv2cXfS1ZJAWNaaAdOFpLvL4TzpIraimLJHph0IIyjJnbUyb5kKIl2+6gJeBGZ68wVE20tEjZM4=; X-YMail-OSG: CAKmfjgVM1lbhBxtVsYm8PmmaXzDt4f2JNjX7VKaA36MjAcqajxJyZLynsuHrjhlXwDT29J77QhbjtClI2eFnFk9oH5dOTbIsBaTOrS5mly0oWMYBt8- Received: from [189.31.103.180] by web52906.mail.re2.yahoo.com via HTTP; Thu, 20 Mar 2008 17:41:38 ART Date: Thu, 20 Mar 2008 17:41:38 -0300 (ART) From: Antonio Giansante Subject: [SPAM] Re: [obm-l] combinatoria dificil To: obm-l@mat.puc-rio.br In-Reply-To: <5bb472220803191956x5985de0cx3e9f90dd4250a71@mail.gmail.com> MIME-Version: 1.0 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 7bit Message-ID: <515441.55123.qm@web52906.mail.re2.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Antonio Giansante X-Spam-Status: Yes, hits=6.4 required=5.0 tests=FORGED_YAHOO_RCVD,IN_REP_TO,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ****** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (6.40 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 16.49.190.206.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 16.49.190.206.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- Pois é joão.... acho q dessa forma a gente acaba contando os casos em que há a mesma matéria duas vezes no dia. Por exemplo: D1: H1: 3 opções--> escolho M; H2 duas opções--> escolho F; D2 --> H1: 3 opções: escolho M H2 --> duas opções: escolho F. Assim, para d3, sobra apenas 2 opções Q, o q não pode ocorrer. Parece que realmente há um erro no gabarito. Veja que a árvore fornece todas as possibilidades. Como eu contei erroneamente duas vezes (conforme observou bem o rafael), a resposta parece ser mesmo 48, não? --- Joao Victor Brasil escreveu: > Estava pensando o seguinte, se D1 é segunda, D2 > quarta e D3 sexta, > e H1 aula de 8-9 hs e H2 aula de 11-12 hs, quantas > possibilidades de > matérias podemos ter por aula? > > D1 H1:3 matérias (MAT, FIS, QUI) > H2:2 matérias (a que não foi escolhida antes) > > D2 H1:3 matérias (MAT, FIS, QUI, pode ser a segunda > aula da semana, > todas voltam) > H2:2 matérias (a que não foi escolhida antes) > > D3 H1:2 matérias (Uma matéria já usou suas duas > aulas semanais) > H2:1 matérias > > Pelo princípio multiplicativo, teremos 3x2x3x2x2x1 = > 72. > Mas D1H1 pode trocar com D1H2 sem prejuízo, teremos > então 72x2x2x2 > (uma multiplicação para cada dia)=576. > Com esse processo, contamos mais de uma vez os > horários, devemos divir > por 3! para corrigir nosso erro. > Logo teremos 96 horários diferentes. > > Joao Victor Brasil > > On 3/19/08, Rafael Cano > wrote: > > Olá Antonio. > > Acho que você contou duas vezes cada horário > possível. > > Da maneira que você fez você já tinha considerado > a ordem das aulas em cada > > dia. A árvore de possibilidades já considera todas > as formas de se preencher > > a primeira aula de cada dia. Por exemplo: suponha > que a primeira aula de > > cada dia é MAT, FIS, QUI, nessa ordem, e que a > segunda aula de cada dia é > > FIS, QUI, MAT. Mas o ramo da árvore que começa com > FIS também considera que > > é possível formar um horário em que a primeira > aula de cada dia é FIS, QUI, > > MAT, e a segunda aula de cada dia é MAT, FIS, QUI, > ou seja, exatamente o > > horário anterior, mas com a ordem das matérias > invertidas. > > Abraços > > > > ----- Original Message ----- > > From: "Antonio Giansante" > > To: > > Sent: Wednesday, March 19, 2008 5:27 PM > > Subject: Re: [obm-l] combinatoria dificil > > > > > > > Desculpem..depois que eu percebi: eu falei que > foi > > > pego a 1a opção, porém a ordem MAT QUI FIS é a > 5a > > > opção. > > > --- Antonio Giansante > > > escreveu: > > > > > >> Olá. Sempre que eu tenho dificuldades em > resolver um > > >> problema de combinatória eu "apelo" para a > árvore de > > >> possibilidades. Ficou assim(Obs: O "tanso" aqui > fez > > >> como MAT, FIS e QUI, ao invés das disciplinas > do > > >> enunciado, mas dá na mesma, ok? Desculpe pela > > >> viajada): > > >> > > >> segunda quarta sexta > > >> > > >> QUI > > >> FIS FIS > > >> MAT > > >> > > >> QUI > > >> MAT QUI FIS > > >> MAT > > >> > > >> QUI > > >> MAT FIS > > >> > > >> Dessa forma, se a 1a aula do 1o dia for FIS, tb > > >> teremos oito opçoes, e o mesmo para QUI, > perfazendo > > >> um > > >> total de 24 possibilidades. Vamos analisar > agora o > > >> que > > >> acontece com uma dessas escolhas. Supondo que > > >> tenhamos > > >> escolhido a primeira opção da árvore para as > > >> primeiras > > >> aulas: > > >> MAT QUI FIS > > >> > > >> Então, na segunda aula, só poderemos ter as > opções > > >> > > >> FIS MAT QUI ou QUI FIS MAT. > > >> Observe que outras ordens destes não são > possíveis > > >> devido à condição de nõ poder ser matérias > iguais no > > >> mesmo dia. Sendo assim, temos duas opções de > > >> preenchimento das aulas da semana para cada > opção da > > >> árvore. Como são 24 opções iniciais, dá um > total de: > > >> 24x2=48. > > >> Entretanto, nós ainda não consideremaos o fato > de > > >> que > > >> a ordem das duas aulas podem ser trocadas no > dia. > > >> Assim, se começarmos a preencher as opções da > > >> segunda > > >> aula primeiro, teremos mais 48 possibildades, o > que > > >> dá > > >> um total de 96 possibilidades de horário.....Ou > não, > > >> como diria Caetano! (posso ter errado também, > > >> ehehe). > > >> Espero ter ajudado. ABÇS > > > > >> > 2008/3/13 Thelio Gama > : > > >> > > > >> > É pessoal... > > >> > > > >> > Achei muito difícil esta questão. > Agradeço se > > >> > alguém puder explicá-la. > > >> > > > >> > Thelio > > >> > > > >> > uma turma tem aulas às 2ª, 4ª e 6ª > feiras, de > > >> > 8-9 horas e de 11-12 horas. As matérias são > > >> > portugues, matemática e ingles, cada uma com > duas > > >> > aulas semanais, em dias diferentes. De > quantos > > >> modos > > >> > pode ser feito o horário dessa turma? > > >> > a)96 ; b) 144 ; c)192 ; d) 6! ; > e) 120 > > >> > > > >> > > > >> > > >> > > >> > > >> Abra sua conta no Yahoo! Mail, o único > sem > > >> limite de espaço para armazenamento! > > >> http://br.mail.yahoo.com/ > > >> > > > > ========================================================================= > > >> Instruções para entrar na lista, sair da lista > e > > >> usar a lista em > > >> http://www.mat.puc-rio.br/~obmlistas/obm-l.html > > >> > > > > ========================================================================= > > >> > > > > > > > > > > > > Abra sua conta no Yahoo! Mail, o único sem > limite de espaço para > > > armazenamento! > > > http://br.mail.yahoo.com/ > > > > ========================================================================= > > > Instruções para entrar na lista, sair da lista e > usar a lista em > > > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > > > > ========================================================================= > > > > > ========================================================================= > > Instruções para entrar na lista, sair da lista e > usar a lista em > > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > > > ========================================================================= > > > === message truncated === Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! http://br.mail.yahoo.com/ ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Mar 20 18:45:30 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2KLhJsG017532 for ; Thu, 20 Mar 2008 18:43:19 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2KLhJO5017530 for obm-l-MllGbsmmN; Thu, 20 Mar 2008 18:43:19 -0300 Received: from wr-out-0506.google.com (wr-out-0506.google.com [64.233.184.239]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2KLhGsG017518 for ; Thu, 20 Mar 2008 18:43:17 -0300 Received: by wr-out-0506.google.com with SMTP id c46so1479550wra.18 for ; Thu, 20 Mar 2008 14:43:52 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; bh=Iex9wyFW5ZPRxBZGjstbr+mlb0KY2GK7E8DSqdcjMRo=; b=IS3bWQ+JzfCwjH21pnhtJ3cUlRRytjyF+zRx/px2HH4ajDrsSjwYZBylYgFeySeUJEKnfPS5NNp+h46uT35MbXQ1KGQzpPhqTHPCUywhR5q3fV43qKnvxHd4ySL8ZML9q5WXOn+1Nqg5hflq8I1xe/+VHHBG0aLhohfC0r515QA= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; b=iSYL+YMQ6AbOfd29uLH7fxtJvDgD5ugXWRNBB5z4ca0vwAL7Woqkw26vDWxQZLPwKV/zpsgWsLCGJ/3aoSkOE84REQwYeVDBDSg4bQB1Ng1HbjS+fGC8sRa7u+R2EEHrYqem1s9dlELa4osb+P1Ta6LQT2BRl8urqUIy1INMMGk= Received: by 10.114.25.3 with SMTP id 3mr4616405way.22.1206049431971; Thu, 20 Mar 2008 14:43:51 -0700 (PDT) Received: by 10.114.58.13 with HTTP; Thu, 20 Mar 2008 14:43:51 -0700 (PDT) Message-ID: <3e7bcb580803201443r10149ad4n4a3c3d7710b3573@mail.gmail.com> Date: Thu, 20 Mar 2008 18:43:51 -0300 From: "=?ISO-8859-1?Q?Henrique_Renn=F3?=" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] combinatoria dificil In-Reply-To: MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline References: Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m2KLhIsG017527 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "=?ISO-8859-1?Q?Henrique_Renn=F3?=" X-Spam-Status: No, hits=1.1 required=5.0 tests=AWL,GAPPY_TEXT,IN_REP_TO,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SIGNATURE_SHORT_SPARSE, SPAM_PHRASE_00_01,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: * Olá pessoal! Acredito que a solução do Salhab está correta. Seja Di o dia i e Hj o horário j. D1H1: 3 matérias D1H2: 2 matérias (para não repetir a utilizada em D1H1) D1: 6 possibilidades Para D2, se escolhermos uma já utilizada em D1 então não poderemos utilizar a outra matéria utilizada em D1, senão D3 teria as mesmas matérias. Assim, para D2 teríamos uma já utilizada (2 matérias) e uma não utilizada. Logo, 2*1 = 2. Como a ordem importa, temos 2*2 = 4. D3 só possui 2 formas, com as ordens das matérias trocadas. Total: 6*4*2 = 48. Essa é uma forma mais lógica de resolver o problema. Estive tentando utilizar combinatória e também achei a resposta 48. Sejam A,B,C as matérias. Quantas permutações diferentes existem entre A,A,B,B,C,C? Cada posição seria um horário em um dia, ou seja, D1H1_D1H2_D2H1_D2H2_D3H1_D3H2. Bastaria calcular o número de permutações com repetição, ou seja, 6!/(2!*2!*2!) = 720/8 = 90. Sabemos que não podemos ter uma permutação do tipo AABCBC, pois AA representa a mesma matéria em D1H1 e D1H2. Então sabemos que a resposta é menor que 90. As formas inválidas serão: Se as 3 matérias do mesmo tipo estão juntas no mesmo dia, ex: AABBCC. Existem 3! = 6 formas, considerando AA,BB,CC como 3 elementos permutados entre si. Não há necessidade de verificar quando 2 matérias estão no mesmo dia pois cai no caso acima. Quando há apenas 1 matéria repetida em 1 dia, ex: AABCBC, então temos 12 formas para cada par da mesma matéria utilizada no mesmo dia. Se AA está em D1 então D2 pode ser BC ou CB e D3 pode ser BC ou CB, 2*2 = 4. AA pode estar em D1,D2,D3. Assim, 4*3 = 12. Para BB e CC seria o mesmo, dando um total de 3*12 = 36 formas quando há apenas uma matéria que se repete no mesmo dia. Assim, o total seria 90 - (6+36) = 90 - 42 = 48 formas distintas de compor o horário Thelio, você poderia passar a fonte do problema e verificar se as respostas são essas mesmo? On 3/13/08, Thelio Gama wrote: > É pessoal... > > Achei muito difícil esta questão. Agradeço se alguém puder explicá-la. > > Thelio > > uma turma tem aulas às 2ª, 4ª e 6ª feiras, de 8-9 horas e de 11-12 horas. As > matérias são portugues, matemática e ingles, cada uma com duas aulas > semanais, em dias diferentes. De quantos modos pode ser feito o horário > dessa turma? > a)96 ; b) 144 ; c)192 ; d) 6! ; e) 120 -- Henrique ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Mar 20 20:20:53 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2KNIisG024309 for ; Thu, 20 Mar 2008 20:18:44 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2KNIifE024307 for obm-l-MllGbsmmN; Thu, 20 Mar 2008 20:18:44 -0300 Received: from web52906.mail.re2.yahoo.com (web52906.mail.re2.yahoo.com [206.190.49.16]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id m2KNIgsG024291 for ; Thu, 20 Mar 2008 20:18:43 -0300 Received: (qmail 75035 invoked by uid 60001); 20 Mar 2008 23:19:17 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:Date:From:Subject:To:In-Reply-To:MIME-Version:Content-Type:Content-Transfer-Encoding:Message-ID; b=XX6J7+nvmJ0A2IBeLZ0+ELDQAWqe8CwvpysEtGDPRMbDfIPD9l1Jlz4YAziHfjHng1W1R6CmKaHD3rR/udY2VlPGWXYMKYDy1UoN/7uoRtfW+elA5xh+QJOkoctpqCSx7n2qtHGGZNSbGzVIqR+Bq0hYfjH/FSaLzlj7JVU/9fs=; X-YMail-OSG: dE9byzIVM1mqrFTD2rtZNWVKC696HhiKHS15jMiyVBegX6u_UldygxyF7JK7VMtPqQ-- Received: from [189.31.103.180] by web52906.mail.re2.yahoo.com via HTTP; Thu, 20 Mar 2008 20:19:17 ART Date: Thu, 20 Mar 2008 20:19:17 -0300 (ART) From: Antonio Giansante Subject: [SPAM] [obm-l] off toppic: material para o ITA To: obm-l@mat.puc-rio.br In-Reply-To: MIME-Version: 1.0 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 7bit Message-ID: <422775.74580.qm@web52906.mail.re2.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Antonio Giansante X-Spam-Status: Yes, hits=6.4 required=5.0 tests=AWL,FORGED_YAHOO_RCVD,IN_REP_TO,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ****** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (6.40 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 16.49.190.206.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 16.49.190.206.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-0.0 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- creio que muitos já pediram isso: alguém sabe um link onde eu possa conseguir as provas do ITA (ao menos as 10 últimas)? Não precisa ser resolvida, mas pelo menos com o gabarito. Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! http://br.mail.yahoo.com/ ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Mar 20 21:08:42 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2L06asG027066 for ; Thu, 20 Mar 2008 21:06:36 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2L06aCL027064 for obm-l-MllGbsmmN; Thu, 20 Mar 2008 21:06:36 -0300 Received: from wf-out-1314.google.com (wf-out-1314.google.com [209.85.200.174]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2L06XsG027061 for ; Thu, 20 Mar 2008 21:06:33 -0300 Received: by wf-out-1314.google.com with SMTP id 27so1226088wfd.18 for ; Thu, 20 Mar 2008 17:07:08 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=ts6BxleHUwwlvsMhT7U0JC60+YrTs23QrnqihxJ+uQg=; b=jHTDWSnTrfx14mL1f+Gdgn8+TlibnqGd0ZAjPssSEINplgXvAAjASErbDG8a1+Tmxl4NFrN4lvYUUUn0VXB4cvxFUzUG5RAPZz+xubx1u0C3ZDF448DW9zsCyFc3jI2KvouBA1Km2BCgv/LjIdTDF5g/K4gZFRn+BAnJTP4ptqM= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=tGqVYQywamItUgxfjRvGQSbqX99wfl1pNiRw36XkblI6niKz17gGePkqfrd51nmfi3sd5iBZq8Ro8uue+Qw1XprYrTkb8hr4c1CTYxod2ZJ1ujBHHPzneBPqGcPtXU42T7x+q7/BimMdEmvlqkHE6uplMPwR45GAN46sdtCwHis= Received: by 10.142.148.7 with SMTP id v7mr1939958wfd.153.1206058028415; Thu, 20 Mar 2008 17:07:08 -0700 (PDT) Received: by 10.142.80.16 with HTTP; Thu, 20 Mar 2008 17:07:08 -0700 (PDT) Message-ID: <789aac5a0803201707m143f15dbhe68c972fada398d7@mail.gmail.com> Date: Thu, 20 Mar 2008 21:07:08 -0300 From: Iuri To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] off toppic: material para o ITA In-Reply-To: <422775.74580.qm@web52906.mail.re2.yahoo.com> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_3381_17722710.1206058028426" References: <422775.74580.qm@web52906.mail.re2.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Iuri X-Spam-Status: No, hits=4.1 required=5.0 tests=AWL,IN_REP_TO,MAILTO_LINK,MIME_EXCESSIVE_QP, QUOTED_EMAIL_TEXT,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, REFERENCES,SPAM_PHRASE_01_02,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** ------=_Part_3381_17722710.1206058028426 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline http://www.rumoaoita.com/novo/provas.php Iuri 2008/3/20 Antonio Giansante : > creio que muitos j=E1 pediram isso: algu=E9m sabe um link > onde eu possa conseguir as provas do ITA (ao menos as > 10 =FAltimas)? N=E3o precisa ser resolvida, mas pelo menos > com o gabarito. > > > Abra sua conta no Yahoo! Mail, o =FAnico sem limite de espa=E7o para > armazenamento! > http://br.mail.yahoo.com/ > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > Instru=E7=F5es para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > ------=_Part_3381_17722710.1206058028426 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline http://www.rumoaoita.c= om/novo/provas.php

Iuri

2008/3= /20 Antonio Giansante <profcabi= @yahoo.com.br>:
creio que muitos = j=E1 pediram isso: algu=E9m sabe um link
onde eu possa conseguir as provas do ITA (ao menos as
10 =FAltimas)? N=E3o precisa ser resolvida, mas pelo menos
com o gabarito.


     Abra sua conta no Yahoo! Mail, o =FAnico sem limite de= espa=E7o para armazenamento!
http://br.mail.yaho= o.com/
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D
Instru=E7=F5es para entrar na lista, sair da lista e usar a lista em
http://www.mat.puc-rio.br/~obmlistas/obm-l.html
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D

------=_Part_3381_17722710.1206058028426-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Mar 20 21:49:25 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2L0lOsG031032 for ; Thu, 20 Mar 2008 21:47:24 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2L0lOKY031030 for obm-l-MllGbsmmN; Thu, 20 Mar 2008 21:47:24 -0300 Received: from wf-out-1314.google.com (wf-out-1314.google.com [209.85.200.168]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2L0lLsG031026 for ; Thu, 20 Mar 2008 21:47:22 -0300 Received: by wf-out-1314.google.com with SMTP id 27so1240000wfd.18 for ; Thu, 20 Mar 2008 17:47:57 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:mime-version:content-type; bh=I9cdoZMrY9E1m/dGTTh8LZUKMMjgajuyiRoouEtEFDQ=; b=O8CM+v0oN2q8ILXoVfe+vRds/kcaNKueIRwcY8SjeLUh7NmTrKdumfQKMzqvnGZxmrxKZmN3Ic/eWfr10QHDleDioV1LtpR8nWJE+Wg2zALAcQKDNVUFmJrMhy487ftkoZoQpT10ydmPFidPEryLoQjV7cnJCvmxLJMwlEd39Ms= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:mime-version:content-type; b=X/Mtu/Nck5eD23xjM50GABGfmtsl+UcE72J/XWmDxp9KCRTRdzimfpbnKpKwxvxgDNmRIEz6pmGfVpMgrC+GhbX2xxCCxawYxQVAmIgEQTkVeAiJlSiakgV46WMdcoPx1OChHBt6hm7m6fmGLsAMU4uYKqFubG5x3E5I7jCN1+Y= Received: by 10.142.142.16 with SMTP id p16mr1954684wfd.176.1206060476740; Thu, 20 Mar 2008 17:47:56 -0700 (PDT) Received: by 10.142.48.8 with HTTP; Thu, 20 Mar 2008 17:47:56 -0700 (PDT) Message-ID: <4de96b200803201747m653b3e65q6515584bdddf8f75@mail.gmail.com> Date: Thu, 20 Mar 2008 21:47:56 -0300 From: "Antonio Manuel Castro del Rio" To: obm-l@mat.puc-rio.br Subject: [SPAM] [obm-l] Quadrado perfeito MIME-Version: 1.0 Content-Type: text/plain Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Antonio Manuel Castro del Rio" X-Spam-Status: Yes, hits=5.9 required=5.0 tests=AWL,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ***** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_Part_3415_29575117.1206060476733" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (5.90 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 168.200.85.209.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 168.200.85.209.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (0.1 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- ------=_Part_3415_29575117.1206060476733 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Como desenvolvo para que seja um quadrado perfeito o polin=F4mio x4 + x3 + x2 + x + 1 Obrigado, Antonio del Rio ------=_Part_3415_29575117.1206060476733 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline

   &= nbsp;    Como desenvolvo para que seja um quadrado perfeito = o polin=F4mio

       x4  +  x3  +  x2  +  x  <= /span>+  1


       &n= bsp; Obrigado, Antonio del Rio
------=_Part_3415_29575117.1206060476733-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Fri Mar 21 17:00:34 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2LJv0WA002911 for ; Fri, 21 Mar 2008 16:57:00 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2LJv0Iw002909 for obm-l-MllGbsmmN; Fri, 21 Mar 2008 16:57:00 -0300 Received: from fg-out-1718.google.com (fg-out-1718.google.com [72.14.220.158]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2LJuwWA002895 for ; Fri, 21 Mar 2008 16:56:58 -0300 Received: by fg-out-1718.google.com with SMTP id e12so1274751fga.3 for ; Fri, 21 Mar 2008 12:56:33 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=qRWdk3155OkEnxiNEwIqohZo4T+cpYiIsYcmIfGT1hI=; b=ktJoRU936kB0ylStrT3qBknlf2Nv+z362mk4KBBrYHA9//pC4PZjXmcuDloQ+awiyCBh6j18swvnfU7cinsxnzWx9P8+ZGOn66FOcx3H9u3LwqhpIfmytVSQG9ksfEiQzupMjZ7IVbxpJdv2/SfKACVLdSOxm5dHLDLiUROgFr4= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=hRD2huw3BHwwd9LvX7dboSIh9KSwdEOtnk2szTTMs/upnPqQSo8Aq2zvQZkksbbr/JXHhB8nb31hcynhmAjdnrlzqVg5WenNrVKJBxajFDS8cX8J2Ox0riWTDFYZ0GipntUAMAwxjvuFcf3jElElt2LK6w6exOrTIR97iL2Nee0= Received: by 10.86.96.18 with SMTP id t18mr2080241fgb.4.1206127816248; Fri, 21 Mar 2008 12:30:16 -0700 (PDT) Received: by 10.86.74.8 with HTTP; Fri, 21 Mar 2008 12:30:16 -0700 (PDT) Message-ID: Date: Fri, 21 Mar 2008 16:30:16 -0300 From: "saulo nilson" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Quadrado perfeito In-Reply-To: <4de96b200803201747m653b3e65q6515584bdddf8f75@mail.gmail.com> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_2768_11550264.1206127816262" References: <4de96b200803201747m653b3e65q6515584bdddf8f75@mail.gmail.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "saulo nilson" X-Spam-Status: No, hits=-1.9 required=5.0 tests=AWL,EMAIL_ATTRIBUTION,IN_REP_TO,MAILTO_LINK, QUOTED_EMAIL_TEXT,REFERENCES,SPAM_PHRASE_00_01, X_MAILING_LIST version=2.44 X-Spam-Level: ------=_Part_2768_11550264.1206127816262 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline x^2+1/x^2+x+1/x +1=3D0 x+1/x=3Dy y^2-2+y+1=3D0 y^2+y-1=3D0 delta=3D1+4=3D5 y=3D(-1+-rq5)/2 o polinomio pode ser escrito como (2y-rq5+1)(2y+1+rq5)/4=3D =3D((2y+1)^2-5)/4 On Thu, Mar 20, 2008 at 9:47 PM, Antonio Manuel Castro del Rio < antoniomcdelrio@gmail.com> wrote: > Como desenvolvo para que seja um quadrado perfeito o polin=F4mio > > x4 + x3 + x2 + x + 1 > > Obrigado, Antonio del Rio > ------=_Part_2768_11550264.1206127816262 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline
x^2+1/x^2+x+1/x +1=3D0
x+1/x=3Dy
y^2-2+y+1=3D0
y^2+y-1=3D0
delta=3D1+4=3D5
y=3D(-1+-rq5)/2
o polinomio pode ser escrito como
(2y-rq5+1)(2y+1+rq5)/4=3D
=3D((2y+1)^2-5)/4

On Thu, Mar 20, 2008 at 9:47 PM, Antonio Manuel = Castro del Rio <antoniomcde= lrio@gmail.com> wrote:

      &nbs= p; Como desenvolvo para que seja um quadrado perfeito o polin=F4mio

       x4  +  x3 = ; +  x2  + = ; x  +  1


         Obrigado, Antonio d= el Rio

------=_Part_2768_11550264.1206127816262-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Fri Mar 21 17:18:36 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2LKFmWA004670 for ; Fri, 21 Mar 2008 17:15:48 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2LKFmBc004667 for obm-l-MllGbsmmN; Fri, 21 Mar 2008 17:15:48 -0300 Received: from web52904.mail.re2.yahoo.com (web52904.mail.re2.yahoo.com [206.190.49.14]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id m2LKFjWA004657 for ; Fri, 21 Mar 2008 17:15:46 -0300 Received: (qmail 51854 invoked by uid 60001); 21 Mar 2008 14:48:39 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:Date:From:Subject:To:In-Reply-To:MIME-Version:Content-Type:Content-Transfer-Encoding:Message-ID; b=bcUHXRQD/pg3OMXN947+/CNnzImHJz/wkiogOqBACwy/D1eKxUjVXH5klUrpWYtHbR0puJTq8zyCyLcOhNrgdgQ4CE5LbzQHij5Y45izoeM4/QjtApCtNiBSkl9yXFL7Q+ka/Yx5VnColIVneO9NQ5lMM92YAX5E4M8euKfQDUc=; X-YMail-OSG: Y17DkxEVM1knzZMsBlapD9uv.4NEx2EwpzZhRKMRiSy95QppeUcWExJtdSizEA16dQ-- Received: from [189.31.103.180] by web52904.mail.re2.yahoo.com via HTTP; Fri, 21 Mar 2008 11:48:39 ART Date: Fri, 21 Mar 2008 11:48:39 -0300 (ART) From: Antonio Giansante Subject: [SPAM] Re: [obm-l] off toppic: material para o ITA To: obm-l@mat.puc-rio.br In-Reply-To: <789aac5a0803201707m143f15dbhe68c972fada398d7@mail.gmail.com> MIME-Version: 1.0 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 7bit Message-ID: <429069.50450.qm@web52904.mail.re2.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Antonio Giansante X-Spam-Status: Yes, hits=6.4 required=5.0 tests=AWL,FORGED_YAHOO_RCVD,IN_REP_TO,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ****** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (6.40 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 14.49.190.206.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 14.49.190.206.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-0.0 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- Obrigado, Iuri. --- Iuri escreveu: > http://www.rumoaoita.com/novo/provas.php > > Iuri > > 2008/3/20 Antonio Giansante : > > > creio que muitos já pediram isso: alguém sabe um > link > > onde eu possa conseguir as provas do ITA (ao menos > as > > 10 últimas)? Não precisa ser resolvida, mas pelo > menos > > com o gabarito. > > > > > > Abra sua conta no Yahoo! Mail, o único sem > limite de espaço para > > armazenamento! > > http://br.mail.yahoo.com/ > > > ========================================================================= > > Instruções para entrar na lista, sair da lista e > usar a lista em > > > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > > > ========================================================================= > > > Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! http://br.mail.yahoo.com/ ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Fri Mar 21 17:25:51 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2LKMxWA005656 for ; Fri, 21 Mar 2008 17:22:59 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2LKMwp7005654 for obm-l-MllGbsmmN; Fri, 21 Mar 2008 17:22:58 -0300 Received: from web52903.mail.re2.yahoo.com (web52903.mail.re2.yahoo.com [206.190.49.13]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id m2LKMuWA005626 for ; Fri, 21 Mar 2008 17:22:56 -0300 Received: (qmail 65463 invoked by uid 60001); 21 Mar 2008 16:22:33 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:Date:From:Subject:To:In-Reply-To:MIME-Version:Content-Type:Content-Transfer-Encoding:Message-ID; b=K6QRw+7LA16hQpU5Xq/kq7ewnqhVy5RtBvlVXnNB/nbf0xtuzLjYGy+5d3EODQz5mGD+ISRHc14CqsoIv1QtLDc7rihDvI5exf9a04zysIEQmOtLyRMzkhcxyqbWJOyp8pTbjBWpkDJKJkm5XpgV35e7REOrKT8BVqp5HjMkbdE=; X-YMail-OSG: 6vgp_TQVM1lKcmMcq7qSpwfDdvZTAj8rZir151U2bTYvurhESN9ytFHpMYF12wCzGEhKIJh_G4xaTrJwPPWqlsMOZ6PugkE6bwO5TT9ENo3FA6Cy_cA- Received: from [189.31.103.180] by web52903.mail.re2.yahoo.com via HTTP; Fri, 21 Mar 2008 13:22:32 ART Date: Fri, 21 Mar 2008 13:22:32 -0300 (ART) From: Antonio Giansante Subject: [SPAM] Re: [obm-l] Quadrado perfeito To: obm-l@mat.puc-rio.br In-Reply-To: <4de96b200803201747m653b3e65q6515584bdddf8f75@mail.gmail.com> MIME-Version: 1.0 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 7bit Message-ID: <984178.64056.qm@web52903.mail.re2.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Antonio Giansante X-Spam-Status: Yes, hits=6.4 required=5.0 tests=FORGED_YAHOO_RCVD,IN_REP_TO,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ****** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (6.40 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 13.49.190.206.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 13.49.190.206.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- Quando um polinômio é um quadrado perfeito, comparamos com o quadrado de um polinômio cujo grau seja a metade. Nesse caso, como é um polinômio do grau 4: (ax2 + bx + c)2 = x4+x3+x2+x+1. Porém, não será possível para esta situação (S = {}).Tem certeza de que o polinômio do exercício é exatamente este? --- Antonio Manuel Castro del Rio escreveu: > Como desenvolvo para que seja um quadrado > perfeito o polinômio > > x4 + x3 + x2 + x + 1 > > Obrigado, Antonio del Rio > Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! http://br.mail.yahoo.com/ ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Fri Mar 21 17:56:15 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2LKrTWA008810 for ; Fri, 21 Mar 2008 17:53:29 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2LKrSBt008808 for obm-l-MllGbsmmN; Fri, 21 Mar 2008 17:53:28 -0300 Received: from fg-out-1718.google.com (fg-out-1718.google.com [72.14.220.156]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2LKrQWA008798 for ; Fri, 21 Mar 2008 17:53:27 -0300 Received: by fg-out-1718.google.com with SMTP id e12so1291174fga.3 for ; Fri, 21 Mar 2008 13:53:04 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=Zn1vduMKbtnSpEYPVKT7iTrF6JYZB9evnag4fb0vFdM=; b=p9jvlu0UpSxyZZv9Qx6KvYyUzD7HrOUg5yQM+9bcfJRK/LSRA4zW2KZSBfZFKRNit7tex2muiFQyqYNJGg+3tFAZVwhW4SgReY0534rxpKolaOBtFsfPneOtUV0KESYYWy3p7rh8g2OX04UhD5Vb2eQdcsYQ7RehCWmtzNOZj0w= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=UeQ3h+1ouTsYY6atq2U3PMPR/IOmgobKkaA+aVslq2rwMmJ0frLy4mMIhk0HnW7QTzQ/QILaXhBCgQpkk66WIlRLb+Ug9dvbb1izVtdxz7IH5J9cDHEnmA2Sj8+TvHwnRpwL2XYHq45rNROkViHSsSoNJXXZd62LdPj7h9AHpXQ= Received: by 10.86.97.7 with SMTP id u7mr2103418fgb.65.1206132784926; Fri, 21 Mar 2008 13:53:04 -0700 (PDT) Received: by 10.86.74.8 with HTTP; Fri, 21 Mar 2008 13:53:04 -0700 (PDT) Message-ID: Date: Fri, 21 Mar 2008 17:53:04 -0300 From: "saulo nilson" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Quadrado perfeito In-Reply-To: <984178.64056.qm@web52903.mail.re2.yahoo.com> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_2910_25440417.1206132784945" References: <4de96b200803201747m653b3e65q6515584bdddf8f75@mail.gmail.com> <984178.64056.qm@web52903.mail.re2.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "saulo nilson" X-Spam-Status: No, hits=-0.7 required=5.0 tests=AWL,IN_REP_TO,MAILTO_LINK,MIME_EXCESSIVE_QP, QUOTED_EMAIL_TEXT,REFERENCES,SPAM_PHRASE_00_01, X_MAILING_LIST version=2.44 X-Spam-Level: ------=_Part_2910_25440417.1206132784945 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline acho que no caso ele quer que vc ache um valor para x que resulte em um quadrado perfeito. 2008/3/21 Antonio Giansante : > Quando um polin=F4mio =E9 um quadrado perfeito, comparamos > com o quadrado de um polin=F4mio cujo grau seja a > metade. Nesse caso, como =E9 um polin=F4mio do grau 4: > (ax2 + bx + c)2 =3D x4+x3+x2+x+1. Por=E9m, n=E3o ser=E1 > poss=EDvel para esta situa=E7=E3o (S =3D {}).Tem certeza de > que o polin=F4mio do exerc=EDcio =E9 exatamente este? > > --- Antonio Manuel Castro del Rio > escreveu: > > > Como desenvolvo para que seja um quadrado > > perfeito o polin=F4mio > > > > x4 + x3 + x2 + x + 1 > > > > Obrigado, Antonio del Rio > > > > > > Abra sua conta no Yahoo! Mail, o =FAnico sem limite de espa=E7o para > armazenamento! > http://br.mail.yahoo.com/ > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > Instru=E7=F5es para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > ------=_Part_2910_25440417.1206132784945 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline acho que no caso ele quer que vc ache um valor para x que resulte em um qua= drado perfeito.

2008/3/21 Antonio Giansante <profcabi@yahoo.com.br>:
Quando um polin=F4mio =E9 um qua= drado perfeito, comparamos
com o quadrado de um polin=F4mio cujo grau se= ja a
metade. Nesse caso, como =E9 um polin=F4mio do grau 4:
(ax2 + bx + c)2 = =3D x4+x3+x2+x+1. Por=E9m, n=E3o ser=E1
poss=EDvel para esta situa=E7=E3= o (S =3D {}).Tem certeza de
que o polin=F4mio do exerc=EDcio =E9 exatame= nte este?

--- Antonio Manuel Castro del Rio
<antoniomcdelrio@gmail.com<= /a>> escreveu:

>         Como desenvolvo = para que seja um quadrado
> perfeito o polin=F4mio
>
> &n= bsp;      x4  +  x3  +  x2  +  = ;x  +  1
>
>          Obriga= do, Antonio del Rio
>



     Abra sua conta no Yahoo! Mail, = o =FAnico sem limite de espa=E7o para armazenamento!
http://br.mail.yahoo.com/
=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D
Instru=E7=F5es para entrar na lista, sair da lista e usar a lista em
= http://www.mat.puc-rio.br/~obmlistas/obm-l.html
=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D

------=_Part_2910_25440417.1206132784945-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sat Mar 22 00:27:35 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2M3OtWA007927 for ; Sat, 22 Mar 2008 00:24:55 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2M3OtUE007924 for obm-l-MllGbsmmN; Sat, 22 Mar 2008 00:24:55 -0300 Received: from web52201.mail.re2.yahoo.com (web52201.mail.re2.yahoo.com [206.190.48.124]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id m2M3OqWA007917 for ; Sat, 22 Mar 2008 00:24:53 -0300 Received: (qmail 26015 invoked by uid 60001); 22 Mar 2008 03:24:30 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:Date:From:Reply-To:Subject:To:In-Reply-To:MIME-Version:Content-Type:Content-Transfer-Encoding:Message-ID; b=ZMeHiL33NitHfmFm2jnNJolyqEiS+7KwkrS1hrHjynLmAuoteuXOV86L2shV9ciZ7L5MB6iaWuVTRlS0VVoBGzFe6zvIVoRdOyH/KTgIXRi3i4MfPJqPFnYcjcQacsFT7+tzSYr3Xf5zPzi4WKsoqKuroEiaj7fAmmjQPf7VtEM=; X-YMail-OSG: Ee_NjOAVM1lmEiHhJW10N5EOTyPN9bC4V_NPY.wi95yrQ4Pp7lE1Xb81kfypZMsj5enfb39gYt8ZMDZze981_e7VzrVi5JGih2rMVREQKnsDmwuOJw-- Received: from [201.37.13.20] by web52201.mail.re2.yahoo.com via HTTP; Sat, 22 Mar 2008 00:24:30 ART Date: Sat, 22 Mar 2008 00:24:30 -0300 (ART) From: Antonio Santos Subject: [SPAM] Re: [obm-l] off toppic: material para o ITA To: obm-l@mat.puc-rio.br In-Reply-To: <422775.74580.qm@web52906.mail.re2.yahoo.com> MIME-Version: 1.0 Content-Type: text/plain Content-Transfer-Encoding: 7bit Message-ID: <595940.25970.qm@web52201.mail.re2.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Antonio Santos X-Spam-Status: Yes, hits=6.5 required=5.0 tests=FORGED_YAHOO_RCVD,IN_REP_TO,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_01_02,SPAM_REDIRECTOR, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ****** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="0-1096543310-1206156270=:25970" X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (6.50 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_01_02 (0.5 points) BODY: Spam phrases score is 01 to 02 (low) SPAM: [score: 1] SPAM: SPAM_REDIRECTOR (0.4 points) URI: Uses open redirection service SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 124.48.190.206.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 124.48.190.206.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- --0-1096543310-1206156270=:25970 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 8bit Entre no site de algum destes colégios : Poliedro, Etapa , Anglo lLatino etc Antonio Giansante escreveu: creio que muitos já pediram isso: alguém sabe um link onde eu possa conseguir as provas do ITA (ao menos as 10 últimas)? Não precisa ser resolvida, mas pelo menos com o gabarito. Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! http://br.mail.yahoo.com/ ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= --------------------------------- Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-1096543310-1206156270=:25970 Content-Type: text/html; charset=iso-8859-1 Content-Transfer-Encoding: 8bit Entre no site de algum destes colégios : Poliedro, Etapa , Anglo lLatino etc 

Antonio Giansante <profcabi@yahoo.com.br> escreveu:
creio que muitos já pediram isso: alguém sabe um link
onde eu possa conseguir as provas do ITA (ao menos as
10 últimas)? Não precisa ser resolvida, mas pelo menos
com o gabarito.


Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento!
http://br.mail.yahoo.com/
=========================================================================
Instruções para entrar na lista, sair da lista e usar a lista em
http://www.mat.puc-rio.br/~obmlistas/obm-l.html
=========================================================================

Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-1096543310-1206156270=:25970-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sat Mar 22 07:53:11 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2MAoKWA024084 for ; Sat, 22 Mar 2008 07:50:20 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2MAoJCh024081 for obm-l-MllGbsmmN; Sat, 22 Mar 2008 07:50:19 -0300 Received: from web90505.mail.mud.yahoo.com (web90505.mail.mud.yahoo.com [216.252.100.172]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id m2MAoHWA024059 for ; Sat, 22 Mar 2008 07:50:18 -0300 Received: (qmail 56495 invoked by uid 60001); 22 Mar 2008 10:49:56 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:X-Mailer:Date:From:Subject:To:Cc:MIME-Version:Content-Type:Content-Transfer-Encoding:Message-ID; b=dce3s4JjTJDqJr5l1t7oZk0wnzxC+ufPoM1K+vUKIQ3SO2DzP0Ho3dJvpleWY0nSOCk/XmmkHPC32CperlaxitC3lj6gNv3DdTX6X6HhkjZ9T5oBeAl+wrcb94pTTedmmwVGPB28IS1MNjDRib/I6YC15zITJl9llSsLCIKmmiQ=; X-YMail-OSG: 3X7wgV8VM1mUqqcgNkgZZAhDsTp0qzWWfWvKzhPWIuLLHZIf_XojLwp6sUid9FOvjSyg74.E7soUejI0OZ4TEnocUmS9uIgp_azgK6Krdpf3OFd4RCY- Received: from [201.70.128.125] by web90505.mail.mud.yahoo.com via HTTP; Sat, 22 Mar 2008 03:49:56 PDT X-Mailer: YahooMailRC/902.38 YahooMailWebService/0.7.162 Date: Sat, 22 Mar 2008 03:49:56 -0700 (PDT) From: Eric Campos Bastos Guedes Subject: [SPAM] [obm-l] Matematica aplicada - Estatistica To: obm-l@mat.puc-rio.br Cc: Joice Nascimento , lista-psi MIME-Version: 1.0 Content-Type: text/plain; charset=iso-8859-1 Message-ID: <207184.56189.qm@web90505.mail.mud.yahoo.com> Content-Transfer-Encoding: 7bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m2MAoJWA024076 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Eric Campos Bastos Guedes X-Spam-Status: Yes, hits=8.1 required=5.0 tests=FORGED_YAHOO_RCVD,FROM_ENDS_IN_NUMS,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01,SUPERLONG_LINE, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (8.10 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: FROM_ENDS_IN_NUMS (0.9 points) From: ends in numbers SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: SUPERLONG_LINE (0.0 points) BODY: Contains a line >=199 characters long SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 172.100.252.216.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 172.100.252.216.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- Ola, Evidentemente, o desvio de dinheiro da Saude Publica a torna ineficiente. Como quantificar essa "ineficiencia"? Qual a relação entre o número de vidas perdidas e a quantidade de dinheiro desviada da Saude Publica? Como relacionar essas grandezas? Mais especificamente: o desvio de R$1000,00 da Saude Publica acarreta, estatisticamente, a morte de quantas pessoas? [ ]'s Eric Campos Bastos Guedes Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! http://br.mail.yahoo.com/ ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sat Mar 22 08:33:03 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2MBV3WA029384 for ; Sat, 22 Mar 2008 08:31:03 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2MBV3WN029379 for obm-l-MllGbsmmN; Sat, 22 Mar 2008 08:31:03 -0300 Received: from colorado.uspnet.usp.br (colorado.uspnet.usp.br [143.107.254.72]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2MBV2WA029346 for ; Sat, 22 Mar 2008 08:31:02 -0300 Received: (qmail 16513 invoked from network); 22 Mar 2008 11:30:41 -0000 X-Mail-Scanner: Scanned by qSheff-II-2.1-r1 (http://www.enderunix.org/qsheff/) Received: from 201-27-77-192.dsl.telesp.net.br (HELO macmini.local) (fabricio82@[201.27.77.192]) (envelope-sender ) by colorado.uspnet.usp.br (qmail-ldap-1.03) with SMTP for ; 22 Mar 2008 11:30:41 -0000 Message-ID: <47E4ED43.1070006@usp.br> Date: Sat, 22 Mar 2008 08:28:03 -0300 From: "fabricio82@usp.br" User-Agent: Thunderbird 2.0.0.12 (Macintosh/20080213) MIME-Version: 1.0 To: obm-l@mat.puc-rio.br Subject: [SPAM] Re: [obm-l] Matematica aplicada - Estatistica References: <207184.56189.qm@web90505.mail.mud.yahoo.com> In-Reply-To: <207184.56189.qm@web90505.mail.mud.yahoo.com> Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "fabricio82@usp.br" X-Spam-Status: Yes, hits=7.7 required=5.0 tests=FROM_ENDS_IN_NUMS,IN_REP_TO,QUOTED_EMAIL_TEXT,RCVD_IN_DSBL, RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,REFERENCES, SPAM_PHRASE_00_01,SUPERLONG_LINE,USER_AGENT,US_DOLLARS_3, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******* X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (7.70 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: REFERENCES (-0.5 points) Has a valid-looking References header SPAM: USER_AGENT (-0.5 points) Found a User-Agent header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: FROM_ENDS_IN_NUMS (0.9 points) From: ends in numbers SPAM: US_DOLLARS_3 (0.4 points) BODY: Nigerian scam key phrase ($NN,NNN,NNN.NN) SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: QUOTED_EMAIL_TEXT (-0.8 points) BODY: Contains what looks like a quoted email text SPAM: SUPERLONG_LINE (0.0 points) BODY: Contains a line >=199 characters long SPAM: RCVD_IN_DSBL (3.2 points) RBL: Received via a relay in list.dsbl.org SPAM: [RBL check: found 192.77.27.201.list.dsbl.org] SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 72.254.107.143.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 72.254.107.143.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- 2.ln(x).phi, onde x é o valor desviado e phi é o número de ouro. Brincadeiras à parte, acredito que não deva ser fácil determinar essa relação, pois vários fatores estão envolvidos, fatores esses que podem colaborar [ou não] para a mortalidade. Veja, devem ser conhecidos [ao menos] os seguintes fatos: i. Qual a parcela da população que realmente depende da saúde pública? ii. De que doenças morrem as pessoas num determinado Estado? Em quais desses casos uma saúde pública de qualidade poderia evitar o óbito? iii. O tempo médio para que um desvio de dinheiro acarrete em conseqüências para a saúde; isto é, pensando da maneira inversa, se R$ 1.000.000,00 fossem injetados na saúde hoje, daqui quantos dias [meses?] veríamos os resultados? iv. Com uma saúde pública de qualidade, certamente muitos dos que hoje utilizam saúde privada, passariam a usar a pública, aumentando a demanda e implicando em queda da qualidade - se mais investimentos não fossem feitos. Certamente o equacionamento desses fatos [entre alguns outros] pode dar um parâmetro razoável a respeito da taxa de mortalidade relacionada à corrupção. [ ]'s Eric Campos Bastos Guedes wrote: > Ola, > > Evidentemente, o desvio de dinheiro da Saude Publica a torna ineficiente. Como quantificar essa "ineficiencia"? Qual a relação entre o número de vidas perdidas e a quantidade de dinheiro desviada da Saude Publica? Como relacionar essas grandezas? > > Mais especificamente: o desvio de R$1000,00 da Saude Publica acarreta, estatisticamente, a morte de quantas pessoas? > > [ ]'s > > Eric Campos Bastos Guedes > > > > > > > > Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! > http://br.mail.yahoo.com/ > > ========================================================================= > Instruções para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > ========================================================================= > > ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sat Mar 22 12:28:13 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2MFPjWA017906 for ; Sat, 22 Mar 2008 12:25:45 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2MFPiBd017904 for obm-l-MllGbsmmN; Sat, 22 Mar 2008 12:25:44 -0300 Received: from web52909.mail.re2.yahoo.com (web52909.mail.re2.yahoo.com [206.190.49.19]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id m2MFPgWA017899 for ; Sat, 22 Mar 2008 12:25:43 -0300 Received: (qmail 88822 invoked by uid 60001); 22 Mar 2008 15:25:20 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:Date:From:Subject:To:In-Reply-To:MIME-Version:Content-Type:Content-Transfer-Encoding:Message-ID; b=ZsUshky7aIo7W1zaWnnx5aWAXDWg7Mvm1YfULkVkxE/0pKUBTvKsS4oeaQsHriiFGhs2gTA/kxMeQrHsZu3PszMuP4wkDJa+6s2nU5nr3ihs45RD6T0p3oDU4MIaF8agOjgonb2U4Smb0zeEPvQ12hS/JyC7VxIPV9VFfDdCaTs=; X-YMail-OSG: DWbYUKwVM1kFGJY0_Xa4Uic8jSL0ypjE.PrjbKFvL53rC7T8o2AN1bhXvKBRaKEbWlidFCZKuoxWgGQd71PCTLg_qt9XQw8yVh0Pac3GqINmiyzOrDU0kGDgQMEkUQzXjbydqU0anWWyVp8- Received: from [189.31.103.180] by web52909.mail.re2.yahoo.com via HTTP; Sat, 22 Mar 2008 12:25:20 ART Date: Sat, 22 Mar 2008 12:25:20 -0300 (ART) From: Antonio Giansante Subject: [SPAM] Re: [obm-l] off toppic: material para o ITA To: obm-l@mat.puc-rio.br In-Reply-To: <595940.25970.qm@web52201.mail.re2.yahoo.com> MIME-Version: 1.0 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 7bit Message-ID: <827910.86431.qm@web52909.mail.re2.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Antonio Giansante X-Spam-Status: Yes, hits=6.3 required=5.0 tests=AWL,FORGED_YAHOO_RCVD,IN_REP_TO,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_01_02,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ****** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (6.30 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_01_02 (0.5 points) BODY: Spam phrases score is 01 to 02 (low) SPAM: [score: 1] SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 19.49.190.206.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 19.49.190.206.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (0.2 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- Obrigado, Antônio. --- Antonio Santos escreveu: > Entre no site de algum destes colégios : Poliedro, > Etapa , Anglo lLatino etc > > Antonio Giansante escreveu: > creio que muitos já pediram isso: alguém sabe um > link > onde eu possa conseguir as provas do ITA (ao menos > as > 10 últimas)? Não precisa ser resolvida, mas pelo > menos > com o gabarito. > > > Abra sua conta no Yahoo! Mail, o único sem limite de > espaço para armazenamento! > http://br.mail.yahoo.com/ > ========================================================================= > Instruções para entrar na lista, sair da lista e > usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > ========================================================================= > > > > --------------------------------- > Abra sua conta no Yahoo! Mail, o único sem limite de > espaço para armazenamento! Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! http://br.mail.yahoo.com/ ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sat Mar 22 13:37:35 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2MGZNWA022259 for ; Sat, 22 Mar 2008 13:35:23 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2MGZNiF022257 for obm-l-MllGbsmmN; Sat, 22 Mar 2008 13:35:23 -0300 Received: from relay3.bol.com.br (relay3.bol.com.br [200.221.4.107]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2MGZMWA022246 for ; Sat, 22 Mar 2008 13:35:22 -0300 Received: from localhost (localhost [127.0.0.1]) by salsa3.bol.com.br (Postfix) with ESMTP id BB500E0063B1 for ; Sat, 22 Mar 2008 04:09:05 -0300 (BRT) Received: from bol.com.br (whisper10.mail.sys.intranet [172.26.5.91]) by salsa3.bol.com.br (Postfix) with ESMTP id 8D55FE00625F for ; Sat, 22 Mar 2008 04:09:05 -0300 (BRT) Date: Sat, 22 Mar 2008 13:35:01 -0300 Message-Id: Subject: [obm-l] FORMIGA MIME-Version: 1.0 X-Sensitivity: 3 Content-Type: multipart/alternative; boundary="_=__=_XaM3_.1206203701.2A.294025.42.25709.52.42.007.449823478" From: "arkon" To: "obm-l" X-XaM3-API-Version: 4.3(R1) (B10) X-SenderIP: 200.140.133.74 X-SIG5: fb5c9df8c6f9ce6156022a5345caa9b6 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "arkon" X-Spam-Status: No, hits=1.3 required=5.0 tests=AWL,BIG_FONT,HTML_50_70,LINES_OF_YELLING, LINES_OF_YELLING_2,SPAM_PHRASE_00_01,SUPERLONG_LINE, TO_LOCALPART_EQ_REAL,X_MAILING_LIST version=2.44 X-Spam-Level: * --_=__=_XaM3_.1206203701.2A.294025.42.25709.52.42.007.449823478 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable PESSOAL ALGU=C9M PODE RESOLVER, POR FAVOR, ESSA: Num vaso aberto, com formato de um cilindro circular reto, de altura igua= l a 30 cm e raio da base igual a 4 cm, existe uma formiga e uma gota de m= el. A Formiga localiza-se num ponto da superf=EDcie externa do vaso a 4 cm da= sua borda. A gota de mel, por sua vez, localiza-se na superf=EDcie inter= na do vaso, junto =E0 borda, o mais afastado poss=EDvel da formiga. Sabe-se que a gota de mel escorre pela superf=EDcie interna do vaso a uma= velocidade constante de 1 cm/seg e a formiga =E9 capaz de caminhar, no m= =E1ximo, a uma velocidade de 3 cm/seg. Calcular, em d=E9cimos de segundo,= o tempo m=EDnimo que a formiga gastar=E1 para alcan=E7ar a gota de mel. = Despreze a espessura do vaso e adote para c=E1lculos pi =3D 3. GABARITO 50. DESDE J=C1 AGRADE=C7O --_=__=_XaM3_.1206203701.2A.294025.42.25709.52.42.007.449823478 Content-Type: text/html; charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable

PES= SOAL ALGU=C9M PODE RESOLVER, POR FAVOR, ESSA:

&nbs= p;

Num= vaso aberto, com formato de um cilindro circular reto, de altura igual a= 30 cm e raio da base igual a 4 cm, existe uma formiga e u= ma gota de mel.

A F= ormiga localiza-se num ponto da superf=EDcie externa do vaso a 4 cm da s= ua borda. A gota de mel, por sua vez, localiza-se na superf=EDcie interna= do vaso, junto =E0 borda, o mais afastado poss=EDvel da formiga.

Sab= e-se que a gota de mel escorre pela superf=EDcie interna do vaso a uma ve= locidade constante de 1 cm/seg e a formiga =E9 capaz de caminhar, no m=E1= ximo, a uma velocidade de 3 cm/seg. Calcular, em d=E9cimos de segundo, o = tempo m=EDnimo que a formiga gastar=E1 para alcan=E7ar a gota de mel. Des= preze a espessura do vaso e adote para c=E1lculos pi =3D 3.

<= B style=3D"mso-bidi-font-weight: normal"> <= /P>

<= B style=3D"mso-bidi-font-weight: normal">GABARITO 50.<= /FONT>

<= B style=3D"mso-bidi-font-weight: normal"> <= /P>

<= B style=3D"mso-bidi-font-weight: normal">DESDE J=C1 AGRADE=C7O

--_=__=_XaM3_.1206203701.2A.294025.42.25709.52.42.007.449823478-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sat Mar 22 16:16:14 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2MJDiWA029651 for ; Sat, 22 Mar 2008 16:13:44 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2MJDiti029649 for obm-l-MllGbsmmN; Sat, 22 Mar 2008 16:13:44 -0300 Received: from py-out-1112.google.com (py-out-1112.google.com [64.233.166.179]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2MJDgWA029646 for ; Sat, 22 Mar 2008 16:13:43 -0300 Received: by py-out-1112.google.com with SMTP id f47so2116938pye.14 for ; Sat, 22 Mar 2008 12:13:22 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; bh=TgrEQdNgJnVP6XDROGywFnIkEQSH4BA1r+nZWUM9heg=; b=g/JLKn0gPZtjP/G/fqSJ+QPjSeip2RWfdNKC4O0REuJ7ekr8g+rU+1h1xKvPP2VHApawCztwafRzzDLmklgFfoknzAa80Bl2BCs803c0fXkIw6SKEBXDqa7v2CuPlWFBa6DHz04hB4TqgtcogCfHyDA4QDBfiq8vd8G2py0a/wc= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; b=BFB+OXP9Ov0krobtJD+RtV1mQrX3ehOIbmAeJxX2nY5vDBaXo90DS/IYIkSLVUiR3hq8ruTwwa2NgWq8Ct+YsC3zLuQzYMMIQ/a5khHGeLOQQrJUdCmmVsdu25r8TddlSP15HxPps3hIDyaT1MjOjgI8dNw+Z7Yft/p/Xnd2EVU= Received: by 10.114.174.2 with SMTP id w2mr8567235wae.17.1206213201527; Sat, 22 Mar 2008 12:13:21 -0700 (PDT) Received: by 10.114.176.17 with HTTP; Sat, 22 Mar 2008 12:13:21 -0700 (PDT) Message-ID: <1bcd8af0803221213u6a46faecvf79710acf9154402@mail.gmail.com> Date: Sat, 22 Mar 2008 20:13:21 +0100 From: "Bernardo Freitas Paulo da Costa" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Esfera... problema In-Reply-To: MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline References: Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m2MJDhWA029647 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Bernardo Freitas Paulo da Costa" X-Spam-Status: No, hits=3.5 required=5.0 tests=AWL,IN_REP_TO,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: *** Só uma idéia (depois de estar muito tempo ausente da lista...) : o que acontece se fosse um círculo ? (um hemisfério seria então uma metade de disco) Aliás, acho que a maior parte dos arcos dentro de um círculo (e da esfera também) tem comprimento menor do que 2 (isso quer dizer mais ou menos que quase sempre dá pra fazer isso !) Depois que você tiver visto porque funciona no círculo, veja o que você precisa fazer pra "cair" num círculo a partir da tua esfera ! -- Bernardo Freitas Paulo da Costa 2008/3/10 MauZ : > Dois pontos na esfera de raio 1 estão conectados por um arco A contido no > interior da esfera. > Mostre que se o comprimento do arco A é menor do que 2 então existe um > hemisfério H que não intercepta A. > > ______ > > Minha ideia até agora foi simplesmente criar um hemisfério da seguitne > forma: > Acho um ponto P coplanar aos dois pontos B e C que seja arco médio de B e C. > Aí basta achar o l.g. de P' tal que arco(P,P')=pi/2. ai essa circunferencia > determina o hemisferio H. Depois tenho q mostrar que qualquer arco q > intercepte esse hemisferio mede 2 ou +. > > não sei se esse é o caminho.. mas nao estou cosneguindo formalizar... > > Obrigado, > Maurizio > ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sat Mar 22 17:56:36 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2MKs6WA002385 for ; Sat, 22 Mar 2008 17:54:06 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2MKs6gL002383 for obm-l-MllGbsmmN; Sat, 22 Mar 2008 17:54:06 -0300 Received: from smtp.bol.com.br (smtpout2.bol.com.br [200.221.4.213]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2MKs5WA002380 for ; Sat, 22 Mar 2008 17:54:05 -0300 Received: from localhost (localhost [127.0.0.1]) by smart6.bol.com.br (Postfix) with ESMTP id BFDFD328 for ; Sat, 22 Mar 2008 17:53:44 -0300 (BRT) Received: from pai (unknown [201.88.134.242]) by smart6.bol.com.br (Postfix) with ESMTP id 20C2E327 for ; Sat, 22 Mar 2008 17:53:42 -0300 (BRT) Message-ID: <001c01c88c5f$12c5e500$6401a8c0@pai> From: "Tio Cabri st" To: Subject: [SPAM] [obm-l] off topic: exercicios analise real Date: Sat, 22 Mar 2008 17:55:27 -0300 MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: 7bit X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2800.1478 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2800.1478 X-SIG5: 25cc05c6b27702b53d2ffc605f3c9276 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Tio Cabri st" X-Spam-Status: Yes, hits=6.0 required=5.0 tests=AWL,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01, USER_AGENT_OE,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ****** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (6.00 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: USER_AGENT_OE (0.2 points) X-Mailer header indicates a non-spam MUA (Outlook Express) SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 242.134.88.201.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 242.134.88.201.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (0.0 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- Senhores, boa tarde, sei que é off-topic desculpem-me, mas, tá difícil de fazer sozinho, gostaria da ajuda do pessoal da lista. Assunto: exercícios resolvidos do livro de análise do Elon do pequeno ou do grande (volume 1). Sei fazer alguns, outros não sei nem por onde começar. Peço: se você possui alguns resolvidos e puder me ceder agradeço muito. meu e-mail: ilhadepaqueta@bol.com.br Obrigado Hermann Cabri ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sat Mar 22 21:02:04 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2MNxLWA026944 for ; Sat, 22 Mar 2008 20:59:21 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2MNxLeI026942 for obm-l-MllGbsmmN; Sat, 22 Mar 2008 20:59:21 -0300 Received: from smtp.uol.com.br (smtps.uol.com.br [200.221.4.131]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2MNxJWA026936 for ; Sat, 22 Mar 2008 20:59:20 -0300 Received: from localhost (localhost [127.0.0.1]) by socom4.uol.com.br (Postfix) with ESMTP id AE33FE000475 for ; Sat, 22 Mar 2008 20:58:58 -0300 (BRT) Received: from microcf7b75528 (201009203022.user.veloxzone.com.br [201.9.203.22]) by socom4.uol.com.br (Postfix) with SMTP id 65688E000323 for ; Sat, 22 Mar 2008 20:58:57 -0300 (BRT) Message-ID: <000a01c88c78$b11a15a0$01fea8c0@microcf7b75528> From: "Ulysses Coelho de Souza Jr." To: Subject: [SPAM] [obm-l] Probabilidades e o Primeiro Lema de Kaplansky Date: Sat, 22 Mar 2008 20:58:56 -0300 MIME-Version: 1.0 Content-Type: text/plain X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2900.3138 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.3198 X-SIG5: a09eb63b304b7f8a823338246b567443 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Ulysses Coelho de Souza Jr." X-Spam-Status: Yes, hits=6.7 required=5.0 tests=AWL,HTML_70_90,HTML_FONT_COLOR_BLUE,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01,USER_AGENT_OE, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ****** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_NextPart_000_0007_01C88C5F.8B44E8F0" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (6.70 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: USER_AGENT_OE (0.2 points) X-Mailer header indicates a non-spam MUA (Outlook Express) SPAM: HTML_70_90 (0.9 points) BODY: Message is 70-90% HTML tags SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: HTML_FONT_COLOR_BLUE (0.2 points) BODY: HTML font color is blue SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 22.203.9.201.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 22.203.9.201.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-0.4 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- This is a multi-part message in MIME format. ------=_NextPart_000_0007_01C88C5F.8B44E8F0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Ol=E1 a todos, A quest=E3o abaixo =E9 de um vestibular recente. Acredito que o = examinador quis dizer "pelo menos um par" ao inv=E9s de "um par". Coment=E1rios ser=E3o bem-vindos.=20 No Concurso da Mega-Sena s=E3o sorteados 6 n=FAmeros de 01 a 60. Por exemplo, o concurso 924 teve como n=FAmeros sorteados 02,20,21,27,51 e 60, ou seja, houve um par de n=FAmeros consecutivos, 20 e 21. A probabilidade de que no jogo da Mega-Sena haja um par de n=FAmeros consecutivos sorteados =E9: =20 (A) 54!/60! (B) 53!/59! (C) 1-(56!55!)/(49!60!) (D) 1-(54!53!)/(48!60!) (E) 1-(55!54!)/(49!60!) Um abra=E7o, Ulysses C. de Souza. ------=_NextPart_000_0007_01C88C5F.8B44E8F0 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable

Ol=E1 a todos,

 

A quest=E3o abaixo =E9 de um vestibular = recente. Acredito=20 que o examinador quis dizer "pelo menos um par" ao inv=E9s de "um=20 par".

 

Coment=E1rios ser=E3o = bem-vindos. 

 

No Concurso da Mega-Sena s=E3o = sorteados

6 n=FAmeros de 01 a 60. Por exemplo, o=20 concurso

924 teve como n=FAmeros=20 sorteados

02,20,21,27,51 e 60, ou seja, houve um = par=20 de

n=FAmeros consecutivos, 20 e 21. A=20 probabilidade

de que no jogo da Mega-Sena haja um par=20 de

n=FAmeros consecutivos sorteados=20 =E9:

 

(A)=20 54!/60!

(B)=20 53!/59!

(C)=20 1-(56!55!)/(49!60!)

(D)=20 1-(54!53!)/(48!60!)

(E)=20 1-(55!54!)/(49!60!)
 
Um = abra=E7o,
 
Ulysses C. de=20 Souza.
------=_NextPart_000_0007_01C88C5F.8B44E8F0-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sat Mar 22 21:43:37 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2N0feWA029440 for ; Sat, 22 Mar 2008 21:41:40 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2N0fe7T029438 for obm-l-MllGbsmmN; Sat, 22 Mar 2008 21:41:40 -0300 Received: from web32703.mail.mud.yahoo.com (web32703.mail.mud.yahoo.com [68.142.207.247]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id m2N0fbWA029435 for ; Sat, 22 Mar 2008 21:41:38 -0300 Received: (qmail 85892 invoked by uid 60001); 23 Mar 2008 00:41:11 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:Date:From:Subject:To:In-Reply-To:MIME-Version:Content-Type:Content-Transfer-Encoding:Message-ID; b=Qc7S6tpY0Y4GROys+1a7mC5tAnJHBu532xe03jWs5nB8PIrWYjKSHv8uivpyN6LQaYxWwPeQqD4EAbqI7F4hKE8Os4/GGRl0D0Now7UlpI8jgEp2jVy+zRcWTSraCxsGQHaL0JQH/Upq+3SSdeBcKzqies7OJGQfnmtUqfWLo9A=; X-YMail-OSG: Z2ACHfUVM1mEoVtMjhCIfvBT9iKoVvXR7BcWI_4wOt5pJTkXso2_fH0TiQI2zWF.lR3skMyA3XZ6umSI1ZFqwVce5S_kC4x2dWZQUViK5iEyOkph1XCxQg-- Received: from [201.9.27.56] by web32703.mail.mud.yahoo.com via HTTP; Sat, 22 Mar 2008 21:41:11 ART Date: Sat, 22 Mar 2008 21:41:11 -0300 (ART) From: alexmay nunes soares Subject: [SPAM] Re: [obm-l] FORMIGA To: obm-l@mat.puc-rio.br In-Reply-To: MIME-Version: 1.0 Content-Type: text/plain Content-Transfer-Encoding: 7bit Message-ID: <231378.84816.qm@web32703.mail.mud.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: alexmay nunes soares X-Spam-Status: Yes, hits=7.2 required=5.0 tests=AWL,BIG_FONT,FORGED_YAHOO_RCVD,GAPPY_TEXT,HTML_50_70, IN_REP_TO,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, SPAM_PHRASE_00_01,SPAM_REDIRECTOR,SUPERLONG_LINE, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******* X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="0-1887890573-1206232871=:84816" X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (7.20 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: GAPPY_TEXT (0.0 points) BODY: Contains 'G.a.p.p.y-T.e.x.t' SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: BIG_FONT (0.3 points) BODY: FONT Size +2 and up or 3 and up SPAM: HTML_50_70 (0.3 points) BODY: Message is 50-70% HTML tags SPAM: SUPERLONG_LINE (0.0 points) BODY: Contains a line >=199 characters long SPAM: SPAM_REDIRECTOR (0.4 points) URI: Uses open redirection service SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 247.207.142.68.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 247.207.142.68.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-0.2 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- --0-1887890573-1206232871=:84816 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 8bit Tente acompanhar com a figura abaixo: Qdo vc planificar o cilindro vc terá um retângulo de dimensões 30cm por 24cm (H por 2pi*raio). Dos dados do exercícios constatamos q a planificação pode ser dada com a Formiga F no "meio" do retângulo e o mel no ponto M. Para a formiga entrar no menor tempo possível ela terá que sair de F e caminhar ate um ponto P, na borda, e desse ponto P entrar no cilindro e caminhar sobre a superfície interna até um ponto T, onde ela deverá encontrar o Mel, a distância mínima implicará um tempo mínimo, logo MP + PT deve ser mínimo, usando alinhamento dos pontos, podemos prolongar PQ (veja figura abaixo) de modo a termos FQ = QF', daí F'P = FP, mas temos F', P e T alinhados! Trace um reta ligando os pontos F' , P e T, se vc prolongar TM até um ponto R, com RF' ortogonal a MR, teremos um triângulo retângulo TRF', sabemos que MQ = 24/2, isto é: MQ = 12 cm, como RF' = MQ, temos RF' = 12 cm, por outro lado F'T é a distância percorrida pela formiga, se t for o tempo necessário para o encontro temos (distância = velocidade * tempo) F'T = 3*t e MT = 1*t, note que MT é a distãncia percorrida pela gota de mel, como TR = TM + MR vem que TR = t+4, pronto agora é só o teorema de pitágoras, com: hipotenusa F'T = 3t e catetos TR = t+4 e RF' = 12 (3t)^2 = (t+4)^2+12^2 9t^2=t^2+8t+16+144 8t^2-8t-160=0 t^2-t-20=0 t=-4(não serve) ou t=5segundos como t deve ser expresso em décimos de segundos vem que t = 50décimos de segundos! Fiz uma tentativa de figura abaixo: R F' I I4cm M______P__ I Q____________ Borda I I I I I4cm I I I I I F I I I I I T I I I I I I arkon escreveu: PESSOAL ALGUÉM PODE RESOLVER, POR FAVOR, ESSA: Num vaso aberto, com formato de um cilindro circular reto, de altura igual a 30 cm e raio da base igual a 4 cm, existe uma formiga e uma gota de mel. A Formiga localiza-se num ponto da superfície externa do vaso a 4 cm da sua borda. A gota de mel, por sua vez, localiza-se na superfície interna do vaso, junto à borda, o mais afastado possível da formiga. Sabe-se que a gota de mel escorre pela superfície interna do vaso a uma velocidade constante de 1 cm/seg e a formiga é capaz de caminhar, no máximo, a uma velocidade de 3 cm/seg. Calcular, em décimos de segundo, o tempo mínimo que a formiga gastará para alcançar a gota de mel. Despreze a espessura do vaso e adote para cálculos pi = 3. GABARITO 50. DESDE JÁ AGRADEÇO --------------------------------- Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-1887890573-1206232871=:84816 Content-Type: text/html; charset=iso-8859-1 Content-Transfer-Encoding: 8bit
Tente acompanhar com a figura abaixo:
 
 
Qdo vc planificar o cilindro vc terá um retângulo de dimensões 30cm por 24cm (H por 2pi*raio). Dos dados do exercícios constatamos q a planificação pode ser dada com a Formiga F no "meio" do retângulo e o mel no ponto M. Para a formiga entrar no menor tempo possível ela terá que sair de F e caminhar ate um ponto P, na borda, e desse ponto P entrar no cilindro e caminhar sobre a superfície interna até um ponto T, onde ela deverá encontrar o Mel, a distância mínima implicará um tempo mínimo, logo MP + PT deve ser mínimo, usando alinhamento dos pontos, podemos prolongar PQ (veja figura abaixo) de modo a termos FQ = QF', daí F'P = FP, mas temos F', P e T alinhados! Trace um reta ligando os pontos F' , P e T, se vc prolongar TM até um ponto R, com RF' ortogonal a MR, teremos um triângulo retângulo TRF', sabemos que MQ = 24/2, isto é: MQ = 12 cm, como RF' = MQ, temos RF' = 12 cm, por outro lado F'T é a distância percorrida pela formiga, se t for o tempo necessário para o encontro temos (distância = velocidade * tempo)
F'T = 3*t e MT = 1*t, note que MT é a distãncia percorrida pela gota de mel, como TR = TM + MR vem que TR = t+4, pronto agora é só o teorema de pitágoras, com: hipotenusa F'T = 3t e catetos TR = t+4 e RF' = 12
 
(3t)^2 = (t+4)^2+12^2
9t^2=t^2+8t+16+144
8t^2-8t-160=0
t^2-t-20=0
t=-4(não serve) ou t=5segundos
como t deve ser expresso em décimos de segundos vem que t = 50décimos de segundos! Fiz uma tentativa de figura abaixo:                                    
 
                     R                  F'
                                         I                     
                                         I4cm              
                    M______P__ I Q____________ Borda
                      I                  I                    I
                      I                  I4cm              I
                      I                  I                    I
                      I                 F                    I
                      I                                       I
                      I                                       I
                   T I                                       I
                      I                                       I
                      I                                       I
 
 


arkon <arkon@bol.com.br> escreveu:
PESSOAL ALGUÉM PODE RESOLVER, POR FAVOR, ESSA:
 
Num vaso aberto, com formato de um cilindro circular reto, de altura igual a 30 cm e raio da base igual a 4 cm, existe uma formiga e uma gota de mel.
A Formiga localiza-se num ponto da superfície externa do vaso a 4 cm da sua borda. A gota de mel, por sua vez, localiza-se na superfície interna do vaso, junto à borda, o mais afastado possível da formiga.
Sabe-se que a gota de mel escorre pela superfície interna do vaso a uma velocidade constante de 1 cm/seg e a formiga é capaz de caminhar, no máximo, a uma velocidade de 3 cm/seg. Calcular, em décimos de segundo, o tempo mínimo que a formiga gastará para alcançar a gota de mel. Despreze a espessura do vaso e adote para cálculos pi = 3.
 
GABARITO 50.
 
DESDE JÁ AGRADEÇO

Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-1887890573-1206232871=:84816-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sun Mar 23 00:51:06 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2N3mWWA006191 for ; Sun, 23 Mar 2008 00:48:32 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2N3mVIm006189 for obm-l-MllGbsmmN; Sun, 23 Mar 2008 00:48:31 -0300 Received: from relay3.bol.com.br (relay3.bol.com.br [200.221.4.107]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2N3mUWA006179 for ; Sun, 23 Mar 2008 00:48:30 -0300 Received: from localhost (localhost [127.0.0.1]) by salsa3.bol.com.br (Postfix) with ESMTP id 9C1D3E006136 for ; Sat, 22 Mar 2008 15:22:14 -0300 (BRT) Received: from bol.com.br (whisper6.mail.sys.intranet [172.26.5.78]) by salsa3.bol.com.br (Postfix) with ESMTP id 7C6FEE005E9D for ; Sat, 22 Mar 2008 15:22:14 -0300 (BRT) Date: Sun, 23 Mar 2008 00:48:10 -0300 Message-Id: Subject: [obm-l] BURRO DA ESCOLA NAVAL MIME-Version: 1.0 X-Sensitivity: 3 Content-Type: multipart/alternative; boundary="_=__=_XaM3_.1206244090.2A.266590.42.3744.52.42.007.472639600" From: "arkon" To: "obm-l" X-XaM3-API-Version: 4.3(R1) (B10) X-SenderIP: 200.140.133.73 X-SIG5: f6640336dc5a04fe71413ddce23ceee7 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "arkon" X-Spam-Status: No, hits=1.5 required=5.0 tests=AWL,BIG_FONT,HTML_50_70,LINES_OF_YELLING, LINES_OF_YELLING_2,LINES_OF_YELLING_3,SPAM_PHRASE_00_01, SUPERLONG_LINE,TO_LOCALPART_EQ_REAL,X_MAILING_LIST version=2.44 X-Spam-Level: * --_=__=_XaM3_.1206244090.2A.266590.42.3744.52.42.007.472639600 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable PESSOAL ALGU=C9M PODE ENVIAR A RESOLU=C7=C3O DESSA, POR FAVOR (EN-86) Um pasto homog=EAneo tem a forma de um c=EDrculo. Um burro est=E1= preso por uma corda de comprimento igual ao raio do c=EDrculo, amarrada = a uma estaca na circunfer=EAncia do c=EDrculo. A melhor aproxima=E7=E3o d= a porcentagem da grama do pasto que o burro consegue comer =E9: a) 45%. b) 42%. c) 39%. d) 36%. e) 32%. MAIS UMA VEZ MUITO OBRIGADO --_=__=_XaM3_.1206244090.2A.266590.42.3744.52.42.007.472639600 Content-Type: text/html; charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable

PESSOAL ALGU=C9M PODE ENVIAR A RESOLU=C7=C3O DESSA, = POR FAVOR

 

(EN-86) Um pasto homog=EAneo tem a forma de um c=EDr= culo. Um burro est=E1 preso por uma corda de comprimento igual ao raio do= c=EDrculo, amarrada a uma estaca na circunfer=EAncia do c=EDrculo. A mel= hor aproxima=E7=E3o da porcentagem da grama do pasto que o burro consegue= comer =E9:

 

<= B style=3D"mso-bidi-font-weight: normal">a) 45%.   b) 42%.   c) 39%.   d) 36%.  e) 32%.

=

<= B style=3D"mso-bidi-font-weight: normal"> 

<= B style=3D"mso-bidi-font-weight: normal">MAIS UMA VEZ MUITO OBRIGADO

--_=__=_XaM3_.1206244090.2A.266590.42.3744.52.42.007.472639600-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sun Mar 23 01:05:56 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2N43vWA006652 for ; Sun, 23 Mar 2008 01:03:57 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2N43v21006648 for obm-l-MllGbsmmN; Sun, 23 Mar 2008 01:03:57 -0300 Received: from py-out-1112.google.com (py-out-1112.google.com [64.233.166.178]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2N43tWA006643 for ; Sun, 23 Mar 2008 01:03:55 -0300 Received: by py-out-1112.google.com with SMTP id f47so2257162pye.14 for ; Sat, 22 Mar 2008 21:03:34 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=DKwiVYQ+zZa8ZxT+07C/wIHhHFKjxwYMInV3WYK/P7M=; b=TPAe3id2U7n51TMvvaI7krwAbz1C+6f+mIIY9M7x8FJgN14uLaplbjLlgJ0Q7zocjujfwRBSw70K41OiECwWF7ShenXlEgy9qCQ2beHNdSQtx5RydTwBdDQm5VmWAu1e0/1mICQSDA+xV520AGoWJ3BAbgjhFayqq4QloAI4zA4= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=iHONE4StYRf1nELZXNOrKOW0RDqWK0N333sMqntCjr0kFUj6s0JNj+XOTiJZ4WzSOtnIbhNw8Plr01jkhCQedlC3w+tlzyP0YW1gPSY3rK34GqU6QZ51ttQnDx9Mo8hcLb4uC+nCkL/JjXbncraKL6M61RYR+yQ98A0czgRSoYQ= Received: by 10.65.214.2 with SMTP id r2mr10000306qbq.86.1206245014131; Sat, 22 Mar 2008 21:03:34 -0700 (PDT) Received: by 10.64.232.4 with HTTP; Sat, 22 Mar 2008 21:03:34 -0700 (PDT) Message-ID: Date: Sun, 23 Mar 2008 01:03:34 -0300 From: "Julio Sousa" To: obm-l@mat.puc-rio.br Subject: [SPAM] Re: [obm-l] BURRO DA ESCOLA NAVAL In-Reply-To: MIME-Version: 1.0 Content-Type: text/plain References: Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Julio Sousa" X-Spam-Status: Yes, hits=5.4 required=5.0 tests=BIG_FONT,IN_REP_TO,LINES_OF_YELLING,LINES_OF_YELLING_2, MAILTO_LINK,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,REFERENCES, SPAM_PHRASE_00_01,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ***** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_Part_2215_11862309.1206245014124" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. 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Um burro est= =E1 preso > por uma corda de comprimento igual ao raio do c=EDrculo, amarrada a uma e= staca > na circunfer=EAncia do c=EDrculo. A melhor aproxima=E7=E3o da porcentagem= da grama > do pasto que o burro consegue comer =E9:* > > * * > > *a) 45%. b) 42%. c) 39%. d) 36%. e) 32%.* > > * * > > *MAIS UMA VEZ MUITO OBRIGADO* > --=20 Atenciosamente J=FAlio Sousa ------=_Part_2215_11862309.1206245014124 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline http://www.orkut.c= om/CommMsgs.aspx?cmm=3D1299345&tid=3D2535709487136738179&kw=3Dburri= nho&na=3D1&nst=3D1

Discuss=E3o interessante sobre uma quest=E3o parecida!

2008/3/23 arkon <a= rkon@bol.com.br>:

PESSOAL ALGU=C9M PODE ENVIAR A RESOLU= =C7=C3O DESSA, POR FAVOR

 

(EN-86) Um pasto homog=EAneo tem a fo= rma de um c=EDrculo. Um burro est=E1 preso por uma corda de comprimento igu= al ao raio do c=EDrculo, amarrada a uma estaca na circunfer=EAncia do c=EDr= culo. A melhor aproxima=E7=E3o da porcentagem da grama do pasto que o burro= consegue comer =E9:

 

= a) 45%.   b) 42%.   c) 39%.   d) 36%.  = e) 32%.

 

= MAIS UMA VEZ MUITO OBRIGADO




--
Atenciosamente
J=FAl= io Sousa ------=_Part_2215_11862309.1206245014124-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sun Mar 23 10:33:51 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2NDUuWA007150 for ; Sun, 23 Mar 2008 10:30:56 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2NDUtvd007148 for obm-l-MllGbsmmN; Sun, 23 Mar 2008 10:30:55 -0300 Received: from web32702.mail.mud.yahoo.com (web32702.mail.mud.yahoo.com [68.142.207.246]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id m2NDUrWA007144 for ; Sun, 23 Mar 2008 10:30:54 -0300 Received: (qmail 6765 invoked by uid 60001); 23 Mar 2008 13:30:32 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:Date:From:Subject:To:In-Reply-To:MIME-Version:Content-Type:Content-Transfer-Encoding:Message-ID; b=kmwVuduUC3eGJg5q0A+pl+A9gsSQoYNd84ubnpeglGv+9m4WcrGTBEQ70O4cJ7LveEjRdAPf3urBltQdzib+YD8Dg5Bk/ymyvXbL54Z3/LlEZT0x+310+iyJCCvLklSjB0WkO9AO80LY1BNCQTX96j0j66Im0CBSgqF+X7zqoug=; X-YMail-OSG: lTrBe0gVM1kjRx1XESBbuTJrUweg7lKGyrZmmWUfdqf0rCNzDjr_uW54Pyh0PAAbv5Cwtsd6lgQ2A3W_JkmkqSFTwa4Pr.zp8Aikc9LHckKi5H6f1KI- Received: from [201.9.93.172] by web32702.mail.mud.yahoo.com via HTTP; Sun, 23 Mar 2008 10:30:31 ART Date: Sun, 23 Mar 2008 10:30:31 -0300 (ART) From: alexmay nunes soares Subject: [SPAM] Re: [obm-l] Probabilidades e o Primeiro Lema de Kaplansky To: obm-l@mat.puc-rio.br In-Reply-To: <000a01c88c78$b11a15a0$01fea8c0@microcf7b75528> MIME-Version: 1.0 Content-Type: text/plain Content-Transfer-Encoding: 7bit Message-ID: <8118.5328.qm@web32702.mail.mud.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: alexmay nunes soares X-Spam-Status: Yes, hits=7.2 required=5.0 tests=AWL,FORGED_YAHOO_RCVD,HTML_50_70,HTML_FONT_COLOR_BLUE, IN_REP_TO,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, SPAM_PHRASE_00_01,SPAM_REDIRECTOR,SUPERLONG_LINE, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******* X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="0-1906243481-1206279031=:5328" X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (7.20 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: HTML_50_70 (0.3 points) BODY: Message is 50-70% HTML tags SPAM: HTML_FONT_COLOR_BLUE (0.2 points) BODY: HTML font color is blue SPAM: SUPERLONG_LINE (0.0 points) BODY: Contains a line >=199 characters long SPAM: SPAM_REDIRECTOR (0.4 points) URI: Uses open redirection service SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 246.207.142.68.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 246.207.142.68.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-0.1 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- --0-1906243481-1206279031=:5328 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 8bit Ulysses, acredito que ao dizer "um par" não esteja sendo excluída a possibilidade de haver mais de um par, certamente que se fosse dito "pelo menos um par" teríamos entendido de imediato a solicitação, mas, na minha opnião, dizer "haja um par" é o mesmo que dizer "haja pelo menos um par", seria diferente se ele tivesse amarrado com "haja extamente um par", ou "haja apenas..." ou "haja somente..." etc. Ademais devemos lembrar que qdo tratamos com conjuntos agimos de forma semelhante, pois ao dizer q x é elemento de A estamos considerando a possibilidade de ele ser elemento de B tb, e qdo queremos nos certificar do contrário dizemos "x é elemento apenas de A" "Ulysses Coelho de Souza Jr." escreveu: Olá a todos, A questão abaixo é de um vestibular recente. Acredito que o examinador quis dizer "pelo menos um par" ao invés de "um par". Comentários serão bem-vindos. No Concurso da Mega-Sena são sorteados 6 números de 01 a 60. Por exemplo, o concurso 924 teve como números sorteados 02,20,21,27,51 e 60, ou seja, houve um par de números consecutivos, 20 e 21. A probabilidade de que no jogo da Mega-Sena haja um par de números consecutivos sorteados é: (A) 54!/60! (B) 53!/59! (C) 1-(56!55!)/(49!60!) (D) 1-(54!53!)/(48!60!) (E) 1-(55!54!)/(49!60!) Um abraço, Ulysses C. de Souza. --------------------------------- Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-1906243481-1206279031=:5328 Content-Type: text/html; charset=iso-8859-1 Content-Transfer-Encoding: 8bit
Ulysses, acredito que ao dizer "um par" não esteja sendo excluída a possibilidade de haver mais de um par, certamente que se fosse dito "pelo menos um par" teríamos entendido de imediato a solicitação, mas, na minha opnião, dizer "haja um par" é o mesmo que dizer "haja pelo menos um par", seria diferente se ele tivesse amarrado com "haja extamente um par", ou "haja apenas..." ou "haja somente..." etc. Ademais devemos lembrar que qdo tratamos com conjuntos agimos de forma semelhante, pois ao dizer q x é elemento de A estamos considerando a possibilidade de ele ser elemento de B tb, e qdo queremos nos certificar do contrário dizemos "x é elemento apenas de A"
 
"Ulysses Coelho de Souza Jr." <ucsjr@uol.com.br> escreveu:
Olá a todos,
 
A questão abaixo é de um vestibular recente. Acredito que o examinador quis dizer "pelo menos um par" ao invés de "um par".
 
Comentários serão bem-vindos. 
 
No Concurso da Mega-Sena são sorteados
6 números de 01 a 60. Por exemplo, o concurso
924 teve como números sorteados
02,20,21,27,51 e 60, ou seja, houve um par de
números consecutivos, 20 e 21. A probabilidade
de que no jogo da Mega-Sena haja um par de
números consecutivos sorteados é:
 
(A) 54!/60!
(B) 53!/59!
(C) 1-(56!55!)/(49!60!)
(D) 1-(54!53!)/(48!60!)
(E) 1-(55!54!)/(49!60!)
 
Um abraço,
 
Ulysses C. de Souza.

Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-1906243481-1206279031=:5328-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sun Mar 23 10:51:50 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2NDnoWA008477 for ; Sun, 23 Mar 2008 10:49:50 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2NDnn6F008465 for obm-l-MllGbsmmN; Sun, 23 Mar 2008 10:49:49 -0300 Received: from web32708.mail.mud.yahoo.com (web32708.mail.mud.yahoo.com [68.142.207.252]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id m2NDnjWA008436 for ; Sun, 23 Mar 2008 10:49:46 -0300 Received: (qmail 7240 invoked by uid 60001); 23 Mar 2008 13:49:25 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:Date:From:Subject:To:In-Reply-To:MIME-Version:Content-Type:Content-Transfer-Encoding:Message-ID; b=i9+xcuVNkOn2VQvuBOGvty5CHRxGMxDLWZiK76+0OlDT8Q5V+EhL1xAOv6bqpoMTWuv2oF9Ev7VbYqL3ds32uUslVnQzcwB4OP4UjVfV5dvjQ5RmroRfdBHexU3zkM0F1YGeeTeLh/YgJYj1H7FrksQKqsHz69EnOhTr+DQRECk=; X-YMail-OSG: s4UcV4kVM1l4U.YhreGNusk1MVDkeL_bRZcBoyNF92iT3z1VA2rgb9HKvfEKrZtPv1vv_RrZlRVKxrZVfuZHnGCWV5zIY4OuIWXumwFGVdVpVQp53Vzg6algeHZjXQ-- Received: from [201.9.93.172] by web32708.mail.mud.yahoo.com via HTTP; Sun, 23 Mar 2008 10:49:25 ART Date: Sun, 23 Mar 2008 10:49:25 -0300 (ART) From: alexmay nunes soares Subject: [SPAM] Re: [obm-l] BURRO DA ESCOLA NAVAL To: obm-l@mat.puc-rio.br In-Reply-To: MIME-Version: 1.0 Content-Type: text/plain Content-Transfer-Encoding: 7bit Message-ID: <262046.6999.qm@web32708.mail.mud.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: alexmay nunes soares X-Spam-Status: Yes, hits=7.2 required=5.0 tests=AWL,BIG_FONT,FORGED_YAHOO_RCVD,IN_REP_TO,MAILTO_LINK, RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01, SPAM_REDIRECTOR,SUPERLONG_LINE,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******* X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="0-552650582-1206280165=:6999" X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (7.20 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: BIG_FONT (0.3 points) BODY: FONT Size +2 and up or 3 and up SPAM: MAILTO_LINK (0.2 points) BODY: Includes a URL link to send an email SPAM: SUPERLONG_LINE (0.0 points) BODY: Contains a line >=199 characters long SPAM: SPAM_REDIRECTOR (0.4 points) URI: Uses open redirection service SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 252.207.142.68.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 252.207.142.68.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-0.1 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- --0-552650582-1206280165=:6999 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 8bit A área é igual a a dois segmentos de circunferência, o ângulo é de 120º ( basta construir dois triângulo equiláteros para verificar isso). COmo queremos saber a porcentagem vamos trabalhar com raio igual a 1. A área do segmento é igual a (setor - triÇangulo) = 2pi*1^2/6 - 1*sen120º/2 como a área do círculo é pi*1^2 divindido "segmento" por "círculo" temos a porcentagem: 2/3 - sqrt3/2*pi = 0,3909...=39,09% Julio Sousa escreveu: http://www.orkut.com/CommMsgs.aspx?cmm=1299345&tid=2535709487136738179&kw=burrinho&na=1&nst=1 Discussão interessante sobre uma questão parecida! 2008/3/23 arkon : PESSOAL ALGUÉM PODE ENVIAR A RESOLUÇÃO DESSA, POR FAVOR (EN-86) Um pasto homogêneo tem a forma de um círculo. Um burro está preso por uma corda de comprimento igual ao raio do círculo, amarrada a uma estaca na circunferência do círculo. A melhor aproximação da porcentagem da grama do pasto que o burro consegue comer é: a) 45%. b) 42%. c) 39%. d) 36%. e) 32%. MAIS UMA VEZ MUITO OBRIGADO -- Atenciosamente Júlio Sousa --------------------------------- Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-552650582-1206280165=:6999 Content-Type: text/html; charset=iso-8859-1 Content-Transfer-Encoding: 8bit
A área é igual a a dois segmentos de circunferência, o ângulo é de 120º ( basta construir dois triângulo equiláteros para verificar isso).
COmo queremos saber a porcentagem vamos trabalhar com raio igual a 1.
A área do segmento é igual a (setor - triÇangulo) = 2pi*1^2/6 - 1*sen120º/2
como a área do círculo é pi*1^2 divindido "segmento" por "círculo" temos a porcentagem:
2/3 - sqrt3/2*pi = 0,3909...=39,09%

Julio Sousa <juliosousajr@gmail.com> escreveu:
http://www.orkut.com/CommMsgs.aspx?cmm=1299345&tid=2535709487136738179&kw=burrinho&na=1&nst=1

Discussão interessante sobre uma questão parecida!

2008/3/23 arkon <arkon@bol.com.br>:
PESSOAL ALGUÉM PODE ENVIAR A RESOLUÇÃO DESSA, POR FAVOR
 
(EN-86) Um pasto homogêneo tem a forma de um círculo. Um burro está preso por uma corda de comprimento igual ao raio do círculo, amarrada a uma estaca na circunferência do círculo. A melhor aproximação da porcentagem da grama do pasto que o burro consegue comer é:
 
a) 45%.   b) 42%.   c) 39%.   d) 36%.  e) 32%.
 
MAIS UMA VEZ MUITO OBRIGADO



--
Atenciosamente
Júlio Sousa

Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-552650582-1206280165=:6999-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sun Mar 23 15:12:08 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2NI9aWA023977 for ; Sun, 23 Mar 2008 15:09:36 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2NI9aHR023975 for obm-l-MllGbsmmN; Sun, 23 Mar 2008 15:09:36 -0300 Received: from smtp.uol.com.br (smtps.uol.com.br [200.221.4.131]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2NI9YWA023966 for ; Sun, 23 Mar 2008 15:09:34 -0300 Received: from localhost (localhost [127.0.0.1]) by socom3.uol.com.br (Postfix) with ESMTP id 1063C7B5 for ; Sun, 23 Mar 2008 15:09:15 -0300 (BRT) Received: from MARTE (unknown [201.12.188.21]) by socom3.uol.com.br (Postfix) with ESMTP id 6D7B72CC for ; Sun, 23 Mar 2008 15:09:14 -0300 (BRT) Message-ID: <462E9A0956E94F1089DC95F25A999652@MARTE> From: "Ojesed Mirror" To: References: <2E2AD4A5B842401BB9820078CDDD50F0@MARTE> In-Reply-To: <2E2AD4A5B842401BB9820078CDDD50F0@MARTE> Subject: [SPAM] Re: [obm-l] SigmaDelta Date: Sun, 23 Mar 2008 15:08:34 -0300 MIME-Version: 1.0 Content-Type: text/plain X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Windows Mail 6.0.6000.16480 X-MimeOLE: Produced By Microsoft MimeOLE V6.0.6000.16545 X-SIG5: e01d460f28854ee6124e9f0ca18a60b8 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Ojesed Mirror" X-Spam-Status: Yes, hits=6.8 required=5.0 tests=IN_REP_TO,MAILTO_LINK,MISSING_OUTLOOK_NAME,RCVD_IN_DSBL, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ****** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_NextPart_000_003C_01C88CF7.C3AFACA0" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (6.80 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: REFERENCES (-0.5 points) Has a valid-looking References header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: MAILTO_LINK (0.2 points) BODY: Includes a URL link to send an email SPAM: RCVD_IN_DSBL (3.2 points) RBL: Received via a relay in list.dsbl.org SPAM: [RBL check: found 21.188.12.201.list.dsbl.org] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 21.188.12.201.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: MISSING_OUTLOOK_NAME (1.1 points) Message looks like Outlook, but isn't SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- This is a multi-part message in MIME format. ------=_NextPart_000_003C_01C88CF7.C3AFACA0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Ol=E1 lista, considerando a import=E2ncia que tem para mim a = resolu=E7=E3o desta quest=E3o, estou reformulando a pergunta na = esperan=E7a de que alguem se interesse por ela. Mostrar que a m=E9dia aritim=E9tica dos valores gerador pela sequencia: = D(1), D(2)....D(n) converge para V quando R > |V| onde D(n) =3D R * I(n) / |I(n)|,=20 e I(n) =3D I(n-1) + V - D(n-1), com: D(0) =3D I(0) =3D 0 R e V reais com R > 0 Ojesed. ----- Original Message -----=20 From: Ojesed Mirror=20 To: obm-l@mat.puc-rio.br=20 Sent: Friday, March 14, 2008 2:43 PM Subject: [obm-l] SigmaDelta Ol=E1 lista, pe=E7o ajuda, n=E3o achei uma sa=EDda anal=EDtica. A(n) =3D A(n-1) + ( D(n) - A(n-1) )/n onde: D(n) =3D sinal( I(n) )*R=20 e I(n) =3D I(n-1) + V - D(n-1) Mostrar que A(n) converge para V quando |V| < R Considerar:=20 A(0) =3D D(0) =3D I(0) =3D 0. n inteiro, R constante real positiva, V constante real. sinal() retorna 1 para argumento positivo, -1 para argumento negativo = e 0 para argumento nulo. Obrigado, Ojesed. ------=_NextPart_000_003C_01C88CF7.C3AFACA0 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable
Ol=E1 lista, considerando a = import=E2ncia que tem para=20 mim a resolu=E7=E3o desta quest=E3o, estou reformulando a pergunta = na esperan=E7a=20 de que alguem se interesse por ela.
 
Mostrar que a m=E9dia aritim=E9tica dos = valores gerador=20 pela sequencia: D(1), D(2)....D(n) converge para V quando R >=20 |V|
 
onde D(n) =3D R *=20 I(n) / |I(n)|,
 
e I(n) =3D I(n-1) + V - = D(n-1),
 
com: D(0) =3D I(0) =3D 0
 
R e V reais com R > 0
 
Ojesed.
 
 
 
----- Original Message -----
From:=20 Ojesed = Mirror=20
Sent: Friday, March 14, 2008 = 2:43=20 PM
Subject: [obm-l] = SigmaDelta

Ol=E1 lista, pe=E7o ajuda, n=E3o = achei uma sa=EDda=20 anal=EDtica.
 
A(n) =3D A(n-1) + ( D(n) - A(n-1) = )/n
 
onde:
 
D(n) =3D sinal( I(n) )*R =
e
I(n) =3D I(n-1) + V - = D(n-1)
 
Mostrar que A(n) converge para V = quando |V|=20 < R
 
Considerar:
A(0) =3D D(0) =3D I(0) =3D = 0.
n inteiro, R constante real positiva, = V constante=20 real.
sinal() retorna 1 para argumento = positivo, -1=20 para argumento negativo e 0 para argumento nulo.
 
 
Obrigado,=20 Ojesed.
------=_NextPart_000_003C_01C88CF7.C3AFACA0-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sun Mar 23 17:21:18 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2NKJ3WA031905 for ; Sun, 23 Mar 2008 17:19:03 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2NKJ2ro031903 for obm-l-MllGbsmmN; Sun, 23 Mar 2008 17:19:02 -0300 Received: from sc2.he.tucows.com (mail06.sc2.he.tucows.com [64.97.154.80]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2NKJ1WA031900 for ; Sun, 23 Mar 2008 17:19:01 -0300 Received: from sc2-out02.emaildefenseservice.com (64.97.201.172) by sc2.he.tucows.com (7.3.127) id 47E4D58400189CD1 for obm-l@mat.puc-rio.br; Sun, 23 Mar 2008 20:18:40 +0000 X-SpamScore: 2 X-Spamcatcher-Summary: 2,0,0,60e5e8fd28907b30,e78590c924dafc7c,cauchy@globo.com,-,RULES_HIT:355:379:541:582:988:989:1152:1260:1277:1311:1313:1314:1345:1513:1515:1516:1518:1521:1534:1536:1559:1593:1594:1711:1714:1730:1747:1766:1792:2393:2559:2562:2828:3165:3869:3876:3877:5007:6114:6312:7652:7904,0,RBL:none,CacheIP:none,Bayesian:0.5,0.5,0.5,Netcheck:none,DomainCache:0,MSF:not bulk,SPF:,MSBL:none,DNSBL:none X-Spamcatcher-Explanation: Received: from sc2.he.tucows.com (mail09.sc2.he.tucows.com [64.97.154.87]) by sc2-out02.emaildefenseservice.com (Postfix) with ESMTP for ; Sun, 23 Mar 2008 20:18:40 +0000 (UTC) Received: from [201.50.243.244] by sc2.he.tucows.com with HTTP; Sun, 23 Mar 2008 20:18:39 +0000 Date: Sun, 23 Mar 2008 17:18:39 -0300 Message-ID: <47C429A700088D75@mail09.sc2.he.tucows.com> From: cauchy@globo.com Subject: [SPAM] [obm-l] teoria dos inteiros-ajuda To: obm-l@mat.puc-rio.br MIME-Version: 1.0 Content-Type: text/plain; charset="ISO-8859-15" X-Mailer: GloboMail X-Originating-IP: 201.50.243.244 Content-Transfer-Encoding: 7bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m2NKJ2WA031901 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: cauchy@globo.com X-Spam-Status: Yes, hits=7.1 required=5.0 tests=AWL,NO_REAL_NAME,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, SPAM_PHRASE_00_01,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******* X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. 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Prove que a=0. ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sun Mar 23 17:44:01 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2NKfwWA001487 for ; Sun, 23 Mar 2008 17:41:58 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2NKfwsH001485 for obm-l-MllGbsmmN; Sun, 23 Mar 2008 17:41:58 -0300 Received: from web33703.mail.mud.yahoo.com (web33703.mail.mud.yahoo.com [68.142.201.200]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id m2NKfsWA001459 for ; Sun, 23 Mar 2008 17:41:55 -0300 Received: (qmail 40886 invoked by uid 60001); 23 Mar 2008 20:41:33 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:X-Mailer:Date:From:Subject:To:MIME-Version:Content-Type:Message-ID; b=oxGSxUQBWYNrBxRgarY6j6yGbhoUgWrWPi8ZjCuVhsJE1RmVcyOhH33ErZqJg1euEuo/ALKXAj8txzA7xq8UxtG9Hdu6qgnnw8BLWEKURKcypNCHThmeKIssb9f7GqE9ych08WklehimRDFMTIFjI4/OV4e7t+te6UhFINcEMy0=; X-YMail-OSG: 9iCEoHkVM1mvA0yitErmWTseYP.hfhdJ2EHKGa5Aj4xG31VWdbVcA9pDwvbFNWdkMpEwHrvFiNAXrlE_cQoyuxo1Rk_FBEyqFxi5ccaePlc8FboVBKs6ItUteYhsug-- Received: from [201.42.104.108] by web33703.mail.mud.yahoo.com via HTTP; Sun, 23 Mar 2008 13:41:33 PDT X-Mailer: YahooMailRC/902.38 YahooMailWebService/0.7.162 Date: Sun, 23 Mar 2008 13:41:33 -0700 (PDT) From: Eduardo Estrada Subject: [SPAM] Res: [obm-l] Probabilidades e o Primeiro Lema de Kaplansky To: obm-l@mat.puc-rio.br MIME-Version: 1.0 Content-Type: text/plain Message-ID: <353537.40862.qm@web33703.mail.mud.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Eduardo Estrada X-Spam-Status: Yes, hits=9.7 required=5.0 tests=AWL,FORGED_YAHOO_RCVD,HTML_50_70,HTML_FONT_COLOR_BLUE, RCVD_IN_DSBL,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, SPAM_PHRASE_00_01,SPAM_REDIRECTOR,SUPERLONG_LINE, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ********* X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="0-18767870-1206304893=:40862" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. 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SPAM: SPAM: Content analysis details: (9.70 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: HTML_50_70 (0.3 points) BODY: Message is 50-70% HTML tags SPAM: HTML_FONT_COLOR_BLUE (0.2 points) BODY: HTML font color is blue SPAM: SUPERLONG_LINE (0.0 points) BODY: Contains a line >=199 characters long SPAM: SPAM_REDIRECTOR (0.4 points) URI: Uses open redirection service SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_DSBL (3.2 points) RBL: Received via a relay in list.dsbl.org SPAM: [RBL check: found 108.104.42.201.list.dsbl.org] SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 200.201.142.68.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 200.201.142.68.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-1.6 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- --0-18767870-1206304893=:40862 Content-Type: text/plain; charset=utf-8 Content-Transfer-Encoding: quoted-printable Fa=C3=A7amos o seguinte, Ulysses:=0A=0AQueremos que haja pelo menos um par = de n=C3=BAmeros consecutivos sorteados. Ent=C3=A3o vamos contar os sorteios= que n=C3=A3o cont=C3=AAm n=C3=BAmeros consecutivos. Para tanto, considerem= os seq=C3=BC=C3=AAncias de 60 d=C3=ADgitos formadas por 54 0's e 6 1's, de = tal maneira que, se o i-=C3=A9simo d=C3=ADgito for 0, ent=C3=A3o o n=C3=BAm= ero i n=C3=A3o foi sorteado e, caso cotr=C3=A1rio, foi sorteado. Por exempl= o:=0A=0A000010001000.....001=0A=0ANa seq=C3=BC=C3=AAncia acima, foram sorte= ados os n=C3=BAmeros 5, 9, 60 etc., pois essas posi=C3=A7=C3=B5es s=C3=A3o = ocupadas por 1's. Assim, se imaginarmos os 54 0's emparelhados, temos:=0A= =0A_0_0_0_0_0_..._0_0_0_=0A=0AOnde os 55 tra=C3=A7os _ indicam posi=C3=A7= =C3=B5es candidatas a serem ocupadas por 6 1's, ou seja, definem os n=C3=BA= meros sorteados. Logo, podemos selecion=C3=A1-las de C(55,6) maneiras. Como= o total de sorteios =C3=A9 C(60,6), segue que a probabilidade de n=C3=A3o = haver n=C3=BAmeros consecutivos =C3=A9 C(55,6)/C(60,6). Portanto, a probabi= lidade de haver n=C3=BAmeros consecutivos =C3=A9:=0A=0A1-C(55,6)/C(60,6) qu= e, ap=C3=B3s algumas manipula=C3=A7=C3=B5es, nos leva =C3=A0 alternativa E.= =0A=0AUm abra=C3=A7o,=0AEduardo Estrada=0A=0A----- Mensagem original ----= =0ADe: Ulysses Coelho de Souza Jr. =0APara: obm-l@mat.puc= -rio.br=0AEnviadas: S=C3=A1bado, 22 de Mar=C3=A7o de 2008 20:58:56=0AAssunt= o: [obm-l] Probabilidades e o Primeiro Lema de Kaplansky=0A=0A =0AOl=C3=A1= a todos,=0A =0AA quest=C3=A3o abaixo =C3=A9 de um vestibular recente. Acre= dito =0Aque o examinador quis dizer "pelo menos um par" ao inv=C3=A9s de "u= m =0Apar".=0A =0AComent=C3=A1rios ser=C3=A3o bem-vindos. =0A =0ANo Concurso= da Mega-Sena s=C3=A3o sorteados=0A=0A=0A =0A6 n=C3=BAmeros de 01 a 60. Por= exemplo, o =0Aconcurso=0A =0A924 teve como n=C3=BAmeros =0Asorteados=0A = =0A02,20,21,27,51 e 60, ou seja, houve um par =0Ade=0A =0An=C3=BAmeros cons= ecutivos, 20 e 21. A =0Aprobabilidade=0A =0Ade que no jogo da Mega-Sena haj= a um par =0Ade=0A =0An=C3=BAmeros consecutivos sorteados =0A=C3=A9:=0A =0A = =0A =0A(A) =0A54!/60!=0A =0A(B) =0A53!/59!=0A =0A(C) =0A1-(56!55!)/(49!60!)= =0A =0A(D) =0A1-(54!53!)/(48!60!)=0A =0A(E) =0A1-(55!54!)/(49!60!)=0A =0AUm= abra=C3=A7o,=0A =0AUlysses C. de =0ASouza.=0A=0A=0A=0A=0A=0A=0A Abra = sua conta no Yahoo! Mail, o =C3=BAnico sem limite de espa=C3=A7o para armaz= enamento!=0Ahttp://br.mail.yahoo.com/ --0-18767870-1206304893=:40862 Content-Type: text/html; charset=utf-8 Content-Transfer-Encoding: quoted-printable
Fa=C3=A7amos o seguinte, Ulysses:

Queremos que = haja pelo menos um par de n=C3=BAmeros consecutivos sorteados. Ent=C3=A3o v= amos contar os sorteios que n=C3=A3o cont=C3=AAm n=C3=BAmeros consecutivos.= Para tanto, consideremos seq=C3=BC=C3=AAncias de 60 d=C3=ADgitos formadas = por 54 0's e 6 1's, de tal maneira que, se o i-=C3=A9simo d=C3=ADgito for 0= , ent=C3=A3o o n=C3=BAmero i n=C3=A3o foi sorteado e, caso cotr=C3=A1rio, f= oi sorteado. Por exemplo:

000010001000.....001

Na seq=C3=BC= =C3=AAncia acima, foram sorteados os n=C3=BAmeros 5, 9, 60 etc., pois essas= posi=C3=A7=C3=B5es s=C3=A3o ocupadas por 1's. Assim, se imaginarmos os 54 = 0's emparelhados, temos:

_0_0_0_0_0_..._0_0_0_

Onde os 55 tra= =C3=A7os _ indicam posi=C3=A7=C3=B5es candidatas a serem ocupadas por 6 1's= , ou seja, definem os n=C3=BAmeros sorteados. Logo, podemos selecion=C3=A1-las de C(55,6) maneir= as. Como o total de sorteios =C3=A9 C(60,6), segue que a probabilidade de <= span style=3D"font-weight: bold;">n=C3=A3o haver n=C3=BAmeros consec= utivos =C3=A9 C(55,6)/C(60,6). Portanto, a probabilidade de haver n=C3=BAme= ros consecutivos =C3=A9:

1-C(55,6)/C(60,6) que, ap=C3=B3s algumas ma= nipula=C3=A7=C3=B5es, nos leva =C3=A0 alternativa E.

Um abra=C3=A7o,=
Eduardo Estrada

----- Mensagem original ----
De: Ulys= ses Coelho de Souza Jr. <ucsjr@uol.com.br>
Para: obm-l@mat.puc-rio= .br
Enviadas: S=C3=A1bado, 22 de Mar=C3=A7o de 2008 20:58:56
Assunto:= [obm-l] Probabilidades e o Primeiro Lema de Kaplansky

=0A=0A =0A = =0A=0A=0A

Ol=C3=A1 a todos,=

=0A

 

=0A

A quest=C3=A3o aba= ixo =C3=A9 de um vestibular recente. Acredito =0Aque o examinador quis= dizer "pelo menos um par" ao inv=C3=A9s de "um =0Apar".

=0A

 

=0A

Coment=C3=A1rios se= r=C3=A3o bem-vindos. 

=0A

 

=0A

No Concurso da Mega-Sena s=C3=A3o sorteados= =0A=0A

=0A6 n=C3= =BAmeros de 01 a 60. Por exemplo, o =0Aconcurso=

=0A

924 teve como n=C3=BAmeros =0Asorteados

=0A

02,20,21,27,5= 1 e 60, ou seja, houve um par =0Ade

=0A

n=C3=BAmeros consecutivos, 20 e 21. A =0Aprobabilidad= e

=0A

de que no jo= go da Mega-Sena haja um par =0Ade

=0A

n=C3=BAmeros consecutivos sorteados =0A=C3=A9:

=0A

 =

=0A

= (A) =0A54!/60!=

=0A

(B) =0A53!/59!=

=0A

= (C) =0A1-(56!55!)/(49!60!)

=0A

(D) =0A1-(54!53!)/(48!60!)

=0A
(E) =0A1-(55!54!)/(= 49!60!)
=0A
 
=0A
Um abra=C3= =A7o,
=0A
 
=0A
Ulysses C. de = =0ASouza.


=0A=0A=0A =
Abra sua conta no Yahoo! Mail, o =C3=BAnico sem li= mite de espa=C3=A7o para armazenamento! =0A --0-18767870-1206304893=:40862-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sun Mar 23 19:44:06 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2NMccXm007190 for ; Sun, 23 Mar 2008 19:40:17 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2NLeicv004548 for obm-l-MllGbsmmN; Sun, 23 Mar 2008 18:40:44 -0300 Received: from sc2.he.tucows.com (mail06.sc2.he.tucows.com [64.97.154.80]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2NLebWA004469 for ; Sun, 23 Mar 2008 18:40:38 -0300 Received: from sc2-out06.emaildefenseservice.com (64.97.201.176) by sc2.he.tucows.com (7.3.127) id 47E4D5840019DA2C for obm-l@mat.puc-rio.br; Sun, 23 Mar 2008 21:40:16 +0000 X-SpamScore: 2 X-Spamcatcher-Summary: 2,0,0,0c04dd144f0def8a,e78590c924dafc7c,cauchy@globo.com,-,RULES_HIT:355:379:541:582:988:989:1152:1260:1277:1311:1313:1314:1345:1513:1515:1516:1518:1521:1534:1536:1559:1593:1594:1711:1714:1730:1747:1766:1792:2393:2559:2562:2828:3165:3869:3876:3877:5007:6114:6312:7652:7904,0,RBL:none,CacheIP:none,Bayesian:0.5,0.5,0.5,Netcheck:none,DomainCache:0,MSF:not bulk,SPF:,MSBL:none,DNSBL:none X-Spamcatcher-Explanation: Received: from sc2.he.tucows.com (mail09.sc2.he.tucows.com [64.97.154.87]) by sc2-out06.emaildefenseservice.com (Postfix) with ESMTP for ; Sun, 23 Mar 2008 21:40:16 +0000 (UTC) Received: from [201.50.243.244] by sc2.he.tucows.com with HTTP; Sun, 23 Mar 2008 21:40:15 +0000 Date: Sun, 23 Mar 2008 18:40:15 -0300 Message-ID: <47C429A700089170@mail09.sc2.he.tucows.com> From: cauchy@globo.com Subject: [SPAM] [obm-l] teoria dos inteiros-ajuda To: obm-l@mat.puc-rio.br MIME-Version: 1.0 Content-Type: text/plain; charset="ISO-8859-15" X-Mailer: GloboMail X-Originating-IP: 201.50.243.244 Content-Transfer-Encoding: 7bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m2NLefWA004526 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: cauchy@globo.com X-Spam-Status: Yes, hits=7.1 required=5.0 tests=NO_REAL_NAME,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, SPAM_PHRASE_00_01,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******* X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (7.10 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: NO_REAL_NAME (1.3 points) From: does not include a real name SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 87.154.97.64.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 87.154.97.64.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- a é inteiro, b inteiro não nulo, tais que (2^n).a + b é um quadrado perfeito para todo n natural. Prove que a=0. ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Mon Mar 24 08:43:46 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2OBg2WA005336 for ; Mon, 24 Mar 2008 08:42:02 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2OBg29A005334 for obm-l-MllGbsmmN; Mon, 24 Mar 2008 08:42:02 -0300 Received: from mail.fazenda.ms.gov.br (mail.fazenda.ms.gov.br [200.181.116.25]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2OBg0WA005330 for ; Mon, 24 Mar 2008 08:42:00 -0300 Received: by mail.fazenda.ms.gov.br (Postfix, from userid 115) id 312427B5C001; Mon, 24 Mar 2008 07:41:41 -0400 (AMT) Received: from mail.fazenda.ms.gov.br (localhost [127.0.0.1]) by mail.fazenda.ms.gov.br (Postfix) with ESMTP id 0841C58B6E5B for ; Mon, 24 Mar 2008 07:41:41 -0400 (AMT) Received: from 10.5.119.29 by mail.fazenda.ms.gov.br with HTTP; Mon, 24 Mar 2008 07:41:41 -0400 (VET) Message-ID: <1161.10.5.119.29.1206358901.squirrel@mail.fazenda.ms.gov.br> In-Reply-To: <99886d920803200945u2e477f6fu6e90547fd91446dc@mail.gmail.com> References: <99886d920803200945u2e477f6fu6e90547fd91446dc@mail.gmail.com> Date: Mon, 24 Mar 2008 07:41:41 -0400 (VET) Subject: [SPAM] Re: [obm-l] Cadastramento OBM-2008 From: jjunior@fazenda.ms.gov.br To: obm-l@mat.puc-rio.br User-Agent: Webmail MS MIME-Version: 1.0 Content-Type: text/plain;charset=iso-8859-1 Content-Transfer-Encoding: 7bit X-Priority: 3 (Normal) Importance: Normal Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: jjunior@fazenda.ms.gov.br X-Spam-Status: Yes, hits=6.2 required=5.0 tests=IN_REP_TO,MAILTO_TO_SPAM_ADDR,NO_REAL_NAME, PRIORITY_NO_NAME,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, USER_AGENT,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ****** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (6.20 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: REFERENCES (-0.5 points) Has a valid-looking References header SPAM: USER_AGENT (-0.5 points) Found a User-Agent header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: NO_REAL_NAME (1.3 points) From: does not include a real name SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: QUOTED_EMAIL_TEXT (-0.8 points) BODY: Contains what looks like a quoted email text SPAM: MAILTO_TO_SPAM_ADDR (0.7 points) URI: Includes a link to a likely spammer email address SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 25.116.181.200.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 25.116.181.200.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: PRIORITY_NO_NAME (1.0 points) Message has priority setting, but no X-Mailer SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- Obrigado, Bruno. > Joao, eu não sei responder à sua pergunta, mas posso te dizer minha > experiência: quando eu estava na 8a. série eu participei. Minha escola > não > participava, nunca teve nada com a OBM (entretanto tem bastante coisa da > OBF > la) por mais que eu insistisse. Eu me inscrevi então num curso > preparatorio > no colegio ETAPA (em Sao Paulo), e acho que eles então que cuidaram da > minha > inscrição. > > Esperto que isso ajude em algo. > > Abraço > Bruno > > 2008/3/18 : > >> Prezada Secretária da OBM, >> Demais competentes a me respoder: >> >> Caso a escola de meu filho não se cadastre, existe alguma forma >> possível >> pela qual ele possa participar? >> >> Fraternalmente, João. >> -----owner-obm-l@mat.puc-rio.br escreveu: ----- >> >> Para: aobm-l@mat.puc-rio.br, Lista de discussao >> De: Olimpiada Brasileira de Matematica >> Enviado por: owner-obm-l@mat.puc-rio.br >> Data: 17/03/2008 9:18 >> Assunto: [obm-l] Cadastramento OBM-2008 >> >> Caros sócios e amigos da OBM, >> >> Estão abertas as inscrições para participar da OBM-2008. >> Todas as escolas das redes pública e privada podem participar. >> >> Período de cadastramento: >> 15 de março até 5 de maio de 2008 >> apenas no site da OBM www.obm.org.br >> >> Importante: Nosso sistema de cadastramento mudou, por favor, se a sua >> escola >> já participou da competição em anos anteriores, também deve realizar >> o >> novo >> cadastramento em 2008. >> >> Cordialmente, >> >> Secretaria da OBM >> >> >> >> >> >> >> >> >> ========================================================================= >> Instruções para entrar na lista, sair da lista e usar a lista em >> http://www.mat.puc-rio.br/~obmlistas/obm-l.html >> ========================================================================= >> >> >> Instruções para entrar na lista, sair da lista e usar a lista em >> http://www.mat.puc-rio.br/~obmlistas/obm-l.html >> > > > > -- > Bruno FRANÇA DOS REIS > > msn: brunoreis666@hotmail.com > skype: brunoreis666 > tel: +33 (0)6 28 43 42 16 > > e^(pi*i)+1=0 > ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Mon Mar 24 10:31:50 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2ODULWA013868 for ; Mon, 24 Mar 2008 10:30:21 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2ODUKWp013866 for obm-l-MllGbsmmN; Mon, 24 Mar 2008 10:30:20 -0300 Received: from ug-out-1314.google.com (ug-out-1314.google.com [66.249.92.174]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2ODUIWA013837 for ; Mon, 24 Mar 2008 10:30:18 -0300 Received: by ug-out-1314.google.com with SMTP id q7so2101753uge.0 for ; Mon, 24 Mar 2008 06:29:58 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=RZTxQUx5+nNmScJR7in45/EUXf2Iq4UcxaSCEUNJjtw=; b=UPfz1xPavEvPKy2qPwpQqiTJ6HljwXXslpihfTxhbrGhMGM1WBuEh+1LMD9+Dg+5nqs/mtvxGy0BH9AbbJlPhgX35xwW/kK0O4Y6xfsH7LHy4VRplJBsc9RiL950MSHH/Yrz1NzzLqNSkVtIgNpIlKNzuWaT9oytOs0coDZdjbk= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=mylncBGGz14j+4ZzcKBx6yIIcOOOKx1Z+hs/ng3Qm6cB1n3SA8qkr9bVuVSuNF2KnEQISeCod0ppiyZgshuPF+hs37rUGVcRtP2AdNhiJgIYZmgOgYKvGsBZkFN8JFF22rdiPdJdEewl1IigAZs06BgcUmprvSacPDkgi4cPvUc= Received: by 10.150.216.8 with SMTP id o8mr3148706ybg.138.1206365397502; Mon, 24 Mar 2008 06:29:57 -0700 (PDT) Received: by 10.150.158.20 with HTTP; Mon, 24 Mar 2008 06:29:57 -0700 (PDT) Message-ID: <5bb472220803240629k4f430aa9v765f20fdbd0bdad2@mail.gmail.com> Date: Mon, 24 Mar 2008 10:29:57 -0300 From: "Joao Victor Brasil" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] combinatoria dificil In-Reply-To: <3e7bcb580803201443r10149ad4n4a3c3d7710b3573@mail.gmail.com> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_7455_15383257.1206365397496" References: <3e7bcb580803201443r10149ad4n4a3c3d7710b3573@mail.gmail.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Joao Victor Brasil" X-Spam-Status: No, hits=4.5 required=5.0 tests=AWL,GAPPY_TEXT,IN_REP_TO,MAILTO_LINK,MIME_EXCESSIVE_QP, QUOTED_EMAIL_TEXT,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, REFERENCES,SPAM_PHRASE_00_01,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** ------=_Part_7455_15383257.1206365397496 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline =C9 verdade pessoal. Errei e muito na minha resolu=E7=E3o. Mas olha s=F3, concordo plenamente com a resposta do Henrique, 48 possibilidades. Usando o princ=EDpio multiplicativo D1H1_D1H2_D2H1_D2H2_D3H1_D3H2 achei 72 possibilidades, me alertaram sobre as repeti=E7=F5es e analisei um modo de retir=E1-las. D1H1:3 disc D1H2: 2 disc D2H1: 2 disc (repetir as mesmas disciplinas do dia 1) D2H2: 1 disc D3H1: 2 disc (apesar de sobrar somente uma disc, temos duas aulas) D3H2: 1 disc 3*2*2*1*2*1 =3D 24. 72 - 24 =3D 48 poss. Joao Victor On 3/20/08, Henrique Renn=F3 wrote: > > Ol=E1 pessoal! > > Acredito que a solu=E7=E3o do Salhab est=E1 correta. Seja Di o dia i e Hj= o > hor=E1rio j. > > D1H1: 3 mat=E9rias > D1H2: 2 mat=E9rias (para n=E3o repetir a utilizada em D1H1) > D1: 6 possibilidades > > Para D2, se escolhermos uma j=E1 utilizada em D1 ent=E3o n=E3o poderemos > utilizar a outra mat=E9ria utilizada em D1, sen=E3o D3 teria as mesmas > mat=E9rias. Assim, para D2 ter=EDamos uma j=E1 utilizada (2 mat=E9rias) e= uma > n=E3o utilizada. Logo, 2*1 =3D 2. Como a ordem importa, temos 2*2 =3D 4. > > D3 s=F3 possui 2 formas, com as ordens das mat=E9rias trocadas. > > Total: 6*4*2 =3D 48. > > Essa =E9 uma forma mais l=F3gica de resolver o problema. Estive tentando > utilizar combinat=F3ria e tamb=E9m achei a resposta 48. > > Sejam A,B,C as mat=E9rias. Quantas permuta=E7=F5es diferentes existem ent= re > A,A,B,B,C,C? Cada posi=E7=E3o seria um hor=E1rio em um dia, ou seja, > D1H1_D1H2_D2H1_D2H2_D3H1_D3H2. Bastaria calcular o n=FAmero de > permuta=E7=F5es com repeti=E7=E3o, ou seja, 6!/(2!*2!*2!) =3D 720/8 =3D 9= 0. > > Sabemos que n=E3o podemos ter uma permuta=E7=E3o do tipo AABCBC, pois AA > representa a mesma mat=E9ria em D1H1 e D1H2. Ent=E3o sabemos que a > resposta =E9 menor que 90. > > As formas inv=E1lidas ser=E3o: > > Se as 3 mat=E9rias do mesmo tipo est=E3o juntas no mesmo dia, ex: AABBCC. > Existem 3! =3D 6 formas, considerando AA,BB,CC como 3 elementos > permutados entre si. > > N=E3o h=E1 necessidade de verificar quando 2 mat=E9rias est=E3o no mesmo = dia > pois cai no caso acima. > > Quando h=E1 apenas 1 mat=E9ria repetida em 1 dia, ex: AABCBC, ent=E3o tem= os > 12 formas para cada par da mesma mat=E9ria utilizada no mesmo dia. Se AA > est=E1 em D1 ent=E3o D2 pode ser BC ou CB e D3 pode ser BC ou CB, 2*2 =3D= 4. > AA pode estar em D1,D2,D3. Assim, 4*3 =3D 12. Para BB e CC seria o > mesmo, dando um total de 3*12 =3D 36 formas quando h=E1 apenas uma mat=E9= ria > que se repete no mesmo dia. > > Assim, o total seria 90 - (6+36) =3D 90 - 42 =3D 48 formas distintas de > compor o hor=E1rio > > Thelio, voc=EA poderia passar a fonte do problema e verificar se as > respostas s=E3o essas mesmo? > > On 3/13/08, Thelio Gama wrote: > > =C9 pessoal... > > > > Achei muito dif=EDcil esta quest=E3o. Agrade=E7o se algu=E9m puder expl= ic=E1-la. > > > > Thelio > > > > uma turma tem aulas =E0s 2=AA, 4=AA e 6=AA feiras, de 8-9 horas e de 11= -12 > horas. As > > mat=E9rias s=E3o portugues, matem=E1tica e ingles, cada uma com duas au= las > > semanais, em dias diferentes. De quantos modos pode ser feito o hor=E1r= io > > dessa turma? > > a)96 ; b) 144 ; c)192 ; d) 6! ; e) 120 > > > -- > Henrique > > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > Instru=E7=F5es para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > ------=_Part_7455_15383257.1206365397496 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline
=C9 verdade pessoal. Errei e muito na minha resolu=E7=E3o.
 
Mas olha s=F3, concordo plenamente com a resposta do Henrique, 48 poss= ibilidades.
 
Usando o princ=EDpio multiplicativo D1H1_D1H2_D2H1_D2H2_D3H1_D3H2 ache= i 72 possibilidades, me alertaram sobre as repeti=E7=F5es e analisei um mod= o de retir=E1-las.
D1H1:3 disc
D1H2: 2 disc
D2H1: 2 disc (repetir as mesmas disciplinas do dia 1)
D2H2: 1 disc
D3H1: 2 disc (apesar de sobrar somente uma disc, temos duas aulas)
D3H2: 1 disc
 
3*2*2*1*2*1 =3D 24.        &nb= sp;  72 - 24 =3D 48 poss.
 
Joao Victor

 
On 3/20/08, = Henrique Renn=F3 <henriq= ue.renno@gmail.com> wrote:
Ol=E1 pessoal!

Acredito q= ue a solu=E7=E3o do Salhab est=E1 correta. Seja Di o dia i e Hj o hor=E1rio= j.

D1H1: 3 mat=E9rias
D1H2: 2 mat=E9rias (para n=E3o repetir a utilizada em= D1H1)
D1: 6 possibilidades

Para D2, se escolhermos uma j=E1 util= izada em D1 ent=E3o n=E3o poderemos
utilizar a outra mat=E9ria utilizada= em D1, sen=E3o D3 teria as mesmas
mat=E9rias. Assim, para D2 ter=EDamos uma j=E1 utilizada (2 mat=E9rias) e u= ma
n=E3o utilizada. Logo, 2*1 =3D 2. Como a ordem importa, temos 2*2 =3D= 4.

D3 s=F3 possui 2 formas, com as ordens das mat=E9rias trocadas.<= br>
Total: 6*4*2 =3D 48.

Essa =E9 uma forma mais l=F3gica de resolver o problema. Estive tentand= o
utilizar combinat=F3ria e tamb=E9m achei a resposta 48.

Sejam A= ,B,C as mat=E9rias. Quantas permuta=E7=F5es diferentes existem entre
A,A= ,B,B,C,C? Cada posi=E7=E3o seria um hor=E1rio em um dia, ou seja,
D1H1_D1H2_D2H1_D2H2_D3H1_D3H2. Bastaria calcular o n=FAmero de
permuta= =E7=F5es com repeti=E7=E3o, ou seja, 6!/(2!*2!*2!) =3D 720/8 =3D 90.
Sabemos que n=E3o podemos ter uma permuta=E7=E3o do tipo AABCBC, pois AArepresenta a mesma mat=E9ria em D1H1 e D1H2. Ent=E3o sabemos que a
resposta =E9 menor que 90.

As formas inv=E1lidas ser=E3o:

Se = as 3 mat=E9rias do mesmo tipo est=E3o juntas no mesmo dia, ex: AABBCC.
E= xistem 3! =3D 6 formas, considerando AA,BB,CC como 3 elementos
permutado= s entre si.

N=E3o h=E1 necessidade de verificar quando 2 mat=E9rias est=E3o no mesm= o dia
pois cai no caso acima.

Quando h=E1 apenas 1 mat=E9ria repe= tida em 1 dia, ex: AABCBC, ent=E3o temos
12 formas para cada par da mesm= a mat=E9ria utilizada no mesmo dia. Se AA
est=E1 em D1 ent=E3o D2 pode ser BC ou CB e D3 pode ser BC ou CB, 2*2 =3D 4= .
AA pode estar em D1,D2,D3. Assim, 4*3 =3D 12. Para BB e CC seria o
= mesmo, dando um total de 3*12 =3D 36 formas quando h=E1 apenas uma mat=E9ri= a
que se repete no mesmo dia.

Assim, o total seria 90 - (6+36) =3D 90 - 42 =3D 48 formas distintas de=
compor o hor=E1rio

Thelio, voc=EA poderia passar a fonte do prob= lema e verificar se as
respostas s=E3o essas mesmo?

On 3/13/08, T= helio Gama <teliogama@gmail.com> wrote:
> =C9 pessoal...
>
> Achei muito dif=EDcil esta quest=E3o. A= grade=E7o se algu=E9m puder explic=E1-la.
>
> Thelio
>> uma turma tem aulas =E0s 2=AA, 4=AA e 6=AA feiras, de 8-9 horas e de = 11-12 horas. As
> mat=E9rias s=E3o portugues, matem=E1tica e ingles, cada uma com duas a= ulas
> semanais, em dias diferentes. De quantos modos pode ser feito = o hor=E1rio
> dessa turma?
> a)96  ; b) 144 &nbs= p; ; c)192   ; d) 6!    ; e) 120


--
Henrique

=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D
Instru=E7=F5es para entrar na lista, sair da li= sta e usar a lista em
http://www.mat.puc-rio.br/~obmlistas/obm-l.html
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D

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(VPS 080127-1, 27/01/2008), Outbound message X-Antivirus-Status: Clean Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Fernando" X-Spam-Status: Yes, hits=7.2 required=5.0 tests=GAPPY_TEXT,HTML_FONT_COLOR_RED,LINES_OF_YELLING, LINES_OF_YELLING_2,MAILTO_LINK,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, USER_AGENT_OE,X_MAILING_LIST,X_MSMAIL_PRIORITY_HIGH, X_OSIRU_OPEN_RELAY,X_PRIORITY_HIGH version=2.44 X-Spam-Flag: YES X-Spam-Level: ******* X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_NextPart_000_0018_01C88DAC.11B38C50" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. 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SPAM: SPAM: Content analysis details: (7.20 hits, 5 required) SPAM: REFERENCES (-0.5 points) Has a valid-looking References header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: X_PRIORITY_HIGH (0.4 points) Sent with 'X-Priority' set to high SPAM: X_MSMAIL_PRIORITY_HIGH (0.4 points) Sent with 'X-Msmail-Priority' set to high SPAM: USER_AGENT_OE (0.2 points) X-Mailer header indicates a non-spam MUA (Outlook Express) SPAM: GAPPY_TEXT (0.0 points) BODY: Contains 'G.a.p.p.y-T.e.x.t' SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: HTML_FONT_COLOR_RED (0.3 points) BODY: HTML font color is red SPAM: LINES_OF_YELLING_2 (0.2 points) BODY: 2 WHOLE LINES OF YELLING DETECTED SPAM: LINES_OF_YELLING (0.2 points) BODY: A WHOLE LINE OF YELLING DETECTED SPAM: MAILTO_LINK (0.2 points) BODY: Includes a URL link to send an email SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 174.201.97.64.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 174.201.97.64.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- This is a multi-part message in MIME format. ------=_NextPart_000_0018_01C88DAC.11B38C50 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Ol=E1 Jo=E3o Victor, boa tarde! Voc=EA possui a solu=E7=E3o do problema abaixo? Se SIM, poderia envi=E1-la para mim? Sociedade Brasileira de Matem=E1tica EUREKA! N=B014, 2002 VIII OLIMP=CDADA DE MAIO Enunciados e Resultado Brasileiro PRIMEIRO N=CDVEL 11/05/2002 PROBLEMA 1 Um grupo de homens, alguns dos quais acompanhados pelas esposas, = gastaram 1000 d=F3lares num hotel. Cada homem gastou 19 d=F3lares e cada mulher, 13 = d=F3lares. Determine quantas mulheres e quantos homens estavam no hotel. http://www.obm.org.br/eureka/eureka14.pdf acesso em 23/03/2008 Agrade=E7o sua aten=E7=E3o. Amplexo. Fernando Pinto -------------------------------------------------------------------------= ------- -------------------------------------------------------------------------= ------- ----- Original Message -----=20 From: Joao Victor Brasil=20 To: obm-l@mat.puc-rio.br=20 Sent: Monday, March 24, 2008 10:29 AM Subject: Re: [obm-l] combinatoria dificil =C9 verdade pessoal. Errei e muito na minha resolu=E7=E3o. Mas olha s=F3, concordo plenamente com a resposta do Henrique, 48 = possibilidades. Usando o princ=EDpio multiplicativo D1H1_D1H2_D2H1_D2H2_D3H1_D3H2 = achei 72 possibilidades, me alertaram sobre as repeti=E7=F5es e analisei = um modo de retir=E1-las. D1H1:3 disc D1H2: 2 disc=20 D2H1: 2 disc (repetir as mesmas disciplinas do dia 1) D2H2: 1 disc D3H1: 2 disc (apesar de sobrar somente uma disc, temos duas aulas) D3H2: 1 disc 3*2*2*1*2*1 =3D 24. 72 - 24 =3D 48 poss. Joao Victor =20 On 3/20/08, Henrique Renn=F3 wrote:=20 Ol=E1 pessoal! Acredito que a solu=E7=E3o do Salhab est=E1 correta. Seja Di o dia i = e Hj o hor=E1rio j. D1H1: 3 mat=E9rias D1H2: 2 mat=E9rias (para n=E3o repetir a utilizada em D1H1) D1: 6 possibilidades Para D2, se escolhermos uma j=E1 utilizada em D1 ent=E3o n=E3o = poderemos utilizar a outra mat=E9ria utilizada em D1, sen=E3o D3 teria as = mesmas mat=E9rias. Assim, para D2 ter=EDamos uma j=E1 utilizada (2 = mat=E9rias) e uma n=E3o utilizada. Logo, 2*1 =3D 2. Como a ordem importa, temos 2*2 = =3D 4. D3 s=F3 possui 2 formas, com as ordens das mat=E9rias trocadas. Total: 6*4*2 =3D 48. Essa =E9 uma forma mais l=F3gica de resolver o problema. Estive = tentando utilizar combinat=F3ria e tamb=E9m achei a resposta 48. Sejam A,B,C as mat=E9rias. Quantas permuta=E7=F5es diferentes = existem entre A,A,B,B,C,C? Cada posi=E7=E3o seria um hor=E1rio em um dia, ou seja, D1H1_D1H2_D2H1_D2H2_D3H1_D3H2. Bastaria calcular o n=FAmero de permuta=E7=F5es com repeti=E7=E3o, ou seja, 6!/(2!*2!*2!) =3D 720/8 = =3D 90. Sabemos que n=E3o podemos ter uma permuta=E7=E3o do tipo AABCBC, = pois AA representa a mesma mat=E9ria em D1H1 e D1H2. Ent=E3o sabemos que a resposta =E9 menor que 90. As formas inv=E1lidas ser=E3o: Se as 3 mat=E9rias do mesmo tipo est=E3o juntas no mesmo dia, ex: = AABBCC. Existem 3! =3D 6 formas, considerando AA,BB,CC como 3 elementos permutados entre si. N=E3o h=E1 necessidade de verificar quando 2 mat=E9rias est=E3o no = mesmo dia pois cai no caso acima. Quando h=E1 apenas 1 mat=E9ria repetida em 1 dia, ex: AABCBC, = ent=E3o temos 12 formas para cada par da mesma mat=E9ria utilizada no mesmo dia. = Se AA est=E1 em D1 ent=E3o D2 pode ser BC ou CB e D3 pode ser BC ou CB, = 2*2 =3D 4. AA pode estar em D1,D2,D3. Assim, 4*3 =3D 12. Para BB e CC seria o mesmo, dando um total de 3*12 =3D 36 formas quando h=E1 apenas uma = mat=E9ria que se repete no mesmo dia. Assim, o total seria 90 - (6+36) =3D 90 - 42 =3D 48 formas distintas = de compor o hor=E1rio Thelio, voc=EA poderia passar a fonte do problema e verificar se as respostas s=E3o essas mesmo? On 3/13/08, Thelio Gama wrote: > =C9 pessoal... > > Achei muito dif=EDcil esta quest=E3o. Agrade=E7o se algu=E9m puder = explic=E1-la. > > Thelio > > uma turma tem aulas =E0s 2=AA, 4=AA e 6=AA feiras, de 8-9 horas e = de 11-12 horas. As > mat=E9rias s=E3o portugues, matem=E1tica e ingles, cada uma com = duas aulas > semanais, em dias diferentes. De quantos modos pode ser feito o = hor=E1rio > dessa turma? > a)96 ; b) 144 ; c)192 ; d) 6! ; e) 120 -- Henrique = =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D Instru=E7=F5es para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html = =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D ------=_NextPart_000_0018_01C88DAC.11B38C50 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable
Ol=E1 Jo=E3o Victor, boa = tarde!
 
Voc=EA possui a solu=E7=E3o do problema = abaixo?
Se SIM, poderia envi=E1-la para = mim?
 

Sociedade Brasileira de Matem=E1tica

EUREKA! N=B014, = 2002

VIII OLIMP=CDADA DE=20 MAIO

Enunciados e Resultado=20 Brasileiro

PRIMEIRO N=CDVEL

11/05/2002

PROBLEMA 1

Um grupo de homens, alguns dos quais = acompanhados=20 pelas esposas, gastaram 1000

d=F3lares num hotel. Cada homem gastou = 19 d=F3lares e=20 cada mulher, 13 d=F3lares.

Determine quantas mulheres e quantos = homens=20 estavam no hotel.

 

http://www.obm.org.br/eureka/eureka14.pdf

acesso em=20 23/03/2008

 
 
Agrade=E7o sua = aten=E7=E3o.
 
Amplexo.
Fernando Pinto
 
----- Original Message -----
From:=20 Joao = Victor=20 Brasil
Sent: Monday, March 24, 2008 = 10:29=20 AM
Subject: Re: [obm-l] = combinatoria=20 dificil

=C9 verdade pessoal. Errei e muito na minha resolu=E7=E3o.
 
Mas olha s=F3, concordo plenamente com a resposta do Henrique, 48 = possibilidades.
 
Usando o princ=EDpio multiplicativo D1H1_D1H2_D2H1_D2H2_D3H1_D3H2 = achei 72=20 possibilidades, me alertaram sobre as repeti=E7=F5es e analisei um = modo de=20 retir=E1-las.
D1H1:3 disc
D1H2: 2 disc
D2H1: 2 disc (repetir as mesmas disciplinas do dia 1)
D2H2: 1 disc
D3H1: 2 disc (apesar de sobrar somente uma disc, temos duas = aulas)
D3H2: 1 disc
 
3*2*2*1*2*1 =3D=20 24.           72 - = 24 =3D 48=20 poss.
 
Joao Victor

 
On 3/20/08, Henrique=20 Renn=F3 <henrique.renno@gmail.com>= =20 wrote:=20
Ol=E1=20 pessoal!

Acredito que a solu=E7=E3o do Salhab est=E1 correta. = Seja Di o dia=20 i e Hj o hor=E1rio j.

D1H1: 3 mat=E9rias
D1H2: 2 = mat=E9rias (para n=E3o=20 repetir a utilizada em D1H1)
D1: 6 possibilidades

Para D2, = se=20 escolhermos uma j=E1 utilizada em D1 ent=E3o n=E3o = poderemos
utilizar a outra=20 mat=E9ria utilizada em D1, sen=E3o D3 teria as mesmas
mat=E9rias. = Assim, para=20 D2 ter=EDamos uma j=E1 utilizada (2 mat=E9rias) e uma
n=E3o = utilizada. Logo, 2*1=20 =3D 2. Como a ordem importa, temos 2*2 =3D 4.

D3 s=F3 possui = 2 formas, com=20 as ordens das mat=E9rias trocadas.

Total: 6*4*2 =3D = 48.

Essa =E9 uma=20 forma mais l=F3gica de resolver o problema. Estive = tentando
utilizar=20 combinat=F3ria e tamb=E9m achei a resposta 48.

Sejam A,B,C as = mat=E9rias.=20 Quantas permuta=E7=F5es diferentes existem entre
A,A,B,B,C,C? = Cada posi=E7=E3o=20 seria um hor=E1rio em um dia, ou = seja,
D1H1_D1H2_D2H1_D2H2_D3H1_D3H2.=20 Bastaria calcular o n=FAmero de
permuta=E7=F5es com = repeti=E7=E3o, ou seja,=20 6!/(2!*2!*2!) =3D 720/8 =3D 90.

Sabemos que n=E3o podemos ter = uma=20 permuta=E7=E3o do tipo AABCBC, pois AA
representa a mesma = mat=E9ria em D1H1 e=20 D1H2. Ent=E3o sabemos que a
resposta =E9 menor que 90.

As = formas=20 inv=E1lidas ser=E3o:

Se as 3 mat=E9rias do mesmo tipo est=E3o = juntas no mesmo=20 dia, ex: AABBCC.
Existem 3! =3D 6 formas, considerando AA,BB,CC = como 3=20 elementos
permutados entre si.

N=E3o h=E1 necessidade de = verificar=20 quando 2 mat=E9rias est=E3o no mesmo dia
pois cai no caso=20 acima.

Quando h=E1 apenas 1 mat=E9ria repetida em 1 dia, ex: = AABCBC,=20 ent=E3o temos
12 formas para cada par da mesma mat=E9ria = utilizada no mesmo=20 dia. Se AA
est=E1 em D1 ent=E3o D2 pode ser BC ou CB e D3 pode = ser BC ou CB,=20 2*2 =3D 4.
AA pode estar em D1,D2,D3. Assim, 4*3 =3D 12. Para BB = e CC seria=20 o
mesmo, dando um total de 3*12 =3D 36 formas quando h=E1 apenas = uma=20 mat=E9ria
que se repete no mesmo dia.

Assim, o total seria = 90 -=20 (6+36) =3D 90 - 42 =3D 48 formas distintas de
compor o = hor=E1rio

Thelio,=20 voc=EA poderia passar a fonte do problema e verificar se = as
respostas s=E3o=20 essas mesmo?

On 3/13/08, Thelio Gama <teliogama@gmail.com> = wrote:
>=20 =C9 pessoal...
>
> Achei muito dif=EDcil esta quest=E3o. = Agrade=E7o se=20 algu=E9m puder explic=E1-la.
>
> Thelio
>
> = uma turma=20 tem aulas =E0s 2=AA, 4=AA e 6=AA feiras, de 8-9 horas e de 11-12 = horas. As
>=20 mat=E9rias s=E3o portugues, matem=E1tica e ingles, cada uma com duas = aulas
>=20 semanais, em dias diferentes. De quantos modos pode ser feito o=20 hor=E1rio
> dessa turma?
> a)96  ; b) = 144   ;=20 c)192   ; d) 6!    ; e)=20 = 120


--
Henrique

=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D
Instru=E7=F5es=20 para entrar na lista, sair da lista e usar a lista em
http://www.mat.p= uc-rio.br/~obmlistas/obm-l.html
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D

= ------=_NextPart_000_0018_01C88DAC.11B38C50-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Mon Mar 24 13:10:09 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2OG93WA031309 for ; Mon, 24 Mar 2008 13:09:03 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2OG922R031306 for obm-l-MllGbsmmN; Mon, 24 Mar 2008 13:09:02 -0300 Received: from ti-out-0910.google.com (ti-out-0910.google.com [209.85.142.189]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2OG8vWA031245 for ; Mon, 24 Mar 2008 13:08:58 -0300 Received: by ti-out-0910.google.com with SMTP id y6so742827tia.13 for ; Mon, 24 Mar 2008 09:08:37 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=qJ8eHznPhd8UHBO1LcxSZ5uQjUUTO32JiC3V0E4uZaM=; b=MVFiPbZq5XNM18GfKE1x4ZSrYT0zoyVk7NpgWFGCTvobdp7YL8YoIkGklx8mJnvX9YdKpfHqSPp3mQUFJvhiqgZsomBHXNcSygBHWupgc+Kb2rbrMKibDydqnkJ7Th2s14KGdsi4Qx3zFrJURrjbjJtvENuriK5UjzqGhwlEqk4= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=K9vbmhtZ77ntMrHJvG8FslfUA9LNaEVLDwu+OPlep+GJ+5C7S5T6k9UZeOIwztyeHVFjYwLrbqT2sEyZ7lqh97KuzmRMCBga/VqyQnnAVwQRzOIWg8iAYsDlYuudjp3LP9csNYMNHP2pk/U6v9sIYOMBoFXblacC/TyxLxKHVXw= Received: by 10.150.123.16 with SMTP id v16mr3252395ybc.156.1206374915608; Mon, 24 Mar 2008 09:08:35 -0700 (PDT) Received: by 10.150.158.20 with HTTP; Mon, 24 Mar 2008 09:08:35 -0700 (PDT) Message-ID: <5bb472220803240908y48701b01y7b8cfeae9d66eeed@mail.gmail.com> Date: Mon, 24 Mar 2008 13:08:35 -0300 From: "Joao Victor Brasil" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] combinatoria dificil In-Reply-To: <001b01c88dc5$3863fdd0$d400a8c0@AMD> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_7832_6124383.1206374915598" References: <3e7bcb580803201443r10149ad4n4a3c3d7710b3573@mail.gmail.com> <5bb472220803240629k4f430aa9v765f20fdbd0bdad2@mail.gmail.com> <001b01c88dc5$3863fdd0$d400a8c0@AMD> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Joao Victor Brasil" X-Spam-Status: No, hits=4.4 required=5.0 tests=AWL,GAPPY_TEXT,HTML_FONT_COLOR_RED,IN_REP_TO, JAVASCRIPT_UNSAFE,LINES_OF_YELLING,MAILTO_LINK, QUOTED_EMAIL_TEXT,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, REFERENCES,SPAM_PHRASE_00_01,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** ------=_Part_7832_6124383.1206374915598 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Fernando, Infelizmente n=E3o tenho, mas tenta ver algo nesse sentido: 19H + 13M =3D 1000, H=3D Homem e M=3DMulher Joao Victor On 3/24/08, Fernando wrote: > > Ol=E1 Jo=E3o Victor, boa tarde! > > Voc=EA possui a solu=E7=E3o do problema abaixo? > Se SIM, poderia envi=E1-la para mim? > > * > > Sociedade Brasileira de Matem=E1tica > > EUREKA! N=B014, 2002 > * > > *VIII OLIMP=CDADA DE MAIO* > * > > Enunciados e Resultado Brasileiro > * > > *PRIMEIRO N=CDVEL* > > *11/05/2002* > > *PROBLEMA 1* > > *Um grupo de homens, alguns dos quais acompanhados pelas esposas, gastara= m > 1000* > > *d=F3lares num hotel. Cada homem gastou 19 d=F3lares e cada mulher, 13 > d=F3lares.* > > *Determine quantas mulheres e quantos homens estavam no hotel.* > > ** > > *http://www.obm.org.br/eureka/eureka14.pdf* > > *acesso em 23/03/2008* > ** > > Agrade=E7o sua aten=E7=E3o. > > Amplexo. > Fernando Pinto > > ------------------------------ > ------------------------------ > > ----- Original Message ----- > *From:* Joao Victor Brasil > *To:* obm-l@mat.puc-rio.br > *Sent:* Monday, March 24, 2008 10:29 AM > *Subject:* Re: [obm-l] combinatoria dificil > > > =C9 verdade pessoal. Errei e muito na minha resolu=E7=E3o. > > Mas olha s=F3, concordo plenamente com a resposta do Henrique, 48 > possibilidades. > > Usando o princ=EDpio multiplicativo D1H1_D1H2_D2H1_D2H2_D3H1_D3H2 achei 7= 2 > possibilidades, me alertaram sobre as repeti=E7=F5es e analisei um modo d= e > retir=E1-las. > D1H1:3 disc > D1H2: 2 disc > D2H1: 2 disc (repetir as mesmas disciplinas do dia 1) > D2H2: 1 disc > D3H1: 2 disc (apesar de sobrar somente uma disc, temos duas aulas) > D3H2: 1 disc > > 3*2*2*1*2*1 =3D 24. 72 - 24 =3D 48 poss. > > Joao Victor > > > On 3/20/08, Henrique Renn=F3 wrote: > > > > Ol=E1 pessoal! > > > > Acredito que a solu=E7=E3o do Salhab est=E1 correta. Seja Di o dia i e = Hj o > > hor=E1rio j. > > > > D1H1: 3 mat=E9rias > > D1H2: 2 mat=E9rias (para n=E3o repetir a utilizada em D1H1) > > D1: 6 possibilidades > > > > Para D2, se escolhermos uma j=E1 utilizada em D1 ent=E3o n=E3o poderemo= s > > utilizar a outra mat=E9ria utilizada em D1, sen=E3o D3 teria as mesmas > > mat=E9rias. Assim, para D2 ter=EDamos uma j=E1 utilizada (2 mat=E9rias)= e uma > > n=E3o utilizada. Logo, 2*1 =3D 2. Como a ordem importa, temos 2*2 =3D 4= . > > > > D3 s=F3 possui 2 formas, com as ordens das mat=E9rias trocadas. > > > > Total: 6*4*2 =3D 48. > > > > Essa =E9 uma forma mais l=F3gica de resolver o problema. Estive tentand= o > > utilizar combinat=F3ria e tamb=E9m achei a resposta 48. > > > > Sejam A,B,C as mat=E9rias. Quantas permuta=E7=F5es diferentes existem e= ntre > > A,A,B,B,C,C? Cada posi=E7=E3o seria um hor=E1rio em um dia, ou seja, > > D1H1_D1H2_D2H1_D2H2_D3H1_D3H2. Bastaria calcular o n=FAmero de > > permuta=E7=F5es com repeti=E7=E3o, ou seja, 6!/(2!*2!*2!) =3D 720/8 =3D= 90. > > > > Sabemos que n=E3o podemos ter uma permuta=E7=E3o do tipo AABCBC, pois A= A > > representa a mesma mat=E9ria em D1H1 e D1H2. Ent=E3o sabemos que a > > resposta =E9 menor que 90. > > > > As formas inv=E1lidas ser=E3o: > > > > Se as 3 mat=E9rias do mesmo tipo est=E3o juntas no mesmo dia, ex: AABBC= C. > > Existem 3! =3D 6 formas, considerando AA,BB,CC como 3 elementos > > permutados entre si. > > > > N=E3o h=E1 necessidade de verificar quando 2 mat=E9rias est=E3o no mesm= o dia > > pois cai no caso acima. > > > > Quando h=E1 apenas 1 mat=E9ria repetida em 1 dia, ex: AABCBC, ent=E3o t= emos > > 12 formas para cada par da mesma mat=E9ria utilizada no mesmo dia. Se A= A > > est=E1 em D1 ent=E3o D2 pode ser BC ou CB e D3 pode ser BC ou CB, 2*2 = =3D 4. > > AA pode estar em D1,D2,D3. Assim, 4*3 =3D 12. Para BB e CC seria o > > mesmo, dando um total de 3*12 =3D 36 formas quando h=E1 apenas uma mat= =E9ria > > que se repete no mesmo dia. > > > > Assim, o total seria 90 - (6+36) =3D 90 - 42 =3D 48 formas distintas de > > compor o hor=E1rio > > > > Thelio, voc=EA poderia passar a fonte do problema e verificar se as > > respostas s=E3o essas mesmo? > > > > On 3/13/08, Thelio Gama wrote: > > > =C9 pessoal... > > > > > > Achei muito dif=EDcil esta quest=E3o. Agrade=E7o se algu=E9m puder ex= plic=E1-la. > > > > > > Thelio > > > > > > uma turma tem aulas =E0s 2=AA, 4=AA e 6=AA feiras, de 8-9 horas e de = 11-12 > > horas. As > > > mat=E9rias s=E3o portugues, matem=E1tica e ingles, cada uma com duas = aulas > > > semanais, em dias diferentes. De quantos modos pode ser feito o > > hor=E1rio > > > dessa turma? > > > a)96 ; b) 144 ; c)192 ; d) 6! ; e) 120 > > > > > > -- > > Henrique > > > > > > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > > Instru=E7=F5es para entrar na lista, sair da lista e usar a lista em > > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > > > > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > > > > ------=_Part_7832_6124383.1206374915598 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline
Fernando,
 
Infelizmente n=E3o tenho, mas tenta ver algo nesse sentido:
19H + 13M =3D 1000, H=3D Homem  e M=3DMulher
 
Joao Victor

 
On 3/24/08, = Fernando <artesmatemati= ca@globo.com> wrote:
Ol=E1 Jo=E3o Victor, boa tarde!=
 
Voc=EA possui a solu=E7=E3o do problem= a abaixo?
Se SIM, poderia envi=E1-la para mim?
 

Sociedade Brasileira de Matem=E1tica

EUREKA! N=B014, 2002

=

VIII OLIMP=CDADA DE MAIO=

Enunciados e Resultado Brasileiro

PRIMEIRO N=CDVEL

11/05/2002

PROBLEMA 1

Um grupo de homens, alguns dos quais aco= mpanhados pelas esposas, gastaram 1000

d=F3lares num hotel. Cada homem gastou 1= 9 d=F3lares e cada mulher, 13 d=F3lares.

Determine quantas mulheres e quantos hom= ens estavam no hotel.

 

http://www.obm.org.br/eureka/eureka14.pdf=

acesso em 23/03/2008

=
 
 
Agrade=E7o sua aten=E7=E3o.
 
Amplexo.
Fernando Pinto
 
----- Original Message -----
Sent: Monday, March 24, 2008 10:29 A= M
Subject: Re: [obm-l] combinatoria di= ficil

 
=C9 verdade pessoal. Errei e muito na minha resolu=E7=E3o.
 
Mas olha s=F3, concordo plenamente com a resposta do Henrique, 48 poss= ibilidades.
 
Usando o princ=EDpio multiplicativo D1H1_D1H2_D2H1_D2H2_D3H1_D3H2 ache= i 72 possibilidades, me alertaram sobre as repeti=E7=F5es e analisei um mod= o de retir=E1-las.
D1H1:3 disc
D1H2: 2 disc
D2H1: 2 disc (repetir as mesmas disciplinas do dia 1)
D2H2: 1 disc
D3H1: 2 disc (apesar de sobrar somente uma disc, temos duas aulas)
D3H2: 1 disc
 
3*2*2*1*2*1 =3D 24.        &nb= sp;  72 - 24 =3D 48 poss.
 
Joao Victor

 
On 3/20/08, = Henrique Renn=F3 <henriq= ue.renno@gmail.com> wrote:=20
Ol=E1 pessoal!

Acredito q= ue a solu=E7=E3o do Salhab est=E1 correta. Seja Di o dia i e Hj o hor=E1rio= j.

D1H1: 3 mat=E9rias
D1H2: 2 mat=E9rias (para n=E3o repetir a utilizada em= D1H1)
D1: 6 possibilidades

Para D2, se escolhermos uma j=E1 util= izada em D1 ent=E3o n=E3o poderemos
utilizar a outra mat=E9ria utilizada= em D1, sen=E3o D3 teria as mesmas
mat=E9rias. Assim, para D2 ter=EDamos uma j=E1 utilizada (2 mat=E9rias) e u= ma
n=E3o utilizada. Logo, 2*1 =3D 2. Como a ordem importa, temos 2*2 =3D= 4.

D3 s=F3 possui 2 formas, com as ordens das mat=E9rias trocadas.<= br>
Total: 6*4*2 =3D 48.

Essa =E9 uma forma mais l=F3gica de resolver o problema. Estive tentand= o
utilizar combinat=F3ria e tamb=E9m achei a resposta 48.

Sejam A= ,B,C as mat=E9rias. Quantas permuta=E7=F5es diferentes existem entre
A,A= ,B,B,C,C? Cada posi=E7=E3o seria um hor=E1rio em um dia, ou seja,
D1H1_D1H2_D2H1_D2H2_D3H1_D3H2. Bastaria calcular o n=FAmero de
permuta= =E7=F5es com repeti=E7=E3o, ou seja, 6!/(2!*2!*2!) =3D 720/8 =3D 90.
Sabemos que n=E3o podemos ter uma permuta=E7=E3o do tipo AABCBC, pois AArepresenta a mesma mat=E9ria em D1H1 e D1H2. Ent=E3o sabemos que a
resposta =E9 menor que 90.

As formas inv=E1lidas ser=E3o:

Se = as 3 mat=E9rias do mesmo tipo est=E3o juntas no mesmo dia, ex: AABBCC.
E= xistem 3! =3D 6 formas, considerando AA,BB,CC como 3 elementos
permutado= s entre si.

N=E3o h=E1 necessidade de verificar quando 2 mat=E9rias est=E3o no mesm= o dia
pois cai no caso acima.

Quando h=E1 apenas 1 mat=E9ria repe= tida em 1 dia, ex: AABCBC, ent=E3o temos
12 formas para cada par da mesm= a mat=E9ria utilizada no mesmo dia. Se AA
est=E1 em D1 ent=E3o D2 pode ser BC ou CB e D3 pode ser BC ou CB, 2*2 =3D 4= .
AA pode estar em D1,D2,D3. Assim, 4*3 =3D 12. Para BB e CC seria o
= mesmo, dando um total de 3*12 =3D 36 formas quando h=E1 apenas uma mat=E9ri= a
que se repete no mesmo dia.

Assim, o total seria 90 - (6+36) =3D 90 - 42 =3D 48 formas distintas de=
compor o hor=E1rio

Thelio, voc=EA poderia passar a fonte do prob= lema e verificar se as
respostas s=E3o essas mesmo?

On 3/13/08, T= helio Gama <teliogama@gmail.com> wrote:
> =C9 pessoal...
>
> Achei muito dif=EDcil esta quest=E3o. A= grade=E7o se algu=E9m puder explic=E1-la.
>
> Thelio
>> uma turma tem aulas =E0s 2=AA, 4=AA e 6=AA feiras, de 8-9 horas e de = 11-12 horas. As
> mat=E9rias s=E3o portugues, matem=E1tica e ingles, cada uma com duas a= ulas
> semanais, em dias diferentes. De quantos modos pode ser feito = o hor=E1rio
> dessa turma?
> a)96  ; b) 144 &nbs= p; ; c)192   ; d) 6!    ; e) 120


--
Henrique

=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D
Instru=E7=F5es para entrar na lista, sair da li= sta e usar a lista em
http://www.mat.puc-rio.br/~obmlistas/obm-l.html
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D

------=_Part_7832_6124383.1206374915598-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Mon Mar 24 13:48:42 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2OGlNWA008110 for ; Mon, 24 Mar 2008 13:47:23 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2OGlNcx008108 for obm-l-MllGbsmmN; Mon, 24 Mar 2008 13:47:23 -0300 Received: from sc2.he.tucows.com (smtpout2063.sc2.he.tucows.com [64.97.155.63]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2OGlJWA008104 for ; Mon, 24 Mar 2008 13:47:19 -0300 Received: from sc2-out03.emaildefenseservice.com (64.97.201.173) by sc2.he.tucows.com (7.3.127) id 47E4F0770024147C for obm-l@mat.puc-rio.br; Mon, 24 Mar 2008 16:46:59 +0000 X-SpamScore: 11 X-Spamcatcher-Summary: 11,1.093,0,3f1f555302858465,7341d1585440b999,artesmatematica@globo.com,-,RULES_HIT:69:125:327:355:379:476:539:540:541:542:543:547:567:599:600:960:962:967:973:978:979:980:983:988:989:1155:1156:1189:1208:1212:1221:1260:1308:1309:1313:1314:1345:1394:1395:1431:1436:1437:1515:1516:1517:1521:1575:1587:1588:1589:1592:1594:1605:1617:1685:1730:1776:1792:2068:2069:2073:2075:2078:2198:2199:2525:2534:2551:2552:2553:2566:2636:2682:2685:2857:2859:2933:2937:2939:2942:2945: 2947:2951:2954:3022:3027:3362:3521:3522:3523:3586:3635:3636:3657:3769:3770:3862:3867:3869:3934:3936:3938:3941:3944:4250:4321:4383:4605:4622:5007:6117:6119:7514:7576:7679:7809:7875,0,RBL:none,CacheIP:none,Bayesian:0.5,0.5,0.5,Netcheck:none,DomainCache:0,MSF:not bulk,SPF:,MSBL:none,DNSBL:none X-Spamcatcher-Explanation: (100%) SPAM TRICK: contains gapped text; Received: from AMD (bhe200150043171.res-com.wayinternet.com.br [200.150.43.171]) (Authenticated sender: artesmatematica@globo.com) by sc2-out03.emaildefenseservice.com (Postfix) with ESMTP for ; Mon, 24 Mar 2008 16:46:57 +0000 (UTC) Message-ID: <000b01c88dce$d8e27bc0$d400a8c0@AMD> From: "Fernando" To: References: <3e7bcb580803201443r10149ad4n4a3c3d7710b3573@mail.gmail.com> <5bb472220803240629k4f430aa9v765f20fdbd0bdad2@mail.gmail.com> <001b01c88dc5$3863fdd0$d400a8c0@AMD> <5bb472220803240908y48701b01y7b8cfeae9d66eeed@mail.gmail.com> Subject: [SPAM] Re: [obm-l] combinatoria dificil Date: Mon, 24 Mar 2008 13:48:06 -0300 MIME-Version: 1.0 Content-Type: text/plain X-Priority: 1 X-MSMail-Priority: High X-Mailer: Microsoft Outlook Express 6.00.2900.2869 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.2869 X-Antivirus: avast! (VPS 080127-1, 27/01/2008), Outbound message X-Antivirus-Status: Clean Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Fernando" X-Spam-Status: Yes, hits=7.2 required=5.0 tests=AWL,GAPPY_TEXT,HTML_FONT_COLOR_RED,JAVASCRIPT_UNSAFE, LINES_OF_YELLING,MAILTO_LINK,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, SUPERLONG_LINE,USER_AGENT_OE,X_MAILING_LIST, X_MSMAIL_PRIORITY_HIGH,X_OSIRU_OPEN_RELAY,X_PRIORITY_HIGH version=2.44 X-Spam-Flag: YES X-Spam-Level: ******* X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_NextPart_000_0008_01C88DB5.B07B5990" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. 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SPAM: SPAM: Content analysis details: (7.20 hits, 5 required) SPAM: REFERENCES (-0.5 points) Has a valid-looking References header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: X_PRIORITY_HIGH (0.4 points) Sent with 'X-Priority' set to high SPAM: X_MSMAIL_PRIORITY_HIGH (0.4 points) Sent with 'X-Msmail-Priority' set to high SPAM: USER_AGENT_OE (0.2 points) X-Mailer header indicates a non-spam MUA (Outlook Express) SPAM: GAPPY_TEXT (0.0 points) BODY: Contains 'G.a.p.p.y-T.e.x.t' SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: HTML_FONT_COLOR_RED (0.3 points) BODY: HTML font color is red SPAM: LINES_OF_YELLING (0.2 points) BODY: A WHOLE LINE OF YELLING DETECTED SPAM: JAVASCRIPT_UNSAFE (0.3 points) BODY: Easily-executed JavaScript code SPAM: MAILTO_LINK (0.2 points) BODY: Includes a URL link to send an email SPAM: SUPERLONG_LINE (0.0 points) BODY: Contains a line >=199 characters long SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 173.201.97.64.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 173.201.97.64.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-0.1 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- This is a multi-part message in MIME format. ------=_NextPart_000_0008_01C88DB5.B07B5990 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Oi Jo=E3o Victor, a quest=E3o =E9 que eu j=E1 havia escrito esta = equa=E7=E3o. Acontece que ela =E9 "diofantina", admitindo infinitas = solu=E7=F5es. Claro que, de acordo com as condi=E7=F5es do exerc=EDcio = proposto deve-se conseguir restringir a quantidade delas para um = n=FAmero bem menos (eu creio). Amplexo. Fernando -------------------------------------------------------------------------= ------- -------------------------------------------------------------------------= ------- ----- Original Message -----=20 From: Joao Victor Brasil=20 To: obm-l@mat.puc-rio.br=20 Sent: Monday, March 24, 2008 1:08 PM Subject: Re: [obm-l] combinatoria dificil Fernando, Infelizmente n=E3o tenho, mas tenta ver algo nesse sentido: 19H + 13M =3D 1000, H=3D Homem e M=3DMulher Joao Victor =20 On 3/24/08, Fernando wrote:=20 Ol=E1 Jo=E3o Victor, boa tarde! Voc=EA possui a solu=E7=E3o do problema abaixo? Se SIM, poderia envi=E1-la para mim? Sociedade Brasileira de Matem=E1tica EUREKA! N=B014, 2002 VIII OLIMP=CDADA DE MAIO Enunciados e Resultado Brasileiro PRIMEIRO N=CDVEL 11/05/2002 PROBLEMA 1 Um grupo de homens, alguns dos quais acompanhados pelas esposas, = gastaram 1000 d=F3lares num hotel. Cada homem gastou 19 d=F3lares e cada mulher, = 13 d=F3lares. Determine quantas mulheres e quantos homens estavam no hotel. http://www.obm.org.br/eureka/eureka14.pdf acesso em 23/03/2008 Agrade=E7o sua aten=E7=E3o. Amplexo. Fernando Pinto -------------------------------------------------------------------------= --- -------------------------------------------------------------------------= --- ----- Original Message -----=20 From: Joao Victor Brasil=20 To: obm-l@mat.puc-rio.br=20 Sent: Monday, March 24, 2008 10:29 AM Subject: Re: [obm-l] combinatoria dificil =20 =C9 verdade pessoal. Errei e muito na minha resolu=E7=E3o. Mas olha s=F3, concordo plenamente com a resposta do Henrique, 48 = possibilidades. Usando o princ=EDpio multiplicativo D1H1_D1H2_D2H1_D2H2_D3H1_D3H2 = achei 72 possibilidades, me alertaram sobre as repeti=E7=F5es e analisei = um modo de retir=E1-las. D1H1:3 disc D1H2: 2 disc=20 D2H1: 2 disc (repetir as mesmas disciplinas do dia 1) D2H2: 1 disc D3H1: 2 disc (apesar de sobrar somente uma disc, temos duas aulas) D3H2: 1 disc 3*2*2*1*2*1 =3D 24. 72 - 24 =3D 48 poss. Joao Victor =20 On 3/20/08, Henrique Renn=F3 wrote:=20 Ol=E1 pessoal! Acredito que a solu=E7=E3o do Salhab est=E1 correta. Seja Di o = dia i e Hj o hor=E1rio j. D1H1: 3 mat=E9rias D1H2: 2 mat=E9rias (para n=E3o repetir a utilizada em D1H1) D1: 6 possibilidades Para D2, se escolhermos uma j=E1 utilizada em D1 ent=E3o n=E3o = poderemos utilizar a outra mat=E9ria utilizada em D1, sen=E3o D3 teria as = mesmas mat=E9rias. Assim, para D2 ter=EDamos uma j=E1 utilizada (2 = mat=E9rias) e uma n=E3o utilizada. Logo, 2*1 =3D 2. Como a ordem importa, temos = 2*2 =3D 4. D3 s=F3 possui 2 formas, com as ordens das mat=E9rias trocadas. Total: 6*4*2 =3D 48. Essa =E9 uma forma mais l=F3gica de resolver o problema. Estive = tentando utilizar combinat=F3ria e tamb=E9m achei a resposta 48. Sejam A,B,C as mat=E9rias. Quantas permuta=E7=F5es diferentes = existem entre A,A,B,B,C,C? Cada posi=E7=E3o seria um hor=E1rio em um dia, ou = seja, D1H1_D1H2_D2H1_D2H2_D3H1_D3H2. Bastaria calcular o n=FAmero de permuta=E7=F5es com repeti=E7=E3o, ou seja, 6!/(2!*2!*2!) =3D = 720/8 =3D 90. Sabemos que n=E3o podemos ter uma permuta=E7=E3o do tipo AABCBC, = pois AA representa a mesma mat=E9ria em D1H1 e D1H2. Ent=E3o sabemos que = a resposta =E9 menor que 90. As formas inv=E1lidas ser=E3o: Se as 3 mat=E9rias do mesmo tipo est=E3o juntas no mesmo dia, = ex: AABBCC. Existem 3! =3D 6 formas, considerando AA,BB,CC como 3 elementos permutados entre si. N=E3o h=E1 necessidade de verificar quando 2 mat=E9rias est=E3o = no mesmo dia pois cai no caso acima. Quando h=E1 apenas 1 mat=E9ria repetida em 1 dia, ex: AABCBC, = ent=E3o temos 12 formas para cada par da mesma mat=E9ria utilizada no mesmo = dia. Se AA est=E1 em D1 ent=E3o D2 pode ser BC ou CB e D3 pode ser BC ou = CB, 2*2 =3D 4. AA pode estar em D1,D2,D3. Assim, 4*3 =3D 12. Para BB e CC seria = o mesmo, dando um total de 3*12 =3D 36 formas quando h=E1 apenas = uma mat=E9ria que se repete no mesmo dia. Assim, o total seria 90 - (6+36) =3D 90 - 42 =3D 48 formas = distintas de compor o hor=E1rio Thelio, voc=EA poderia passar a fonte do problema e verificar se = as respostas s=E3o essas mesmo? On 3/13/08, Thelio Gama wrote: > =C9 pessoal... > > Achei muito dif=EDcil esta quest=E3o. Agrade=E7o se algu=E9m = puder explic=E1-la. > > Thelio > > uma turma tem aulas =E0s 2=AA, 4=AA e 6=AA feiras, de 8-9 = horas e de 11-12 horas. As > mat=E9rias s=E3o portugues, matem=E1tica e ingles, cada uma = com duas aulas > semanais, em dias diferentes. De quantos modos pode ser feito = o hor=E1rio > dessa turma? > a)96 ; b) 144 ; c)192 ; d) 6! ; e) 120 -- Henrique = =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D Instru=E7=F5es para entrar na lista, sair da lista e usar a = lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html = =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D ------=_NextPart_000_0008_01C88DB5.B07B5990 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable
Oi Jo=E3o Victor, a quest=E3o =E9 que = eu j=E1 havia escrito=20 esta equa=E7=E3o. Acontece que ela =E9 "diofantina", admitindo infinitas = solu=E7=F5es.=20 Claro que, de acordo com as condi=E7=F5es do exerc=EDcio proposto = deve-se conseguir=20 restringir a quantidade delas para um n=FAmero bem menos (eu = creio).
 
Amplexo.
Fernando
 
----- Original Message -----
From:=20 Joao = Victor=20 Brasil
Sent: Monday, March 24, 2008 = 1:08=20 PM
Subject: Re: [obm-l] = combinatoria=20 dificil

Fernando,
 
Infelizmente n=E3o tenho, mas tenta ver algo nesse sentido:
19H + 13M =3D 1000, H=3D Homem  e M=3DMulher
 
Joao Victor

 
-----Mensagem original-----
De: owner-obm-l@mat.puc-rio.br [mailto:owner-obm-l@mat.puc-rio.br]Em nome de Joel Castro
Enviada em: ter=E7a-feira, 25 de mar=E7o de 2008 09:41
Para: obm-l@mat.puc-rio.br
Assunto: [obm-l] m=F3dulo

tenho pequena d=FAvida:
 
prove: se para todo r maior que zero, o m=F3dulo da diferen=E7a de a e= b =E9 menor que r, ent=E3o a =E9 igual a b.
 
valeu!!!!!!

Abra sua conta no Yahoo! Mail, o =FAnico sem limite de espa=E7o para armazenamento! --_000_E4C89EA639092445A78832509143CCB83908610AEEVENUSmmegovbr_-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Tue Mar 25 10:46:02 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2PDijWA031273 for ; Tue, 25 Mar 2008 10:44:46 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2PDijeZ031263 for obm-l-MllGbsmmN; Tue, 25 Mar 2008 10:44:45 -0300 Received: from correio.mme.gov.br (correio.mme.gov.br [200.198.213.101]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2PDiiWA031256 for ; Tue, 25 Mar 2008 10:44:44 -0300 Received: from VENUS.mme.gov.br ([172.16.1.53]) by srv017.mme.gov.br ([172.16.1.46]) with mapi; Tue, 25 Mar 2008 10:44:28 -0300 From: Artur Costa Steiner To: "obm-l@mat.puc-rio.br" Date: Tue, 25 Mar 2008 10:44:24 -0300 Subject: =?iso-8859-1?Q?RES:_[obm-l]_Fun=E7=F5es_limitadas?= Thread-Topic: =?iso-8859-1?Q?[obm-l]_Fun=E7=F5es_limitadas?= Thread-Index: AciN9IHDZPdVL70NTnqmHt/ftHrCcgAiQv5g Message-ID: In-Reply-To: <657129.82325.qm@web58211.mail.re3.yahoo.com> Accept-Language: pt-BR, en-US Content-Language: pt-BR X-MS-Has-Attach: X-MS-TNEF-Correlator: acceptlanguage: pt-BR, en-US x-tm-as-product-ver: SMEX-8.0.0.1226-5.000.1023-15808.003 x-tm-as-result: No--30.010000-4.000000-31 x-tm-as-user-approved-sender: No x-tm-as-user-blocked-sender: No Content-Type: multipart/alternative; boundary="_000_E4C89EA639092445A78832509143CCB83908610B0CVENUSmmegovbr_" MIME-Version: 1.0 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Artur Costa Steiner X-Spam-Status: No, hits=1.7 required=5.0 tests=AWL,HTML_FONT_COLOR_BLUE,IN_REP_TO,SPAM_PHRASE_00_01, SPAM_REDIRECTOR,TO_ADDRESS_EQ_REAL,X_MAILING_LIST version=2.44 X-Spam-Level: * --_000_E4C89EA639092445A78832509143CCB83908610B0CVENUSmmegovbr_ Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable 1) Para todo x de X, temos que f(x) <=3Dsup(f) e que g(x) <=3D sup(g). Como= f e g tem valores em R+, temos para todo x de X que f(x) g(x) <=3D sup(f) = sup(g). Ou seja, o conjunto {f(x) g(x) | x esta em X} eh limitado superiorm= ente por sup(f) sup(g). Da definicao de supremo, segue-se que sup {f(x) g(= x) | x esta em X} =3D sup(f.g) <=3D sup(f) sup(g). 2) Faca g =3D f e aplique (1). Artur -----Mensagem original----- De: owner-obm-l@mat.puc-rio.br [mailto:owner-obm-l@mat.puc-rio.br]Em nome d= e Douglas Alexandre Enviada em: segunda-feira, 24 de mar=E7o de 2008 17:44 Para: obm-l@mat.puc-rio.br Assunto: [obm-l] Fun=E7=F5es limitadas Como resolvo a seguinte quest=E3o: Sejam f,g : X->R^+, fun=E7=F5es limitada= s superiormente. Prove que sup(f.g)<=3D (menor ou igual)sup(f).sup(g) e que= sup(f^2)=3D(sup(f))^2 _____ Abra sua conta no Yahoo! Mail, o =FAnico sem limite de espa=E7o para armazenamen= to! --_000_E4C89EA639092445A78832509143CCB83908610B0CVENUSmmegovbr_ Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable
1) Para todo x de X, temos que f(x) <=3Dsup(f) e que g(x)= <=3D sup(g). Como f e g tem valores em R+, temos para todo x d= e X que f(x) g(x) <=3D sup(f) sup(g). Ou seja, o conjunto {f(x) g(x) | x esta em X} eh limitado superiormente por sup(f) sup(g). Da defini= cao de supremo, segue-se que sup  {f(x) g(x) | x esta em X} =3D s= up(f.g) <=3D sup(f) sup(g).
 
2) Faca g =3D f e aplique (1).
 
Artur

  -----Mensagem original-----
De: owner-obm-l@mat.puc-rio.br [mailto:owner-obm-l@mat.puc-rio.br]Em nome de Douglas Alexandre
Enviada em: segunda-feira, 24 de mar=E7o de 2008 17:44
Para: obm-l@mat.puc-rio.br
Assunto: [obm-l] Fun=E7=F5es limitadas
Como resolvo a seguinte quest=E3o: Sejam f,g : X->R^+, fun=E7= =F5es limitadas superiormente. Prove que sup(f.g)<=3D (menor ou igual)su= p(f).sup(g) e que sup(f^2)=3D(sup(f))^2

Abra sua conta no Yahoo! Mail, o =FAnico sem limite de espa=E7o para armazenamento! --_000_E4C89EA639092445A78832509143CCB83908610B0CVENUSmmegovbr_-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Tue Mar 25 12:12:22 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2PFArWA003650 for ; Tue, 25 Mar 2008 12:10:53 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2PFArx6003648 for obm-l-MllGbsmmN; Tue, 25 Mar 2008 12:10:53 -0300 Received: from smtp.bol.com.br (smtpout1.bol.com.br [200.221.4.212]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2PFAqWA003644 for ; Tue, 25 Mar 2008 12:10:52 -0300 Received: from localhost (localhost [127.0.0.1]) by smart5.bol.com.br (Postfix) with ESMTP id 7A0CB78F for ; Tue, 25 Mar 2008 12:10:34 -0300 (BRT) Received: from pai (unknown [201.88.134.242]) by smart5.bol.com.br (Postfix) with ESMTP id 6428978B for ; Tue, 25 Mar 2008 12:10:33 -0300 (BRT) Message-ID: <003301c88e8a$a4df7c80$6401a8c0@pai> From: "Tio Cabri st" To: References: <638971.61255.qm@web45906.mail.sp1.yahoo.com> Subject: [SPAM] [obm-l] =?iso-8859-1?Q?Re:_=5Bobm-l=5D_m=F3dulo?= Date: Tue, 25 Mar 2008 12:12:29 -0300 MIME-Version: 1.0 Content-Type: text/plain X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2800.1478 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2800.1478 X-SIG5: 5ecf1be2c854e7cfb08f3628196664aa Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Tio Cabri st" X-Spam-Status: Yes, hits=6.8 required=5.0 tests=AWL,HTML_FONT_FACE_BAD,HTML_FONT_FACE_CAPS, HTML_FONT_FACE_ODD,MAILTO_LINK,MAILTO_TO_SPAM_ADDR, RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,REFERENCES, SPAM_PHRASE_00_01,SPAM_REDIRECTOR,USER_AGENT_OE, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ****** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_NextPart_000_0030_01C88E71.7F2D8F40" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (6.80 hits, 5 required) SPAM: REFERENCES (-0.5 points) Has a valid-looking References header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: USER_AGENT_OE (0.2 points) X-Mailer header indicates a non-spam MUA (Outlook Express) SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: HTML_FONT_FACE_ODD (0.3 points) BODY: HTML font face is not a commonly used face SPAM: HTML_FONT_FACE_CAPS (0.2 points) BODY: HTML font face has excess capital characters SPAM: HTML_FONT_FACE_BAD (0.2 points) BODY: HTML font face is not a word SPAM: MAILTO_LINK (0.2 points) BODY: Includes a URL link to send an email SPAM: MAILTO_TO_SPAM_ADDR (0.7 points) URI: Includes a link to a likely spammer email address SPAM: SPAM_REDIRECTOR (0.4 points) URI: Uses open redirection service SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 242.134.88.201.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 242.134.88.201.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-0.7 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- This is a multi-part message in MIME format. ------=_NextPart_000_0030_01C88E71.7F2D8F40 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Eu acho que isso =E9 falso, logo n=E3o pode provar. O que sei =E9 dado r>0 |a-b| b - r < a < b + r=20 ----- Original Message -----=20 From: Joel Castro=20 To: obm-l@mat.puc-rio.br=20 Sent: Tuesday, March 25, 2008 9:40 AM Subject: [obm-l] m=F3dulo tenho pequena d=FAvida: prove: se para todo r maior que zero, o m=F3dulo da diferen=E7a de a e = b =E9 menor que r, ent=E3o a =E9 igual a b. valeu!!!!!! -------------------------------------------------------------------------= ----- Abra sua conta no Yahoo! Mail, o =FAnico sem limite de espa=E7o para = armazenamento! ------=_NextPart_000_0030_01C88E71.7F2D8F40 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable
Eu acho que isso =E9 falso, logo n=E3o = pode=20 provar.
O que sei =E9 dado r>0
|a-b|<r =3D> b - r < a < b = + r
----- Original Message -----
From:=20 Joel Castro
Sent: Tuesday, March 25, 2008 = 9:40=20 AM
Subject: [obm-l] m=F3dulo

tenho pequena d=FAvida:
 
prove: se para todo r maior que zero, o m=F3dulo da diferen=E7a = de a e b =E9=20 menor que r, ent=E3o a =E9 igual a b.
 
valeu!!!!!!

Abra sua conta no Yahoo!=20 Mail, o =FAnico sem limite de espa=E7o para armazenamento!=20
------=_NextPart_000_0030_01C88E71.7F2D8F40-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Tue Mar 25 13:55:52 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2PGs8WA009184 for ; Tue, 25 Mar 2008 13:54:08 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2PGs87G009182 for obm-l-MllGbsmmN; Tue, 25 Mar 2008 13:54:08 -0300 Received: from gv-out-0910.google.com (gv-out-0910.google.com [216.239.58.186]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2PGs5WA009177 for ; Tue, 25 Mar 2008 13:54:06 -0300 Received: by gv-out-0910.google.com with SMTP id u5so619473gve.25 for ; Tue, 25 Mar 2008 09:53:46 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; bh=tE+NidBvmKYp9VMnejCV63JJNbxN9qs3tbpaQQScgqA=; b=N2cmB4s4wSwA6koO4kJK//MBP2GGmMYV8V9csql04P8YUV4uo4iaEUDxM07tZjBM5Pe/BpfkiTnKrqd60+kzHpE0bfhdtkXGPmuOVIighg+5r/yzj0YxXs4atYIasKOitmOQdnit2Rmbn6hi/XxSQxawcTPrL45WuFy3Gc4M9tk= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; b=HXhe6QIYMjldtRfAcu/ZsVQY9xkC38Af9h+VN8p2Fug16b1fDzIZeeuqut9rNiuInDEK9dPyKQ8NExDnGDzX/f7Hw6TQN6ONqGZhUgIchU60HDRMfrS10GV2YWaIL7J1OJa3TZtnhCQe3o2Ysw070ym64nYzvX1BFkBgq8nSUCs= Received: by 10.151.156.2 with SMTP id i2mr4168711ybo.121.1206464025371; Tue, 25 Mar 2008 09:53:45 -0700 (PDT) Received: by 10.150.144.4 with HTTP; Tue, 25 Mar 2008 09:53:45 -0700 (PDT) Message-ID: Date: Tue, 25 Mar 2008 13:53:45 -0300 From: "Paulo Santa Rita" To: obm-l@mat.puc-rio.br Subject: =?ISO-8859-1?Q?Re:_[obm-l]_m=F3dulo?= In-Reply-To: <638971.61255.qm@web45906.mail.sp1.yahoo.com> MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline References: <638971.61255.qm@web45906.mail.sp1.yahoo.com> Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m2PGs7WA009180 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Paulo Santa Rita" X-Spam-Status: No, hits=4.2 required=5.0 tests=AWL,IN_REP_TO,MAILTO_TO_SPAM_ADDR,QUOTED_EMAIL_TEXT, RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,REFERENCES, SPAM_PHRASE_00_01,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** Ola Joel e demais colegas desta lista ... OBM-L, Suponha que a # b, isto é, suponha que "a" e diferente de "b". Neste caso, s = | a - b | e um real positivo. Entao, fazendo r = s e usando a propriedade enunciada, teremos : | a - b | < s => | a - b | < | a - b | ... absurdo ! Assim, a nossa tese e insustentavel e somos obrigados a admitir que a = b. No endereco abaixo existem muitos problemas olimpicos interessantes : http://www.mat.puc-rio.br/~nicolau/psr/ Um Abraco a Todos Paulo Santa Rita 3,0D31,190308 Em 25/03/08, Joel Castro escreveu: > tenho pequena dúvida: > > prove: se para todo r maior que zero, o módulo da diferença de a e b é menor > que r, então a é igual a b. > > valeu!!!!!! > > ________________________________ > Abra sua conta no Yahoo! Mail, o único sem limite de espaço para > armazenamento! > > ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Tue Mar 25 16:08:25 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2PJ6sWA015794 for ; Tue, 25 Mar 2008 16:06:54 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2PJ6sZU015792 for obm-l-MllGbsmmN; Tue, 25 Mar 2008 16:06:54 -0300 Received: from web55209.mail.re4.yahoo.com (web55209.mail.re4.yahoo.com [206.190.58.173]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id m2PJ6pWA015781 for ; Tue, 25 Mar 2008 16:06:52 -0300 Received: (qmail 3262 invoked by uid 60001); 25 Mar 2008 19:06:32 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:Date:From:Subject:To:MIME-Version:Content-Type:Content-Transfer-Encoding:Message-ID; b=0JreLeznkYOSzNv2RYZWW00jc1FIanjXS9CgpQ6bmqmx0/x/fiCDREnhbfv3zQyy5JrvlCCfx/JX41/FVPCpPISuNUM2Kp6lluaa4Dpsg9CZ/s7+W3zHzZ7OXpz7OS65xZRfgr1IjKVnELnTqMzeHhSG7GE6W3wdCRvsuxG2cHY=; X-YMail-OSG: wKLF508VM1mpSpM5M6un8Rpy5WqB5OJ7L97r_2Hm Received: from [200.147.88.118] by web55209.mail.re4.yahoo.com via HTTP; Tue, 25 Mar 2008 16:06:32 ART Date: Tue, 25 Mar 2008 16:06:32 -0300 (ART) From: =?iso-8859-1?q?C=E9sar=20Santos?= Subject: [SPAM] [obm-l] =?iso-8859-1?q?Integral=20de=20superf=EDcie=20=20(quest=E3o=20s?= =?iso-8859-1?q?imples)?= To: obm-l@mat.puc-rio.br MIME-Version: 1.0 Content-Type: text/plain Content-Transfer-Encoding: 7bit Message-ID: <393603.1422.qm@web55209.mail.re4.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: =?iso-8859-1?q?C=E9sar=20Santos?= X-Spam-Status: Yes, hits=8.1 required=5.0 tests=AWL,FORGED_YAHOO_RCVD,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, SPAM_PHRASE_00_01,SPAM_REDIRECTOR,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="0-640690847-1206471992=:1422" X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (8.10 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: SPAM_REDIRECTOR (0.4 points) URI: Uses open redirection service SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 173.58.190.206.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 173.58.190.206.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (0.5 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- --0-640690847-1206471992=:1422 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 8bit Calcule área da porção do plano 2x + 3y + z =6 que é cortada pelos três planos coordenados. Resp. 3V14 (três raiz de quatorze). Alguém poderia me explicar a resolução da questão, por favor? --------------------------------- Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-640690847-1206471992=:1422 Content-Type: text/html; charset=iso-8859-1 Content-Transfer-Encoding: 8bit Calcule área da porção do plano 2x + 3y + z =6 que é cortada pelos três planos coordenados. Resp. 3V14 (três raiz de quatorze). Alguém poderia me explicar a resolução da questão, por favor?

Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-640690847-1206471992=:1422-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Tue Mar 25 16:11:53 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2PJAmWA015893 for ; Tue, 25 Mar 2008 16:10:48 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2PJAkM5015891 for obm-l-MllGbsmmN; Tue, 25 Mar 2008 16:10:46 -0300 Received: from web55214.mail.re4.yahoo.com (web55214.mail.re4.yahoo.com [206.190.58.178]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id m2PJAWWA015886 for ; Tue, 25 Mar 2008 16:10:33 -0300 Received: (qmail 45371 invoked by uid 60001); 25 Mar 2008 19:10:13 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:Date:From:Subject:To:MIME-Version:Content-Type:Content-Transfer-Encoding:Message-ID; b=oh9ojDqqPHK25cuzyKdKqeDO9ajB0rC6ze0Uc5gyYf7VPgFTkqrJMI/HfBTmNeEbnJf+Cc7ZQSMo6Yu8/mRoaYJoCwkY7zVRgFZfGTD3SE7pxqTURhSqlKwmDsR0OHbWJ4xnsHQXzhdg6WSyEbo4JmpbtSsOdB+nogDan1wrclM=; X-YMail-OSG: xgABE7oVM1ka4LsMrrUVJgXPRl21r37waSBS0yhLX93Zp.qyTeNT2YXC2zhz70Wb6oizzx77U8_9cw6_C.M3a6EDqJ0mwBEyhztBpcOfCjf3zD8QRXYi5RlxkKB6luGI019j7.cxCKSZBtHmIoAW.1ag.Q-- Received: from [200.147.88.118] by web55214.mail.re4.yahoo.com via HTTP; Tue, 25 Mar 2008 16:10:12 ART Date: Tue, 25 Mar 2008 16:10:12 -0300 (ART) From: =?iso-8859-1?q?C=E9sar=20Santos?= Subject: [SPAM] [obm-l] =?iso-8859-1?q?Indica=E7=E3o=20de=20livros=20(C=E1lculo=20num=E9rico=20e?= =?iso-8859-1?q?=20Equa=E7=F5es=20diferenciais)?= To: obm-l@mat.puc-rio.br MIME-Version: 1.0 Content-Type: text/plain Content-Transfer-Encoding: 7bit Message-ID: <212079.44593.qm@web55214.mail.re4.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: =?iso-8859-1?q?C=E9sar=20Santos?= X-Spam-Status: Yes, hits=8.9 required=5.0 tests=AWL,FORGED_YAHOO_RCVD,MIME_BOUND_DIGITS_5,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01,SPAM_REDIRECTOR, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="0-918161263-1206472212=:44593" X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (8.90 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: MIME_BOUND_DIGITS_5 (1.7 points) Spam tool pattern in MIME boundary SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: SPAM_REDIRECTOR (0.4 points) URI: Uses open redirection service SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 178.58.190.206.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 178.58.190.206.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-0.4 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- --0-918161263-1206472212=:44593 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 8bit Poderiam me indicar bons livros de cálculo numérico e de equações diferencias acessíveis para iniciante? --------------------------------- Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-918161263-1206472212=:44593 Content-Type: text/html; charset=iso-8859-1 Content-Transfer-Encoding: 8bit Poderiam me indicar bons livros de cálculo numérico e de equações diferencias acessíveis para iniciante?

Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-918161263-1206472212=:44593-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Tue Mar 25 17:08:05 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2PK6qWA018991 for ; Tue, 25 Mar 2008 17:06:52 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2PK6qtk018989 for obm-l-MllGbsmmN; Tue, 25 Mar 2008 17:06:52 -0300 Received: from smtpi01s.infolink.com.br (smtpi01s.infolink.com.br [200.187.64.121]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2PK6nWA018985 for ; Tue, 25 Mar 2008 17:06:49 -0300 Received: from smtpi01s.infolink.com.br (localhost [127.0.0.1]) by smtpi01s.infolink.com.br (Postfix) with ESMTP id 8E4D01A783E for ; Tue, 25 Mar 2008 17:06:28 -0300 (EST) Received: from [127.0.0.1] (unknown [189.60.112.176]) by smtpi01s.infolink.com.br (Postfix) with ESMTP id 5A7671B1CB4 for ; Tue, 25 Mar 2008 17:06:28 -0300 (EST) Message-ID: <47E95AFE.5000105@infolink.com.br> Date: Tue, 25 Mar 2008 17:05:18 -0300 From: Carlos Nehab User-Agent: Thunderbird 2.0.0.12 (Windows/20080213) MIME-Version: 1.0 To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] =?ISO-8859-1?Q?m=F3dulo?= References: <638971.61255.qm@web45906.mail.sp1.yahoo.com> In-Reply-To: Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: 7bit X-Antivirus: avast! (VPS 080324-0, 24/03/2008), Outbound message X-Antivirus-Status: Clean Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Carlos Nehab X-Spam-Status: No, hits=4.6 required=5.0 tests=AWL,CTYPE_JUST_HTML,IN_REP_TO,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, USER_AGENT,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** Oi, caro Santa Rita,

Qual a origem dos exercícios postados no link citado em seu email?

Abração,
Carlos Nehab

Paulo Santa Rita escreveu: 
.......
No endereco abaixo existem muitos problemas olimpicos interessantes :
http://www.mat.puc-rio.br/~nicolau/psr/

Um Abraco a Todos
Paulo Santa Rita
......
========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Tue Mar 25 18:11:19 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2PL9uWA022279 for ; Tue, 25 Mar 2008 18:09:56 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2PL9uVQ022277 for obm-l-MllGbsmmN; Tue, 25 Mar 2008 18:09:56 -0300 Received: from colorado.uspnet.usp.br (colorado.uspnet.usp.br [143.107.254.72]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2PL9tWA022274 for ; Tue, 25 Mar 2008 18:09:55 -0300 Received: (qmail 30798 invoked from network); 25 Mar 2008 21:09:37 -0000 X-Mail-Scanner: Scanned by qSheff-II-2.1-r1 (http://www.enderunix.org/qsheff/) Received: from dubai.uspnet.usp.br (HELO localhost) ([143.107.254.99]) (envelope-sender ) by colorado.uspnet.usp.br (qmail-ldap-1.03) with SMTP for ; 25 Mar 2008 21:09:37 -0000 Received: from 143.107.45.13 ([143.107.45.13]) by webmail.usp.br (Horde MIME library) with HTTP; Tue, 25 Mar 2008 18:09:37 -0300 Message-ID: <20080325180937.72s6l3suqsscw4co@webmail.usp.br> Date: Tue, 25 Mar 2008 18:09:37 -0300 From: Arlane Manoel S Silva To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Integral de =?iso-8859-1?b?c3VwZXJm7WNpZSA=?= =?iso-8859-1?b?PGT6dmlkYT4g?= =?iso-8859-1?b?KHF1ZXN0428=?= simples) References: <393603.1422.qm@web55209.mail.re4.yahoo.com> In-Reply-To: <393603.1422.qm@web55209.mail.re4.yahoo.com> MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1; DelSp="Yes"; format="flowed" Content-Disposition: inline User-Agent: Internet Messaging Program (IMP) H3 (4.1.5-cvs) Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m2PL9tWA022275 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Arlane Manoel S Silva X-Spam-Status: No, hits=2.9 required=5.0 tests=IN_REP_TO,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SIGNATURE_LONG_SPARSE, SPAM_PHRASE_00_01,USER_AGENT,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: ** Seria ótimo fazer uma figura, primeiro. Note que a equação 2x + 3y + z =6 determina um plano no R^3 e a porção que é corta pelos eixos forma um triângulo de vértices (0,0,6), (3,0,0) e (0,2,0). É possível resolver geometricamente. Um outro modo é usando integral de superfície. Considere a função z:=z(x,y)=6-2x-3y e use a definição. Citando César Santos : > Calcule área da porção do plano 2x + 3y + z =6 que é cortada pelos > três planos coordenados. Resp. 3V14 (três raiz de quatorze). Alguém > poderia me explicar a resolução da questão, por favor? > > --------------------------------- > Abra sua conta no Yahoo! Mail, o único sem limite de espaço para > armazenamento! -- Arlane Manoel S Silva MAT-IME-USP ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Tue Mar 25 19:22:04 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2PMKuWA025280 for ; Tue, 25 Mar 2008 19:20:56 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2PMKutM025278 for obm-l-MllGbsmmN; Tue, 25 Mar 2008 19:20:56 -0300 Received: from ti-out-0910.google.com (ti-out-0910.google.com [209.85.142.185]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2PMKrWA025274 for ; Tue, 25 Mar 2008 19:20:54 -0300 Received: by ti-out-0910.google.com with SMTP id y6so1271993tia.13 for ; Tue, 25 Mar 2008 15:20:34 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; bh=SF86zKIVITr8miwDDQvTv7mYgJRhzPCeRGy25QvwYhE=; b=lGXKTwdlQ4Q0Ayty7ng0piouyyJkBoQ8M4m8r2YtlaetsEjHgPo9WtIIBH471POR7XdrASF29z5xD6lnqTl/+3uOi6vkSHejmpN5S/l64y7YtmYyyI3wGS0iIbRtdiexMGX4LoBVyfzi9FCiziLQ0v+b7l1tyj7L/zQZ6PsJSnY= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; b=D4NE10IcSUflpNizJFtdW/kcpcnbuv6cG7DauaqtW2WP/FQuzYeYQeHZ1bVBU2VvWSRlLK5/h8M68VCu2/XnvC/AJYiEqu7LI7YULZtNRspjT6cew4MOEKGIc0TaCQDpI0e3iU5Y/2KYz/GL6wmnAdc5rwLKK/RZJY3TBTyK89o= Received: by 10.151.147.16 with SMTP id z16mr4371943ybn.196.1206483633565; Tue, 25 Mar 2008 15:20:33 -0700 (PDT) Received: by 10.150.144.4 with HTTP; Tue, 25 Mar 2008 15:20:33 -0700 (PDT) Message-ID: Date: Tue, 25 Mar 2008 19:20:33 -0300 From: "Paulo Santa Rita" To: obm-l@mat.puc-rio.br Subject: =?ISO-8859-1?Q?Re:_[obm-l]_m=F3dulo?= In-Reply-To: <47E95AFE.5000105@infolink.com.br> MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline References: <638971.61255.qm@web45906.mail.sp1.yahoo.com> <47E95AFE.5000105@infolink.com.br> Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m2PMKtWA025276 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Paulo Santa Rita" X-Spam-Status: No, hits=3.9 required=5.0 tests=AWL,IN_REP_TO,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: *** Ola carissimo Nehab e demais colegas desta lista ... OBM-L, A origem dos exercicios são as Olimpiadas Russas ... Falei o obvio ululante ? Bem, voce deve estar querendo saber o endereco eletronico do arquivo que contem os problemas em suas formulacoes originais, certo ? Nao sei : um estudante de uma outra Lista, na qual participavam alguns Matematicos de Princeton, me passou o arquivo original. No espaco cedido pelo Carissimo Prof Nicolau existem apenas 100, mas eu tenho "perdido em meu computador pessoal" o arquivo completo, com milhares de exercicios, escritos no idioma original. "Descobrindo" este arquivo eu posso passa-lo pra voce, caso voce queira. Um Abracao a Todos ! Paulo Santa Rita 3,1312,190308 2008/3/25, Carlos Nehab : > > Oi, caro Santa Rita, > > Qual a origem dos exercícios postados no link citado em seu email? > > Abração, > Carlos Nehab > > Paulo Santa Rita escreveu: > ....... > No endereco abaixo existem muitos problemas olimpicos interessantes : > http://www.mat.puc-rio.br/~nicolau/psr/ > > Um Abraco a Todos > Paulo Santa Rita > ...... > ========================================================================= > Instruções para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > ========================================================================= ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Tue Mar 25 20:59:35 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2PNvFWA030552 for ; Tue, 25 Mar 2008 20:57:15 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2PNvF3G030549 for obm-l-MllGbsmmN; Tue, 25 Mar 2008 20:57:15 -0300 Received: from n65b.bullet.mail.sp1.yahoo.com (n65b.bullet.mail.sp1.yahoo.com [98.136.45.38]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id m2PNvCWA030546 for ; Tue, 25 Mar 2008 20:57:13 -0300 Received: from [216.252.122.217] by n65.bullet.mail.sp1.yahoo.com with NNFMP; 25 Mar 2008 23:56:54 -0000 Received: from [69.147.65.171] by t2.bullet.sp1.yahoo.com with NNFMP; 25 Mar 2008 23:56:54 -0000 Received: from [127.0.0.1] by omp506.mail.sp1.yahoo.com with NNFMP; 25 Mar 2008 23:56:54 -0000 X-Yahoo-Newman-Property: ymail-5 X-Yahoo-Newman-Id: 354966.88238.bm@omp506.mail.sp1.yahoo.com Received: (qmail 85434 invoked by uid 60001); 25 Mar 2008 23:56:54 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:Date:From:Subject:To:MIME-Version:Content-Type:Content-Transfer-Encoding:Message-ID; b=Ig22+YbNOErrMHSUa/oXTPQU4/nmIF3WgDv0RgwVlJZB/VcyPaffAjJKVkMtwEyI4M48GmbApQGjPL4DuLmRKrUEUFvPsu3KSmAjR8+MT1i3JFVmHgXBiK1Mo4RYfblD8rj1MEvoofbfrekREoz3/hKU5LFaC/XZrBXnpKb1714=; X-YMail-OSG: qoONU.cVM1l1HVHBVJC0XF39Yl_O_RM.pMbYDnxF27pEBvAlJPviwR.RRyQ800UsHg-- Received: from [189.71.170.237] by web46208.mail.sp1.yahoo.com via HTTP; Tue, 25 Mar 2008 20:56:54 ART Date: Tue, 25 Mar 2008 20:56:54 -0300 (ART) From: Daniel Madeira Subject: [obm-l] Livros de Geomtria Analitica To: obm-l@mat.puc-rio.br MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="0-1058281523-1206489414=:84676" Content-Transfer-Encoding: 8bit Message-ID: <228699.84676.qm@web46208.mail.sp1.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Daniel Madeira X-Spam-Status: No, hits=4.5 required=5.0 tests=FORGED_YAHOO_RCVD,RCVD_IN_ORBS,SPAM_PHRASE_00_01, SPAM_REDIRECTOR,SUPERLONG_LINE,X_MAILING_LIST version=2.44 X-Spam-Level: **** --0-1058281523-1206489414=:84676 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 8bit Caros amigos da lista, Estou estudando na universidade a disciplina: Geometria Analítica. Estive navegando na internet em busca de livros para e comprar e estudar essa disciplina. Em particular me interessa um livro que aborde problemas sobre parte de vetores como semi-retas (a parte geometrica), a parte referente a vetores Linearmente depedentes e independentes e exercícios de demonstração envolvendo propriedades de operações com vetores. Estive vendo alguns livros. O que acham desses livros ? - Introdução à geomtria analítica no espaço autor: Paulo Boulos e Ivan de Camargo edt: Makron Books - Álgebra Linear e geometria vectorial autor: Rios, Sixto edit: Litexa - Vetores e Geometria Analitica, teoria e exercicios autor: Ana Célia da Costa Loreto e Armando editora: LCTE - Vetores e uma iniciação à geometria análitica autor: Dorival A. de Mello e Renate G. Watanabe editora: Penn - Exercícios de geometria analitica (vale a pena esse livro ?) autor: Blasi editora: Papirus Já tenho os livros: álgebra linear e aplicações do callioli, geometria analítica - um tratamento vetorial do Paulo Boulos e geometria analítica do Steinbruch. Peço desculpas pelo e-mail extenso. Certo da compreensão de vocês e de sua ajuda, agradeço desde já. Cordialmente, Daniel. ps: algum livro do elon lages envolvendo essa parte de geometria analitica ? ele vale a pena ? --------------------------------- Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-1058281523-1206489414=:84676 Content-Type: text/html; charset=iso-8859-1 Content-Transfer-Encoding: 8bit
Caros amigos da lista,
 
   Estou estudando na universidade a disciplina: Geometria Analítica. Estive navegando na internet em busca de livros para e comprar e estudar essa disciplina. Em particular me interessa um livro que aborde problemas sobre parte de vetores como semi-retas (a parte geometrica), a parte referente a vetores Linearmente depedentes e independentes e exercícios de demonstração envolvendo propriedades de operações com vetores. Estive vendo alguns livros. O que acham desses livros ?
 
- Introdução à geomtria analítica no espaço
  autor: Paulo Boulos e Ivan de Camargo
  edt: Makron Books
 
- Álgebra Linear e geometria vectorial
 autor: Rios, Sixto
 edit: Litexa
 
- Vetores e Geometria Analitica, teoria e exercicios
 autor: Ana Célia da Costa Loreto e Armando
 editora: LCTE
 
- Vetores e uma iniciação à geometria análitica
 autor: Dorival A. de Mello e Renate G. Watanabe
editora: Penn
 
- Exercícios de geometria analitica (vale a pena esse livro ?)
 autor: Blasi
editora: Papirus
 
Já tenho os livros: álgebra linear e aplicações do callioli, geometria analítica - um tratamento vetorial do Paulo Boulos e geometria analítica do Steinbruch.
 
  Peço desculpas pelo e-mail extenso. Certo da compreensão de vocês e de sua ajuda, agradeço desde já.
 
 Cordialmente,
 
   Daniel.
 
ps:  algum livro do elon lages envolvendo essa parte de geometria analitica ? ele vale a pena ?
  

Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-1058281523-1206489414=:84676-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Tue Mar 25 21:32:13 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2Q0VAWA032212 for ; Tue, 25 Mar 2008 21:31:10 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2Q0VAOu032210 for obm-l-MllGbsmmN; Tue, 25 Mar 2008 21:31:10 -0300 Received: from ug-out-1314.google.com (ug-out-1314.google.com [66.249.92.169]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2Q0V7WA032202 for ; Tue, 25 Mar 2008 21:31:08 -0300 Received: by ug-out-1314.google.com with SMTP id q7so2623186uge.0 for ; Tue, 25 Mar 2008 17:30:49 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; bh=3ZDNX9nVfa30QBbMLRN6Ihz+G/V28pp2qhAhgGurDhM=; b=a9ps/sJXzTc718F1aorthjCF6KOtEzQe9FD79WbY1YJhIvFjBuRaniJaP5q8yY7FLQFqSkPkKtknJGn6PpKF2jzbh7WxOgAN13BHyahiyZ+hn6Yb8w/TLPjzpi1099MpbpCZAOH5LWMb7c4i9xnxJFoSzz2CUfC91B/W39oXYlA= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; b=oAyVNkxx04wtJofsJgr2LGs10D+L9B6YvS5ebl5qkZhFu2S+d/bE9N+2CZ5xevCHi7IyHTA8Mox032NxBvpZFbNAcl2feUOpEhLB81ZCdkTm99rqfTG7NZPNVqX6DXrq5MnukqqEe4Z5C9ttoGwFu+M3I3dOz2uAa98mzafjWBo= Received: by 10.66.221.6 with SMTP id t6mr986701ugg.0.1206491449084; Tue, 25 Mar 2008 17:30:49 -0700 (PDT) Received: by 10.66.219.5 with HTTP; Tue, 25 Mar 2008 17:30:49 -0700 (PDT) Message-ID: <2d483c770803251730q41df2b4fyd08ee989c0767a0c@mail.gmail.com> Date: Tue, 25 Mar 2008 21:30:49 -0300 From: "Ralph Teixeira" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Livros de Geomtria Analitica In-Reply-To: <228699.84676.qm@web46208.mail.sp1.yahoo.com> MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline References: <228699.84676.qm@web46208.mail.sp1.yahoo.com> Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m2Q0V9WA032206 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Ralph Teixeira" X-Spam-Status: No, hits=2.4 required=5.0 tests=AWL,IN_REP_TO,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS,REFERENCES, SPAM_PHRASE_00_01,X_MAILING_LIST version=2.44 X-Spam-Level: ** Para responder o PS, o Elon escreveu sim um livro "Geometria Analitica e Algebra Linear", publicado pela Colecao Matematica Universitaria do IMPA, cuja intencao era exatamente ensinar Geometria Analitica usando bastante vetores para alunos no comeco da Graduacao, com um olho num proximo segundo curso mais pesado de Algebra Linear. Ele estah aqui neste link: http://www.impa.br/opencms/pt/publicacoes/colecao_matematica_universitaria/livro_geometria_analitica_e_algebra_Linear/index.html Voce tem que gostar do estilo do Elon para aprecia-lo (na minha modesta opiniao, isto significa: correto, elegante e sucinto; mas para ler voce tem que se concentrar e destrinchar devagar cada pagina com papel e caneta do lado o tempo todo). Bom, eu gosto do estilo do Elon, mas minha opiniao eh parcial, jah que eu estudava com ele jah ha mais de 20 anos atras... Vale lembrar que o livro eh bem baratinho, entao custa pouco experimentar e ver... :) Abraco, Ralph 2008/3/25 Daniel Madeira : > Caros amigos da lista, > > Estou estudando na universidade a disciplina: Geometria Analítica. Estive > navegando na internet em busca de livros para e comprar e estudar essa > disciplina. Em particular me interessa um livro que aborde problemas sobre > parte de vetores como semi-retas (a parte geometrica), a parte referente a > vetores Linearmente depedentes e independentes e exercícios de demonstração > envolvendo propriedades de operações com vetores. Estive vendo alguns > livros. O que acham desses livros ? > > - Introdução à geomtria analítica no espaço > autor: Paulo Boulos e Ivan de Camargo > edt: Makron Books > > - Álgebra Linear e geometria vectorial > autor: Rios, Sixto > edit: Litexa > > - Vetores e Geometria Analitica, teoria e exercicios > autor: Ana Célia da Costa Loreto e Armando > editora: LCTE > > - Vetores e uma iniciação à geometria análitica > autor: Dorival A. de Mello e Renate G. Watanabe > editora: Penn > > - Exercícios de geometria analitica (vale a pena esse livro ?) > autor: Blasi > editora: Papirus > > Já tenho os livros: álgebra linear e aplicações do callioli, geometria > analítica - um tratamento vetorial do Paulo Boulos e geometria analítica do > Steinbruch. > > Peço desculpas pelo e-mail extenso. Certo da compreensão de vocês e de sua > ajuda, agradeço desde já. > > Cordialmente, > > Daniel. > > ps: algum livro do elon lages envolvendo essa parte de geometria analitica > ? ele vale a pena ? > > > > ________________________________ > Abra sua conta no Yahoo! Mail, o único sem limite de espaço para > armazenamento! > > ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Tue Mar 25 21:39:31 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2Q0cSWA032533 for ; Tue, 25 Mar 2008 21:38:28 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2Q0cRGg032531 for obm-l-MllGbsmmN; Tue, 25 Mar 2008 21:38:27 -0300 Received: from nf-out-0910.google.com (nf-out-0910.google.com [64.233.182.186]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2Q0cQWA032527 for ; Tue, 25 Mar 2008 21:38:26 -0300 Received: by nf-out-0910.google.com with SMTP id k4so1527840nfd.19 for ; Tue, 25 Mar 2008 17:38:07 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; bh=VkNrDYNBoMia0/zkSJKQkvBRLJHOf2MDLMBkvZ6MhZ8=; b=WNkBnyoKV6W7GePvmlT/8p5FLbsGmH2wapWuR+Pn1uQAi8vsFsrjUFDv9sx6nGDBGX1G+XWvygOHWHuwhS0mdNe8fiVRrE/zlWxpbtGY3OgbimW7RLBFL/hExjb8WFACMY1zuLoTxdwcdPbUpJicpYsSKdlUwP5wE4vfjGjUblY= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; b=pM5bOuvbywVCGtR3GzBmH0YKtPwNQRo8TLk1lgIbPmNV8h8H73N9qzAfQaEt85GeypOoT3ZKakFmjoOPR2WcR9G7tnYq/2/c7hfdtZt1hnEeD8JaLmfo08QYI18hxX6PqzlWfmnZrclXSGotIjhAV74jqNaq/wqC+Xck7o0NQ4k= Received: by 10.78.197.9 with SMTP id u9mr23057265huf.56.1206491886842; Tue, 25 Mar 2008 17:38:06 -0700 (PDT) Received: by 10.78.57.6 with HTTP; Tue, 25 Mar 2008 17:38:06 -0700 (PDT) Message-ID: <8994b830803251738ic3f0183q5341f39f0115e7e2@mail.gmail.com> Date: Tue, 25 Mar 2008 21:38:06 -0300 From: "=?ISO-8859-1?Q?Maur=EDcio_Collares?=" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Livros de Geomtria Analitica In-Reply-To: <228699.84676.qm@web46208.mail.sp1.yahoo.com> MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline References: <228699.84676.qm@web46208.mail.sp1.yahoo.com> Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m2Q0cRWA032528 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "=?ISO-8859-1?Q?Maur=EDcio_Collares?=" X-Spam-Status: No, hits=2.3 required=5.0 tests=AWL,IN_REP_TO,RCVD_IN_ORBS,REFERENCES,SPAM_PHRASE_00_01, X_MAILING_LIST version=2.44 X-Spam-Level: ** On 3/25/08, Daniel Madeira wrote: > ps: algum livro do elon lages envolvendo essa parte de geometria analitica > ? ele vale a pena ? > Sim, o Elon tem um livro chamado "Geometria Analítica e Álgebra Linear". Vale muito a pena, o livro é muito bem escrito. -- Abraços, Maurício ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Tue Mar 25 23:09:24 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2Q282WA004757 for ; Tue, 25 Mar 2008 23:08:06 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2Q27vgJ004753 for obm-l-MllGbsmmN; Tue, 25 Mar 2008 23:07:57 -0300 Received: from smtp.bol.com.br (smtpout1.bol.com.br [200.221.4.212]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2Q27CWA004718 for ; Tue, 25 Mar 2008 23:07:14 -0300 Received: from localhost (localhost [127.0.0.1]) by smart5.bol.com.br (Postfix) with ESMTP id 0619E38E for ; Tue, 25 Mar 2008 23:06:55 -0300 (BRT) Received: from pai (unknown [201.88.134.242]) by smart5.bol.com.br (Postfix) with ESMTP id 8893D2B2 for ; Tue, 25 Mar 2008 23:06:54 -0300 (BRT) Message-ID: <002d01c88ee6$55fe2380$6501a8c0@pai> From: "Tio Cabri st" To: Subject: [obm-l] off topic: resumos analise real Date: Tue, 25 Mar 2008 22:57:14 -0300 MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: 8bit X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2800.1478 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2800.1478 X-SIG5: d4790e227042b75f0a8d2adf69d500d5 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Tio Cabri st" X-Spam-Status: No, hits=4.5 required=5.0 tests=AWL,RCVD_IN_ORBS,SPAM_PHRASE_00_01,USER_AGENT_OE, X_MAILING_LIST version=2.44 X-Spam-Level: **** Senhores, boa noite, tá difícil de fazer sozinho, análise realmente é ingrata, gostaria NOVAMENTE (perdoem-me) da ajuda do pessoal da lista. Pedi há uns dias exercícios resolvidos do livro de análise do Elon do pequeno ou do grande (volume 1). Infelizmente não consegui nem um. Aí, como a situação está braba (estou trabalhando muito, sem tempo para estudar) pensei na possibilidade de estudar por resumos. Peço: se você possui RESUMOS de análise do Elon (grande ou pequeno vol 1) por gentileza mande para meu e-mail ilhadepaquetaARROBAbol.com.br estudar por resumos vai facilitar (acho!). Obrigado mais uma vez Hermann Cabri ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Tue Mar 25 23:09:24 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2Q27pWA004750 for ; Tue, 25 Mar 2008 23:07:57 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2Q27jxQ004740 for obm-l-MllGbsmmN; Tue, 25 Mar 2008 23:07:45 -0300 Received: from smtp.bol.com.br (smtpout1.bol.com.br [200.221.4.212]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2Q27DWA004719 for ; Tue, 25 Mar 2008 23:07:14 -0300 Received: from localhost (localhost [127.0.0.1]) by smart5.bol.com.br (Postfix) with ESMTP id 454276C7 for ; Tue, 25 Mar 2008 23:06:56 -0300 (BRT) Received: from pai (unknown [201.88.134.242]) by smart5.bol.com.br (Postfix) with ESMTP id DE9FE2B2 for ; Tue, 25 Mar 2008 23:06:54 -0300 (BRT) Message-ID: <002e01c88ee6$56cf2f20$6501a8c0@pai> From: "Tio Cabri st" To: References: <638971.61255.qm@web45906.mail.sp1.yahoo.com> Subject: [obm-l] =?iso-8859-1?Q?Re:_=5Bobm-l=5D_m=F3dulo?= Date: Tue, 25 Mar 2008 23:08:51 -0300 MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: 8bit X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2800.1478 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2800.1478 X-SIG5: c20f83547c14e7bc920778588446964a Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Tio Cabri st" X-Spam-Status: No, hits=4.1 required=5.0 tests=AWL,MAILTO_TO_SPAM_ADDR,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, REFERENCES,SPAM_PHRASE_00_01,USER_AGENT_OE,X_MAILING_LIST version=2.44 X-Spam-Level: **** Não entendi não. Isso aí está certo??????????? Suponha que a # b, isto é, suponha que "a" e diferente de "b". Neste caso, s = | a - b | e um real positivo. (OK, tudo bem) ?????mas...??????? Entao, fazendo r = s e usando (ué, não era para todo r>0????????) (não entendi) Se puder explicar de outra forma agradeceria. Abraços Hermann Cabri ----- Original Message ----- From: "Paulo Santa Rita" To: Sent: Tuesday, March 25, 2008 1:53 PM Subject: Re: [obm-l] módulo Ola Joel e demais colegas desta lista ... OBM-L, Suponha que a # b, isto é, suponha que "a" e diferente de "b". Neste caso, s = | a - b | e um real positivo. Entao, fazendo r = s e usando a propriedade enunciada, teremos : | a - b | < s => | a - b | < | a - b | ... absurdo ! Assim, a nossa tese e insustentavel e somos obrigados a admitir que a = b. No endereco abaixo existem muitos problemas olimpicos interessantes : http://www.mat.puc-rio.br/~nicolau/psr/ Um Abraco a Todos Paulo Santa Rita 3,0D31,190308 Em 25/03/08, Joel Castro escreveu: > tenho pequena dúvida: > > prove: se para todo r maior que zero, o módulo da diferença de a e b é menor > que r, então a é igual a b. > > valeu!!!!!! > > ________________________________ > Abra sua conta no Yahoo! Mail, o único sem limite de espaço para > armazenamento! > > ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Tue Mar 25 23:26:41 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2Q2PgWA006144 for ; Tue, 25 Mar 2008 23:25:42 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2Q2PgnS006142 for obm-l-MllGbsmmN; Tue, 25 Mar 2008 23:25:42 -0300 Received: from web52903.mail.re2.yahoo.com (web52903.mail.re2.yahoo.com [206.190.49.13]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id m2Q2PdWA006128 for ; Tue, 25 Mar 2008 23:25:40 -0300 Received: (qmail 67213 invoked by uid 60001); 26 Mar 2008 02:25:20 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:Date:From:Subject:To:In-Reply-To:MIME-Version:Content-Type:Content-Transfer-Encoding:Message-ID; b=deAFawk3IFFfurFcOIqe0j7CzbFo2ePTyxfONr26YqhvE+DyTDGPcpncMIXZCK908xtN5VzvlkdQXwWcu5J17Q/W9ycAJzilAce69/3mH14pH/aBnVavOygJkE8Xp85D90sIQ0hUnKmh3byH5Zn10neUvUBtcyY+TO2mJb/tvQo=; X-YMail-OSG: E9YQL.IVM1kbG.f8hPeA5SGwwme.DfkOe8khkowyocLIaaneIVQ2rd6d2UtGXyfL6ah6xnqRHT9XsXEylBw0E5Knwr9C9Uyz7HKr_ryq0SX6jvs8TfE- Received: from [189.30.80.236] by web52903.mail.re2.yahoo.com via HTTP; Tue, 25 Mar 2008 23:25:20 ART Date: Tue, 25 Mar 2008 23:25:20 -0300 (ART) From: Antonio Giansante Subject: =?iso-8859-1?q?Re:=20[obm-l]=20m=F3dulo?= To: obm-l@mat.puc-rio.br In-Reply-To: MIME-Version: 1.0 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 8bit Message-ID: <889896.67173.qm@web52903.mail.re2.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Antonio Giansante X-Spam-Status: No, hits=4.0 required=5.0 tests=FORGED_YAHOO_RCVD,IN_REP_TO,MAILTO_TO_SPAM_ADDR, RCVD_IN_ORBS,SPAM_PHRASE_00_01,X_MAILING_LIST version=2.44 X-Spam-Level: **** Creio que você incorreu em um erro muito comum da argumentação lógica, justamente por ser ele muito sutil de ser percebido (e por isso ser muito usado em concursos públicos): Você não pode usar a tese para prová-la. Por exemplo: Prove que se um número é divisível por 2, então ele é par. Aí você começa fazendo: suponha que n é par, logo é divisível por 2. Por isso não pode fazer "suponha r=s". creio que essa afirmação da tese é dito modus tollens. Em um exemplo um pouco mais didático: pense na afirmação: Se chove, então molha. Assim, se eu afirmar que se molhou, então choveu, vou estar errando, pois poderia ter molhado com um copo d'água, uma mangueira, etc Eu posso dizer que se chove, com certeza molha, mas se molha, nem sempre foi porque choveu. Espero que este chove-e-não-molha (que é a negação da frase inicial) E creio que essa afirmação é falsa, pois encontramos um contra-exemplo: Seja a#0, b = 2a e r = 3a veja que | a - b | escreveu: > Ola Joel e demais colegas > desta lista ... OBM-L, > > > Suponha que a # b, isto é, suponha que "a" e > diferente de "b". Neste > caso, s = | a - b | e um real positivo. Entao, > fazendo r = s e usando > a propriedade enunciada, teremos : > > | a - b | < s => | a - b | < | a - b | ... absurdo ! > > Assim, a nossa tese e insustentavel e somos > obrigados a admitir que a = b. > > No endereco abaixo existem muitos problemas > olimpicos interessantes : > http://www.mat.puc-rio.br/~nicolau/psr/ > > Um Abraco a Todos > Paulo Santa Rita > 3,0D31,190308 > > > > Em 25/03/08, Joel Castro > escreveu: > > tenho pequena dúvida: > > > > prove: se para todo r maior que zero, o módulo da > diferença de a e b é menor > > que r, então a é igual a b. > > > > valeu!!!!!! > > > > ________________________________ > > Abra sua conta no Yahoo! Mail, o único sem limite > de espaço para > > armazenamento! > > > > > > ========================================================================= > Instruções para entrar na lista, sair da lista e > usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > ========================================================================= > Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! http://br.mail.yahoo.com/ ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Mar 26 00:59:22 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2Q3vYWA010916 for ; Wed, 26 Mar 2008 00:57:34 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2Q3vSO7010914 for obm-l-MllGbsmmN; Wed, 26 Mar 2008 00:57:28 -0300 Received: from hm171.locaweb.com.br (hm171-2.locaweb.com.br [200.234.205.179]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id m2Q3vHWA010909 for ; Wed, 26 Mar 2008 00:57:17 -0300 Received: (qmail 20074 invoked from network); 26 Mar 2008 03:57:01 -0000 Received: from unknown (10.1.10.169) by hm171.locaweb.com.br with QMQP; 26 Mar 2008 03:57:01 -0000 Received: from unknown (HELO lattes) (paulo@uniredes.org@189.25.240.94) by hm169.locaweb.com.br with SMTP; 26 Mar 2008 03:57:00 -0000 From: "Paulo - Uniredes" To: Subject: [SPAM] RES: [obm-l] Livros de Geomtria Analitica Date: Wed, 26 Mar 2008 00:57:18 -0300 Organization: Uniredes Message-ID: MIME-Version: 1.0 Content-Type: text/plain X-Mailer: Microsoft Office Outlook, Build 11.0.5510 In-Reply-To: <228699.84676.qm@web46208.mail.sp1.yahoo.com> X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.3198 thread-index: AciO14kj1cAHkqgFRuKfT8v9jH1AqQAHXyrg Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Paulo - Uniredes" X-Spam-Status: Yes, hits=8.2 required=5.0 tests=HTML_FONT_COLOR_BLUE,IN_REP_TO,MISSING_OUTLOOK_NAME, MSGID_CHARS_SPAM,MSGID_CHARS_WEIRD,NOSPAM_INC,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01,SPAM_REDIRECTOR, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_NextPart_000_0036_01C88EDC.57948680" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (8.20 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: NOSPAM_INC (-0.2 points) Where are you working at? SPAM: MSGID_CHARS_WEIRD (1.6 points) Message-Id has characters often found in spam SPAM: MSGID_CHARS_SPAM (0.1 points) Message-Id has characters indicating spam SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: HTML_FONT_COLOR_BLUE (0.2 points) BODY: HTML font color is blue SPAM: SPAM_REDIRECTOR (0.4 points) URI: Uses open redirection service SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 179.205.234.200.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 179.205.234.200.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: MISSING_OUTLOOK_NAME (1.1 points) Message looks like Outlook, but isn't SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- This is a multi-part message in MIME format. ------=_NextPart_000_0036_01C88EDC.57948680 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Olha, Daniel... =20 Eu recomendo o Boldrini. Eu tenho um exemplar (edi=E7=E3o antiga) em meu "sebinho". Se estiver interessado a gente se fala. =C9 o melhor at=E9 hoje: http://www.livrariamelhoramentos.com.br/supercart/cgi-bin/supercart.exe/s= ear chID?ok=3Ddetalhes_livros.htm ¬hing=3Dlivros_nada.htm&b=3D168&id_est=3D77583&depto=3D68 =20 =20 []s =20 --- Paulo C. Santos (PC) e-mail: paulo@uniredes.org Homepage: http://uniredes.org =20 Tel.: (21) 2510.8783 - Cel.: (21) 8753-0729 -------------------------------------------- MS-Messenger: Uniredes_Br@hotmail.Com=20 =20 _____ =20 De: owner-obm-l@mat.puc-rio.br [mailto:owner-obm-l@mat.puc-rio.br] Em = nome de Daniel Madeira Enviada em: ter=E7a-feira, 25 de mar=E7o de 2008 20:57 Para: obm-l@mat.puc-rio.br Assunto: [obm-l] Livros de Geomtria Analitica Caros amigos da lista, =20 Estou estudando na universidade a disciplina: Geometria Anal=EDtica. = Estive navegando na internet em busca de livros para e comprar e estudar essa disciplina. Em particular me interessa um livro que aborde problemas = sobre parte de vetores como semi-retas (a parte geometrica), a parte referente = a vetores Linearmente depedentes e independentes e exerc=EDcios de = demonstra=E7=E3o envolvendo propriedades de opera=E7=F5es com vetores. Estive vendo = alguns livros. O que acham desses livros ? =20 - Introdu=E7=E3o =E0 geomtria anal=EDtica no espa=E7o autor: Paulo Boulos e Ivan de Camargo edt: Makron Books =20 - =C1lgebra Linear e geometria vectorial autor: Rios, Sixto edit: Litexa =20 - Vetores e Geometria Analitica, teoria e exercicios autor: Ana C=E9lia da Costa Loreto e Armando editora: LCTE =20 - Vetores e uma inicia=E7=E3o =E0 geometria an=E1litica autor: Dorival A. de Mello e Renate G. Watanabe editora: Penn =20 - Exerc=EDcios de geometria analitica (vale a pena esse livro ?) autor: Blasi editora: Papirus =20 J=E1 tenho os livros: =E1lgebra linear e aplica=E7=F5es do callioli, = geometria anal=EDtica - um tratamento vetorial do Paulo Boulos e geometria = anal=EDtica do Steinbruch. =20 Pe=E7o desculpas pelo e-mail extenso. Certo da compreens=E3o de = voc=EAs e de sua ajuda, agrade=E7o desde j=E1. =20 Cordialmente, =20 Daniel. =20 ps: algum livro do elon lages envolvendo essa parte de geometria = analitica ? ele vale a pena ? =20 _____ =20 Abra sua conta no Yahoo! = Mail, o =FAnico sem limite de espa=E7o para armazenamento!=20 ------=_NextPart_000_0036_01C88EDC.57948680 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable
Olha, Daniel...
 
Eu recomendo o Boldrini. Eu tenho um exemplar = (edi=E7=E3o=20 antiga) em meu "sebinho". Se estiver interessado a gente se=20 fala.
=C9 o melhor at=E9 hoje: http://www.livrariamelhorame= ntos.com.br/supercart/cgi-bin/supercart.exe/searchID?ok=3Ddetalhes_livros= .htm&nothing=3Dlivros_nada.htm&b=3D168&id_est=3D77583&dep= to=3D68
 
 
[]s
 

---
Paulo C. Santos (PC)
e-mail:=20 paulo@uniredes.org
Homepage: http://uniredes.org
Tel.: (21) = 2510.8783 -=20 Cel.: (21)=20 8753-0729
--------------------------------------------
MS-Messenger= :=20 Uniredes_Br@hotmail.Com


 


De: owner-obm-l@mat.puc-rio.br=20 [mailto:owner-obm-l@mat.puc-rio.br] Em nome de Daniel=20 Madeira
Enviada em: ter=E7a-feira, 25 de mar=E7o de 2008=20 20:57
Para: obm-l@mat.puc-rio.br
Assunto: [obm-l] = Livros de=20 Geomtria Analitica

Caros amigos da lista,
 
   Estou estudando na universidade a disciplina: = Geometria=20 Anal=EDtica. Estive navegando na internet em busca de livros para e = comprar e=20 estudar essa disciplina. Em particular me interessa um livro que = aborde=20 problemas sobre parte de vetores como semi-retas (a parte = geometrica), a=20 parte referente a vetores Linearmente depedentes e independentes=20 e exerc=EDcios de demonstra=E7=E3o envolvendo propriedades de = opera=E7=F5es com=20 vetores. Estive vendo alguns livros. O que acham desses=20 livros ?
 
- Introdu=E7=E3o =E0 geomtria anal=EDtica no espa=E7o
  autor: Paulo Boulos e Ivan de Camargo
  edt: Makron Books
 
- =C1lgebra Linear e geometria vectorial
 autor: Rios, Sixto
 edit: Litexa
 
- Vetores e Geometria Analitica, teoria e exercicios
 autor: Ana C=E9lia da Costa Loreto e Armando
 editora: LCTE
 
- Vetores e uma inicia=E7=E3o =E0 geometria an=E1litica
 autor: Dorival A. de Mello e Renate G. Watanabe
editora: Penn
 
- Exerc=EDcios de geometria analitica (vale a pena esse = livro=20 ?)
 autor: Blasi
editora: Papirus
 
J=E1 tenho os livros: =E1lgebra linear e aplica=E7=F5es do = callioli, geometria=20 anal=EDtica - um tratamento vetorial do Paulo Boulos e geometria = anal=EDtica do=20 Steinbruch.
 
  Pe=E7o desculpas pelo e-mail extenso. Certo da compreens=E3o = de voc=EAs e=20 de sua ajuda, agrade=E7o desde j=E1.
 
 Cordialmente,
 
   Daniel.
 
ps:  algum livro do elon lages envolvendo essa parte = de=20 geometria analitica ? ele vale a pena ?
  

Abra sua conta no Yahoo!=20 Mail, o =FAnico sem limite de espa=E7o para armazenamento! = ------=_NextPart_000_0036_01C88EDC.57948680-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Mar 26 01:01:25 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2Q40MWA010985 for ; Wed, 26 Mar 2008 01:00:22 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2Q40FRI010981 for obm-l-MllGbsmmN; Wed, 26 Mar 2008 01:00:15 -0300 Received: from hm171.locaweb.com.br (hm171-2.locaweb.com.br [200.234.205.179]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id m2Q402WA010964 for ; Wed, 26 Mar 2008 01:00:03 -0300 Message-Id: <200803260400.m2Q402WA010964@saci.mat.puc-rio.br> Received: (qmail 19294 invoked from network); 26 Mar 2008 03:53:05 -0000 Received: from unknown (10.1.10.169) by hm171.locaweb.com.br with QMQP; 26 Mar 2008 03:53:05 -0000 Received: from unknown (HELO lattes) (paulo@uniredes.org@189.25.240.94) by hm169.locaweb.com.br with SMTP; 26 Mar 2008 03:53:05 -0000 From: "Paulo - Uniredes" To: Subject: [SPAM] [obm-l] =?iso-8859-1?Q?RES:_=5Bobm-l=5D_Indica=E7=E3o_de_livros_=28C=E1lcul?= =?iso-8859-1?Q?o_num=E9rico_e_Equa=E7=F5es_diferenciais=29?= Date: Wed, 26 Mar 2008 00:53:23 -0300 Organization: Uniredes MIME-Version: 1.0 Content-Type: text/plain X-Mailer: Microsoft Office Outlook, Build 11.0.5510 In-Reply-To: <212079.44593.qm@web55214.mail.re4.yahoo.com> X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.3198 thread-index: AciOsgk3GG+MwtTGShKvm60HOqO6pgAQqASA Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Paulo - Uniredes" X-Spam-Status: Yes, hits=7.4 required=5.0 tests=AWL,HTML_FONT_COLOR_BLUE,IN_REP_TO,MISSING_OUTLOOK_NAME, MSG_ID_ADDED_BY_MTA_2,NOSPAM_INC,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01,SPAM_REDIRECTOR, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******* X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_NextPart_000_0032_01C88EDB.CB3F6290" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (7.40 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: NOSPAM_INC (-0.2 points) Where are you working at? SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: HTML_FONT_COLOR_BLUE (0.2 points) BODY: HTML font color is blue SPAM: SPAM_REDIRECTOR (0.4 points) URI: Uses open redirection service SPAM: MSG_ID_ADDED_BY_MTA_2 (0.1 points) 'Message-Id' was added by a relay (2) SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 179.205.234.200.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 179.205.234.200.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: MISSING_OUTLOOK_NAME (1.1 points) Message looks like Outlook, but isn't SPAM: AWL (0.8 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- This is a multi-part message in MIME format. ------=_NextPart_000_0032_01C88EDB.CB3F6290 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable C=E1lculo num=E9rico eu tenho um usado do T=E9rcio Pacitti. Muito bom, = mas os exemplos est=E3o em Fortran, que =E9 a linguagem mais usada at=E9 hoje = para C=E1lculo num=E9rico. T=E1 interessado ? =20 []s =20 PS.: Arrumar um compilador Fortran gratuito para Windows ou Linux =E9 = muito f=E1cil... =20 --- Paulo C. Santos (PC) e-mail: paulo@uniredes.org Homepage: http://uniredes.org =20 Tel.: (21) 2510.8783 - Cel.: (21) 8753-0729 -------------------------------------------- MS-Messenger: Uniredes_Br@hotmail.Com=20 _____ =20 De: owner-obm-l@mat.puc-rio.br [mailto:owner-obm-l@mat.puc-rio.br] Em = nome de C=E9sar Santos Enviada em: ter=E7a-feira, 25 de mar=E7o de 2008 16:10 Para: obm-l@mat.puc-rio.br Assunto: [obm-l] Indica=E7=E3o de livros (C=E1lculo num=E9rico e = Equa=E7=F5es diferenciais) Poderiam me indicar bons livros de c=E1lculo num=E9rico e de = equa=E7=F5es diferencias acess=EDveis para iniciante?=20 _____ =20 Abra sua conta no Yahoo! = Mail, o =FAnico sem limite de espa=E7o para armazenamento!=20 ------=_NextPart_000_0032_01C88EDB.CB3F6290 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable
C=E1lculo num=E9rico eu tenho um usado do = T=E9rcio Pacitti. Muito=20 bom, mas os exemplos est=E3o em Fortran, que =E9 a linguagem mais usada = at=E9 hoje=20 para C=E1lculo num=E9rico. T=E1 interessado ?
 
[]s
 
PS.: Arrumar um compilador Fortran gratuito = para Windows ou=20 Linux =E9 muito f=E1cil...
 

---
Paulo C. Santos (PC)
e-mail:=20 paulo@uniredes.org
Homepage: http://uniredes.org
Tel.: (21) = 2510.8783 -=20 Cel.: (21)=20 8753-0729
--------------------------------------------
MS-Messenger= :=20 Uniredes_Br@hotmail.Com


De: owner-obm-l@mat.puc-rio.br=20 [mailto:owner-obm-l@mat.puc-rio.br] Em nome de C=E9sar = Santos
Enviada=20 em: ter=E7a-feira, 25 de mar=E7o de 2008 16:10
Para:=20 obm-l@mat.puc-rio.br
Assunto: [obm-l] Indica=E7=E3o de livros = (C=E1lculo=20 num=E9rico e Equa=E7=F5es diferenciais)

Poderiam me indicar bons livros de c=E1lculo num=E9rico e de = equa=E7=F5es=20 diferencias acess=EDveis para iniciante?

Abra sua conta no Yahoo!=20 Mail, o =FAnico sem limite de espa=E7o para armazenamento! = ------=_NextPart_000_0032_01C88EDB.CB3F6290-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Mar 26 01:05:45 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2Q44nWA011152 for ; Wed, 26 Mar 2008 01:04:49 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2Q44nU1011150 for obm-l-MllGbsmmN; Wed, 26 Mar 2008 01:04:49 -0300 Received: from hm171.locaweb.com.br (hm171-2.locaweb.com.br [200.234.205.179]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id m2Q44mWA011147 for ; Wed, 26 Mar 2008 01:04:48 -0300 Received: (qmail 22326 invoked from network); 26 Mar 2008 04:04:31 -0000 Received: from unknown (10.1.10.169) by hm171.locaweb.com.br with QMQP; 26 Mar 2008 04:04:31 -0000 Received: from unknown (HELO lattes) (paulo@uniredes.org@189.25.240.94) by hm169.locaweb.com.br with SMTP; 26 Mar 2008 04:04:32 -0000 From: "Paulo - Uniredes" To: Subject: [SPAM] [obm-l] =?iso-8859-1?Q?RES:_=5Bobm-l=5D_Indica=E7=E3o_de_livros_=28C=E1lcul?= =?iso-8859-1?Q?o_num=E9rico_e_Equa=E7=F5es_diferenciais=29?= Date: Wed, 26 Mar 2008 01:04:49 -0300 Organization: Uniredes Message-ID: MIME-Version: 1.0 Content-Type: text/plain X-Mailer: Microsoft Office Outlook, Build 11.0.5510 In-Reply-To: <212079.44593.qm@web55214.mail.re4.yahoo.com> X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.3198 thread-index: AciOsgk3GG+MwtTGShKvm60HOqO6pgAQ6PVg Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Paulo - Uniredes" X-Spam-Status: Yes, hits=7.8 required=5.0 tests=AWL,HTML_FONT_COLOR_BLUE,IN_REP_TO,MISSING_OUTLOOK_NAME, MSGID_CHARS_SPAM,MSGID_CHARS_WEIRD,NOSPAM_INC,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01,SPAM_REDIRECTOR, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******* X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_NextPart_000_003A_01C88EDD.645DBAC0" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (7.80 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: NOSPAM_INC (-0.2 points) Where are you working at? SPAM: MSGID_CHARS_WEIRD (1.6 points) Message-Id has characters often found in spam SPAM: MSGID_CHARS_SPAM (0.1 points) Message-Id has characters indicating spam SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: HTML_FONT_COLOR_BLUE (0.2 points) BODY: HTML font color is blue SPAM: SPAM_REDIRECTOR (0.4 points) URI: Uses open redirection service SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 179.205.234.200.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 179.205.234.200.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: MISSING_OUTLOOK_NAME (1.1 points) Message looks like Outlook, but isn't SPAM: AWL (-0.4 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- This is a multi-part message in MIME format. ------=_NextPart_000_003A_01C88EDD.645DBAC0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Oi Cesar, =20 Para c=E1lculo I e II, eu recomendo o Piskunov: http://www.traca.com.br/seboslivrosusados.cgi?mod=3DLV62211 &origem=3Dresultadodetalhada Eu tenho os volumes I e II em espanhol no meu sebo. S=E3o muito legais. = O volume II =E9 =F3timo em equa=E7=F5es diferenciais. A obra, em 2 = volumes, foi usada na UFRJ. =20 Tem tamb=E9m o do Tom M. Apostol em portugu=EAs...: =20 http://www.livrariadafisica.com.br/produto_detalhe.asp?id_produto=3D19209= =20 Estudei pelo Apostol e a qualidade =E9 muito boa. Apesar de eu ser meio "burro" (S=F3 passei em c=E1lculo I ap=F3s fazer um curso de ver=E3o na = UFRJ. Muito legal...mas meu neg=F3cio =E9 redes de computadores). =20 Fa=E7o pre=E7o camarada nos 3 livros. Camarada mesmo ! =20 =20 []s =20 --- Paulo C. Santos (PC) e-mail: paulo@uniredes.org Homepage: http://uniredes.org =20 Tel.: (21) 2510.8783 - Cel.: (21) 8753-0729 -------------------------------------------- MS-Messenger: Uniredes_Br@hotmail.Com=20 _____ =20 De: owner-obm-l@mat.puc-rio.br [mailto:owner-obm-l@mat.puc-rio.br] Em = nome de C=E9sar Santos Enviada em: ter=E7a-feira, 25 de mar=E7o de 2008 16:10 Para: obm-l@mat.puc-rio.br Assunto: [obm-l] Indica=E7=E3o de livros (C=E1lculo num=E9rico e = Equa=E7=F5es diferenciais) Poderiam me indicar bons livros de c=E1lculo num=E9rico e de = equa=E7=F5es diferencias acess=EDveis para iniciante?=20 _____ =20 Abra sua conta no Yahoo! = Mail, o =FAnico sem limite de espa=E7o para armazenamento!=20 ------=_NextPart_000_003A_01C88EDD.645DBAC0 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable
Oi Cesar,
 
Para c=E1lculo I e II, eu recomendo o Piskunov: = http://www.traca.com.br/seboslivrosusados.cgi= ?mod=3DLV62211&origem=3Dresultadodetalhada
Eu tenho os volumes I e II em espanhol no meu = sebo. S=E3o=20 muito legais. O volume II =E9 =F3timo em equa=E7=F5es diferenciais. A = obra, em 2=20 volumes, foi usada na UFRJ.
 
Tem tamb=E9m o do Tom M. Apostol em=20 portugu=EAs...:
 
http://www.livrariadafisica.com.br/produto_detalhe.asp?id_produ= to=3D19209
 
Estudei pelo Apostol e a qualidade =E9 = muito boa. Apesar=20 de eu ser meio "burro" (S=F3 passei em c=E1lculo I ap=F3s fazer um curso = de ver=E3o na=20 UFRJ. Muito legal...mas meu neg=F3cio =E9 redes de=20 computadores).
 
Fa=E7o pre=E7o camarada nos 3 livros. Camarada = mesmo=20 !
 
 
[]s
 

---
Paulo C. Santos (PC)
e-mail:=20 paulo@uniredes.org
Homepage: http://uniredes.org
Tel.: (21) = 2510.8783 -=20 Cel.: (21)=20 8753-0729
--------------------------------------------
MS-Messenger= :=20 Uniredes_Br@hotmail.Com


De: owner-obm-l@mat.puc-rio.br=20 [mailto:owner-obm-l@mat.puc-rio.br] Em nome de C=E9sar = Santos
Enviada=20 em: ter=E7a-feira, 25 de mar=E7o de 2008 16:10
Para:=20 obm-l@mat.puc-rio.br
Assunto: [obm-l] Indica=E7=E3o de livros = (C=E1lculo=20 num=E9rico e Equa=E7=F5es diferenciais)

Poderiam me indicar bons livros de c=E1lculo num=E9rico e de = equa=E7=F5es=20 diferencias acess=EDveis para iniciante?

Abra sua conta no Yahoo!=20 Mail, o =FAnico sem limite de espa=E7o para armazenamento! = ------=_NextPart_000_003A_01C88EDD.645DBAC0-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Mar 26 01:28:12 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2Q4REWA012181 for ; Wed, 26 Mar 2008 01:27:14 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2Q4RElq012179 for obm-l-MllGbsmmN; Wed, 26 Mar 2008 01:27:14 -0300 Received: from fg-out-1718.google.com (fg-out-1718.google.com [72.14.220.155]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2Q4RBWA012176 for ; Wed, 26 Mar 2008 01:27:12 -0300 Received: by fg-out-1718.google.com with SMTP id e12so3125994fga.3 for ; Tue, 25 Mar 2008 21:26:53 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; bh=3TAgol8X+JXplnKVrUqUqOe+eJAR28WmJUFS08HChJ0=; b=Y4gsB9sgct/U5l2RGLkhsdZd0LpJiDAghHtqBYAiZ2Gz/xgtACBJNCaYup1lXvbX73ZB/jrJv8AoA23DjjZLBURzmUhn6EnWK7mKm3ti6SpaIy9R9VgirPiJFX1J8nMLTlzabNfrnwRmU0ZXbju/M+qjgzzzNXMqL/vRQGFfhak= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; b=oR7j/zpoLfwAdiy469Rdlh5nqXOsouXoF41zvoJ3nXX589nIYDuaxFsjaFWGdskL5jd4TV0OnLH1VVMKm1Tjj/0QZOZG30UQwhYoOXH9ohUh/mvD3a2+ol1Wj3q5jcZrIQVFnKhFprn+seuHa9QzZM7jp/Bj5SE857HClYBVJYg= Received: by 10.82.124.10 with SMTP id w10mr23225431buc.18.1206505612903; Tue, 25 Mar 2008 21:26:52 -0700 (PDT) Received: by 10.82.127.13 with HTTP; Tue, 25 Mar 2008 21:26:52 -0700 (PDT) Message-ID: Date: Wed, 26 Mar 2008 01:26:52 -0300 From: "Johann Peter Gustav Lejeune Dirichlet" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] combinatoria dificil In-Reply-To: <000b01c88dce$d8e27bc0$d400a8c0@AMD> MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline References: <3e7bcb580803201443r10149ad4n4a3c3d7710b3573@mail.gmail.com> <5bb472220803240629k4f430aa9v765f20fdbd0bdad2@mail.gmail.com> <001b01c88dc5$3863fdd0$d400a8c0@AMD> <5bb472220803240908y48701b01y7b8cfeae9d66eeed@mail.gmail.com> <000b01c88dce$d8e27bc0$d400a8c0@AMD> Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m2Q4RDWA012177 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Johann Peter Gustav Lejeune Dirichlet" X-Spam-Status: No, hits=-0.1 required=5.0 tests=AWL,FROM_ENDS_IN_NUMS,GAPPY_TEXT,IN_REP_TO, QUOTED_EMAIL_TEXT,REFERENCES,SIGNATURE_LONG_SPARSE, SPAM_PHRASE_00_01,X_MAILING_LIST version=2.44 X-Spam-Level: Não é tão escabroso quanto parece: 19H + 13M = 1000 Módulo 13, temos 19H=1000 7H=1000=-14 H=-2=(mod 13) Entao H=13x+2 Substitui: 19(13x+2) + 13M = 1000 247x+13M=962 19x+M=74 M=74-19x H=13x+2 Agora que parametrizou, faz com que ambos sejam positivos, ou 74-19x>0 74>19x x<74/19<4 Bem, daí é só testar! Em 24/03/08, Fernando escreveu: > > > Oi João Victor, a questão é que eu já havia escrito esta equação. Acontece > que ela é "diofantina", admitindo infinitas soluções. Claro que, de acordo > com as condições do exercício proposto deve-se conseguir restringir a > quantidade delas para um número bem menos (eu creio). > P.S.: Nem toda diofantiona tem infinitas soluções. Diofantina significa somente `resolva em Z={0,1,-1,2,-2,3,-3,...}´ Ou seja, até mesmo x=2 pode ser diofantina, bem como x^3=5 > Amplexo. > Fernando > > ________________________________ > ________________________________ > > > ----- Original Message ----- > From: Joao Victor Brasil > To: obm-l@mat.puc-rio.br > Sent: Monday, March 24, 2008 1:08 PM > Subject: Re: [obm-l] combinatoria dificil > > > Fernando, > > Infelizmente não tenho, mas tenta ver algo nesse sentido: > 19H + 13M = 1000, H= Homem e M=Mulher > > Joao Victor > > > On 3/24/08, Fernando wrote: > > > > > > Olá João Victor, boa tarde! > > > > Você possui a solução do problema abaixo? > > Se SIM, poderia enviá-la para mim? > > > > > > > > Sociedade Brasileira de Matemática > > > > EUREKA! N°14, 2002 > > > > VIII OLIMPÍADA DE MAIO > > > > Enunciados e Resultado Brasileiro > > > > PRIMEIRO NÍVEL > > > > 11/05/2002 > > > > PROBLEMA 1 > > > > Um grupo de homens, alguns dos quais acompanhados pelas esposas, gastaram > 1000 > > > > dólares num hotel. Cada homem gastou 19 dólares e cada mulher, 13 dólares. > > > > Determine quantas mulheres e quantos homens estavam no hotel. > > > > > > > > http://www.obm.org.br/eureka/eureka14.pdf > > > > acesso em 23/03/2008 > > > > > > Agradeço sua atenção. > > > > Amplexo. > > Fernando Pinto > > > > ________________________________ > ________________________________ > > > > > ----- Original Message ----- > > From: Joao Victor Brasil > > To: obm-l@mat.puc-rio.br > > Sent: Monday, March 24, 2008 10:29 AM > > Subject: Re: [obm-l] combinatoria dificil > > > > > > > > É verdade pessoal. Errei e muito na minha resolução. > > > > Mas olha só, concordo plenamente com a resposta do Henrique, 48 > possibilidades. > > > > Usando o princípio multiplicativo D1H1_D1H2_D2H1_D2H2_D3H1_D3H2 achei 72 > possibilidades, me alertaram sobre as repetições e analisei um modo de > retirá-las. > > D1H1:3 disc > > D1H2: 2 disc > > D2H1: 2 disc (repetir as mesmas disciplinas do dia 1) > > D2H2: 1 disc > > D3H1: 2 disc (apesar de sobrar somente uma disc, temos duas aulas) > > D3H2: 1 disc > > > > 3*2*2*1*2*1 = 24. 72 - 24 = 48 poss. > > > > Joao Victor > > > > > > On 3/20/08, Henrique Rennó wrote: > > > Olá pessoal! > > > > > > Acredito que a solução do Salhab está correta. Seja Di o dia i e Hj o > horário j. > > > > > > D1H1: 3 matérias > > > D1H2: 2 matérias (para não repetir a utilizada em D1H1) > > > D1: 6 possibilidades > > > > > > Para D2, se escolhermos uma já utilizada em D1 então não poderemos > > > utilizar a outra matéria utilizada em D1, senão D3 teria as mesmas > > > matérias. Assim, para D2 teríamos uma já utilizada (2 matérias) e uma > > > não utilizada. Logo, 2*1 = 2. Como a ordem importa, temos 2*2 = 4. > > > > > > D3 só possui 2 formas, com as ordens das matérias trocadas. > > > > > > Total: 6*4*2 = 48. > > > > > > Essa é uma forma mais lógica de resolver o problema. Estive tentando > > > utilizar combinatória e também achei a resposta 48. > > > > > > Sejam A,B,C as matérias. Quantas permutações diferentes existem entre > > > A,A,B,B,C,C? Cada posição seria um horário em um dia, ou seja, > > > D1H1_D1H2_D2H1_D2H2_D3H1_D3H2. Bastaria calcular o número de > > > permutações com repetição, ou seja, 6!/(2!*2!*2!) = 720/8 = 90. > > > > > > Sabemos que não podemos ter uma permutação do tipo AABCBC, pois AA > > > representa a mesma matéria em D1H1 e D1H2. Então sabemos que a > > > resposta é menor que 90. > > > > > > As formas inválidas serão: > > > > > > Se as 3 matérias do mesmo tipo estão juntas no mesmo dia, ex: AABBCC. > > > Existem 3! = 6 formas, considerando AA,BB,CC como 3 elementos > > > permutados entre si. > > > > > > Não há necessidade de verificar quando 2 matérias estão no mesmo dia > > > pois cai no caso acima. > > > > > > Quando há apenas 1 matéria repetida em 1 dia, ex: AABCBC, então temos > > > 12 formas para cada par da mesma matéria utilizada no mesmo dia. Se AA > > > está em D1 então D2 pode ser BC ou CB e D3 pode ser BC ou CB, 2*2 = 4. > > > AA pode estar em D1,D2,D3. Assim, 4*3 = 12. Para BB e CC seria o > > > mesmo, dando um total de 3*12 = 36 formas quando há apenas uma matéria > > > que se repete no mesmo dia. > > > > > > Assim, o total seria 90 - (6+36) = 90 - 42 = 48 formas distintas de > > > compor o horário > > > > > > Thelio, você poderia passar a fonte do problema e verificar se as > > > respostas são essas mesmo? > > > > > > On 3/13/08, Thelio Gama wrote: > > > > É pessoal... > > > > > > > > Achei muito difícil esta questão. Agradeço se alguém puder explicá-la. > > > > > > > > Thelio > > > > > > > > uma turma tem aulas às 2ª, 4ª e 6ª feiras, de 8-9 horas e de 11-12 > horas. As > > > > matérias são portugues, matemática e ingles, cada uma com duas aulas > > > > semanais, em dias diferentes. De quantos modos pode ser feito o > horário > > > > dessa turma? > > > > a)96 ; b) 144 ; c)192 ; d) 6! ; e) 120 > > > > > > > > > -- > > > Henrique > > > > > > > ========================================================================= > > > Instruções para entrar na lista, sair da lista e usar a lista em > > > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > > > > ========================================================================= > > > > > > > > > -- Ideas are bulletproof. V ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Mar 26 03:59:43 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2Q6wBWA032130 for ; Wed, 26 Mar 2008 03:58:11 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2Q6wB3Y032127 for obm-l-MllGbsmmN; Wed, 26 Mar 2008 03:58:11 -0300 Received: from fg-out-1718.google.com (fg-out-1718.google.com [72.14.220.156]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2Q6w9WA032122 for ; Wed, 26 Mar 2008 03:58:09 -0300 Received: by fg-out-1718.google.com with SMTP id e12so3171847fga.3 for ; Tue, 25 Mar 2008 23:57:51 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:mime-version:content-type:content-transfer-encoding:content-disposition; bh=7UGP+/HxJ4VCy/wUfPBfxOqoolU45O8iI2cQrOYukHk=; b=HN1+6Njt/t8cbrxM3ngoR3XOVHprRaabGPo/ppZ8/g7ShgGY/rqT2GuvyDqG4uXbjI5ugtho5evsrsHXrs4gteuO7XtioTeZszuD1K6HKVgv4ljdEhUIZuoL0nAJ/b/7dLjzDGZPFC7qYW+bAi6C54+dn9PypJUknF5xzQpRTv4= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:mime-version:content-type:content-transfer-encoding:content-disposition; b=JAewS03o4aL9P5Tqy1A3nuiUcr8Q3GvAv4x06lsCdDMQIxvdG3Sr8vBJiQhNP9X4ImRl3hgJfHTj5vCl/K8S/X0SREr6s23trJ7mi2PIetHGCJqOdAOgJa4jeLrjiiyLHU9sj7lybRznoQGYIJm+dvHtL0qott94CHQAQcges8I= Received: by 10.82.105.1 with SMTP id d1mr23525997buc.29.1206514670144; Tue, 25 Mar 2008 23:57:50 -0700 (PDT) Received: by 10.82.127.13 with HTTP; Tue, 25 Mar 2008 23:57:50 -0700 (PDT) Message-ID: Date: Wed, 26 Mar 2008 03:57:50 -0300 From: "Johann Peter Gustav Lejeune Dirichlet" To: obm-l@mat.puc-rio.br Subject: [obm-l] =?ISO-8859-1?Q?Meu_livro_-_Constru=E7=F5es_Geom=E9tricas?= MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m2Q6wAWA032125 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Johann Peter Gustav Lejeune Dirichlet" X-Spam-Status: No, hits=1.0 required=5.0 tests=AWL,FROM_ENDS_IN_NUMS,SPAM_PHRASE_00_01,X_MAILING_LIST version=2.44 X-Spam-Level: * Olá pessoas! Estou escrevendo um livro sobre construções geométricas, entre minhas horas vagas. Ele pretende falar mais da parte algébrica, mas sem tirar a beleza da construção ao vivo. Por exemplo, já imaginou usar dobraduras, réguas marcadas, compassos travados, palitos de dente, marcadores de distâncias, etc.? Pois tem várias destas surpresas no livro. Por ora não há aquela porrada de coisas nele, pois não acabei ainda (estou no primeiro capítulo). Mas, para uma prévia, deve valer a pena. Por ora, os arquivos em LaTeX precisam de uma limpeza, mas devem compilar sem maiores problemas. Ainda estou pensando na licença a aplicar nele, depois eu decido. Link: http://www.icmc.usp.br/~richelet/stuff/math Até mais! --- Meu blog! http://tavernadofimdomundo.blogspot.com >> Quadrinhos, poemas, histórias e afins ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Mar 26 07:56:24 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2QAsrWA015062 for ; Wed, 26 Mar 2008 07:54:53 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2QAsq1A015060 for obm-l-MllGbsmmN; Wed, 26 Mar 2008 07:54:52 -0300 Received: from web.fbinfo.com.br (www.fbinfo.com.br [200.245.31.215]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2QAspWA015048 for ; Wed, 26 Mar 2008 07:54:51 -0300 Received: from web.fbinfo.com.br (web [127.0.0.1]) by web.fbinfo.com.br (8.14.1/8.13.4) with ESMTP id m2QAsHwn027255 for ; Wed, 26 Mar 2008 07:54:17 -0300 Received: (from apache@localhost) by web.fbinfo.com.br (8.14.1/8.14.1/Submit) id m2QAsHGu027254; Wed, 26 Mar 2008 07:54:17 -0300 X-Authentication-Warning: web.fbinfo.com.br: apache set sender to buso@fbinfo.com.br using -f Received: from 10.1.3.1 (proxying for 10.1.2.207) (SquirrelMail authenticated user buso) by www.fbinfo.com.br with HTTP; Wed, 26 Mar 2008 07:54:17 -0300 (BRT) Message-ID: <43040.10.1.3.1.1206528857.squirrel@www.fbinfo.com.br> Date: Wed, 26 Mar 2008 07:54:17 -0300 (BRT) Subject: [SPAM] [obm-l] Prove From: buso@fbinfo.com.br To: obm-l@mat.puc-rio.br User-Agent: SquirrelMail/1.4.10a-1.fc7 MIME-Version: 1.0 Content-Type: text/plain;charset=utf-8 Content-Transfer-Encoding: 7bit X-Priority: 3 (Normal) Importance: Normal Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: buso@fbinfo.com.br X-Spam-Status: Yes, hits=7.4 required=5.0 tests=NO_REAL_NAME,PRIORITY_NO_NAME,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01,USER_AGENT, X_AUTH_WARNING,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******* X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. 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Ajuda!!! Eduardo. ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Mar 26 08:04:15 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2QB2JWA015442 for ; Wed, 26 Mar 2008 08:02:19 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2QB2JFv015440 for obm-l-MllGbsmmN; Wed, 26 Mar 2008 08:02:19 -0300 Received: from web56902.mail.re3.yahoo.com (web56902.mail.re3.yahoo.com [66.196.97.91]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id m2QB2HWA015422 for ; Wed, 26 Mar 2008 08:02:17 -0300 Received: (qmail 11395 invoked by uid 60001); 26 Mar 2008 11:01:58 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:Date:From:Subject:To:In-Reply-To:MIME-Version:Content-Type:Content-Transfer-Encoding:Message-ID; b=z0PXvSdBFBpTaqIthQKtpfmq2PdrJphCvkOMg5466CAf+t2/gwtjVcLj0gDhyogZOLb6rulGPYLDglUvQCMBY0wwNIV4729tsgke0UJckrCqzBQ+BdA7zkNw1z/STo266f53/uQflUDnisTZzmC8qTb6EdPp/KYEeT3nkXMLBhI=; X-YMail-OSG: MO5lsacVM1lfKcednGD2mCrL7y6gGBEAPI3t3s51RP8Sh7h4DxOJ5cn4WToFONSf2hbSvDOEAqLEPV_SwiBpsTj1ytHMAEaohyNYBWwrjFWqowaQM.7OOJb3EFUh Received: from [189.62.141.221] by web56902.mail.re3.yahoo.com via HTTP; Wed, 26 Mar 2008 08:01:57 ART Date: Wed, 26 Mar 2008 08:01:57 -0300 (ART) From: cleber vieira Subject: [SPAM] [obm-l] =?iso-8859-1?q?Qual=20o=20valor=20do=20=E2ngulo=3F?= To: obm-l@mat.puc-rio.br In-Reply-To: MIME-Version: 1.0 Content-Type: text/plain Content-Transfer-Encoding: 7bit Message-ID: <206410.11049.qm@web56902.mail.re3.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: cleber vieira X-Spam-Status: Yes, hits=8.7 required=5.0 tests=FORGED_YAHOO_RCVD,HTML_FONT_COLOR_BLUE,IN_REP_TO, MIME_BOUND_DIGITS_5,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, SPAM_PHRASE_00_01,SPAM_REDIRECTOR,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="0-890025571-1206529317=:11049" X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. 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SPAM: SPAM: Content analysis details: (8.70 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: MIME_BOUND_DIGITS_5 (1.7 points) Spam tool pattern in MIME boundary SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: HTML_FONT_COLOR_BLUE (0.2 points) BODY: HTML font color is blue SPAM: SPAM_REDIRECTOR (0.4 points) URI: Uses open redirection service SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 91.97.196.66.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 91.97.196.66.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- --0-890025571-1206529317=:11049 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 8bit O triângulo ABC, retângulo em A, é tal que o < ABC é maior que < ACB. A bissetriz interna de
O triângulo ABC, retângulo em A, é tal que o < ABC é maior que < ACB.
A bissetriz interna de <A, intercepta o lado BC em D. Seja HD perpendicular a BC ( H entre A e C). Nestas condições podemos afirmar que o ângulo <HBD mede, em graus:
a) 25
b) 65
c) 35
d) 45
 
Obrigado!!!

Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-890025571-1206529317=:11049-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Mar 26 08:05:46 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2QB3vWA015552 for ; Wed, 26 Mar 2008 08:03:57 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2QB3ueN015550 for obm-l-MllGbsmmN; Wed, 26 Mar 2008 08:03:56 -0300 Received: from yw-out-2324.google.com (yw-out-2324.google.com [74.125.46.31]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2QB3rWA015546 for ; Wed, 26 Mar 2008 08:03:55 -0300 Received: by yw-out-2324.google.com with SMTP id 3so13221ywj.9 for ; Wed, 26 Mar 2008 04:03:35 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; bh=ikiobeYPhBjyBJwGOxns6J0K9PvaDIRiMSajZ3G6J1Q=; b=jiKWjIJV3GXZIt1ma8HNFnaP+yF6ub2uQJrvzUDAInjDvzptbJ+8PZDwbOeEASlkl++NVpLI7QqnB/u/Wzw7vQ/fMaz8ZchOY4SsYgQhQgSMLpDH2Pi3uBoUoNCQUBj3Xu26s9BaoO6iOkQh6BM8/2zzcjVSBXCdfPFRnJUDsns= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; b=slXY6Pk62fzm700ynCXiMrABt4gHHR06dQRxu7/VHzagbUmhpoMbJiTe098QanEXRqUrrpjrqR4QYyXTiiqkzrv7LaQUDfVDkud31tbuAOPTTqoBGYjcJCr2Cuv2hbVwUNNGzVoNtKGWhkiYAgaxhucZvEjWwsjzkHvUj+i7XxA= Received: by 10.150.135.2 with SMTP id i2mr161626ybd.197.1206529415490; Wed, 26 Mar 2008 04:03:35 -0700 (PDT) Received: by 10.150.144.4 with HTTP; Wed, 26 Mar 2008 04:03:35 -0700 (PDT) Message-ID: Date: Wed, 26 Mar 2008 08:03:35 -0300 From: "Paulo Santa Rita" To: obm-l@mat.puc-rio.br Subject: =?ISO-8859-1?Q?Re:_[obm-l]_m=F3dulo?= In-Reply-To: <889896.67173.qm@web52903.mail.re2.yahoo.com> MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline References: <889896.67173.qm@web52903.mail.re2.yahoo.com> Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m2QB3tWA015548 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Paulo Santa Rita" X-Spam-Status: No, hits=1.6 required=5.0 tests=AWL,IN_REP_TO,MAILTO_TO_SPAM_ADDR,QUOTED_EMAIL_TEXT, REFERENCES,SPAM_PHRASE_00_01,X_MAILING_LIST version=2.44 X-Spam-Level: * Ola Antonio e demais colegas desta lista ... OBM-L, Nao incorri em erro algum. Qualquer pessoa que tenha um minimo de conhecimento nao superficial de Matematica vai atestar que a demonstracao que eu fiz esta correta. O que acho realmente incrivel e que voce nao tenha percebido isso ... Alias, esta questao e tao trivial que nao merece ser proposta aqui, uma lista de discussao de PROBLEMAS DE MATEMATICA OLIMPICA. Queremos provar que "a = b" sob a hipotese de que para todo real "r" positivo o modulo da diferenca entre "a" e "b" e menor que "r". Vamos portanto supor o contrario e mostrar que isso leva a um absurdo. Alias, esta tecnica e muito comum em Matematica, conhecida por "REDUCAO AO ABSURDO". Suponha que "a" e diferente de "b", isto e, a # b. Admitindo isso, necessariamente, teremos que s = | a - b | e um real positivo. Tomaremos ele como o "r", vale dizer, faremos r=s. Neste caso, teriamos : | a - b | < r => | a- b | < | a - b | ... ABSURDO ! Assim, nao pode ser a # b, ou seja, a = b, como queriamos demonstrar. Um Abraco a Todos Paulo Santa Rita 4,0738,1A0308 Em 25/03/08, Antonio Giansante escreveu: > Creio que você incorreu em um erro muito comum da > argumentação lógica, justamente por ser ele muito > sutil de ser percebido (e por isso ser muito usado em > concursos públicos): Você não pode usar a tese para > prová-la. Por exemplo: Prove que se um número é > divisível por 2, então ele é par. Aí você começa > fazendo: suponha que n é par, logo é divisível por 2. > Por isso não pode fazer "suponha r=s". creio que essa > afirmação da tese é dito modus tollens. Em um exemplo > um pouco mais didático: pense na afirmação: Se chove, > então molha. Assim, se eu afirmar que se molhou, > então choveu, vou estar errando, pois poderia ter > molhado com um copo d'água, uma mangueira, etc Eu > posso dizer que se chove, com certeza molha, mas se > molha, nem sempre foi porque choveu. Espero que este > chove-e-não-molha (que é a negação da frase inicial) > E creio que essa afirmação é falsa, pois encontramos > um contra-exemplo: Seja a#0, b = 2a e r = 3a veja que > | a - b | > > > > --- Paulo Santa Rita > escreveu: > > > > Ola Joel e demais colegas > > desta lista ... OBM-L, > > > > > > Suponha que a # b, isto é, suponha que "a" e > > diferente de "b". Neste > > caso, s = | a - b | e um real positivo. Entao, > > fazendo r = s e usando > > a propriedade enunciada, teremos : > > > > | a - b | < s => | a - b | < | a - b | ... absurdo ! > > > > Assim, a nossa tese e insustentavel e somos > > obrigados a admitir que a = b. > > > > No endereco abaixo existem muitos problemas > > olimpicos interessantes : > > http://www.mat.puc-rio.br/~nicolau/psr/ > > > > Um Abraco a Todos > > Paulo Santa Rita > > 3,0D31,190308 > > > > > > > > Em 25/03/08, Joel Castro > > escreveu: > > > tenho pequena dúvida: > > > > > > prove: se para todo r maior que zero, o módulo da > > diferença de a e b é menor > > > que r, então a é igual a b. > > > > > > valeu!!!!!! > > > > > > ________________________________ > > > Abra sua conta no Yahoo! Mail, o único sem limite > > de espaço para > > > armazenamento! > > > > > > > > > > > > ========================================================================= > > Instruções para entrar na lista, sair da lista e > > usar a lista em > > > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > > > ========================================================================= > > > > > > > Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! > > http://br.mail.yahoo.com/ > > ========================================================================= > Instruções para entrar na lista, sair da lista e usar a lista em > > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > ========================================================================= > ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Mar 26 08:29:50 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2QBSmWA016686 for ; Wed, 26 Mar 2008 08:28:48 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2QBSmNq016684 for obm-l-MllGbsmmN; Wed, 26 Mar 2008 08:28:48 -0300 Received: from rn-out-0910.google.com (rn-out-0910.google.com [64.233.170.191]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2QBSiWA016680 for ; Wed, 26 Mar 2008 08:28:46 -0300 Received: by rn-out-0910.google.com with SMTP id e11so2319304rng.7 for ; Wed, 26 Mar 2008 04:28:25 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; bh=pAHhOTu2I5M0QguHK/3gVfJU4lnfKhhlDPOIS45XwwM=; b=L17ko6r94DlmYLxxwRcMidqPLVLya38Iv3Ba12WRkbeuTTQQ30rNlnct/wEpwvFOqqNFROs7FmHVYIj6PqVUAh2kSWPNg5sNeOPF6dBje8y4MJLywGMxBFyTvRbT5slzMbgURgirOCQ5HLLmYOvnKdNmWXnqjrhfT7d3rzpdhiY= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; b=KCEYs/EMdTlgdt29wFY2PtHhNU0MLP6SkZUnSHd4Vd6q4yhVlXFo/Bno3KZZIXjw2AAUZU0i6TmWva1PEJApvzCy6mRO1j44cZc7APRPXCqssh/ZkTwZURFJjghGyeM2s8ahLd06e83/DMhU1z12qnkFV5UrIlDaiNmn6mrfXDE= Received: by 10.150.133.17 with SMTP id g17mr4728195ybd.27.1206530905544; Wed, 26 Mar 2008 04:28:25 -0700 (PDT) Received: by 10.150.144.4 with HTTP; Wed, 26 Mar 2008 04:28:25 -0700 (PDT) Message-ID: Date: Wed, 26 Mar 2008 08:28:25 -0300 From: "Paulo Santa Rita" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] off topic: resumos analise real In-Reply-To: <002d01c88ee6$55fe2380$6501a8c0@pai> MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline References: <002d01c88ee6$55fe2380$6501a8c0@pai> Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m2QBSlWA016682 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Paulo Santa Rita" X-Spam-Status: No, hits=3.5 required=5.0 tests=AWL,IN_REP_TO,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: *** Ola Hermann e demais colegas desta lisa ... OBM-L, A melhor maneira de aprender Analise e estudar a teoria com atencao, vale dizer, repetindo com suas proprias palavras e recursos as demonstracoes, verificando os limites de aplicacoes dos teoremas e, sobretudo e mais que tudo, FAZER BASTANTE EXERCICIOS INTELIGENTES. O Livro do Prof Elon ( Vol 1, Colecao Projeto Euclides ) e excelente. Eu pensei em divulgar as solucoes, mas, vou repetir aqui o que o proprio Elon me falou : "... nao sei se e uma boa ideia publicar as solucoes, embora eu nao tenha o poder, nem a intencao de proibi-lo de fazer isto.Na verdade, ha uns 25 anos uma aluna do IMPA redigiu todas as solucoes (algumas com minha ajuda) mas nem me lembro onde joguei o manuscrito ... " Veja portanto que o proprio autor tem duvidas sobre o valor de se publicar as solucoes. Se voce aceita um conselho, vai publicando aqui os problemas que voce achar mais dificeis e os fatos que voce nao esta conseguindo entender. Isso vai elevar o atual nivel desta nossa LISTA DE DISCUSSAO DE PROBLEMAS OLIMPICOS e, alem disso, ha pessoas aqui que gostam muito de Analise. O Artur Steiner, por exemplo. Acredito que voce publicando ele vai ajudar. Um Abracao Paulo Santa Rita 4,0819,1A0308 Em 25/03/08, Tio Cabri st escreveu: > Senhores, boa noite, tá difícil de fazer sozinho, análise realmente é > ingrata, > gostaria NOVAMENTE (perdoem-me) da ajuda do pessoal da lista. > > Pedi há uns dias exercícios resolvidos do livro de análise do Elon do > pequeno ou do grande (volume 1). > Infelizmente não consegui nem um. > > Aí, como a situação está braba (estou trabalhando muito, sem tempo para > estudar) > pensei na possibilidade de estudar por resumos. > Peço: > se você possui RESUMOS de análise do Elon (grande ou pequeno vol 1) > por gentileza mande para meu e-mail ilhadepaquetaARROBAbol.com.br > estudar por resumos vai facilitar (acho!). > > Obrigado mais uma vez > Hermann Cabri > > > ========================================================================= > Instruções para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > ========================================================================= > ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Mar 26 08:31:58 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2QBV4WA016783 for ; Wed, 26 Mar 2008 08:31:04 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2QBV39c016774 for obm-l-MllGbsmmN; Wed, 26 Mar 2008 08:31:03 -0300 Received: from el-out-1112.google.com (el-out-1112.google.com [209.85.162.180]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2QBV0WA016742 for ; Wed, 26 Mar 2008 08:31:00 -0300 Received: by el-out-1112.google.com with SMTP id o28so2078096ele.3 for ; Wed, 26 Mar 2008 04:30:42 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=yBKRwfqKXk6QtOVxc5XwTUX8mLCXkHgVI6EIsGYzEHA=; b=Q1eNCJ/2FNQbA7RvLwulubHZ+Qi64Ivm38+8XIIDlXOLwlsk1K70xwK1FUToGHFLeWxpI21DF5JM9JYjRlKQLYfGcKaIR+MeaFCV0FBO0P8ee6b62mkS31dqJrUt7DzCboe9Tq4Jr8xwAulC/NnRL1tbs1DdqSUZRYdYanD5s7o= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=J0EYXzIPaY19E0I/6uErT5qIGoPpZ0w+cMquffK65OjXnuq0+x7PwvRtyRGUduXF6sFfRP0+st5iBfXSZ6rwUDfMql5sM8hURl8XQF1lMQUc7WoobVql+jqiGWwpeoweecI5dqsmXhvwIyJG0tvfIcoTRa3z3nEdEC45NP8zTWo= Received: by 10.150.52.2 with SMTP id z2mr4742088ybz.47.1206531040571; Wed, 26 Mar 2008 04:30:40 -0700 (PDT) Received: by 10.150.158.20 with HTTP; Wed, 26 Mar 2008 04:30:40 -0700 (PDT) Message-ID: <5bb472220803260430r477d89f3ye1066bd076953c7d@mail.gmail.com> Date: Wed, 26 Mar 2008 08:30:40 -0300 From: "Joao Victor Brasil" To: obm-l@mat.puc-rio.br Subject: =?ISO-8859-1?Q?Re:_[obm-l]_RES:_[obm-l]_Indica=E7=E3o_de_livro?= =?ISO-8859-1?Q?s_(C=E1lculo_num=E9rico_e_Equa=E7=F5es_diferenciais)?= In-Reply-To: MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_16580_395219.1206531040496" References: <212079.44593.qm@web55214.mail.re4.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Joao Victor Brasil" X-Spam-Status: No, hits=4.5 required=5.0 tests=AWL,HTML_FONT_COLOR_BLUE,IN_REP_TO,JAVASCRIPT_UNSAFE, MAILTO_LINK,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, SPAM_REDIRECTOR,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** ------=_Part_16580_395219.1206531040496 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Paulo, Quanto voc=EA quer neste livros? Os do Piskonov, Apostol e Pacitti. Joao Victor On 3/26/08, Paulo - Uniredes wrote: > > Oi Cesar, > > Para c=E1lculo I e II, eu recomendo o Piskunov: > http://www.traca.com.br/seboslivrosusados.cgi?mod=3DLV62211&origem=3Dresu= ltadodetalhada > Eu tenho os volumes I e II em espanhol no meu sebo. S=E3o muito legais. O > volume II =E9 =F3timo em equa=E7=F5es diferenciais. A obra, em 2 volumes,= foi usada > na UFRJ. > > Tem tamb=E9m o do Tom M. Apostol em portugu=EAs...: > > http://www.livrariadafisica.com.br/produto_detalhe.asp?id_produto=3D19209 > > Estudei pelo Apostol e a qualidade =E9 muito boa. Apesar de eu ser meio > "burro" (S=F3 passei em c=E1lculo I ap=F3s fazer um curso de ver=E3o na U= FRJ. Muito > legal...mas meu neg=F3cio =E9 redes de computadores). > > Fa=E7o pre=E7o camarada nos 3 livros. Camarada mesmo ! > > > []s > > > --- > Paulo C. Santos (PC) > e-mail: paulo@uniredes.org > Homepage: http://uniredes.org > Tel.: (21) 2510.8783 - Cel.: (21) 8753-0729 > -------------------------------------------- > MS-Messenger: Uniredes_Br@hotmail.Com > > ------------------------------ > *De:* owner-obm-l@mat.puc-rio.br [mailto:owner-obm-l@mat.puc-rio.br] *Em > nome de *C=E9sar Santos > *Enviada em:* ter=E7a-feira, 25 de mar=E7o de 2008 16:10 > *Para:* obm-l@mat.puc-rio.br > *Assunto:* [obm-l] Indica=E7=E3o de livros (C=E1lculo num=E9rico e Equa= =E7=F5es > diferenciais) > > > Poderiam me indicar bons livros de c=E1lculo num=E9rico e de equa=E7=F5es > diferencias acess=EDveis para iniciante? > > ------------------------------ > Abra sua conta no Yahoo! Mail, > o =FAnico sem limite de espa=E7o para armazenamento! > > ------=_Part_16580_395219.1206531040496 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline
Paulo,
 
Quanto voc=EA quer neste livros? Os do Piskonov, Apostol e Pacitti.
 
Joao Victor

 
On 3/26/08, = Paulo - Uniredes <paulo@unired= es.org> wrote:
Oi Cesar,
 
Eu tenho os volumes I e II em espanhol no meu sebo. S=E3o muit= o legais. O volume II =E9 =F3timo em equa=E7=F5es diferenciais. A obra, em = 2 volumes, foi usada na UFRJ.
 
Tem tamb=E9m o do Tom M. Apostol em portugu=EAs...:
 
 
Estudei pelo Apostol e a qualidade =E9 muito boa. Apesar = de eu ser meio "burro" (S=F3 passei em c=E1lculo I ap=F3s fazer u= m curso de ver=E3o na UFRJ. Muito legal...mas meu neg=F3cio =E9 redes de co= mputadores).
 
Fa=E7o pre=E7o camarada nos 3 livros. Camarada mesmo !<= /span>
 
 
[]s
 

---
Paulo C. Santos (PC)
e-mail: paulo@uniredes.org
Homepage: http://uniredes.org
Tel.: (21) 2510.8783 - Cel.: (21) 8753-0729
----------------------------= ----------------
MS-Messenger: Uniredes_Br@hotmail.Com


De: owner-obm-l@mat.puc-rio.br [mailto:owner-obm-l@mat.puc-rio.br] Em nome de = C=E9sar Santos
Enviada em: ter=E7a-feira, 25 de mar=E7o de 2008 16:10
Para: obm-l@mat.puc-rio.br
A= ssunto: [obm-l] Indica=E7=E3o de livros (C=E1lculo num=E9rico e Equa=E7= =F5es diferenciais)

 
Poderiam me indicar bons livros de c=E1= lculo num=E9rico e de equa=E7=F5es diferencias acess=EDveis para iniciante?= =20

Abra sua conta no Yahoo! Mail, o =FAnico sem limite de espa=E7o p= ara armazenamento!=20


------=_Part_16580_395219.1206531040496-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Mar 26 08:46:05 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2QBj5WA017967 for ; Wed, 26 Mar 2008 08:45:05 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2QBj5HE017965 for obm-l-MllGbsmmN; Wed, 26 Mar 2008 08:45:05 -0300 Received: from yw-out-2324.google.com (yw-out-2324.google.com [74.125.46.30]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2QBj3WA017954 for ; Wed, 26 Mar 2008 08:45:03 -0300 Received: by yw-out-2324.google.com with SMTP id 3so14447ywj.9 for ; Wed, 26 Mar 2008 04:44:45 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=7SftHjjfllfNq2g64Wn8P/MZnyPoCwUGr51e9nlnNRs=; b=GHqRrnhpa/2VaUUyI+RIlHCiZgVPthY3uJssAet67vmmVs+nA6r2rBoK6DGciRpGyfg+4nTTY8+UU4j/ebHSfrxz7dYqqy1CD1FMDqNTIcMYYxgs+yO5JnGGKx83gldi+AVrGza2EtCygDGpsCkCedyVWxjaYXd1ODi0VpL9diY= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=VlC6zmmknJUZMyYVjgf/5klA9R8iH262UudI2Kspg/xvzTYIIJIi7DDBBP2MfHePcONjzB/itl8Qt4xzqUz1HX1aQMzvttE/0sj17galJbP1TuCLRjqSBtg+Ahol6gjdsxCPDQbUUJT3tI8ibki7Tm/r4Pry52GdkOuYT7gcvDY= Received: by 10.151.150.13 with SMTP id c13mr4730330ybo.173.1206531885138; Wed, 26 Mar 2008 04:44:45 -0700 (PDT) Received: by 10.150.158.20 with HTTP; Wed, 26 Mar 2008 04:44:45 -0700 (PDT) Message-ID: <5bb472220803260444i2ee8d07fh62fcceab23558a59@mail.gmail.com> Date: Wed, 26 Mar 2008 08:44:45 -0300 From: "Joao Victor Brasil" To: obm-l@mat.puc-rio.br Subject: =?ISO-8859-1?Q?Re:_[obm-l]_Qual_o_valor_do_=E2ngulo=3F?= In-Reply-To: <206410.11049.qm@web56902.mail.re3.yahoo.com> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_16640_24748687.1206531885121" References: <206410.11049.qm@web56902.mail.re3.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Joao Victor Brasil" X-Spam-Status: No, hits=1.7 required=5.0 tests=AWL,HTML_FONT_COLOR_BLUE,IN_REP_TO,JAVASCRIPT_UNSAFE, MAILTO_LINK,QUOTED_EMAIL_TEXT,REFERENCES,SPAM_PHRASE_01_02, SPAM_REDIRECTOR,X_MAILING_LIST version=2.44 X-Spam-Level: * ------=_Part_16640_24748687.1206531885121 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline A resposta =E9 a letra D, 45=B0. Quando voc=EA montar o tri=E2ngulo j=E1 com os segmentos, poderemos ver o quadril=E1tero ABDH. Onde wrote: > > > O tri=E2ngulo ABC, ret=E2ngulo em A, =E9 tal que o < ABC =E9 maior que < = ACB. > A bissetriz interna de perpendicular a BC ( H entre A e C). Nestas condi=E7=F5es podemos afirmar= que o > =E2ngulo a) 25 > b) 65 > c) 35 > d) 45 > > Obrigado!!! > > ------------------------------ > Abra sua conta no Yahoo! Mail, > o =FAnico sem limite de espa=E7o para armazenamento! > > ------=_Part_16640_24748687.1206531885121 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline
A resposta =E9 a letra D, 45=B0.
 
Quando voc=EA montar o tri=E2ngulo j=E1 com os segmentos, poderemos ve= r o quadril=E1tero ABDH.
Onde <HAB =3D <HDB =3D 90=B0 e <ABD + <AHD =3D 180=B0. Com= o a soma dos =E2ngulos opostos =E9 180=B0, podemos inscrever este quadrilat= ero num c=EDrculo e verificar pelos arcos que o arco HD determina os =E2ngu= los <HAD e <HBD.
 
Joao Victor

 
On 3/26/08, = cleber vieira <vieira_usp= @yahoo.com.br> wrote:

O tri=E2ngulo ABC, ret=E2ngulo em A, =E9 t= al que o < ABC =E9 maior que < ACB.
A bissetriz interna de <A, intercepta o lad= o BC em D. Seja HD perpendicular a BC ( H entre A e C). Nestas condi=E7=F5e= s podemos afirmar que o =E2ngulo <HBD mede, em graus:
a) 25
b) 65
c) 35
d) 45
 
Obrigado!!!

Abra sua conta no Yahoo! Mail, o =FAnico sem l= imite de espa=E7o para armazenamento!


------=_Part_16640_24748687.1206531885121-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Mar 26 08:58:03 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2QBucWA018629 for ; Wed, 26 Mar 2008 08:56:38 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2QBucIC018627 for obm-l-MllGbsmmN; Wed, 26 Mar 2008 08:56:38 -0300 Received: from wr-out-0506.google.com (wr-out-0506.google.com [64.233.184.228]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2QBuZWA018622 for ; Wed, 26 Mar 2008 08:56:36 -0300 Received: by wr-out-0506.google.com with SMTP id c46so3945392wra.18 for ; Wed, 26 Mar 2008 04:56:18 -0700 (PDT) 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<26fc77ef0803260456l4def1858h8d1390ce4ae7c69c@mail.gmail.com> Date: Wed, 26 Mar 2008 08:56:16 -0300 From: "Palmerim Soares" To: obm-l@mat.puc-rio.br Subject: =?UTF-8?Q?Re:_[obm-l]_RES:_[obm-l]_Indica=C3=A7=C3=A3o_de_livro?= =?UTF-8?Q?s_(C=C3=A1lculo_num=C3=A9rico_e_?= =?UTF-8?Q?Equa=C3=A7=C3=B5es_diferenciais)?= In-Reply-To: MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_19560_14611184.1206532576387" References: <212079.44593.qm@web55214.mail.re4.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Palmerim Soares" X-Spam-Status: No, hits=4.1 required=5.0 tests=IN_REP_TO,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, SPAM_REDIRECTOR,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** ------=_Part_19560_14611184.1206532576387 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: base64 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aXY+PGJyPgo= ------=_Part_19560_14611184.1206532576387-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Mar 26 09:35:36 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2QCYWWA021840 for ; Wed, 26 Mar 2008 09:34:32 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2QCYWOe021835 for obm-l-MllGbsmmN; Wed, 26 Mar 2008 09:34:32 -0300 Received: from hm171.locaweb.com.br (hm171-2.locaweb.com.br [200.234.205.179]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id m2QCYRWA021807 for ; Wed, 26 Mar 2008 09:34:28 -0300 Message-Id: <200803261234.m2QCYRWA021807@saci.mat.puc-rio.br> Received: (qmail 28968 invoked from network); 26 Mar 2008 12:34:14 -0000 Received: from unknown (10.1.10.169) by hm171.locaweb.com.br with QMQP; 26 Mar 2008 12:34:14 -0000 Received: from unknown (HELO lattes) (paulo@uniredes.org@201.8.60.197) by hm169.locaweb.com.br with SMTP; 26 Mar 2008 12:34:15 -0000 From: "Paulo - Uniredes" To: Subject: [SPAM] [obm-l] =?iso-8859-1?Q?RES:_=5Bobm-l=5D_RES:_=5Bobm-l=5D_Indica=E7=E3o_de_livros_?= =?iso-8859-1?Q?=28C=E1lculo_num=E9rico_e_Equa=E7=F5es_diferenciais=29?= Date: Wed, 26 Mar 2008 09:34:30 -0300 Organization: Uniredes MIME-Version: 1.0 Content-Type: text/plain X-Mailer: Microsoft Office Outlook, Build 11.0.5510 In-Reply-To: <5bb472220803260430r477d89f3ye1066bd076953c7d@mail.gmail.com> X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.3198 thread-index: AciPOGGx8ImhUcaRQCWuOrTDDqKmvgABGcIg Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Paulo - Uniredes" X-Spam-Status: Yes, hits=7.1 required=5.0 tests=HTML_FONT_COLOR_BLUE,IN_REP_TO,JAVASCRIPT_UNSAFE, MAILTO_LINK,MISSING_OUTLOOK_NAME,MSG_ID_ADDED_BY_MTA_2, NOSPAM_INC,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, SPAM_PHRASE_00_01,SPAM_REDIRECTOR,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******* X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_NextPart_000_0015_01C88F24.97B33D40" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (7.10 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: NOSPAM_INC (-0.2 points) Where are you working at? SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: HTML_FONT_COLOR_BLUE (0.2 points) BODY: HTML font color is blue SPAM: JAVASCRIPT_UNSAFE (0.3 points) BODY: Easily-executed JavaScript code SPAM: MAILTO_LINK (0.2 points) BODY: Includes a URL link to send an email SPAM: SPAM_REDIRECTOR (0.4 points) URI: Uses open redirection service SPAM: MSG_ID_ADDED_BY_MTA_2 (0.1 points) 'Message-Id' was added by a relay (2) SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 179.205.234.200.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 179.205.234.200.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: MISSING_OUTLOOK_NAME (1.1 points) Message looks like Outlook, but isn't SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- This is a multi-part message in MIME format. ------=_NextPart_000_0015_01C88F24.97B33D40 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Olha Jo=E3o, =20 Provavelmente tem uns amigos a=ED chateados comigo, pois eu ainda n=E3o = estava preparado para os pedidos que iam chegar. Meu pequeno sebo tem muitos = livros legais mas eu precisava de uma loja eletr=F4nica, para organizar as = coisas. Ela est=E1 em http://uniredes.org/loja01. =C9 ainda incipiente mas vai = ajudar muito. Estou migrando o cadastro das obras que tenho. N=E3o =E9 um = esquema rigorosamente comercial. Quando acabar o estoque particular acabou, mas = eu quero atender direitinho, deixando tudo documentado. Assim posso indicar = no ano que vem quem tem o que para vender. Ser=E1 muito legal e um = servi=E7o de utilidade. =20 Os pre=E7os que voc=EA deseja estar=E3o dispon=EDveis na loja, amanh=E3 = de manh=E3, prometo. =20 Espero que todos gostem e j=E1 pe=E7o desculpas pela demora. =20 --- Paulo C. Santos (PC) e-mail: paulo@uniredes.org Homepage: http://uniredes.org =20 Tel.: (21) 2510.8783 - Cel.: (21) 8753-0729 -------------------------------------------- MS-Messenger: Uniredes_Br@hotmail.Com=20 =20 _____ =20 De: owner-obm-l@mat.puc-rio.br [mailto:owner-obm-l@mat.puc-rio.br] Em = nome de Joao Victor Brasil Enviada em: quarta-feira, 26 de mar=E7o de 2008 08:31 Para: obm-l@mat.puc-rio.br Assunto: Re: [obm-l] RES: [obm-l] Indica=E7=E3o de livros (C=E1lculo = num=E9rico e Equa=E7=F5es diferenciais) Paulo,=20 =20 Quanto voc=EA quer neste livros? Os do Piskonov, Apostol e Pacitti. =20 Joao Victor =20 On 3/26/08, Paulo - Uniredes wrote:=20 Oi Cesar, =20 Para c=E1lculo I e II, eu recomendo o Piskunov: http://www.traca.com.br/seboslivrosusados.cgi?mod=3DLV62211 &origem=3Dresultadodetalhada Eu tenho os volumes I e II em espanhol no meu sebo. S=E3o muito legais. = O volume II =E9 =F3timo em equa=E7=F5es diferenciais. A obra, em 2 = volumes, foi usada na UFRJ. =20 Tem tamb=E9m o do Tom M. Apostol em portugu=EAs...: =20 http://www.livrariadafisica.com.br/produto_detalhe.asp?id_produto=3D19209= =20 Estudei pelo Apostol e a qualidade =E9 muito boa. Apesar de eu ser meio "burro" (S=F3 passei em c=E1lculo I ap=F3s fazer um curso de ver=E3o na = UFRJ. Muito legal...mas meu neg=F3cio =E9 redes de computadores). =20 Fa=E7o pre=E7o camarada nos 3 livros. Camarada mesmo ! =20 =20 []s =20 --- Paulo C. Santos (PC) e-mail: paulo@uniredes.org Homepage: http://uniredes.org =20 Tel.: (21) 2510.8783 - Cel.: (21) 8753-0729 -------------------------------------------- MS-Messenger: Uniredes_Br@hotmail.Com=20 _____ =20 De: owner-obm-l@mat.puc-rio.br [mailto:owner-obm-l@mat.puc-rio.br] Em = nome de C=E9sar Santos Enviada em: ter=E7a-feira, 25 de mar=E7o de 2008 16:10 Para: obm-l@mat.puc-rio.br Assunto: [obm-l] Indica=E7=E3o de livros (C=E1lculo num=E9rico e = Equa=E7=F5es diferenciais) =20 Poderiam me indicar bons livros de c=E1lculo num=E9rico e de = equa=E7=F5es diferencias acess=EDveis para iniciante?=20 _____ =20 Abra sua conta no Yahoo! Mail , = o =FAnico sem limite de espa=E7o para armazenamento!=20 ------=_NextPart_000_0015_01C88F24.97B33D40 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable
Olha Jo=E3o,
 
Provavelmente tem uns amigos a=ED chateados = comigo, pois eu=20 ainda n=E3o estava preparado para os pedidos que iam chegar. Meu pequeno = sebo tem=20 muitos livros legais mas eu precisava de uma loja eletr=F4nica, para = organizar as=20 coisas. Ela est=E1 em http://uniredes.org/loja01. =C9 = ainda=20 incipiente mas vai ajudar muito. Estou migrando o cadastro = das obras que=20 tenho. N=E3o=20 =E9 um esquema rigorosamente comercial. Quando acabar o estoque = particular acabou,=20 mas eu quero atender direitinho, deixando tudo documentado. Assim posso = indicar=20 no ano que vem quem tem o que para vender. Ser=E1 muito legal e um = servi=E7o de=20 utilidade.
 
Os pre=E7os que voc=EA deseja estar=E3o = dispon=EDveis na loja,=20 amanh=E3 de manh=E3, prometo.
 
Espero que todos gostem e j=E1 pe=E7o desculpas = pela=20 demora.
 

---
Paulo C. Santos (PC)
e-mail:=20 paulo@uniredes.org
Homepage: http://uniredes.org
Tel.: (21) = 2510.8783 -=20 Cel.: (21)=20 8753-0729
--------------------------------------------
MS-Messenger= :=20 Uniredes_Br@hotmail.Com

 
De:=20 owner-obm-l@mat.puc-rio.br [mailto:owner-obm-l@mat.puc-rio.br] Em = nome de=20 Joao Victor Brasil
Enviada em: quarta-feira, 26 de mar=E7o = de 2008=20 08:31
Para: obm-l@mat.puc-rio.br
Assunto: Re: = [obm-l] RES:=20 [obm-l] Indica=E7=E3o de livros (C=E1lculo num=E9rico e Equa=E7=F5es=20 diferenciais)

Paulo,
 
Quanto voc=EA quer neste livros? Os do Piskonov, Apostol e = Pacitti.
 
Joao Victor

 
On 3/26/08, Paulo -=20 Uniredes <paulo@uniredes.org>=20 wrote:=20
Oi=20 Cesar,
 
Para=20 c=E1lculo I e II, eu recomendo o Piskunov: http://www.traca.com.br/seboslivrosusados.cgi?mod=3DLV622= 11&origem=3Dresultadodetalhada
Eu tenho=20 os volumes I e II em espanhol no meu sebo. S=E3o muito legais. O = volume II =E9=20 =F3timo em equa=E7=F5es diferenciais. A obra, em 2 volumes, foi usada = na=20 UFRJ.
 
Tem tamb=E9m=20 o do Tom M. Apostol em portugu=EAs...:
 
http://www.livrariadafisica.com.br/produto_detalhe.asp?id= _produto=3D19209
 
Estudei=20 pelo Apostol e a qualidade =E9 muito boa. Apesar de eu ser meio = "burro" (S=F3=20 passei em c=E1lculo I ap=F3s fazer um curso de ver=E3o na UFRJ. Muito = legal...mas=20 meu neg=F3cio =E9 redes de computadores).
 
Fa=E7o pre=E7o=20 camarada nos 3 livros. Camarada mesmo !
 
 
[]s
 

---
Paulo C. Santos (PC)
e-mail: paulo@uniredes.org
Homepage: http://uniredes.org
Tel.:=20 (21) 2510.8783 - Cel.: (21)=20 = 8753-0729
--------------------------------------------
MS-Messenger= : Uniredes_Br@hotmail.Com =


De: owner-obm-l@mat.puc-rio.br [mailto:owner-obm-l@mat.puc-rio.br] Em nome de = C=E9sar=20 Santos
Enviada em: ter=E7a-feira, 25 de mar=E7o de 2008=20 16:10
Para: obm-l@mat.puc-rio.br
Assunto: [obm-l] = Indica=E7=E3o de=20 livros (C=E1lculo num=E9rico e Equa=E7=F5es = diferenciais)

 
Poderiam me indicar bons livros de = c=E1lculo=20 num=E9rico e de equa=E7=F5es diferencias acess=EDveis para iniciante?=20

Abra sua conta no Yahoo! Mail, o =FAnico sem limite de espa=E7o para = armazenamento!=20


------=_NextPart_000_0015_01C88F24.97B33D40-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Mar 26 09:50:07 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2QCn5WA023388 for ; Wed, 26 Mar 2008 09:49:05 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2QCn5oB023382 for obm-l-MllGbsmmN; Wed, 26 Mar 2008 09:49:05 -0300 Received: from hm171.locaweb.com.br (hm171-2.locaweb.com.br [200.234.205.179]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id m2QCn2WA023344 for ; Wed, 26 Mar 2008 09:49:02 -0300 Message-Id: <200803261249.m2QCn2WA023344@saci.mat.puc-rio.br> Received: (qmail 6575 invoked from network); 26 Mar 2008 12:41:28 -0000 Received: from unknown (10.1.10.169) by hm171.locaweb.com.br with QMQP; 26 Mar 2008 12:41:28 -0000 Received: from unknown (HELO lattes) (paulo@uniredes.org@201.8.60.197) by hm169.locaweb.com.br with SMTP; 26 Mar 2008 12:41:30 -0000 From: "Paulo - Uniredes" To: Subject: [SPAM] [obm-l] =?iso-8859-1?Q?Essa_=E9_a_=FAltima_vez=2C_professor=2C_prometo.?= Date: Wed, 26 Mar 2008 09:41:43 -0300 Organization: Uniredes MIME-Version: 1.0 Content-Type: text/plain X-Mailer: Microsoft Office Outlook, Build 11.0.5510 In-Reply-To: <26fc77ef0803260456l4def1858h8d1390ce4ae7c69c@mail.gmail.com> X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.3198 thread-index: AciPPJa/FyXwVScKTOKPL1MFNafBRwAAT+aw Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Paulo - Uniredes" X-Spam-Status: Yes, hits=7.1 required=5.0 tests=HTML_FONT_COLOR_BLUE,IN_REP_TO,JAVASCRIPT_UNSAFE, MAILTO_LINK,MISSING_OUTLOOK_NAME,MSG_ID_ADDED_BY_MTA_2, NOSPAM_INC,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, SPAM_PHRASE_00_01,SPAM_REDIRECTOR,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******* X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_NextPart_000_001F_01C88F25.9AA33BD0" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (7.10 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: NOSPAM_INC (-0.2 points) Where are you working at? SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: HTML_FONT_COLOR_BLUE (0.2 points) BODY: HTML font color is blue SPAM: JAVASCRIPT_UNSAFE (0.3 points) BODY: Easily-executed JavaScript code SPAM: MAILTO_LINK (0.2 points) BODY: Includes a URL link to send an email SPAM: SPAM_REDIRECTOR (0.4 points) URI: Uses open redirection service SPAM: MSG_ID_ADDED_BY_MTA_2 (0.1 points) 'Message-Id' was added by a relay (2) SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 179.205.234.200.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 179.205.234.200.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: MISSING_OUTLOOK_NAME (1.1 points) Message looks like Outlook, but isn't SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- This is a multi-part message in MIME format. ------=_NextPart_000_001F_01C88F25.9AA33BD0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Prezado Palmerim =20 Desculpe-me (publicamente) pelo embara=E7o que causei. =C9 =F3bvio que = eu deveria responder em PVT. Eu tamb=E9m detesto SPAM e a lista =E9 muito preciosa = para eu ficar fora dela. =20 Prometo que n=E3o se trata mais dessas coisas por aqui. Foi tolice = minha. Pode ter certeza de que n=E3o =E9 m=E1 f=E9 ou "esperteza". =20 Obrigado pela "bronca" e vamos em frente. =20 =20 Cordial abra=E7o, =20 --- Paulo C. Santos (PC) e-mail: paulo@uniredes.org Homepage: http://uniredes.org =20 Tel.: (21) 2510.8783 - Cel.: (21) 8753-0729 -------------------------------------------- MS-Messenger: Uniredes_Br@hotmail.Com=20 _____ =20 De: owner-obm-l@mat.puc-rio.br [mailto:owner-obm-l@mat.puc-rio.br] Em = nome de Palmerim Soares Enviada em: quarta-feira, 26 de mar=E7o de 2008 08:56 Para: obm-l@mat.puc-rio.br Assunto: Re: [obm-l] RES: [obm-l] Indica=E7=E3o de livros (C=E1lculo = num=E9rico e Equa=E7=F5es diferenciais) Prezado Sr. Paulo, n=E3o me entenda mal, mas acho que voc=EA deveria saber que esta lista = n=E3o =E9 o local adequado para fazer com=E9rcio. Nenhum de n=F3s aqui est=E1 = interessado em acompanhar os detalhes de suas vendas, n=E3o parece =F3bvio? Se voc=EA = est=E1 realmente interessado em ajudar um colega, e n=E3o em usar a lista com = fins comerciais e de propaganda, ent=E3o, fa=E7a a gentileza (todos n=F3s agradeceremos!!) de tratar desses assuntos individualmente, enviando um e-mail somente para quem estiver interessado, sem jamais divulgar na = lista que voc=EA possui um sebo e que pode "fazer pre=E7os camaradas". Esse = tipo de atitude n=E3o =E9 bem-vinda e nem mesmo permitida nesta lista. Sem mais para o momento, subscrevo-me, Atenciosamente, Palmerim =20 Em 26/03/08, Paulo - Uniredes escreveu:=20 Oi Cesar, =20 Para c=E1lculo I e II, eu recomendo o Piskunov: http://www.traca.com.br/seboslivrosusados.cgi?mod=3DLV62211 &origem=3Dresultadodetalhada Eu tenho os volumes I e II em espanhol no meu sebo. S=E3o muito legais. = O volume II =E9 =F3timo em equa=E7=F5es diferenciais. A obra, em 2 = volumes, foi usada na UFRJ. =20 Tem tamb=E9m o do Tom M. Apostol em portugu=EAs...: =20 http://www.livrariadafisica.com.br/produto_detalhe.asp?id_produto=3D19209= =20 Estudei pelo Apostol e a qualidade =E9 muito boa. Apesar de eu ser meio "burro" (S=F3 passei em c=E1lculo I ap=F3s fazer um curso de ver=E3o na = UFRJ. Muito legal...mas meu neg=F3cio =E9 redes de computadores). =20 Fa=E7o pre=E7o camarada nos 3 livros. Camarada mesmo ! =20 =20 []s =20 --- Paulo C. Santos (PC) e-mail: paulo@uniredes.org Homepage: http://uniredes.org =20 Tel.: (21) 2510.8783 - Cel.: (21) 8753-0729 -------------------------------------------- MS-Messenger: Uniredes_Br@hotmail.Com=20 _____ =20 De: owner-obm-l@mat.puc-rio.br [mailto:owner-obm-l@mat.puc-rio.br] Em = nome de C=E9sar Santos Enviada em: ter=E7a-feira, 25 de mar=E7o de 2008 16:10 Para: obm-l@mat.puc-rio.br Assunto: [obm-l] Indica=E7=E3o de livros (C=E1lculo num=E9rico e = Equa=E7=F5es diferenciais) =20 Poderiam me indicar bons livros de c=E1lculo num=E9rico e de = equa=E7=F5es diferencias acess=EDveis para iniciante?=20 _____ =20 Abra sua conta no Yahoo! Mail , = o =FAnico sem limite de espa=E7o para armazenamento!=20 ------=_NextPart_000_001F_01C88F25.9AA33BD0 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable
Prezado Palmerim
 
Desculpe-me (publicamente) pelo embara=E7o = que causei. =C9=20 =F3bvio que eu deveria responder em PVT. Eu tamb=E9m detesto SPAM e a = lista =E9 muito=20 preciosa para eu ficar fora dela.
 
Prometo que n=E3o se trata mais dessas coisas = por aqui.=20 Foi tolice minha. Pode ter certeza de que n=E3o =E9 m=E1 f=E9 ou=20 "esperteza".
 
Obrigado pela "bronca" e vamos em=20 frente.
 
 
Cordial abra=E7o,
 

---
Paulo C. Santos (PC)
e-mail:=20 paulo@uniredes.org
Homepage: http://uniredes.org
Tel.: (21) = 2510.8783 -=20 Cel.: (21)=20 8753-0729
--------------------------------------------
MS-Messenger= :=20 Uniredes_Br@hotmail.Com


De: owner-obm-l@mat.puc-rio.br=20 [mailto:owner-obm-l@mat.puc-rio.br] Em nome de Palmerim=20 Soares
Enviada em: quarta-feira, 26 de mar=E7o de 2008=20 08:56
Para: obm-l@mat.puc-rio.br
Assunto: Re: = [obm-l] RES:=20 [obm-l] Indica=E7=E3o de livros (C=E1lculo num=E9rico e Equa=E7=F5es=20 diferenciais)

Prezado Sr. Paulo,
n=E3o me entenda mal, mas acho que voc=EA deveria saber que esta = lista n=E3o =E9 o=20 local adequado para fazer com=E9rcio. Nenhum de n=F3s aqui est=E1 = interessado em=20 acompanhar os detalhes de suas vendas, n=E3o parece =F3bvio? Se voc=EA = est=E1 realmente=20 interessado em ajudar um colega, e n=E3o em usar a lista com fins = comerciais e de=20 propaganda, ent=E3o, fa=E7a a gentileza (todos n=F3s agradeceremos!!) de = tratar desses=20 assuntos individualmente, enviando um e-mail somente para quem estiver=20 interessado, sem jamais divulgar na lista que voc=EA possui um sebo e = que pode=20 "fazer pre=E7os camaradas". Esse tipo de atitude n=E3o =E9 bem-vinda e = nem mesmo=20 permitida nesta lista.
Sem mais para o momento, subscrevo-me,
Atenciosamente,
Palmerim

 
Em 26/03/08, Paulo -=20 Uniredes <paulo@uniredes.org>=20 escreveu:=20
Oi=20 Cesar,
 
Para=20 c=E1lculo I e II, eu recomendo o Piskunov: http://www.traca.com.br/seboslivrosusados.cgi?mod=3DLV622= 11&origem=3Dresultadodetalhada
Eu tenho=20 os volumes I e II em espanhol no meu sebo. S=E3o muito legais. O = volume II =E9=20 =F3timo em equa=E7=F5es diferenciais. A obra, em 2 volumes, foi usada = na=20 UFRJ.
 
Tem tamb=E9m=20 o do Tom M. Apostol em portugu=EAs...:
 
http://www.livrariadafisica.com.br/produto_detalhe.asp?id= _produto=3D19209
 
Estudei=20 pelo Apostol e a qualidade =E9 muito boa. Apesar de eu ser meio = "burro" (S=F3=20 passei em c=E1lculo I ap=F3s fazer um curso de ver=E3o na UFRJ. Muito = legal...mas=20 meu neg=F3cio =E9 redes de computadores).
 
Fa=E7o pre=E7o=20 camarada nos 3 livros. Camarada mesmo !
 
 
[]s
 

---
Paulo C. Santos (PC)
e-mail: paulo@uniredes.org
Homepage: http://uniredes.org
Tel.:=20 (21) 2510.8783 - Cel.: (21)=20 = 8753-0729
--------------------------------------------
MS-Messenger= : Uniredes_Br@hotmail.Com =


De: owner-obm-l@mat.puc-rio.br [mailto:owner-obm-l@mat.puc-rio.br] Em nome de = C=E9sar=20 Santos
Enviada em: ter=E7a-feira, 25 de mar=E7o de 2008=20 16:10
Para: obm-l@mat.puc-rio.br
Assunto: [obm-l] = Indica=E7=E3o de=20 livros (C=E1lculo num=E9rico e Equa=E7=F5es = diferenciais)

 
Poderiam me indicar bons livros de = c=E1lculo=20 num=E9rico e de equa=E7=F5es diferencias acess=EDveis para iniciante?=20

Abra sua conta no Yahoo! Mail, o =FAnico sem limite de espa=E7o para = armazenamento!=20


------=_NextPart_000_001F_01C88F25.9AA33BD0-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Mar 26 10:02:11 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2QD0vWA026465 for ; Wed, 26 Mar 2008 10:00:57 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2QD0vER026463 for obm-l-MllGbsmmN; Wed, 26 Mar 2008 10:00:57 -0300 Received: from web55208.mail.re4.yahoo.com (web55208.mail.re4.yahoo.com [206.190.58.172]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id m2QD0rWA026421 for ; Wed, 26 Mar 2008 10:00:55 -0300 Received: (qmail 48542 invoked by uid 60001); 26 Mar 2008 13:00:34 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:Date:From:Subject:To:In-Reply-To:MIME-Version:Content-Type:Content-Transfer-Encoding:Message-ID; b=4Y8B9V4QqyPHxCSAdnLdBbjSD/69hwQhXtDVJUY8MUjMphW0lokiHFwaqEi3F9c1f7L3X482+JgqJgVnUbXN/9pMulCJxtYDURRB4jQunhZN1uvAFe8AgGT/3lR9EZKN24mgYCjVrjlgZj6RZEv6J/kJCPFJHmSN1KcnetYw4B8=; X-YMail-OSG: VB_aXt8VM1md2Z5fLKOJD2r_f8Z0O5p7.ZHYx12rVaFyqC33F63zRl5AzDPZb0iWUQ-- Received: from [200.17.143.33] by web55208.mail.re4.yahoo.com via HTTP; Wed, 26 Mar 2008 10:00:34 ART Date: Wed, 26 Mar 2008 10:00:34 -0300 (ART) From: =?iso-8859-1?q?C=E9sar=20Santos?= Subject: [SPAM] =?iso-8859-1?q?Re:=20[obm-l]=20Integral=20de=20superf=EDcie=20?= =?iso-8859-1?q?=20(quest=E3o=20simples)?= To: obm-l@mat.puc-rio.br In-Reply-To: <20080325180937.72s6l3suqsscw4co@webmail.usp.br> MIME-Version: 1.0 Content-Type: text/plain Content-Transfer-Encoding: 7bit Message-ID: <884134.27287.qm@web55208.mail.re4.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: =?iso-8859-1?q?C=E9sar=20Santos?= X-Spam-Status: Yes, hits=6.0 required=5.0 tests=FORGED_YAHOO_RCVD,IN_REP_TO,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01,SPAM_REDIRECTOR, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ****** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="0-1920139426-1206536434=:27287" X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (6.00 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: QUOTED_EMAIL_TEXT (-0.8 points) BODY: Contains what looks like a quoted email text SPAM: SPAM_REDIRECTOR (0.4 points) URI: Uses open redirection service SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 172.58.190.206.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 172.58.190.206.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- --0-1920139426-1206536434=:27287 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 8bit Obrigado Arlane pela resposta, mas sobre isso eu já sabia, o que eu quero saber é quais são os limites de integraçao para x e y. Arlane Manoel S Silva escreveu: Seria ótimo fazer uma figura, primeiro. Note que a equação 2x + 3y + z =6 determina um plano no R^3 e a porção que é corta pelos eixos forma um triângulo de vértices (0,0,6), (3,0,0) e (0,2,0). É possível resolver geometricamente. Um outro modo é usando integral de superfície. Considere a função z:=z(x,y)=6-2x-3y e use a definição. Citando César Santos : > Calcule área da porção do plano 2x + 3y + z =6 que é cortada pelos > três planos coordenados. Resp. 3V14 (três raiz de quatorze). Alguém > poderia me explicar a resolução da questão, por favor? > > --------------------------------- > Abra sua conta no Yahoo! Mail, o único sem limite de espaço para > armazenamento! -- Arlane Manoel S Silva MAT-IME-USP ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= --------------------------------- Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-1920139426-1206536434=:27287 Content-Type: text/html; charset=iso-8859-1 Content-Transfer-Encoding: 8bit  Obrigado Arlane pela resposta, mas sobre isso eu já sabia, o que eu quero saber é quais são os limites de integraçao para x e y.

Arlane Manoel S Silva <arlan@usp.br> escreveu:
Seria ótimo fazer uma figura, primeiro. Note que a equação 2x + 3y + z =6
determina um plano no R^3 e a porção que é corta pelos eixos forma um
triângulo de vértices (0,0,6), (3,0,0) e (0,2,0). É possível resolver
geometricamente.
Um outro modo é usando integral de superfície.
Considere a função z:=z(x,y)=6-2x-3y e use a definição.

Citando César Santos :

> Calcule área da porção do plano 2x + 3y + z =6 que é cortada pelos
> três planos coordenados. Resp. 3V14 (três raiz de quatorze). Alguém
> poderia me explicar a resolução da questão, por favor?
>
> ---------------------------------
> Abra sua conta no Yahoo! Mail, o único sem limite de espaço para
> armazenamento!



--
Arlane Manoel S Silva
MAT-IME-USP


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Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-1920139426-1206536434=:27287-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Mar 26 11:15:26 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2QEDPWA032326 for ; Wed, 26 Mar 2008 11:13:25 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2QEDMNS032318 for obm-l-MllGbsmmN; Wed, 26 Mar 2008 11:13:22 -0300 Received: from an-out-0708.google.com (an-out-0708.google.com [209.85.132.250]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2QEDDWA032311 for ; Wed, 26 Mar 2008 11:13:14 -0300 Received: by an-out-0708.google.com with SMTP id c31so862725ana.120 for ; Wed, 26 Mar 2008 07:12:55 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:mime-version:content-type; bh=XMFQGWuG9J7Bn1Y37CiAzUIbSMjCULTOGbXHH4yCsY8=; b=Pzw1ZPabPJYtCvOez3hB1sP86hF4fXatTxdtSw30AzehjVqYGRVVwPLPEoeF/6OuaqrwRLxuAZCGDMs4QQK5FMD+LfaTxkWgY8qZyuHZ6Uq+xr7FV6IQUXs7yMEDCOWeIKt1hwmlAoHYHdW1Uf0js8AOQzjROLYdJ9zSTsmdde4= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:mime-version:content-type; b=SHJg9DDRajATdreTvvkXs42RONN+Ea5bB+NpY6PhniC72FMKDG/aIbqmqbzYGQDqUCzVArMGj13yrvGYlRUDqKtL7Dx25+g+TPmZotneq5eCSPkfyaX1bJSV+14+tBgF0CPXpWRYqlNMGDJ2LF3U//Q8OarTtFfGbd+/+WgNHjk= Received: by 10.100.32.8 with SMTP id f8mr45853anf.29.1206540775196; Wed, 26 Mar 2008 07:12:55 -0700 (PDT) Received: by 10.100.135.4 with HTTP; Wed, 26 Mar 2008 07:12:55 -0700 (PDT) Message-ID: Date: Wed, 26 Mar 2008 11:12:55 -0300 From: "Thelio Gama" To: obm-l@mat.puc-rio.br Subject: [SPAM] [obm-l] =?ISO-8859-1?Q?zero_=E9_divisor_de_zero=3F?= MIME-Version: 1.0 Content-Type: text/plain Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Thelio Gama" X-Spam-Status: Yes, hits=5.8 required=5.0 tests=RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ***** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_Part_18745_30399745.1206540775184" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (5.80 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 250.132.85.209.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 250.132.85.209.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- ------=_Part_18745_30399745.1206540775184 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Bom dia, professores, Estou um pouco confuso sobre isso: tem livro que diz que zero NUNCA divide, n=E3o =E9 divisor de nenhum n=FAmero. Outros dizem que zero pode dividir ze= ro, j=E1 que 0 =3D n . 0. Neste caso ent=E3o o zero pode ser divisor sim ( mas somen= te do zero). Afinal, =E9 certo afirmar que zero NUNCA pode dividir nenhum n=FAmer= o ou que o zero pode ser divisor do zero??? E qual o significado de zero dividid= o por zero??? Agrade=E7o se puder ter este exclarecimento dos mestres da lista. Thelio ------=_Part_18745_30399745.1206540775184 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline
Bom dia, professores,
Estou um pouco confuso sobre isso: tem livro que diz que zero NUNCA di= vide, n=E3o =E9 divisor de nenhum n=FAmero. Outros dizem que zero pode divi= dir zero, j=E1 que 0 =3D n . 0. Neste caso ent=E3o o zero pode ser divisor = sim ( mas somente do zero). Afinal, =E9 certo afirmar que zero NUNCA pode d= ividir nenhum n=FAmero ou que o zero pode ser divisor do zero??? E qual o s= ignificado de zero dividido por zero???
Agrade=E7o se puder ter este exclarecimento dos mestres da lista.
 
Thelio
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<99886d920803260716p30a09d25ydd325e87283ca285@mail.gmail.com> Date: Wed, 26 Mar 2008 15:16:47 +0100 From: "=?UTF-8?Q?Bruno_Fran=C3=A7a_dos_Reis?=" To: obm-l@mat.puc-rio.br Subject: =?UTF-8?Q?Re:_[obm-l]_m=C3=B3dulo?= In-Reply-To: <889896.67173.qm@web52903.mail.re2.yahoo.com> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_24354_8235847.1206541007322" References: <889896.67173.qm@web52903.mail.re2.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "=?UTF-8?Q?Bruno_Fran=C3=A7a_dos_Reis?=" X-Spam-Status: No, hits=1.3 required=5.0 tests=AWL,IN_REP_TO,MAILTO_TO_SPAM_ADDR,QUOTED_EMAIL_TEXT, REFERENCES,SPAM_PHRASE_00_01,X_MAILING_LIST version=2.44 X-Spam-Level: * ------=_Part_24354_8235847.1206541007322 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: base64 Content-Disposition: inline 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========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Mar 26 11:57:23 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2QEtOWA004602 for ; Wed, 26 Mar 2008 11:55:26 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2QEtFSv004594 for obm-l-MllGbsmmN; Wed, 26 Mar 2008 11:55:15 -0300 Received: from colorado.uspnet.usp.br (colorado.uspnet.usp.br [143.107.254.72]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2QEslWA004571 for ; Wed, 26 Mar 2008 11:54:47 -0300 Received: (qmail 6033 invoked from network); 26 Mar 2008 14:54:30 -0000 X-Mail-Scanner: Scanned by qSheff-II-2.1-r1 (http://www.enderunix.org/qsheff/) Received: from siberia.uspnet.usp.br (HELO localhost) ([143.107.254.70]) (envelope-sender ) by colorado.uspnet.usp.br (qmail-ldap-1.03) with SMTP for ; 26 Mar 2008 14:54:30 -0000 Received: from 192.168.240.100 (192.168.240.100 [192.168.240.100]) by webmail.usp.br (Horde MIME library) with HTTP; Wed, 26 Mar 2008 11:54:30 -0300 Message-ID: <20080326115430.21iynmskr48oscog@webmail.usp.br> Date: Wed, 26 Mar 2008 11:54:30 -0300 From: Arlane Manoel S Silva To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Integral de =?iso-8859-1?b?c3VwZXJm7WNpZSA=?= =?iso-8859-1?b?PGT6dmlkYT4g?= =?iso-8859-1?b?KHF1ZXN0428=?= simples) References: <884134.27287.qm@web55208.mail.re4.yahoo.com> In-Reply-To: <884134.27287.qm@web55208.mail.re4.yahoo.com> MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1; DelSp="Yes"; format="flowed" Content-Disposition: inline User-Agent: Internet Messaging Program (IMP) H3 (4.1.5-cvs) Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m2QEswWA004580 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Arlane Manoel S Silva X-Spam-Status: No, hits=2.4 required=5.0 tests=AWL,IN_REP_TO,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SIGNATURE_LONG_SPARSE, SPAM_PHRASE_00_01,USER_AGENT,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: ** Quando z=0 temos a variação entre x e y, ou seja, 2x+3y=6. Assim, y=2x/3 + 2. Logo, x varia de 0 até 3 e y varia de 0 até 2x/3 + 2 . Acho que é isso. Citando César Santos : > Obrigado Arlane pela resposta, mas sobre isso eu já sabia, o que eu > quero saber é quais são os limites de integraçao para x e y. > > Arlane Manoel S Silva escreveu: Seria ótimo fazer > uma figura, primeiro. Note que a equação 2x + 3y + z =6 > determina um plano no R^3 e a porção que é corta pelos eixos forma um > triângulo de vértices (0,0,6), (3,0,0) e (0,2,0). É possível resolver > geometricamente. > Um outro modo é usando integral de superfície. > Considere a função z:=z(x,y)=6-2x-3y e use a definição. > > Citando César Santos : > >> Calcule área da porção do plano 2x + 3y + z =6 que é cortada pelos >> três planos coordenados. Resp. 3V14 (três raiz de quatorze). Alguém >> poderia me explicar a resolução da questão, por favor? >> >> --------------------------------- >> Abra sua conta no Yahoo! Mail, o único sem limite de espaço para >> armazenamento! > > > > -- > Arlane Manoel S Silva > MAT-IME-USP > > > ========================================================================= > Instruções para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > ========================================================================= > > > > --------------------------------- > Abra sua conta no Yahoo! Mail, o único sem limite de espaço para > armazenamento! -- Arlane Manoel S Silva MAT-IME-USP ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Mar 26 13:15:26 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2QGE3WA010404 for ; Wed, 26 Mar 2008 13:14:03 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2QGE3Js010402 for obm-l-MllGbsmmN; Wed, 26 Mar 2008 13:14:03 -0300 Received: from fk-out-0910.google.com (fk-out-0910.google.com [209.85.128.185]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2QGE1WA010393 for ; Wed, 26 Mar 2008 13:14:01 -0300 Received: by fk-out-0910.google.com with SMTP id 22so4684292fkq.13 for ; Wed, 26 Mar 2008 09:13:43 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; bh=MmjwcdDDtBFOkF2t2YZFkJkOWnlqdqyI2ggSilT1y+k=; b=WKPXfJBYI1XfVWGmSnc/dCL0U+Am4tQHGoaPwVLbPlc0ZJ8TZouZHPhavivzbwm4uuN3ESr2zWmWbpacwDkLVjXB6MjY2QB5aGfU9aF6kj+BUmL/METBsrMZBdVMNoYKU2/9Aca11xj1g74NgksYjrOfIpChTgC5Ti+y5q3qK3M= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; b=COaIxc7kuRWkiCey+plDDncRm60hsYa9QywLTz3N1jreWX1nWi+SflTX/St7d6olCaXfOD39clm5zpAm//0swZeywMW9vAukkx9le3MEsGOx9edvPNiglxM1gXPPM4oe5nzHCl2byFeqpvpIqYy9kfk9OFx+Swa82RFiNDP7QF4= Received: by 10.82.113.6 with SMTP id l6mr330113buc.20.1206548022408; Wed, 26 Mar 2008 09:13:42 -0700 (PDT) Received: by 10.82.127.13 with HTTP; Wed, 26 Mar 2008 09:13:42 -0700 (PDT) Message-ID: Date: Wed, 26 Mar 2008 13:13:42 -0300 From: "Johann Peter Gustav Lejeune Dirichlet" To: obm-l@mat.puc-rio.br Subject: =?ISO-8859-1?Q?Re:_[obm-l]_zero_=E9_divisor_de_zero=3F?= In-Reply-To: MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline References: Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m2QGE2WA010398 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Johann Peter Gustav Lejeune Dirichlet" X-Spam-Status: No, hits=2.7 required=5.0 tests=AWL,FROM_ENDS_IN_NUMS,IN_REP_TO,QUOTED_EMAIL_TEXT, RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,REFERENCES, SPAM_PHRASE_00_01,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: ** Bem, em Teoria dos Números, um número é múltiplo do outro se é possível achar uma solução inteira para ax=b Se a=b=0 então qualquer x é solução. Mas é errôneo tentar fazer a conta 0/0, bem como 5/0. O porque disso é uma dicussão longa e cheia de farpas, que nunca vai levar a lugar nenhum. Até porque usando aritmética módulo 6, 2*3 é congruente a 0 módulo 6, e nenhum deles é zero. Ou seja, 2 e 3 são divisores não-triviais do zero. Em 26/03/08, Thelio Gama escreveu: > Bom dia, professores, > Estou um pouco confuso sobre isso: tem livro que diz que zero NUNCA divide, > não é divisor de nenhum número. Outros dizem que zero pode dividir zero, já > que 0 = n . 0. Neste caso então o zero pode ser divisor sim ( mas somente do > zero). Afinal, é certo afirmar que zero NUNCA pode dividir nenhum número ou > que o zero pode ser divisor do zero??? E qual o significado de zero dividido > por zero??? > Agradeço se puder ter este exclarecimento dos mestres da lista. > > Thelio ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Mar 26 13:40:24 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2QGbtWA013105 for ; Wed, 26 Mar 2008 13:37:55 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2QGbtJp013103 for obm-l-MllGbsmmN; Wed, 26 Mar 2008 13:37:55 -0300 Received: from el-out-1112.google.com (el-out-1112.google.com [209.85.162.177]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2QGbqWA013092 for ; Wed, 26 Mar 2008 13:37:53 -0300 Received: by el-out-1112.google.com with SMTP id o28so2196771ele.3 for ; Wed, 26 Mar 2008 09:37:34 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:mime-version:content-type; bh=q8s5EJUJH8kJWZrJeMzGC099L97WmAlANrW9DnbPMqA=; b=JWNFLoGxij910V2tpF3vx3vW6c+P0cJZVKq088potpRzQX9mBbVRrdctH0N9KQH6Px96h6Lp+8YEC4hxf6mqsn5Sgp7JP9X1jzei3wuwUkUCiXw13V+WEktNs2U1ydMIMRk5xUuwS3VycqNOvbZZq9rXVFxTQzshJggZi298ZeQ= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:mime-version:content-type; b=Q4TAEz0VuWvcXcIRLC5c9HmU2fDcK7U+kV5PJ/eLFwHVWRTfPaS8w3RTSHfmgNsWAmzK5aW61L5q9a2aC6w0UdRdNCUo9CAKjxqbQyHwsEcf3Br3qRZJSg5Nr3rL/UbCiZ5ZQ35zBkrYEGtWApVX8xJuQvXn3OswIVxw7Ns3ZXg= Received: by 10.141.122.20 with SMTP id z20mr204794rvm.160.1206549453523; Wed, 26 Mar 2008 09:37:33 -0700 (PDT) Received: by 10.140.128.9 with HTTP; Wed, 26 Mar 2008 09:37:33 -0700 (PDT) Message-ID: Date: Wed, 26 Mar 2008 13:37:33 -0300 From: MauZ To: obm-l@mat.puc-rio.br Subject: [SPAM] [obm-l] =?ISO-8859-1?Q?Problema_Combinat=F3ria?= MIME-Version: 1.0 Content-Type: text/plain Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: MauZ X-Spam-Status: Yes, hits=5.8 required=5.0 tests=RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ***** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_Part_25205_17335952.1206549453540" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (5.80 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 177.162.85.209.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 177.162.85.209.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- ------=_Part_25205_17335952.1206549453540 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Ol=E1 a todos! Numa estante com 24 livros, de quantas maneiras posso retirar 5 livros sem ter nenhum consecutivo? E no caso de n livros, quantas maneiras retiro p livros sem ter nenhum consecutivo? Pra completar vou colocar parte da minha tentativa de solu=E7=E3o, preciso = de ajuda pra saber se est=E1 certo at=E9 onde fiz e como finalizar pois empaqu= ei. Fiz dessa forma: Todas Combina=E7=F5es - Combina=E7=F5es c/ Consecutivos Todas: 24!/5!19! Consecutivos: 23!/4!19! + 22!/3!19! + 21!/2!19! + 20!/1!19! Fiz uma formula geral com n e p e deu o seguinte: n!/p!(n-p!) - [(n-1)!/(p-1)!(n-p)! + (n-2)!/(p-2)!(n-p)!+...+(n-p+1)!/(n-p)!] Fatorando deu: (1/(n-p)!)[n!/p!-(n-1)!/(p-1)!-(n-2)!/(p-2)-...-(n-p+1)!/(n-p)!] Dae empaquei de vez... N=E3o consegui continuar! Quem souber fazer por favor me d=EA a luz! Ou simplesmente indique o erro n= o meu racioc=EDnio. Agrade=E7o antecipadamente, Maurizio ------=_Part_25205_17335952.1206549453540 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Ol=E1 a todos!

Numa estante com 24 livros, de quantas maneiras posso= retirar 5 livros sem ter nenhum consecutivo? E no caso de n livros, quanta= s maneiras retiro p livros sem ter nenhum consecutivo?



Pra c= ompletar vou colocar parte da minha tentativa de solu=E7=E3o, preciso de aj= uda pra saber se est=E1 certo at=E9 onde fiz e como finalizar pois empaquei= .

Fiz dessa forma: Todas Combina=E7=F5es - Combina=E7=F5es c/ Consecutivo= s

Todas: 24!/5!19!
Consecutivos: 23!/4!19! + 22!/3!19! + 21!/2!1= 9! + 20!/1!19!

Fiz uma formula geral com n e p e deu o seguinte:
=
n!/p!(n-p!) - [(n-1)!/(p-1)!(n-p)! + (n-2)!/(p-2)!(n-p)!+...+(n-p+1)!/(n-p)= !]

Fatorando deu:

(1/(n-p)!)[n!/p!-(n-1)!/(p-1)!-(n-2)!/(p-2)= -...-(n-p+1)!/(n-p)!]

Dae empaquei de vez... N=E3o consegui continua= r!
Quem souber fazer por favor me d=EA a luz! Ou simplesmente indique o erro n= o meu racioc=EDnio.

Agrade=E7o antecipadamente,
Maurizio

------=_Part_25205_17335952.1206549453540-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Mar 26 14:20:05 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2QHIgWA016133 for ; Wed, 26 Mar 2008 14:18:42 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2QHIg9w016131 for obm-l-MllGbsmmN; Wed, 26 Mar 2008 14:18:42 -0300 Received: from ti-out-0910.google.com (ti-out-0910.google.com [209.85.142.189]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2QHIbWA016124 for ; Wed, 26 Mar 2008 14:18:39 -0300 Received: by ti-out-0910.google.com with SMTP id y6so1461644tia.13 for ; Wed, 26 Mar 2008 10:18:19 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; bh=8dQ9CnPKkgPlX+P/h50g3P8E+vIOAbmugL+UDcLle/Y=; b=FuDmvHOO1zmwNiMpBuk5hpxUCPRhL4wirkLv8hoCanJ2pQAe/F0Qb7X5bQubaSh/zGoROjlI4S/OwFdpuyp5iWcBzq0VXsAEL7MTpXiKFwpaXh6Xm4oAo5yv5LHiH54q5cySJx2WLNYy7lgyBHpofGZIP8qIZ8ETil0CJp0igc4= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; b=DIw+J3PQ0LywMilb6sUHW9jBkcxY2d6Q9GcRqnTPp7BrsXf4i/R85yqTsWezR5fGlpbGifG71hKgkHG+vUHEsTLSZFnzPb01opoUxQ6x135B7hdAmZkBWmx27AYXT5l6tA8fmS6qLZ9Bk2Xl9+7kUDS0IOIg0fhHQKRmTNQ2lZo= Received: by 10.110.52.5 with SMTP id z5mr433035tiz.17.1206551898785; Wed, 26 Mar 2008 10:18:18 -0700 (PDT) Received: by 10.70.60.1 with HTTP; Wed, 26 Mar 2008 10:18:18 -0700 (PDT) Message-ID: <7e31215a0803261018t377c7fc3oe8d6e0bef04928ca@mail.gmail.com> Date: Wed, 26 Mar 2008 14:18:18 -0300 From: "Rodrigo Renji" To: obm-l@mat.puc-rio.br Subject: =?ISO-8859-1?Q?Re:_[obm-l]_RES:_[obm-l]_RES:_[obm-l]_Indica=E7=E3o_de?= =?ISO-8859-1?Q?_livros_(C=E1lculo_num=E9rico_e_Equa=E7=F5es_diferenciais)?= In-Reply-To: <200803261234.m2QCYRWA021807@saci.mat.puc-rio.br> MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline References: <5bb472220803260430r477d89f3ye1066bd076953c7d@mail.gmail.com> <200803261234.m2QCYRWA021807@saci.mat.puc-rio.br> Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m2QHIfWA016128 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Rodrigo Renji" X-Spam-Status: No, hits=3.8 required=5.0 tests=AWL,IN_REP_TO,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: *** De equações diferenciais(livros) eu conheço poucos, mas dos poucos que conheço um que me agradou foi o livro, William E. Boyce e Richard C. Diprima, Equações diferenciais elementares e problemas de valores de contorno, um de cálculo númerico que me agradou foi Cálculo númerico de Victor Mirshawka Em 26/03/08, Paulo - Uniredes escreveu: > > > Olha João, > > Provavelmente tem uns amigos aí chateados comigo, pois eu ainda não estava > preparado para os pedidos que iam chegar. Meu pequeno sebo tem muitos livros > legais mas eu precisava de uma loja eletrônica, para organizar as coisas. > Ela está em http://uniredes.org/loja01. É ainda incipiente mas vai ajudar > muito. Estou migrando o cadastro das obras que tenho. Não é um esquema > rigorosamente comercial. Quando acabar o estoque particular acabou, mas eu > quero atender direitinho, deixando tudo documentado. Assim posso indicar no > ano que vem quem tem o que para vender. Será muito legal e um serviço de > utilidade. > > Os preços que você deseja estarão disponíveis na loja, amanhã de manhã, > prometo. > > Espero que todos gostem e já peço desculpas pela demora. > > > > --- > Paulo C. Santos (PC) > e-mail: paulo@uniredes.org > Homepage: http://uniredes.org > Tel.: (21) 2510.8783 - Cel.: (21) 8753-0729 > -------------------------------------------- > MS-Messenger: Uniredes_Br@hotmail.Com > > ________________________________ > > De: owner-obm-l@mat.puc-rio.br [mailto:owner-obm-l@mat.puc-rio.br] Em nome > de Joao Victor Brasil > Enviada em: quarta-feira, 26 de março de 2008 08:31 > Para: obm-l@mat.puc-rio.br > Assunto: Re: [obm-l] RES: [obm-l] Indicação de livros (Cálculo numérico e > Equações diferenciais) > > > > Paulo, > > Quanto você quer neste livros? Os do Piskonov, Apostol e Pacitti. > > Joao Victor > > > On 3/26/08, Paulo - Uniredes wrote: > > > > > > Oi Cesar, > > > > Para cálculo I e II, eu recomendo o Piskunov: > http://www.traca.com.br/seboslivrosusados.cgi?mod=LV62211&origem=resultadodetalhada > > Eu tenho os volumes I e II em espanhol no meu sebo. São muito legais. O > volume II é ótimo em equações diferenciais. A obra, em 2 volumes, foi usada > na UFRJ. > > > > Tem também o do Tom M. Apostol em português...: > > > > > http://www.livrariadafisica.com.br/produto_detalhe.asp?id_produto=19209 > > > > Estudei pelo Apostol e a qualidade é muito boa. Apesar de eu ser meio > "burro" (Só passei em cálculo I após fazer um curso de verão na UFRJ. Muito > legal...mas meu negócio é redes de computadores). > > > > Faço preço camarada nos 3 livros. Camarada mesmo ! > > > > > > []s > > > > > > > > --- > > Paulo C. Santos (PC) > > e-mail: paulo@uniredes.org > > Homepage: http://uniredes.org > > Tel.: (21) 2510.8783 - Cel.: (21) 8753-0729 > > -------------------------------------------- > > MS-Messenger: Uniredes_Br@hotmail.Com > > > > ________________________________ > De: owner-obm-l@mat.puc-rio.br [mailto:owner-obm-l@mat.puc-rio.br] Em nome > de César Santos > > Enviada em: terça-feira, 25 de março de 2008 16:10 > > Para: obm-l@mat.puc-rio.br > > Assunto: [obm-l] Indicação de livros (Cálculo numérico e Equações > diferenciais) > > > > > > Poderiam me indicar bons livros de cálculo numérico e de equações > diferencias acessíveis para iniciante? > > > > ________________________________ > Abra sua conta no Yahoo! Mail, o único sem limite de espaço para > armazenamento! > > > > > > > > > > > > > > ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Mar 26 16:01:04 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2QIxaWA024208 for ; Wed, 26 Mar 2008 15:59:36 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2QIxaVG024206 for obm-l-MllGbsmmN; Wed, 26 Mar 2008 15:59:36 -0300 Received: from relay3.bol.com.br (relay3.bol.com.br [200.221.4.107]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2QIxZWA024203 for ; Wed, 26 Mar 2008 15:59:35 -0300 Received: from localhost (localhost [127.0.0.1]) by salsa3.bol.com.br (Postfix) with ESMTP id 54A90E005FB5 for ; Wed, 26 Mar 2008 06:33:22 -0300 (BRT) Received: from bol.com.br (whisper6.mail.sys.intranet [172.26.5.78]) by salsa3.bol.com.br (Postfix) with ESMTP id 33CFEE00634C for ; Wed, 26 Mar 2008 06:33:22 -0300 (BRT) Date: Wed, 26 Mar 2008 15:59:17 -0300 Message-Id: Subject: [obm-l] =?iso-8859-1?b?TEFET1MgRE8gVFJJwk5HVUxP?= MIME-Version: 1.0 X-Sensitivity: 3 Content-Type: multipart/alternative; boundary="_=__=_XaM3_.1206557957.2A.895015.42.12819.52.42.007.1552099933" From: "arkon" To: "obm-l" X-XaM3-API-Version: 4.3(R1) (B10) X-SenderIP: 200.140.133.74 X-SIG5: 9b050593224f168eaf58bba1350d90e4 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "arkon" X-Spam-Status: No, hits=1.3 required=5.0 tests=AWL,BIG_FONT,HTML_50_70,LINES_OF_YELLING, LINES_OF_YELLING_2,SPAM_PHRASE_00_01,TO_LOCALPART_EQ_REAL, X_MAILING_LIST version=2.44 X-Spam-Level: * --_=__=_XaM3_.1206557957.2A.895015.42.12819.52.42.007.1552099933 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable Pessoal algu=E9m pode me enviar, por favor, a resolu=E7=E3o dessa quest=E3= o (EN-84) As medidas dos lados de um tri=E2ngulo ABC s=E3o 3 n=FAmeros inte= iros e consecutivos e o =E2ngulo maior A =E9 o dobro do menor C. Os lados= deste tri=E2ngulo s=E3o: a) 2, 3 e 4. b) 3, 4 e 5. c) 8, 9 e 10. d) 4, 5 e 6. e) 5, 6 = e 7. DESDE J=C1 MUITO OBRIGADO --_=__=_XaM3_.1206557957.2A.895015.42.12819.52.42.007.1552099933 Content-Type: text/html; charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable

<= B style=3D"mso-bidi-font-weight: normal">Pessoal algu=E9m pode me enviar, por favor, a resolu=E7=E3o= dessa quest=E3o

<= B style=3D"mso-bidi-font-weight: normal"> 

<= B style=3D"mso-bidi-font-weight: normal">(EN-84) As medidas dos la= dos de um tri=E2ngulo ABC s=E3o 3 n=FAmeros inteiros e consecutivo= s e o =E2ngulo maior A =E9 o dobro do menor C. Os lados des= te tri=E2ngulo s=E3o:

 

a) 2, 3 e 4.=     b) 3, = 4 e 5.    c) 8, 9 e 10.    d) 4, 5 e 6.    e) 5, 6 e 7.

 

DESDE J=C1 MUITO OBRIGADO

--_=__=_XaM3_.1206557957.2A.895015.42.12819.52.42.007.1552099933-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Mar 26 16:26:58 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2QJPdWA026183 for ; Wed, 26 Mar 2008 16:25:39 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2QJPcNJ026181 for obm-l-MllGbsmmN; Wed, 26 Mar 2008 16:25:38 -0300 Received: from web52906.mail.re2.yahoo.com (web52906.mail.re2.yahoo.com [206.190.49.16]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id m2QJPYWA026164 for ; Wed, 26 Mar 2008 16:25:34 -0300 Received: (qmail 7839 invoked by uid 60001); 26 Mar 2008 19:25:15 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:Date:From:Subject:To:In-Reply-To:MIME-Version:Content-Type:Content-Transfer-Encoding:Message-ID; b=cqZsADuDzkLnPv9J2nMXaERVyA/OKWheqow1O0g4u7JJottjcko/vAoxGcocPeRQARyA04QaIpn1iXn3sg+J57w68NvK9f8rWTbsiAN0KApCcOcCEe/ev7X03a+mKP8B49yVEVNWZMfS4CxA5M+pCQmWlRjTburvzksycKrJNxU=; X-YMail-OSG: X7rVm7cVM1lF4FPGrytdW4SawTFJzRjkQ4GYtLwvrUjU588XyHBjgjPHO4deRXXkKW.FkiYTXrEocbtVyzxVZsLWgthYMVIHeuc_lgJmqUeHjQ7nXpaHrKEEDDG9BFk_bXpNhRKyIraIXCg- Received: from [189.30.80.236] by web52906.mail.re2.yahoo.com via HTTP; Wed, 26 Mar 2008 16:25:15 ART Date: Wed, 26 Mar 2008 16:25:15 -0300 (ART) From: Antonio Giansante Subject: [SPAM] =?iso-8859-1?q?Re:=20[obm-l]=20m=C3=B3dulo?= To: obm-l@mat.puc-rio.br In-Reply-To: <99886d920803260716p30a09d25ydd325e87283ca285@mail.gmail.com> MIME-Version: 1.0 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 7bit Message-ID: <639458.6086.qm@web52906.mail.re2.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Antonio Giansante X-Spam-Status: Yes, hits=5.5 required=5.0 tests=AWL,FORGED_YAHOO_RCVD,IN_REP_TO,MAILTO_TO_SPAM_ADDR, RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ***** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (5.50 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: MAILTO_TO_SPAM_ADDR (0.7 points) URI: Includes a link to a likely spammer email address SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 16.49.190.206.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 16.49.190.206.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-1.6 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- Caro Bruno: Você está certo. Acho que eu tenho é mesmo de parar de tentar me divertir com estes exercícios antes de dormir. É obvio que o q o Paulo fez está, além de correto, muito bem explicado e resumido, o q certamente decorre de sua grande capacidade e qualidade. O erro EXTREMAMENTE CRASSO com certeza foi meu. Agradeço por ter observado. Vc não sabe como eu fiquei pasmo ao ver a parvoíce, a sandice que escrevi. Foi realmente uma falta de atenção ao ler o enunciado (coisa que eu reforço sempre aos meus alunos para tomarem cuidado) e perceber que é PARA TODO r maior q zero. Esta é uma daquelas situações em que vc tropeça na rua e olha pra trás para conferir o çhão, incrédulo que vc se atrapalhou com um coisa tão básica como andar. Creio q, na opinião d Erdös, eu deveria tomar mais café. ABçs. --- Bruno França dos Reis escreveu: > Antonio, > > acho que foi você quem não leu direito nem a questão > e muito menos a > resposta do Paulo Santa Rita. > Em momento algum o Paulo usou a tese para prova-la, > como você afirma. Isso é > realmente um erro comum, mas para pessoas de um > nivel de matematica mais > baixo do que o do Paulo, certamente. > O que ele fez foi admitir a hipotese e que esta > implica a NEGACAO da tese e > em seguida provar que esta é falsa, e a partir dai, > ter a obrigacao de > concluir a veracidade da tese. > > Vou te devolver um exemplo muito parecido com o que > você deu, mas para > explicar o que o Paulo fez. Quero provar: n = 5 ==> > n é impar. > Vamos, para evidenciar a tecnica, definir um numero > par como aquele que pode > ser decomposto como a soma de duas parcelas iguais e > inteiras. > Vamos então admitir a hipotese (n = 5) e supor a > negacao da tese: n é par. > Sendo n par, temos que ser capazes de exibir um > inteiro que somado a si > mesmo de 5. > Ora, 1 + 1 = 2, 2 + 2 = 4, 3 + 3 = 6, e a partir > daqui, k + k > 5. Então não > existe inteiro que somado a si mesmo dê 5. Logo foi > um erro admitir que n é > par, isto é, dado que n = 5, não vale que n é par, > vale a negação disso, > isto é: n não é par. Um número inteiro que não é par > é necessariamente > ímpar, o que conclue a demonstração. > > > O seu contra-exemplo para negar a afirmação proposta > pelo exercicio não vale > pelo simples fato de que para o seu a e o seu b vc > tomou APENAS UM valor de > r, e a hipotese inclue " | a - b | DE r MAIOR QUE ZERO". > Não satisfeita a hipótese, não há obrigação nenhuma > de que a tese valha. > > > > Para finalizar, um simples argumento (e não mais uma > prova, essas vc ja tem > o suficiente) para tentar convencer a veracidade da > afirmação: > > Temos dois numeros positivos, a e b. Calculamos o > modulo de sua diferença: d > = |b - a|. > Temos então que d >= 0. > Mas eu afirmo pra vc (hipotese): dado um numero real > r positivo (maior que > zero), d < r. Quanto vale d? > Ora, r = 0.5 implica d < 0.5. Mas e se diminuirmos > r? Tomemos então r = > 10^-219287391873. Ora, d < r. Como d será menor do > que QUALQUER valor > positivo, temos então que d é NO MAXIMO 0. Mas pela > definição de d, ele > também é NO MINIMO 0. Ora, nessas condições, d vale > exatamente 0, o que > implica a = b. > > > > Espero que a questão tenha ficado clara agora para > você. Qualquer coisa, > pergunte! > > Abraço > Bruno > 2008/3/26 Antonio Giansante : > > > Creio que você incorreu em um erro muito comum da > > argumentação lógica, justamente por ser ele muito > > sutil de ser percebido (e por isso ser muito usado > em > > concursos públicos): Você não pode usar a tese > para > > prová-la. Por exemplo: Prove que se um número é > > divisível por 2, então ele é par. Aí você começa > > fazendo: suponha que n é par, logo é divisível por > 2. > > Por isso não pode fazer "suponha r=s". creio que > essa > > afirmação da tese é dito modus tollens. Em um > exemplo > > um pouco mais didático: pense na afirmação: Se > chove, > > então molha. Assim, se eu afirmar que se molhou, > > então choveu, vou estar errando, pois poderia ter > > molhado com um copo d'água, uma mangueira, etc Eu > > posso dizer que se chove, com certeza molha, mas > se > > molha, nem sempre foi porque choveu. Espero que > este > > chove-e-não-molha (que é a negação da frase > inicial) > > E creio que essa afirmação é falsa, pois > encontramos > > um contra-exemplo: Seja a#0, b = 2a e r = 3a veja > que > > | a - b | > > > > > > > > > --- Paulo Santa Rita > > escreveu: > > > > > Ola Joel e demais colegas > > > desta lista ... OBM-L, > > > > > > > > > Suponha que a # b, isto é, suponha que "a" e > > > diferente de "b". Neste > > > caso, s = | a - b | e um real positivo. Entao, > > > fazendo r = s e usando > > > a propriedade enunciada, teremos : > > > > > > | a - b | < s => | a - b | < | a - b | ... > absurdo ! > > > > > > Assim, a nossa tese e insustentavel e somos > > > obrigados a admitir que a = b. > > > > > > No endereco abaixo existem muitos problemas > > > olimpicos interessantes : > > > > http://www.mat.puc-rio.br/~nicolau/psr/ > > > > > > Um Abraco a Todos > > > Paulo Santa Rita > > > 3,0D31,190308 > > > > > > > > > > > > Em 25/03/08, Joel > Castro > > > escreveu: > > > > tenho pequena dúvida: > > > > > > > > prove: se para todo r maior que zero, o módulo > da > > > diferença de a e b é menor > > > > que r, então a é igual a b. > > > > > > > > valeu!!!!!! > > > > > > > > ________________________________ > > > > Abra sua conta no Yahoo! Mail, o único sem > limite > > > de espaço para > > > > armazenamento! > > > > > > > > > > > > > > > > > ========================================================================= > > > Instruções para entrar na lista, sair da lista e > > > usar a lista em > > > > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > > > > > > ========================================================================= > > > > > > > > > > > Abra sua conta no Yahoo! Mail, o único sem > limite de espaço para > > armazenamento! > > http://br.mail.yahoo.com/ > > > ========================================================================= > > Instruções para entrar na lista, sair da lista e > usar a lista em > > > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > > > ========================================================================= > > > > > > -- > Bruno FRANÇA DOS REIS > > msn: brunoreis666@hotmail.com > === message truncated === Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! http://br.mail.yahoo.com/ ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Mar 26 16:48:33 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2QJlMWA028344 for ; Wed, 26 Mar 2008 16:47:22 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2QJlM72028342 for obm-l-MllGbsmmN; Wed, 26 Mar 2008 16:47:22 -0300 Received: from yw-out-2324.google.com (yw-out-2324.google.com [74.125.46.28]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2QJlKWA028335 for ; Wed, 26 Mar 2008 16:47:21 -0300 Received: by yw-out-2324.google.com with SMTP id 3so32974ywj.9 for ; Wed, 26 Mar 2008 12:47:03 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; bh=qeQe+vID4PPjE+9u7bhVtYvuxg05JXyQOhW6H/KQCmU=; b=fzfA2M9VJrDBIMR1706n6vlRw+pnVKMQQ5RWPEzSnMfgM8tPs7yz1YxicY+3jB39in99ftBHB218Y+fzwOSGhFJP4KIvwH+oBkHltcmYsHQZUZoLGIr9ML7c2U7crzZwDZEB/Vz2u2pDw8bMFdx45KT2E4JNieWkvM6Z/aD0sKQ= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; b=XC82Zpn02NpQ/3eVK07zKc85dFUBByzUyDloN1ZPSq6FCX/d1sncLa14sJl5cWQ4X6G4OMOtX4ZUXyIZvaqy53V3fB8eikhYxCsItAAiVlq5C93CqDj/aVDzZOYM67BvMoF1TchCjZWxqmxV9I1Yo0E8wwhqVr6vCVxPM10GTTw= Received: by 10.142.156.2 with SMTP id d2mr629336wfe.219.1206560396121; Wed, 26 Mar 2008 12:39:56 -0700 (PDT) Received: by 10.66.219.5 with HTTP; Wed, 26 Mar 2008 12:39:55 -0700 (PDT) Message-ID: <2d483c770803261239w3150011dna0832fa8bfcdd642@mail.gmail.com> Date: Wed, 26 Mar 2008 16:39:55 -0300 From: "Ralph Teixeira" To: obm-l@mat.puc-rio.br Subject: =?ISO-8859-1?Q?Re:_[obm-l]_LADOS_DO_TRI=C2NGULO?= In-Reply-To: MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline References: Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m2QJlMWA028340 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Ralph Teixeira" X-Spam-Status: No, hits=1.1 required=5.0 tests=AWL,IN_REP_TO,QUOTED_EMAIL_TEXT,REFERENCES, SPAM_PHRASE_00_01,X_MAILING_LIST version=2.44 X-Spam-Level: * Os lados sao c, b=c+1 e a=c+2 (pois A=2C eh o maior angulo, e C eh o menor; o outro eh B=180-3C). Entao, pela lei dos senos: (c+2)/sin2C=c/sinC Daqui, tiramos cosC=(c+2)/2c. Agora eu vou logo na Lei dos Cossenos: c^2=a^2+b^2-2abcosC c^2=(c+2)^2+(c+1)^2-2(c+1)(c+2)(c+2)/2c (c+1)(c+2)^2=c(c^2+6c+5) (Que bom que o termo em c^3 vai cortar, entao teremos uma quadratica em c. Vai sair!) 5c^2+8c+4=6c^2+5c c^2-3c+4=0 c=4 ou c=-1 Entao c=4, b=5 e a=6 eh a unica solucao possivel... (Para multipla escolha, tah bom aqui, mas para o problema ficar correto mesmo, agora a gente teria que checar se, no triangulo de lados 4, 5 e 6, o angulo A eh o dobro de C mesmo; mas dah para calcular cosC=3/4 e cosA=1/8, isto eh, dah para ver que cosA=cos2C, donde sai que A=2C). Abraco, Ralph 2008/3/26 arkon : > > > > Pessoal alguém pode me enviar, por favor, a resolução dessa questão > > > > (EN-84) As medidas dos lados de um triângulo ABC são 3 números inteiros e > consecutivos e o ângulo maior A é o dobro do menor C. Os lados deste > triângulo são: > > > > a) 2, 3 e 4. b) 3, 4 e 5. c) 8, 9 e 10. d) 4, 5 e 6. e) 5, 6 e > 7. > > > > DESDE JÁ MUITO OBRIGADO ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Mar 26 17:02:58 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2QK1hWA029228 for ; Wed, 26 Mar 2008 17:01:43 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2QK1hop029226 for obm-l-MllGbsmmN; Wed, 26 Mar 2008 17:01:43 -0300 Received: from colorado.uspnet.usp.br (colorado.uspnet.usp.br [143.107.254.72]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2QK1gWA029214 for ; Wed, 26 Mar 2008 17:01:42 -0300 Received: (qmail 28933 invoked from network); 26 Mar 2008 20:01:24 -0000 X-Mail-Scanner: Scanned by qSheff-II-2.1-r1 (http://www.enderunix.org/qsheff/) Received: from negev.uspnet.usp.br (HELO localhost) ([143.107.254.65]) (envelope-sender ) by colorado.uspnet.usp.br (qmail-ldap-1.03) with SMTP for ; 26 Mar 2008 20:01:24 -0000 Received: from kama.ime.usp.br (kama.ime.usp.br [143.107.45.43]) by webmail.usp.br (Horde MIME library) with HTTP; Wed, 26 Mar 2008 17:01:24 -0300 Message-ID: <20080326170124.u0k3knrps84s08wg@webmail.usp.br> Date: Wed, 26 Mar 2008 17:01:24 -0300 From: Arlane Manoel S Silva To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] LADOS DO =?iso-8859-1?b?VFJJwk5HVUxP?= References: In-Reply-To: MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1; DelSp="Yes"; format="flowed" Content-Disposition: inline User-Agent: Internet Messaging Program (IMP) H3 (4.1.5-cvs) Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m2QK1gWA029224 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Arlane Manoel S Silva X-Spam-Status: No, hits=2.9 required=5.0 tests=AWL,IN_REP_TO,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SIGNATURE_LONG_SPARSE, SPAM_PHRASE_00_01,USER_AGENT,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: ** Considere o triângulo ABC cujos lados são dados por: AB=n-1 AC=n BC=n+1 Se x é a medida do menor ângulo, então ângulo(BCA)=x e ângulo(BAC)=2x Pela Lei dos senos sen(x)/(n-1) = sen(2x)/(n+1) = [2sen(x)cos(x)]/(n+1) Supondo que o triângulo não é degenerado, i.e., a medida de cada ângulo é maior que 0 e menor que pi, podemos cancelar sen(x) na igualdade acima, o que nos dá 1/(n-1) = [2cos(x)]/(n+1), ou melhor, cos(x)=2[(n+1)/(n-1)] (*) Aplicando, agora, a Lei dos cossenos (n-1)^2 = n^2 + (n+1)^2 - 2n(n+1)cos(x). Substituindo o resultado obtido em (*) e resolvendo a equação em n obtemos n=5, e portanto os lados valem 4, 5 e 6, se não houver erros de contas! inté, Citando arkon : > Pessoal alguém pode me enviar, por favor, a resolução dessa questão > > (EN-84) As medidas dos lados de um triângulo ABC são 3 números > inteiros e consecutivos e o ângulo maior A é o dobro do menor C. Os > lados deste triângulo são: > > a) 2, 3 e 4. b) 3, 4 e 5. c) 8, 9 e 10. d) 4, 5 e 6. e) 5, 6 e 7. > > DESDE JÁ MUITO OBRIGADO > -- Arlane Manoel S Silva MAT-IME-USP ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Mar 26 17:09:43 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2QK8bWA029699 for ; Wed, 26 Mar 2008 17:08:37 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2QK8aag029695 for obm-l-MllGbsmmN; Wed, 26 Mar 2008 17:08:36 -0300 Received: from gv-out-0910.google.com (gv-out-0910.google.com [216.239.58.189]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2QK8XWA029684 for ; Wed, 26 Mar 2008 17:08:34 -0300 Received: by gv-out-0910.google.com with SMTP id u5so850969gve.25 for ; Wed, 26 Mar 2008 13:08:15 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=ccliZm9LYab96AERqY8TR3x2NogEixgNYg4eU+TkTaQ=; b=SwUn51PGBr7AjDdBH7Oh9kigKojY4F/IwAuL+LrZfJ5nZMAdqpyESSa5IfDuDcF8eOC+H0DluDebr5/DsAkumcpGgIWbDfIWFs2Li3aiHwh/8SMhm3kAcQUjGigOaRKI5bQCEGtF5y4fGJ6BWywpMGFbWg7qETm0TCAm8KS+xvs= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=Al8UeZtK0sLWeZPKk3x1QVFZsyXMonYI+TaNi1eSPa43wkyYzzuIycP2VhayG3jxTv/u2ChmjS54/xH3ySyWzNkAwmpyUZS0u7rLFzeA9mAbkgb625reQKbikGfySMXxG5Ye2MexybnE39hm9mnRp0BuBcTmCIao5DCu2cYjqVc= Received: by 10.151.101.20 with SMTP id d20mr273130ybm.193.1206562093877; Wed, 26 Mar 2008 13:08:13 -0700 (PDT) Received: by 10.150.156.12 with HTTP; Wed, 26 Mar 2008 13:08:13 -0700 (PDT) Message-ID: <71c5e1520803261308t28150f09xccc2c6be7d1f4e26@mail.gmail.com> Date: Wed, 26 Mar 2008 17:08:13 -0300 From: "Nicolau C. Saldanha" To: obm-l@mat.puc-rio.br Subject: [SPAM] =?ISO-8859-1?Q?Re:_[obm-l]_RES:_[obm-l]_Indica=E7=E3o_de_livro?= =?ISO-8859-1?Q?s_(C=E1lculo_num=E9rico_e_Equa=E7=F5es_diferenciais)?= In-Reply-To: <5bb472220803260430r477d89f3ye1066bd076953c7d@mail.gmail.com> MIME-Version: 1.0 Content-Type: text/plain References: <212079.44593.qm@web55214.mail.re4.yahoo.com> <5bb472220803260430r477d89f3ye1066bd076953c7d@mail.gmail.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Nicolau C. Saldanha" X-Spam-Status: Yes, hits=5.1 required=5.0 tests=HTML_FONT_COLOR_BLUE,HTML_FONT_COLOR_GRAY, HTML_FONT_COLOR_UNSAFE,IN_REP_TO,MAILTO_LINK, QUOTED_EMAIL_TEXT,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, REFERENCES,SPAM_PHRASE_00_01,SPAM_REDIRECTOR, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ***** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_Part_2873_20974636.1206562093856" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. 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Por favor trat= em disso em particular. Nicolau (administrador da lista, ainda que atualmente sem muito tempo para acompanhar o que nela acontece) 2008/3/26 Joao Victor Brasil : > Paulo, > > Quanto voc=EA quer neste livros? Os do Piskonov, Apostol e Pacitti. > > Joao Victor > > > On 3/26/08, Paulo - Uniredes wrote: > > > > Oi Cesar, > > > > Para c=E1lculo I e II, eu recomendo o Piskunov: > > http://www.traca.com.br/seboslivrosusados.cgi?mod=3DLV62211&origem=3Dre= sultadodetalhada > > Eu tenho os volumes I e II em espanhol no meu sebo. S=E3o muito legais.= O > > volume II =E9 =F3timo em equa=E7=F5es diferenciais. A obra, em 2 volume= s, foi usada > > na UFRJ. > > > > Tem tamb=E9m o do Tom M. Apostol em portugu=EAs...: > > > > http://www.livrariadafisica.com.br/produto_detalhe.asp?id_produto=3D192= 09 > > > > Estudei pelo Apostol e a qualidade =E9 muito boa. Apesar de eu ser meio > > "burro" (S=F3 passei em c=E1lculo I ap=F3s fazer um curso de ver=E3o na= UFRJ. Muito > > legal...mas meu neg=F3cio =E9 redes de computadores). > > > > Fa=E7o pre=E7o camarada nos 3 livros. Camarada mesmo ! > > > > > > []s > > > > > > --- > > Paulo C. Santos (PC) > > e-mail: paulo@uniredes.org > > Homepage: http://uniredes.org > > Tel.: (21) 2510.8783 - Cel.: (21) 8753-0729 > > -------------------------------------------- > > MS-Messenger: Uniredes_Br@hotmail.Com > > > > ------------------------------ > > *De:* owner-obm-l@mat.puc-rio.br [mailto:owner-obm-l@mat.puc-rio.br] *E= m > > nome de *C=E9sar Santos > > *Enviada em:* ter=E7a-feira, 25 de mar=E7o de 2008 16:10 > > *Para:* obm-l@mat.puc-rio.br > > *Assunto:* [obm-l] Indica=E7=E3o de livros (C=E1lculo num=E9rico e Equa= =E7=F5es > > diferenciais) > > > > > > Poderiam me indicar bons livros de c=E1lculo num=E9rico e de equa=E7=F5= es > > diferencias acess=EDveis para iniciante? > > > > ------------------------------ > > Abra sua conta no Yahoo! Mail, > > o =FAnico sem limite de espa=E7o para armazenamento! > > > > > ------=_Part_2873_20974636.1206562093856 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Refor=E7ando o que outros disseram: recomendar ou criticar livros est=E1 de= ntro do prop=F3sito desta lista,
anunciar n=E3o est=E1 e negociar compra= e venda menos ainda. Por favor tratem disso em particular.

Nicolau = (administrador da lista, ainda que atualmente sem muito tempo para acompanh= ar o que nela acontece)

2008/3/26 Joao Victor Brasil <jvbrasil@gmail.com>:
Paulo,
 
Quanto voc=EA quer neste livros? Os do Piskonov, Apostol e Pacitti.
 
Joao Victor

 
On 3/26/08, = Paulo - Uniredes <paulo@uniredes.org> wrote:
Oi Cesar,
 
Eu tenho os volumes I e II em espanhol no meu sebo. S=E3o muit= o legais. O volume II =E9 =F3timo em equa=E7=F5es diferenciais. A obra, em = 2 volumes, foi usada na UFRJ.
 
Tem tamb=E9m o do Tom M. Apostol em portugu=EAs...:
 
 
Estudei pelo Apostol e a qualidade =E9 muito boa. Apesar = de eu ser meio "burro" (S=F3 passei em c=E1lculo I ap=F3s fazer u= m curso de ver=E3o na UFRJ. Muito legal...mas meu neg=F3cio =E9 redes de co= mputadores).
 
Fa=E7o pre=E7o camarada nos 3 livros. Camarada mesmo !<= /span>
 
 
[]s
 

---
Paulo C. Santos (PC)
e-mail: paulo@uniredes.org
Homepage:= http://uniredes.org=
Tel.: (21) 2510.8783 - Cel.: (21) 8753-0729
----------------------------= ----------------
MS-Messenger: Uniredes_Br@hotmail.Com


De: owner-obm-l@mat.puc-rio.br [mailto:owner-obm-l@ma= t.puc-rio.br] Em nome de C=E9sar Santos
Enviada em: ter=E7a-feira, 25 de mar=E7o de 2008 16:10
Para: obm-l@mat.puc-= rio.br
Assunto: [obm-l] Indica=E7=E3o de livros (C=E1lculo nu= m=E9rico e Equa=E7=F5es diferenciais)

 
Poderiam me indicar bons livros de c=E1lculo num=E9= rico e de equa=E7=F5es diferencias acess=EDveis para iniciante?=20

Abra sua conta no Yahoo! Mail, o =FAnico sem li= mite de espa=E7o para armazenamento!=20



------=_Part_2873_20974636.1206562093856-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Mar 26 18:55:26 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2QLrpWA005380 for ; Wed, 26 Mar 2008 18:53:52 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2QLrp8S005378 for obm-l-MllGbsmmN; Wed, 26 Mar 2008 18:53:51 -0300 Received: from smtp.uol.com.br (smtps.uol.com.br [200.221.4.131]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2QLrfWA005363 for ; Wed, 26 Mar 2008 18:53:42 -0300 Received: from localhost (localhost [127.0.0.1]) by socom4.uol.com.br (Postfix) with ESMTP id 6DEA0E000B12 for ; Wed, 26 Mar 2008 18:53:24 -0300 (BRT) Received: from microcf7b75528 (201009220011.user.veloxzone.com.br [201.9.220.11]) by socom4.uol.com.br (Postfix) with SMTP id 7A4D3E0042FE for ; Wed, 26 Mar 2008 18:53:23 -0300 (BRT) Message-ID: <000c01c88f8b$d14475d0$01fea8c0@microcf7b75528> From: "Ulysses Coelho de Souza Jr." To: Subject: [SPAM] [obm-l] Re: off topic: resumos analise real Date: Wed, 26 Mar 2008 18:53:24 -0300 MIME-Version: 1.0 Content-Type: text/plain X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2900.3138 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.3198 X-SIG5: 3f489544c45c211ef05b40ae9efef230 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Ulysses Coelho de Souza Jr." X-Spam-Status: Yes, hits=6.3 required=5.0 tests=AWL,HTML_FONT_COLOR_BLUE,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01,SUPERLONG_LINE, USER_AGENT_OE,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ****** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_NextPart_000_0009_01C88F72.AB6AB540" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (6.30 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: USER_AGENT_OE (0.2 points) X-Mailer header indicates a non-spam MUA (Outlook Express) SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: HTML_FONT_COLOR_BLUE (0.2 points) BODY: HTML font color is blue SPAM: SUPERLONG_LINE (0.0 points) BODY: Contains a line >=199 characters long SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 11.220.9.201.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 11.220.9.201.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (0.1 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- This is a multi-part message in MIME format. ------=_NextPart_000_0009_01C88F72.AB6AB540 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Ol=E1 a todos, Na minha opini=E3o, todos os livros de Matem=E1tica deveriam = ter todas as respostas sem exce=E7=E3o. Al=E9m disso, no caso de livros = para o N=EDvel Superior de disciplinas importantes como An=E1lise na = Reta, ou as solu=E7=F5es deveriam ser publicadas no mesmo livro ou num = manual vendido =E0 parte. Como disse o Doutor Elon em uma palestra: = "Propor um problema =E9 muito f=E1cil, o dif=EDcil =E9 apresentar uma = solu=E7=E3o". Abra=E7os. =20 Ola Hermann e demais colegas desta lisa ... OBM-L, A melhor maneira de aprender Analise e estudar a teoria com atencao, vale dizer, repetindo com suas proprias palavras e recursos as demonstracoes, verificando os limites de aplicacoes dos teoremas e, sobretudo e mais que tudo, FAZER BASTANTE EXERCICIOS INTELIGENTES. O Livro do Prof Elon ( Vol 1, Colecao Projeto Euclides ) e excelente. Eu pensei em divulgar as solucoes, mas, vou repetir aqui o que o proprio Elon me falou : "... nao sei se e uma boa ideia publicar as solucoes, embora eu nao tenha o poder, nem a intencao de proibi-lo de fazer isto.Na verdade, ha uns 25 anos uma aluna do IMPA redigiu todas as solucoes (algumas com minha ajuda) mas = nem me lembro onde joguei o manuscrito ... " Veja portanto que o proprio autor tem duvidas sobre o valor de se publicar as solucoes. Se voce aceita um conselho, vai publicando aqui os problemas que voce achar mais dificeis e os fatos que voce nao esta conseguindo entender. Isso vai elevar o atual nivel desta nossa LISTA DE DISCUSSAO DE PROBLEMAS OLIMPICOS e, alem disso, ha pessoas aqui que gostam muito de Analise. O Artur Steiner, por exemplo. Acredito que voce publicando ele vai ajudar. Um Abracao Paulo Santa Rita ------=_NextPart_000_0009_01C88F72.AB6AB540 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable
Ol=E1 a todos,
 
    =    =20     Na minha opini=E3o, todos os livros de Matem=E1tica = deveriam ter=20 todas as respostas sem exce=E7=E3o. Al=E9m disso, no caso de = livros para o N=EDvel=20 Superior de disciplinas importantes como An=E1lise na Reta, ou as = solu=E7=F5es=20 deveriam ser publicadas no mesmo livro ou num manual vendido =E0 = parte. Como=20 disse o Doutor Elon em uma palestra: "Propor um problema =E9 = muito=20 f=E1cil, o dif=EDcil =E9 apresentar uma solu=E7=E3o".
 
Abra=E7os.  
 
 
Ola Hermann e demais colegas
desta lisa ... OBM-L,

A = melhor=20 maneira de aprender Analise e estudar a teoria com atencao,
vale = dizer,=20 repetindo com suas proprias palavras e recursos as
demonstracoes, = verificando=20 os limites de aplicacoes dos teoremas e,
sobretudo e mais que tudo, = FAZER=20 BASTANTE EXERCICIOS INTELIGENTES.

O Livro do Prof Elon ( Vol 1, = Colecao=20 Projeto Euclides ) e excelente.
Eu pensei em divulgar  as = solucoes, mas,=20 vou repetir aqui o que o
proprio Elon me falou :

"... nao sei = se e uma=20 boa ideia publicar as solucoes, embora eu nao
tenha o poder,
nem a = intencao de proibi-lo de fazer isto.Na verdade, ha uns 25 anos = uma
aluna do=20 IMPA redigiu todas as solucoes (algumas com minha ajuda)  mas=20 nem
me  lembro onde joguei o manuscrito ... "

Veja = portanto que o=20 proprio autor tem duvidas sobre o valor de se
publicar as = solucoes.

Se=20 voce aceita um conselho, vai publicando aqui os problemas que = voce
achar mais=20 dificeis e os fatos que voce nao esta conseguindo entender.
Isso vai = elevar o=20 atual nivel desta nossa LISTA DE DISCUSSAO DE
PROBLEMAS OLIMPICOS e, = alem=20 disso, ha pessoas aqui que gostam muito de
Analise. O Artur Steiner, = por=20 exemplo. Acredito que voce publicando
ele vai ajudar.

Um=20 Abracao
Paulo Santa Rita
------=_NextPart_000_0009_01C88F72.AB6AB540-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Mar 26 19:11:18 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2QMACWA006091 for ; Wed, 26 Mar 2008 19:10:12 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2QMACJ2006089 for obm-l-MllGbsmmN; Wed, 26 Mar 2008 19:10:12 -0300 Received: from wa-out-1112.google.com (wa-out-1112.google.com [209.85.146.180]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2QMAAWA006085 for ; Wed, 26 Mar 2008 19:10:11 -0300 Received: by wa-out-1112.google.com with SMTP id m28so4469481wag.13 for ; Wed, 26 Mar 2008 15:09:53 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:mime-version:content-type:content-transfer-encoding:content-disposition; bh=c0E/JCja0hA9tG5qZMgPmk3KWYck99j85fONHo0Dm9I=; b=Cx6513hRFJhIugfWtdcn5iOMvhYmg9HjPiqgetuePnX6Teqrlzw1RBQkzDjVzRD9I5X4pJcT136ofeYIuQoe92FGduU/g1dW9rZSj0tPsgsMSgXoVaFlkdV4GnLkeaGJk/UdNOjUrM2CAntrlz6sgLKYu5nmSfd7377stJq8Ya0= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:mime-version:content-type:content-transfer-encoding:content-disposition; b=Be23W9cO6f24KsEz6W1moFvvOc0lpUUNi7WvSV+CTuSmghhRECmzc5panNHbSRjpX+71Xn/ddE5tyn5YXnrMh1WT/1jI9LrhYQE5FzJ7skniki+wlMZghI7nfHKBiayIGSB9hCQJnimhz5Wcd1169qDUjMzsPxFznm33od9bJwo= Received: by 10.115.111.1 with SMTP id o1mr252178wam.87.1206569393242; Wed, 26 Mar 2008 15:09:53 -0700 (PDT) Received: by 10.114.193.10 with HTTP; Wed, 26 Mar 2008 15:09:53 -0700 (PDT) Message-ID: Date: Wed, 26 Mar 2008 19:09:53 -0300 From: "Eike Santos" To: ccppbrasil@googlegroups.com, obm-l@mat.puc-rio.br Subject: [SPAM] [obm-l] Computaca Grafica!!! MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline Content-Transfer-Encoding: 7bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m2QMACWA006087 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Eike Santos" X-Spam-Status: Yes, hits=5.6 required=5.0 tests=AWL,PLING_PLING,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, SIGNATURE_LONG_SPARSE,SPAM_PHRASE_00_01,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ***** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (5.60 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: SIGNATURE_LONG_SPARSE (-0.3 points) Long signature present (empty lines) SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 180.146.85.209.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 180.146.85.209.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: PLING_PLING (1.5 points) Subject has lots of exclamation marks SPAM: AWL (-1.4 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- Alguem esta trabalhando ou gosta de computacao gráfica em geral aqui na lista? Vamos trocas info? Dúvidas e coisas afim? Ats, -- Marcos Eike Tinen dos Santos +559881176565 OpenSuse- Comunidade Open do Suse www.opensuse.org OpenSolaris- Comunidade Open do Solaris www.opensolaris.org ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Mar 26 19:29:39 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2QMSKWA007102 for ; Wed, 26 Mar 2008 19:28:20 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2QMSEAR007091 for obm-l-MllGbsmmN; Wed, 26 Mar 2008 19:28:14 -0300 Received: from el-out-1112.google.com (el-out-1112.google.com [209.85.162.177]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2QMRPWA007011 for ; Wed, 26 Mar 2008 19:27:29 -0300 Received: by el-out-1112.google.com with SMTP id z25so2157950ele.15 for ; Wed, 26 Mar 2008 15:26:53 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; bh=9N87Fiold5lH/XKox8IwFHDscu3aM5/TY6Im9KWGL4s=; b=EeHKBdcMf5QI44jddpAlnOb8PYdsXmzBpHKXvwBa9dtfmMc3tYSknspkwKivN4qpeWM/Fwge1OkwfrPIsJM7bWFjRbfSfOUmILu0lB12AN6vzkObbPVqDUrDFVZnsBzQpg6OrKgv0RytrcnCE7cVQavppsJtbSeBT9uyX9q0tLY= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; b=KOy+SfkRNEkDeonw+SWQK9AiWn8Lmij4DPkWObnCMPuSn88R1uKayB9iMXeVjQuJf550usXHP/rWCnnqZrNplOfs4ewwyiBTy7zlcVEVyP3CmwyatNMq/wIct+QsyYEhEpO1MjnTgbV5r2f8vTqAtdAxwr+GTt1c812xDh6oWdY= Received: by 10.151.108.10 with SMTP id k10mr370775ybm.123.1206570413143; Wed, 26 Mar 2008 15:26:53 -0700 (PDT) Received: by 10.150.144.4 with HTTP; Wed, 26 Mar 2008 15:26:53 -0700 (PDT) Message-ID: Date: Wed, 26 Mar 2008 19:26:53 -0300 From: "Paulo Santa Rita" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Re: off topic: resumos analise real In-Reply-To: <000c01c88f8b$d14475d0$01fea8c0@microcf7b75528> MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline References: <000c01c88f8b$d14475d0$01fea8c0@microcf7b75528> Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m2QMS1WA007058 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Paulo Santa Rita" X-Spam-Status: No, hits=3.5 required=5.0 tests=AWL,IN_REP_TO,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: *** Ola Ulisses, Tio Cabri e demais colegas desta lista ... OBM-L, Voces acham que seria valioso apenas ver as solucoes do Livro de Analise do Prof Elon ( Vol 1, Projeto Euclides, IMPA ) sem tentar raciocinar por si mesmo e encontrar a solucao ? Eu nao estaria fazendo um mal de fosse divulgando as solucoes ? Um Abraco a Todos Paulo Santa Rita 4,1319,1A0308 Em 26/03/08, Ulysses Coelho de Souza Jr. escreveu: > > > Olá a todos, > > Na minha opinião, todos os livros de Matemática deveriam ter > todas as respostas sem exceção. Além disso, no caso de livros para o Nível > Superior de disciplinas importantes como Análise na Reta, ou as soluções > deveriam ser publicadas no mesmo livro ou num manual vendido à parte. Como > disse o Doutor Elon em uma palestra: "Propor um problema é muito fácil, o > difícil é apresentar uma solução". > > Abraços. > > > Ola Hermann e demais colegas > desta lisa ... OBM-L, > > A melhor maneira de aprender Analise e estudar a teoria com atencao, > vale dizer, repetindo com suas proprias palavras e recursos as > demonstracoes, verificando os limites de aplicacoes dos teoremas e, > sobretudo e mais que tudo, FAZER BASTANTE EXERCICIOS INTELIGENTES. > > O Livro do Prof Elon ( Vol 1, Colecao Projeto Euclides ) e excelente. > Eu pensei em divulgar as solucoes, mas, vou repetir aqui o que o > proprio Elon me falou : > > "... nao sei se e uma boa ideia publicar as solucoes, embora eu nao > tenha o poder, > nem a intencao de proibi-lo de fazer isto.Na verdade, ha uns 25 anos uma > aluna do IMPA redigiu todas as solucoes (algumas com minha ajuda) mas nem > me lembro onde joguei o manuscrito ... " > > Veja portanto que o proprio autor tem duvidas sobre o valor de se > publicar as solucoes. > > Se voce aceita um conselho, vai publicando aqui os problemas que voce > achar mais dificeis e os fatos que voce nao esta conseguindo entender. > Isso vai elevar o atual nivel desta nossa LISTA DE DISCUSSAO DE > PROBLEMAS OLIMPICOS e, alem disso, ha pessoas aqui que gostam muito de > Analise. O Artur Steiner, por exemplo. Acredito que voce publicando > ele vai ajudar. > > Um Abracao > Paulo Santa Rita ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Mar 26 20:48:57 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2QNliWA026494 for ; Wed, 26 Mar 2008 20:47:44 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2QNliOQ026492 for obm-l-MllGbsmmN; Wed, 26 Mar 2008 20:47:44 -0300 Received: from qb-out-0506.google.com (qb-out-0506.google.com [72.14.204.225]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2QNlfWA026487 for ; Wed, 26 Mar 2008 20:47:42 -0300 Received: by qb-out-0506.google.com with SMTP id a10so7205195qbd.7 for ; Wed, 26 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<99886d920803261647j3b6a1e0vb9c47d07e8d25d09@mail.gmail.com> Date: Thu, 27 Mar 2008 00:47:21 +0100 From: "=?UTF-8?Q?Bruno_Fran=C3=A7a_dos_Reis?=" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Re: off topic: resumos analise real In-Reply-To: MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_27996_18119276.1206575241287" References: <000c01c88f8b$d14475d0$01fea8c0@microcf7b75528> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "=?UTF-8?Q?Bruno_Fran=C3=A7a_dos_Reis?=" X-Spam-Status: No, hits=1.1 required=5.0 tests=AWL,IN_REP_TO,MAILTO_TO_SPAM_ADDR,QUOTED_EMAIL_TEXT, REFERENCES,SPAM_PHRASE_00_01,X_MAILING_LIST version=2.44 X-Spam-Level: * ------=_Part_27996_18119276.1206575241287 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: base64 Content-Disposition: inline T2kuCgpFdSBhY2hvIHF1ZSBuw6NvIGVzdGFyaWEgZmF6ZW5kbyBtYWwgZGl2dWxnYW5kby4gTWFs 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with ESMTP id m2R0G7WA028584 for ; Wed, 26 Mar 2008 21:16:08 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2R0G5GE028580 for obm-l-MllGbsmmN; Wed, 26 Mar 2008 21:16:05 -0300 Received: from wx-out-0506.google.com (wx-out-0506.google.com [66.249.82.233]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2R0FcWA028543 for ; Wed, 26 Mar 2008 21:15:41 -0300 Received: by wx-out-0506.google.com with SMTP id t4so4398243wxc.18 for ; Wed, 26 Mar 2008 17:15:21 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:reply-to:to:subject:in-reply-to:mime-version:content-type:references; bh=mL7FE6k3ZuoWE4dhPRxlOtUh8XEztSl67Cl64redc4M=; b=VAOcUifmAnf9/sUK5uMWtYjZBqZ5S6LVS3EsKJYK7S23FwSftvOi2ZxoSi2lRzoDxohr2m+DwZ1Rs3AxdQ1Ecd+jwm1LJPMiEu7/qCgDWQ+raqzp68NX2jzeEGluDaNIPC+v6jG64mUoe+UCS/8F5Z12/RNNkrjmWZkk4udwJBo= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:reply-to:to:subject:in-reply-to:mime-version:content-type:references; b=f1+G8H7yNv/ABfX1Ngb2uq7u7N+j3xvPlqHE23ACTVsedoVjgl9qrYyIDnq1pRQk90b9DOsAfeu7mt++XkT/yeVKnn5QfpNA7bdEOWtgXR4+HnBQiqS+xAq4TPMhnhcUIEN67ekka228JW1zdFrOTNO0+nQizrt8wtmpQAcsmto= Received: by 10.65.224.11 with SMTP id b11mr1636117qbr.42.1206576920446; Wed, 26 Mar 2008 17:15:20 -0700 (PDT) Received: by 10.65.122.4 with HTTP; Wed, 26 Mar 2008 17:15:20 -0700 (PDT) Message-ID: Date: Wed, 26 Mar 2008 21:15:20 -0300 From: "=?ISO-8859-1?Q?Vin=EDcius_Almeida?=" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Re: off topic: resumos analise real In-Reply-To: <99886d920803261647j3b6a1e0vb9c47d07e8d25d09@mail.gmail.com> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_10531_9002982.1206576920378" References: <000c01c88f8b$d14475d0$01fea8c0@microcf7b75528> <99886d920803261647j3b6a1e0vb9c47d07e8d25d09@mail.gmail.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "=?ISO-8859-1?Q?Vin=EDcius_Almeida?=" X-Spam-Status: No, hits=4.5 required=5.0 tests=IN_REP_TO,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,REFERENCES, SPAM_PHRASE_00_01,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** ------=_Part_10531_9002982.1206576920378 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Sou novo no grupo e sobre fazer exerc=EDcios inteligentes eu tenho um que = =E9 dif=EDcil por demais. Segundo me consta =E9 de uma olimp=EDada mundial. Seja um tri=E2ngulo ABC aonde =C2 =3D 100=BA e existe um ponto D, sobre o = lado AC tal que AC =3D BD. Sabe-se ainda que AD =3D AB. Qual o valor do =C2ngulo C? aquele abra=E7o ------=_Part_10531_9002982.1206576920378 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline
Sou novo no grupo e sobre fazer exerc=EDcios inteligentes eu tenho um = que =E9 dif=EDcil por demais. Segundo me consta =E9 de uma olimp=EDada mund= ial.
Seja um tri=E2ngulo ABC aonde =C2 =3D 100=BA e existe u= m ponto D, sobre o lado AC tal que AC =3D BD. Sabe-se ainda que AD =3D AB. = Qual o valor do =C2ngulo C?
aquele abra=E7o
------=_Part_10531_9002982.1206576920378-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Mar 26 21:34:21 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2R0XSWA029516 for ; Wed, 26 Mar 2008 21:33:28 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2R0XSqk029514 for obm-l-MllGbsmmN; Wed, 26 Mar 2008 21:33:28 -0300 Received: from po-out-1718.google.com (po-out-1718.google.com [72.14.252.153]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2R0XOWA029510 for ; Wed, 26 Mar 2008 21:33:26 -0300 Received: by po-out-1718.google.com with SMTP id a23so821059poh.4 for ; Wed, 26 Mar 2008 17:33:07 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:mime-version:content-type; bh=V8cb9UANWm5ckj7byPYB4OWcRIXO2AFejacoU/RC3R0=; b=kIf++pTVxvE4HBK0VGRj+oicWrXn4l3v9hFH3TzHxmJ9uyPaE3yCt3GF9/8UL9NlFLbwAgDT3wo2Rvy41pY81rK1HQqeBGeHq8ynyL2fy2YPRtymyHx1mXP+0hlR+87GkYWiZr12/26Xv4LFYIcyydlapvh7nmCVhZtZJ5tidCM= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:mime-version:content-type; b=jXEe0oV+fPepUt/6Tx++as7Z/bEC2iGxkspqJYhckAkHd0x8bCDKNI0dq37Ydeyfl1LsBczrccPNacaDdSXtYPjXGfU41qTQmG2wpEffi+3g0WqLEGxP+BaxmI+SM9LFGH9gTKaGRIft4bDRbMdjHdyWN7fULefcjqW+RrpLe5c= Received: by 10.140.201.1 with SMTP id y1mr603327rvf.200.1206577986797; Wed, 26 Mar 2008 17:33:06 -0700 (PDT) Received: by 10.140.143.11 with HTTP; Wed, 26 Mar 2008 17:33:06 -0700 (PDT) Message-ID: <99886d920803261733m20957fdcwead8e048e725b6fe@mail.gmail.com> Date: Thu, 27 Mar 2008 01:33:06 +0100 From: "=?UTF-8?Q?Bruno_Fran=C3=A7a_dos_Reis?=" To: OBM Subject: [obm-l] T. dos Numeros, olimpico! MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_28201_18247679.1206577986784" Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "=?UTF-8?Q?Bruno_Fran=C3=A7a_dos_Reis?=" X-Spam-Status: No, hits=1.9 required=5.0 tests=AWL,MAILTO_TO_SPAM_ADDR,SPAM_PHRASE_00_01,X_MAILING_LIST version=2.44 X-Spam-Level: * ------=_Part_28201_18247679.1206577986784 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: base64 Content-Disposition: inline UHJvYmxlbWE6CgpQcm92ZSBxdWUgbsOjbyBleGlzdGVtIG51bWVyb3MgZmF0b3JpYWlzIGNvbnNl Y3V0aXZvcyBjb20gcHJpbWVpcm9zIGRpZ2l0b3MKaWd1YWlzIGEgMSwgMiwgLi4uLCA5LgpFbSBv dXRyYXMgcGFsYXZyYXM6IHByb3ZlIHF1ZSBuw6NvIGV4aXN0ZSBLIHRhbCBxdWUgKEsraikhIGNv bWVjZSBwZWxvCmFsZ2FyaXNtbyBqLCBwYXJhIHRvZG8gaiA9IDEsIC4uLiwgOS4KCkFicmHDp28K QnJ1bm8KCi0tIApCcnVubyBGUkFOw4dBIERPUyBSRUlTCgptc246IGJydW5vcmVpczY2NkBob3Rt YWlsLmNvbQpza3lwZTogYnJ1bm9yZWlzNjY2CnRlbDogKzMzICgwKTYgMjggNDMgNDIgMTYKCmVe KHBpKmkpKzE9MAo= ------=_Part_28201_18247679.1206577986784 Content-Type: text/html; charset=UTF-8 Content-Transfer-Encoding: base64 Content-Disposition: inline UHJvYmxlbWE6PGJyPjxicj5Qcm92ZSBxdWUgbsOjbyBleGlzdGVtIG51bWVyb3MgZmF0b3JpYWlz IGNvbnNlY3V0aXZvcyBjb20gcHJpbWVpcm9zIGRpZ2l0b3MgaWd1YWlzIGEgMSwgMiwgLi4uLCA5 Ljxicj5FbSBvdXRyYXMgcGFsYXZyYXM6IHByb3ZlIHF1ZSBuw6NvIGV4aXN0ZSBLIHRhbCBxdWUg KEsraikhIGNvbWVjZSBwZWxvIGFsZ2FyaXNtbyBqLCBwYXJhIHRvZG8gaiA9IDEsIC4uLiwgOS48 YnI+Cjxicj5BYnJhw6dvPGJyPkJydW5vPGJyIGNsZWFyPSJhbGwiPjxicj4tLSA8YnI+QnJ1bm8g RlJBTsOHQSBET1MgUkVJUzxicj48YnI+bXNuOiA8YSBocmVmPSJtYWlsdG86YnJ1bm9yZWlzNjY2 QGhvdG1haWwuY29tIj5icnVub3JlaXM2NjZAaG90bWFpbC5jb208L2E+PGJyPnNreXBlOiBicnVu b3JlaXM2NjY8YnI+dGVsOiArMzMgKDApNiAyOCA0MyA0MiAxNjxicj48YnI+ZV4ocGkqaSkrMT0w Cg== ------=_Part_28201_18247679.1206577986784-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Mar 26 21:34:17 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2R0XHWA029498 for ; Wed, 26 Mar 2008 21:33:17 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2R0XHbU029496 for obm-l-MllGbsmmN; Wed, 26 Mar 2008 21:33:17 -0300 Received: from fk-out-0910.google.com (fk-out-0910.google.com [209.85.128.185]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2R0XFWA029491 for ; Wed, 26 Mar 2008 21:33:15 -0300 Received: by fk-out-0910.google.com with SMTP id 22so4895611fkq.13 for ; Wed, 26 Mar 2008 17:32:57 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=tGTr8ksysXtIP3tJJg885wgM27ih50MEIf2gTmluZFg=; b=g7Q1f4PgrCbG9RjQlcqh9cqmkZvGlsLihGi/IyKhqPRTpMDwM2ECYICUnuhIL9ykY8XmbR84cfaB5CjdvpWMB54BxD1gT/8GtObIlE/RzjdfYPJt20I5JmtVu0v4becRoaONTQf4/YqbBS7M8hfAFmAJa8Bs6kHNNzeM9DNAkzc= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=axKslgEk/yRldAKu1ZDk82ztcy9JBLPTvYtLCvqS4ofHVDY5qkBmMIIzcRGT8EzYlKxH6LXrscMuCd0BM8ThKq07SlFg1cGQsiR19fgnQlpVqStjL1JymNFnCEv5ISgWhBRdtJRFIQ3D0Wluql73T0OFlR4TQ+d+eVWob9Rw+M4= Received: by 10.82.170.3 with SMTP id s3mr339449bue.18.1206577977037; Wed, 26 Mar 2008 17:32:57 -0700 (PDT) Received: by 10.82.170.15 with HTTP; Wed, 26 Mar 2008 17:32:57 -0700 (PDT) Message-ID: Date: Wed, 26 Mar 2008 21:32:57 -0300 From: "Tiago Machado" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Computaca Grafica!!! In-Reply-To: MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_27822_29454065.1206577977040" References: Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Tiago Machado" X-Spam-Status: No, hits=4.4 required=5.0 tests=AWL,EMAIL_ATTRIBUTION,IN_REP_TO,MAILTO_LINK, MIME_EXCESSIVE_QP,PLING_PLING,QUOTED_EMAIL_TEXT, RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,REFERENCES, SPAM_PHRASE_00_01,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** ------=_Part_27822_29454065.1206577977040 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Oi Eike, Fa=E7o IC na area de computa=E7=E3o gr=E1fica. On Wed, Mar 26, 2008 at 7:09 PM, Eike Santos wrote: > Alguem esta trabalhando ou gosta de computacao gr=E1fica em geral aqui > na lista? Vamos trocas info? D=FAvidas e coisas afim? > > Ats, > -- > Marcos Eike Tinen dos Santos > +559881176565 > > OpenSuse- Comunidade Open do Suse > www.opensuse.org > OpenSolaris- Comunidade Open do Solaris > www.opensolaris.org > > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > Instru=E7=F5es para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > ------=_Part_27822_29454065.1206577977040 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Oi Eike,

Fa=E7o IC na area de computa=E7=E3o gr=E1fica.

On Wed, Mar 26, 2008 at 7:09 PM, Eike Santos <eiketinen@gmail.com> wrote:
Alguem esta trabalhando ou gosta de computacao gr=E1fica em geral aqui
na lista? Vamos trocas info? D=FAvidas e coisas afim?

Ats,
--
Marcos Eike Tinen dos Santos
+559881176565

OpenSuse- Comunidade Open do Suse
www.opensuse.org<= br> OpenSolaris- Comunidade Open do Solaris
www.opensolaris.or= g

=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D
Instru=E7=F5es para entrar na lista, sair da lista e usar a lista em
http://www.mat.puc-rio.br/~obmlistas/obm-l.html
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D

------=_Part_27822_29454065.1206577977040-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Mar 26 22:09:17 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2R17xWA031750 for ; Wed, 26 Mar 2008 22:07:59 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2R17wOZ031748 for obm-l-MllGbsmmN; Wed, 26 Mar 2008 22:07:58 -0300 Received: from wa-out-1112.google.com (wa-out-1112.google.com [209.85.146.179]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2R17sWA031740 for ; Wed, 26 Mar 2008 22:07:55 -0300 Received: by wa-out-1112.google.com with SMTP id m28so4537113wag.13 for ; Wed, 26 Mar 2008 18:07:36 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; bh=aNqeoA151kP8J+srYiebVGcYamG46LE+eMektb0+u4s=; b=bcOwDlRc7yzOkStN2+XpJ1cK4i20zXQAU7hk/YvRCNysLRPA9b3D5EH5hSOEL4HDtsXIhpe0kamLegCZ0+yBm0akxiIAWHYZzTjzTlqvKTzFDZNXUmCPNQaz9C/cXgli3Wchx6Csx4qPUXVpm/Zt5fPt24WnDwuLWu9ICTbQ7o0= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; b=Wa8wd7RLWzMU04pkg2J4d5DGJVXw471fhgtu0Ac3+kZ7dkIkc1QrEvuXRdu08gEXTpkqFPVE7529pnADFhGfV+EY/bLioBWGPlCWO+EUf61PpQS8kR6tuifM6zUVxtL/p1hG0CJg0GVjTpVpqtP5/RumpsIKM9s0gg/VGsA6vnM= Received: by 10.114.191.1 with SMTP id o1mr409243waf.117.1206580056377; Wed, 26 Mar 2008 18:07:36 -0700 (PDT) Received: by 10.114.193.10 with HTTP; Wed, 26 Mar 2008 18:07:36 -0700 (PDT) Message-ID: Date: Wed, 26 Mar 2008 22:07:36 -0300 From: "Eike Santos" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Computaca Grafica!!! In-Reply-To: MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline References: Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m2R17vWA031744 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Eike Santos" X-Spam-Status: No, hits=4.8 required=5.0 tests=AWL,IN_REP_TO,PLING_PLING,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SIGNATURE_LONG_SPARSE, SPAM_PHRASE_00_01,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** Blz. Rapaz... Tem msn? Trabalha em que área? Atualmente estou estudando Rendering! Ats, Marcos Eike 2008/3/26 Tiago Machado : > Oi Eike, > > Faço IC na area de computação gráfica. > > > > On Wed, Mar 26, 2008 at 7:09 PM, Eike Santos wrote: > > > > > > > > Alguem esta trabalhando ou gosta de computacao gráfica em geral aqui > > na lista? Vamos trocas info? Dúvidas e coisas afim? > > > > Ats, > > -- > > Marcos Eike Tinen dos Santos > > +559881176565 > > > > OpenSuse- Comunidade Open do Suse > > www.opensuse.org > > OpenSolaris- Comunidade Open do Solaris > > www.opensolaris.org > > > > ========================================================================= > > Instruções para entrar na lista, sair da lista e usar a lista em > > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > > ========================================================================= > > > > -- Marcos Eike Tinen dos Santos +559881176565 OpenSuse- Comunidade Open do Suse www.opensuse.org OpenSolaris- Comunidade Open do Solaris www.opensolaris.org ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Mar 26 23:26:26 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2R2PCWA002535 for ; Wed, 26 Mar 2008 23:25:12 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2R2PBxq002533 for obm-l-MllGbsmmN; Wed, 26 Mar 2008 23:25:11 -0300 Received: from sc2.he.tucows.com (mail06.sc2.he.tucows.com [64.97.154.80]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2R2P9WA002530 for ; Wed, 26 Mar 2008 23:25:10 -0300 Received: from sc2-out07.emaildefenseservice.com (64.97.201.177) by sc2.he.tucows.com (7.3.127) id 47E4D5840041FADB for obm-l@mat.puc-rio.br; Thu, 27 Mar 2008 02:24:52 +0000 X-SpamScore: 10 X-Spamcatcher-Summary: 10,1,0,4b9ae5297d6c0e5b,089906b11c168474,marcusaurelio80@globo.com,-,RULES_HIT:10:46:355:379:541:542:960:962:967:973:980:988:989:1021:1029:1155:1160:1189:1221:1260:1308:1309:1313:1314:1345:1436:1437:1515:1516:1517:1521:1533:1534:1541:1575:1588:1589:1592:1594:1691:1711:1714:1730:1748:1777:1792:2525:2528:2559:2564:2682:2685:2857:2859:2902:2917:2933:2937:2939:2942:2945:2947:2951:2954:3022:3466:3869:3876:3877:3934:3936:3938:3941:3944:4321:4379:5007:6114:6117: 6261:7679:7688,0,RBL:none,CacheIP:none,Bayesian:0.5,0.5,0.5,Netcheck:none,DomainCache:0,MSF:not bulk,SPF:,MSBL:none,DNSBL:none X-Spamcatcher-Explanation: (100%) SUBJ: subject is iso-8859-b encoded; Received: from jambock9acfddd (20151252208.user.veloxzone.com.br [201.51.252.208]) (Authenticated sender: marcusaurelio80@globo.com) by sc2-out07.emaildefenseservice.com (Postfix) with ESMTP for ; Thu, 27 Mar 2008 02:24:51 +0000 (UTC) From: "Marcus Aurelio" To: Subject: [SPAM] [obm-l] =?iso-8859-1?B?ZnVu5+Nv?= Date: Wed, 26 Mar 2008 23:24:44 -0300 Message-ID: <004901c88fb1$b9f98520$2dec8f60$@com> MIME-Version: 1.0 Content-Type: text/plain X-Mailer: Microsoft Office Outlook 12.0 thread-index: AciPsbgQI3aEJ7B+QA6RvWaBLMp4FQ== Content-Language: pt-br Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Marcus Aurelio" X-Spam-Status: Yes, hits=8.6 required=5.0 tests=AWL,FROM_ENDS_IN_NUMS,HTML_50_70,RCVD_IN_DSBL,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_NextPart_000_004A_01C88F98.94AC4D20" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (8.60 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: FROM_ENDS_IN_NUMS (0.9 points) From: ends in numbers SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: HTML_50_70 (0.3 points) BODY: Message is 50-70% HTML tags SPAM: RCVD_IN_DSBL (3.2 points) RBL: Received via a relay in list.dsbl.org SPAM: [RBL check: found 208.252.51.201.list.dsbl.org] SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 177.201.97.64.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 177.201.97.64.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-1.6 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- Esta é uma mensagem em várias partes no formato MIME. ------=_NextPart_000_004A_01C88F98.94AC4D20 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Algu=E9m pode me ajudar nessa f(x) + f(x-1) =3D x^2 se f(19) =3D 94 calcule f(94)? =20 ------=_NextPart_000_004A_01C88F98.94AC4D20 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable

Algu=E9m pode me ajudar nessa

f(x) + f(x-1) =3D x^2 se f(19) =3D 94 calcule = f(94)?

 

------=_NextPart_000_004A_01C88F98.94AC4D20-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Wed Mar 26 23:40:05 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2R2cxWA003066 for ; Wed, 26 Mar 2008 23:39:00 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2R2cxam003057 for obm-l-MllGbsmmN; Wed, 26 Mar 2008 23:38:59 -0300 Received: from smtp.uol.com.br (smtps.uol.com.br [200.221.4.131]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2R2cqWA002979 for ; Wed, 26 Mar 2008 23:38:53 -0300 Received: from localhost (localhost [127.0.0.1]) by socom1.uol.com.br (Postfix) with ESMTP id D13A0FB6 for ; Wed, 26 Mar 2008 23:38:35 -0300 (BRT) Received: from [127.0.0.1] (unknown [189.81.124.20]) by socom1.uol.com.br (Postfix) with ESMTP id 2B233A7A for ; Wed, 26 Mar 2008 23:38:33 -0300 (BRT) Message-ID: <47EB08A8.8070007@uol.com.br> Date: Wed, 26 Mar 2008 23:38:32 -0300 From: Saulo User-Agent: Thunderbird 2.0.0.12 (Windows/20080213) MIME-Version: 1.0 To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Computaca Grafica!!! References: In-Reply-To: Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 8bit X-Antivirus: avast! (VPS 080326-3, 26/03/2008), Outbound message X-Antivirus-Status: Clean X-SIG5: c3db4c5beec92c0bcc79ac844e64f7b6 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Saulo X-Spam-Status: No, hits=4.7 required=5.0 tests=IN_REP_TO,PLING_PLING,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, USER_AGENT,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** Eike Santos escreveu: > Blz. Rapaz... Tem msn? > Trabalha em que área? Atualmente estou estudando Rendering! > > Ats, > Marcos Eike > > 2008/3/26 Tiago Machado : > >> Oi Eike, >> >> Faço IC na area de computação gráfica. >> >> >> >> On Wed, Mar 26, 2008 at 7:09 PM, Eike Santos wrote: >> >>> >>> Alguem esta trabalhando ou gosta de computacao gráfica em geral aqui >>> na lista? Vamos trocas info? Dúvidas e coisas afim? >>> >>> Ats, >>> -- >>> Marcos Eike Tinen dos Santos >>> +559881176565 >>> >>> OpenSuse- Comunidade Open do Suse >>> www.opensuse.org >>> OpenSolaris- Comunidade Open do Solaris >>> www.opensolaris.org >>> >>> ========================================================================= >>> Instruções para entrar na lista, sair da lista e usar a lista em >>> http://www.mat.puc-rio.br/~obmlistas/obm-l.html >>> ========================================================================= >>> >>> >> > > > > Sou aluno do CEFET-RJ faço Eng. Mecânica e faço diversos trabalhos pra empresas no ramo de desenhos 3D e marquetes virtuais. Em breve irei fazer um curso de desenvolvedor de games. Estou estudando por conta própria o 3D Studio Max. Abraços. ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Mar 27 00:18:01 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2R3GwWA005144 for ; Thu, 27 Mar 2008 00:16:58 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2R3Gwlu005142 for obm-l-MllGbsmmN; Thu, 27 Mar 2008 00:16:58 -0300 Received: from fg-out-1718.google.com (fg-out-1718.google.com [72.14.220.155]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2R3GtWA005139 for ; Thu, 27 Mar 2008 00:16:56 -0300 Received: by fg-out-1718.google.com with SMTP id e12so3521684fga.3 for ; Wed, 26 Mar 2008 20:16:38 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=8LRsVTb8VBulYwYQ0rI5dQZ3VeaPDQ0F5WnnJd9DfMc=; b=qfnGl3J1lvctjSdZYT0x6aePGoVnGESyjKBRZ3lSnZMnB3rGcvPGWS3dKqklCT5j2cJUh5hdCZ/HPcM56x0sL8TzBPdC9MT2Xmd7/q1EC23JOUksqmf8sWyEziA9N9ItOdzd04ZMSfTiuftxb9svqdIDtFSySSMv/b1cLnwlt6o= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=VlPENhFNRjgKyHUFyxqZ9lWp4HEB6FLCNv9x+wooJ1A0yvNrdxg6oSnE6WiBV4zQ9N1Z2BClKOPKOCUSFFbaaJLWqVsNQqpYC8FZKpQY8kMf0wRgYKr4SgY2eTX1LXPzqym4Ws4qP6ra3KQcQriU8H+t/Qn+GXXQony/Wj/wOr8= Received: by 10.82.121.20 with SMTP id t20mr707647buc.20.1206587797854; Wed, 26 Mar 2008 20:16:37 -0700 (PDT) Received: by 10.82.170.15 with HTTP; Wed, 26 Mar 2008 20:16:37 -0700 (PDT) Message-ID: Date: Thu, 27 Mar 2008 00:16:37 -0300 From: "Tiago Machado" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Computaca Grafica!!! In-Reply-To: MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_28332_13129420.1206587797862" References: Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Tiago Machado" X-Spam-Status: No, hits=2.8 required=5.0 tests=AWL,IN_REP_TO,MAILTO_LINK,MIME_EXCESSIVE_QP,PLING_PLING, QUOTED_EMAIL_TEXT,REFERENCES,SPAM_PHRASE_00_01, X_MAILING_LIST version=2.44 X-Spam-Level: ** ------=_Part_28332_13129420.1206587797862 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Atualmente estou trabalhando na area de computa=E7=E3o gr=E1fica e t=E9cnic= as interativas. 2008/3/26 Eike Santos : > Blz. Rapaz... Tem msn? > Trabalha em que =E1rea? Atualmente estou estudando Rendering! > > Ats, > Marcos Eike > > 2008/3/26 Tiago Machado : > > Oi Eike, > > > > Fa=E7o IC na area de computa=E7=E3o gr=E1fica. > > > > > > > > On Wed, Mar 26, 2008 at 7:09 PM, Eike Santos > wrote: > > > > > > > > > > > > Alguem esta trabalhando ou gosta de computacao gr=E1fica em geral aqu= i > > > na lista? Vamos trocas info? D=FAvidas e coisas afim? > > > > > > Ats, > > > -- > > > Marcos Eike Tinen dos Santos > > > +559881176565 > > > > > > OpenSuse- Comunidade Open do Suse > > > www.opensuse.org > > > OpenSolaris- Comunidade Open do Solaris > > > www.opensolaris.org > > > > > > > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > > > Instru=E7=F5es para entrar na lista, sair da lista e usar a lista em > > > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > > > > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > > > > > > > > > > > -- > Marcos Eike Tinen dos Santos > +559881176565 > > OpenSuse- Comunidade Open do Suse > www.opensuse.org > OpenSolaris- Comunidade Open do Solaris > www.opensolaris.org > > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > Instru=E7=F5es para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > ------=_Part_28332_13129420.1206587797862 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Atualmente estou trabalhando na area de computa=E7=E3o gr=E1fica e t=E9cnic= as interativas.

2008/3/26 Eike Santos <= ;eiketinen@gmail.com>:
Blz. Rapaz... Tem msn?
Trabalha em que =E1rea? Atualmente estou estudando Rendering!

Ats,
Marcos Eike

2008/3/26 Tiago Machado <jaspier@gm= ail.com>:
> Oi Eike,
>
> Fa=E7o IC na area de computa=E7=E3o gr=E1fica.
>
>
>
> On Wed, Mar 26, 2008 at 7:09 PM, Eike Santos <eiketinen@gmail.com> wrote:
> >
> >
> >
> > Alguem esta trabalhando ou gosta de computacao gr=E1fica em geral= aqui
> > na lista? Vamos trocas info? D=FAvidas e coisas afim?
> >
> > Ats,
> > --
> > Marcos Eike Tinen dos Santos
> > +559881176565
> >
> > OpenSuse- Comunidade Open do Suse
> > www.opensus= e.org
> > OpenSolaris- Comunidade Open do Solaris
> > www.open= solaris.org
> >
> > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D
> > Instru=E7=F5es para entrar na lista, sair da lista e usar a lista= em
> > http://www.mat.puc-rio.br/~obmlistas/obm-l.html
> > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D
> >
>
>



--
Marcos Eike Tinen dos Santos
+559881176565

OpenSuse- Comunidade Open do Suse
www.opensuse.org<= br> OpenSolaris- Comunidade Open do Solaris
www.opensolaris.or= g

=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D
Instru=E7=F5es para entrar na lista, sair da lista e usar a lista em
http://www.mat.puc-rio.br/~obmlistas/obm-l.html
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D

------=_Part_28332_13129420.1206587797862-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Mar 27 01:50:27 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2R4n4WA008899 for ; Thu, 27 Mar 2008 01:49:04 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2R4n3o9008895 for obm-l-MllGbsmmN; Thu, 27 Mar 2008 01:49:03 -0300 Received: from smtp.uol.com.br (smtps.uol.com.br [200.221.4.131]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2R4n0WA008890 for ; Thu, 27 Mar 2008 01:49:00 -0300 Received: from localhost (localhost [127.0.0.1]) by socom5.uol.com.br (Postfix) with ESMTP id F1FB09AC for ; Thu, 27 Mar 2008 01:48:43 -0300 (BRT) Received: from microcf7b75528 (201009200107.user.veloxzone.com.br [201.9.200.107]) by socom5.uol.com.br (Postfix) with SMTP id 8A6014D7 for ; Thu, 27 Mar 2008 01:48:38 -0300 (BRT) Message-ID: <000d01c88fc5$d74b6170$01fea8c0@microcf7b75528> From: "Ulysses Coelho de Souza Jr." To: Subject: [SPAM] Re:[obm-l] Re: off topic: resumos analise real Date: Thu, 27 Mar 2008 01:48:41 -0300 MIME-Version: 1.0 Content-Type: text/plain X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2900.3138 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.3198 X-SIG5: c8bc9aad6b28f0541099fdcd679ee503 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Ulysses Coelho de Souza Jr." X-Spam-Status: Yes, hits=6.3 required=5.0 tests=AWL,HTML_FONT_COLOR_BLUE,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01,SUPERLONG_LINE, USER_AGENT_OE,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ****** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_NextPart_000_000A_01C88FAC.AEE6B040" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (6.30 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: USER_AGENT_OE (0.2 points) X-Mailer header indicates a non-spam MUA (Outlook Express) SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: HTML_FONT_COLOR_BLUE (0.2 points) BODY: HTML font color is blue SPAM: SUPERLONG_LINE (0.0 points) BODY: Contains a line >=199 characters long SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 107.200.9.201.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 107.200.9.201.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (0.1 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- This is a multi-part message in MIME format. ------=_NextPart_000_000A_01C88FAC.AEE6B040 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Ol=E1 a todos, Caro Paulo, O que eu estou tentando dizer, =E9 que muitas vezes = simplesmente n=E3o conseguimos encontrar uma solu=E7=E3o para um = problema. Al=E9m disso, muitas vezes enfrentamos dificuldades que nosso = orientador ou professor n=E3o disp=F5e de tempo para resolver. Para mim = e muitos outros colegas da gradua=E7=E3o a cadeira An=E1lise Real foi um = completo desastre. At=E9 hoje n=E3o sei como fui aprovado. Acho que h=E1 = uma car=EAncia muito grande de bons livros (em portugu=EAs) para o = Ensino Superior. Acredito que um livro para ser bom, entre outras qualidades, = deve conter as respostas (e como j=E1 disse antes, em alguns casos, = solu=E7=F5es). Com o manual de solu=E7=F5es podemos apreender t=E9cnicas = que s=E3o alcan=E7adas apenas com muita pr=E1tica e experi=EAncia, = pontos de vista diferentes, etc. Al=E9m de avaliar o real progresso na = compreens=E3o dos t=F3picos estudados. A id=E9ia de que alunos = pregui=E7osos podem ir direto =E0s solu=E7=F5es ao inv=E9s de tentar = resolver os problemas servir como desculpa para n=E3o publicar as = solu=E7=F5es, com o perd=E3o do rigor, =E9 absolutamente estapaf=FArdia = e descabida. N=E3o se pode penalizar os interessados por conta dos = pregui=E7osos.=20 =20 Um abra=E7o. Ulysses Coelho de Souza. =20 Ola Ulisses, Tio Cabri e demais colegas desta lista ... OBM-L, Voces acham que seria valioso apenas ver as solucoes do Livro de Analise do Prof Elon ( Vol 1, Projeto Euclides, IMPA ) sem tentar raciocinar por si mesmo e encontrar a solucao ? Eu nao estaria fazendo um mal de fosse divulgando as solucoes ? Um Abraco a Todos Paulo Santa Rita ------=_NextPart_000_000A_01C88FAC.AEE6B040 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable
Ol=E1 a todos,
 
Caro Paulo,
 
    =    =20     O que eu estou tentando dizer, =E9 que muitas vezes=20 simplesmente n=E3o conseguimos encontrar uma solu=E7=E3o para um = problema. Al=E9m=20 disso, muitas vezes enfrentamos dificuldades que nosso orientador = ou=20 professor n=E3o disp=F5e de tempo para resolver. Para mim e muitos = outros=20 colegas da gradua=E7=E3o a cadeira An=E1lise Real foi um = completo desastre.=20 At=E9 hoje n=E3o sei como fui aprovado. Acho que h=E1 uma car=EAncia = muito grande de=20 bons livros (em portugu=EAs) para o Ensino Superior.
          &nbs= p;=20 Acredito que um livro para ser bom, entre outras = qualidades, deve=20 conter as respostas (e como j=E1 disse antes, em alguns casos, = solu=E7=F5es).=20 Com o manual de solu=E7=F5es podemos apreender t=E9cnicas que s=E3o = alcan=E7adas=20 apenas com muita pr=E1tica e experi=EAncia, pontos de vista = diferentes, etc.=20 Al=E9m de avaliar o real progresso na compreens=E3o dos t=F3picos = estudados. A id=E9ia=20 de que alunos pregui=E7osos podem ir direto =E0s solu=E7=F5es ao inv=E9s = de tentar=20 resolver os problemas servir como desculpa para n=E3o publicar as = solu=E7=F5es, com o=20 perd=E3o do rigor, =E9 absolutamente estapaf=FArdia e descabida. N=E3o = se pode penalizar=20 os interessados por conta dos pregui=E7osos. 
          &nbs= p;=20
 
Um abra=E7o.
Ulysses Coelho de = Souza.
    =   
 
 
Ola Ulisses, Tio Cabri e
demais colegas desta lista ...=20 OBM-L,

Voces acham que seria valioso apenas ver as solucoes do = Livro=20 de
Analise do Prof Elon ( Vol 1,  Projeto Euclides, IMPA ) sem=20 tentar
raciocinar por si mesmo e encontrar a solucao ? Eu nao estaria = fazendo
um mal de fosse divulgando as solucoes ?

Um Abraco a=20 Todos
Paulo Santa Rita
------=_NextPart_000_000A_01C88FAC.AEE6B040-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Mar 27 02:44:02 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2R5gxWA013738 for ; Thu, 27 Mar 2008 02:42:59 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2R5gwSJ013727 for obm-l-MllGbsmmN; Thu, 27 Mar 2008 02:42:58 -0300 Received: from fg-out-1718.google.com (fg-out-1718.google.com [72.14.220.155]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2R5gsWA013667 for ; Thu, 27 Mar 2008 02:42:55 -0300 Received: by fg-out-1718.google.com with SMTP id e12so3563122fga.3 for ; Wed, 26 Mar 2008 22:42:37 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; bh=5xoplEw6sVGgMXhNnhHwoA92GvnlsmwoRl7W1GOIN/Y=; b=NzBIybRcimAMcyetk4iJRgpkNxsITP3SGku2jpy3KUSNnMzg7jEvhAC2NDN1mfdbqbqIKgfmrhGMIhAaJvBxKKGQGVmgRDM0rCmCu6LTzEcEiJw2XAwqej7qHeUnr/elVFWXwKG0eqrjBIy+WIq7rBfgZUbLLenaiMJbDenXh5k= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; b=QirwnxxCLHU9sIEbdx72P5UGRtA6tj+Un2pmcqXByuLFogzQ1Ukp8khiaczRD9rLCf39Iy38dKgNxEhv19e15X8BhI9USjw2i6nSKRGvUi14EyWXZ1m/X+2BPoU/nI2lzrM3NExnEZLawsh6bjBd2MkBW9AldHRbPQgEzoE0QT0= Received: by 10.82.159.2 with SMTP id h2mr1000931bue.33.1206596557468; Wed, 26 Mar 2008 22:42:37 -0700 (PDT) Received: by 10.82.178.20 with HTTP; Wed, 26 Mar 2008 22:42:37 -0700 (PDT) Message-ID: Date: Thu, 27 Mar 2008 02:42:37 -0300 From: "Igor Battazza" To: obm-l@mat.puc-rio.br Subject: =?ISO-8859-1?Q?Re:_[obm-l]_fun=E7=E3o?= In-Reply-To: MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline References: <004901c88fb1$b9f98520$2dec8f60$@com> Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m2R5guWA013714 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Igor Battazza" X-Spam-Status: No, hits=-0.9 required=5.0 tests=IN_REP_TO,MAILTO_TO_SPAM_ADDR,QUOTED_EMAIL_TEXT,REFERENCES, SPAM_PHRASE_00_01,X_MAILING_LIST version=2.44 X-Spam-Level: 2008/3/27, Igor Battazza : > 2008/3/26, Marcus Aurelio : > > > > > > > > > > > Alguém pode me ajudar nessa > > > > f(x) + f(x-1) = x^2 se f(19) = 94 calcule f(94)? > > > > > > > Olá > > f(x) = x^2 - f(x - 1), então f(94) = 94^2 - f(93), > f(93) = 93^2 - f(92), > f(92) = 92^2 - f(91). > .... > f(20) = 20^2 - f(19) > > Perceba que substituindo os valores, teremos a seguinte soma: f(94) = > (94^2 - 93^2) + (92^2 - 91^2) + ... + (22^2 - 21^2) + 20^2 - 94 > > mas (n + 1)^2 - n^2 = [(n + 1) - n][(n + 1) + n], portanto a soma fica: > f(94) = 1*(94 + 93) + 1*(92 + 91) + 1*(90 + 89) + ... + 20^2 - 94 -> > -> f(94) = (94 + 93 + 92 + ... + 21) + 20^2 - 94 = 4225 + 400 - 94 = 4561 > > (a soma de 21 até 94 é uma P.A. de razão 1) > > "acho" que é isso > Só pra ficar claro as passagens dos termos que eu n coloquei: f(94) = 94^2 - f(93) e f(93) = 93^2 - f(92) Substituindo, teremos f(94) = 94^2 - [93^2 - f(92)] = 94^2 - 93^2 + f(92), e assim por diante ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Mar 27 05:42:47 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2R8ceY4025039 for ; Thu, 27 Mar 2008 05:40:12 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2R5deSi012425 for obm-l-MllGbsmmN; Thu, 27 Mar 2008 02:39:40 -0300 Received: from fg-out-1718.google.com (fg-out-1718.google.com [72.14.220.156]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2R5dSWA012336 for ; Thu, 27 Mar 2008 02:39:30 -0300 Received: by fg-out-1718.google.com with SMTP id e12so3562107fga.3 for ; Wed, 26 Mar 2008 22:39:10 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; bh=1GPGgd37cc+ABsu00+bgbYkMcjq5mqr/P75qz83eKc4=; b=jx/tKhS7wRySLOKQPaQgVXOyh9Osgocmg4nr7p2ZISvv7lo6CBFzgW8AKNA3iay7v59Xdk3IaYuHmi9mKqCiS4eYdkI+unWumpYAzsI9j9jpAK2n5aj3BJxgaiW09wwS+anFff8uaLlQMUTpxODb77VsEiEwlsFWOleZoGXoeeo= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; b=M26nxoKpPUDKbQ9x/KXCl646Ea/L5fC/fi6T0jbc5UorJ3cNmV32eWf+BN30Ip0YFL2ESaeSDUkHtTUFidS5hANLAO/32Okfa7Mo1avy57iv3K5JvuKL22XW6knLVjTgLXZYJ9ZZPNPT5v3T0ljpo5KNmXWjubixarkANsms7sg= Received: by 10.82.175.7 with SMTP id x7mr996018bue.36.1206596350502; Wed, 26 Mar 2008 22:39:10 -0700 (PDT) Received: by 10.82.178.20 with HTTP; Wed, 26 Mar 2008 22:39:10 -0700 (PDT) Message-ID: Date: Thu, 27 Mar 2008 02:39:10 -0300 From: "Igor Battazza" To: obm-l@mat.puc-rio.br Subject: =?ISO-8859-1?Q?Re:_[obm-l]_fun=E7=E3o?= In-Reply-To: <004901c88fb1$b9f98520$2dec8f60$@com> MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline References: <004901c88fb1$b9f98520$2dec8f60$@com> Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m2R5dZWA012396 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Igor Battazza" X-Spam-Status: No, hits=-0.5 required=5.0 tests=AWL,IN_REP_TO,MAILTO_TO_SPAM_ADDR,REFERENCES, SPAM_PHRASE_00_01,X_MAILING_LIST version=2.44 X-Spam-Level: 2008/3/26, Marcus Aurelio : > > > > > Alguém pode me ajudar nessa > > f(x) + f(x-1) = x^2 se f(19) = 94 calcule f(94)? > > Olá f(x) = x^2 - f(x - 1), então f(94) = 94^2 - f(93), f(93) = 93^2 - f(92), f(92) = 92^2 - f(91). .... f(20) = 20^2 - f(19) Perceba que substituindo os valores, teremos a seguinte soma: f(94) = (94^2 - 93^2) + (92^2 - 91^2) + ... + (22^2 - 21^2) + 20^2 - 94 mas (n + 1)^2 - n^2 = [(n + 1) - n][(n + 1) + n], portanto a soma fica: f(94) = 1*(94 + 93) + 1*(92 + 91) + 1*(90 + 89) + ... + 20^2 - 94 -> -> f(94) = (94 + 93 + 92 + ... + 21) + 20^2 - 94 = 4225 + 400 - 94 = 4561 (a soma de 21 até 94 é uma P.A. de razão 1) "acho" que é isso ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Mar 27 08:45:13 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2RBhfWA009954 for ; Thu, 27 Mar 2008 08:43:41 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2RBhepa009944 for obm-l-MllGbsmmN; Thu, 27 Mar 2008 08:43:40 -0300 Received: from wr-out-0506.google.com (wr-out-0506.google.com [64.233.184.231]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2RBhaWA009916 for ; Thu, 27 Mar 2008 08:43:37 -0300 Received: by wr-out-0506.google.com with SMTP id c46so4703277wra.18 for ; Thu, 27 Mar 2008 04:43:19 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; bh=vyrV0iE6JvmHhH39Yi9PUsE1EZAyQ/Pzu5gyHjDMznk=; b=SbdcY6AyzyOI4312OITnd6DF/8TREPYz6qf5OZDUxALzZgRLDnhsXvokOw87T1vTF2TPGvtoKJqwQJKnHQA/gV93rPmKzEPji6WHhAdYTLUfmp04LL195KBKA0NUCXJUW1aejSfJDio0c0jwy5i4UE28LY6vje/4T+6LsBOyOsI= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; b=kDSoAW6ElsjXNDSzQDYS/RU6bQ47n3DhgBhd8+huen5vKhHy2YIxTyJ1MCKOKIpemIUcFBUmizTH792a4+5PSIfZ7XJnTNLUObF41cL/VxYqC2wUvMW9YDCJrkxmws9ZlYoYWzZJJt2SrN9N168VAAS5dgmc9qXT9/YEi6HFRe0= Received: by 10.114.197.1 with SMTP id u1mr1215273waf.61.1206618199236; Thu, 27 Mar 2008 04:43:19 -0700 (PDT) Received: by 10.114.193.10 with HTTP; Thu, 27 Mar 2008 04:43:19 -0700 (PDT) Message-ID: Date: Thu, 27 Mar 2008 08:43:19 -0300 From: "Eike Santos" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Computaca Grafica!!! In-Reply-To: MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline References: Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m2RBhdWA009936 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Eike Santos" X-Spam-Status: No, hits=4.8 required=5.0 tests=AWL,IN_REP_TO,PLING_PLING,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SIGNATURE_LONG_SPARSE, SPAM_PHRASE_00_01,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** Mas, vc tem estudado ou estudou Rendering? Ats, Marcos Eike 2008/3/27 Tiago Machado : > Atualmente estou trabalhando na area de computação gráfica e técnicas > interativas. > > 2008/3/26 Eike Santos : > > > > Blz. Rapaz... Tem msn? > > Trabalha em que área? Atualmente estou estudando Rendering! > > > > Ats, > > Marcos Eike > > > > 2008/3/26 Tiago Machado : > > > > > > > > > Oi Eike, > > > > > > Faço IC na area de computação gráfica. > > > > > > > > > > > > On Wed, Mar 26, 2008 at 7:09 PM, Eike Santos > wrote: > > > > > > > > > > > > > > > > Alguem esta trabalhando ou gosta de computacao gráfica em geral aqui > > > > na lista? Vamos trocas info? Dúvidas e coisas afim? > > > > > > > > Ats, > > > > -- > > > > Marcos Eike Tinen dos Santos > > > > +559881176565 > > > > > > > > OpenSuse- Comunidade Open do Suse > > > > www.opensuse.org > > > > OpenSolaris- Comunidade Open do Solaris > > > > www.opensolaris.org > > > > > > > > > ========================================================================= > > > > Instruções para entrar na lista, sair da lista e usar a lista em > > > > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > > > > > ========================================================================= > > > > > > > > > > > > > > > > > > -- > > > > > > > > Marcos Eike Tinen dos Santos > > +559881176565 > > > > OpenSuse- Comunidade Open do Suse > > www.opensuse.org > > OpenSolaris- Comunidade Open do Solaris > > www.opensolaris.org > > > > ========================================================================= > > Instruções para entrar na lista, sair da lista e usar a lista em > > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > > ========================================================================= > > > > -- Marcos Eike Tinen dos Santos +559881176565 OpenSuse- Comunidade Open do Suse www.opensuse.org OpenSolaris- Comunidade Open do Solaris www.opensolaris.org ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Mar 27 08:46:14 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2RBjKWA010060 for ; Thu, 27 Mar 2008 08:45:20 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2RBjK7P010058 for obm-l-MllGbsmmN; Thu, 27 Mar 2008 08:45:20 -0300 Received: from wf-out-1314.google.com (wf-out-1314.google.com [209.85.200.171]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2RBjHWA010044 for ; Thu, 27 Mar 2008 08:45:18 -0300 Received: by wf-out-1314.google.com with SMTP id 27so3467085wfd.18 for ; Thu, 27 Mar 2008 04:45:00 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; bh=vyrV0iE6JvmHhH39Yi9PUsE1EZAyQ/Pzu5gyHjDMznk=; b=LXYEdpm9O6vqPWknXiJDcEqLGKMdHlftAMQTyIwj7qV4wBOPSQSBOJEaKhmEJ55rjALyNR1wgpHl4n2bhFjDm9cRuYFH528cECIDt49LDWUJA0XNnsUKB/5NT3RmgLVCsUhK/RyoCV4w+uwn+GX5CED8UVx1yoNVZzCfbKd6HhQ= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; b=LfuGhSmIV8xdZvFD1v97uj0wJF4Ad5NBzd2u49DRMV+4Y9Ld0/rWFJru22ztJJ945KUaqhb+jUhWzJHf4qgl+QGPXGJbSePdO4434sTUI54/LK+ZBXCeoNop4hSnIOaJjOxWBs65v5szbZBFNIXuJM+7TeIvxjqYjvMWVH8TgDo= Received: by 10.142.103.6 with SMTP id a6mr981769wfc.109.1206618300179; Thu, 27 Mar 2008 04:45:00 -0700 (PDT) Received: by 10.143.5.12 with HTTP; Thu, 27 Mar 2008 04:44:59 -0700 (PDT) Message-ID: Date: Thu, 27 Mar 2008 08:44:59 -0300 From: "Eike Santos" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Computaca Grafica!!! In-Reply-To: MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline References: Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m2RBjJWA010056 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Eike Santos" X-Spam-Status: No, hits=4.9 required=5.0 tests=IN_REP_TO,PLING_PLING,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SIGNATURE_LONG_SPARSE, SPAM_PHRASE_00_01,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** Mas, vc tem estudado ou estudou Rendering? Ats, Marcos Eike 2008/3/27 Tiago Machado : > Atualmente estou trabalhando na area de computação gráfica e técnicas > interativas. > > 2008/3/26 Eike Santos : > > > > Blz. Rapaz... Tem msn? > > Trabalha em que área? Atualmente estou estudando Rendering! > > > > Ats, > > Marcos Eike > > > > 2008/3/26 Tiago Machado : > > > > > > > > > Oi Eike, > > > > > > Faço IC na area de computação gráfica. > > > > > > > > > > > > On Wed, Mar 26, 2008 at 7:09 PM, Eike Santos > wrote: > > > > > > > > > > > > > > > > Alguem esta trabalhando ou gosta de computacao gráfica em geral aqui > > > > na lista? Vamos trocas info? Dúvidas e coisas afim? > > > > > > > > Ats, > > > > -- > > > > Marcos Eike Tinen dos Santos > > > > +559881176565 > > > > > > > > OpenSuse- Comunidade Open do Suse > > > > www.opensuse.org > > > > OpenSolaris- Comunidade Open do Solaris > > > > www.opensolaris.org > > > > > > > > > ========================================================================= > > > > Instruções para entrar na lista, sair da lista e usar a lista em > > > > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > > > > > ========================================================================= > > > > > > > > > > > > > > > > > > -- > > > > > > > > Marcos Eike Tinen dos Santos > > +559881176565 > > > > OpenSuse- Comunidade Open do Suse > > www.opensuse.org > > OpenSolaris- Comunidade Open do Solaris > > www.opensolaris.org > > > > ========================================================================= > > Instruções para entrar na lista, sair da lista e usar a lista em > > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > > ========================================================================= > > > > -- Marcos Eike Tinen dos Santos +559881176565 OpenSuse- Comunidade Open do Suse www.opensuse.org OpenSolaris- Comunidade Open do Solaris www.opensolaris.org ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Mar 27 08:53:54 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2RBquWA010539 for ; Thu, 27 Mar 2008 08:52:56 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2RBqtY3010537 for obm-l-MllGbsmmN; Thu, 27 Mar 2008 08:52:55 -0300 Received: from ik-out-1112.google.com (ik-out-1112.google.com [66.249.90.181]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2RBqrWA010513 for ; Thu, 27 Mar 2008 08:52:53 -0300 Received: by ik-out-1112.google.com with SMTP id c28so1381454ika.5 for ; Thu, 27 Mar 2008 04:52:36 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:mime-version:content-type:content-transfer-encoding:content-disposition; bh=aCXXCGA1QJ9052I+TUDsYVIFpGgzan6GiQb8OVX9DPY=; b=e8Vuq+dMjvCm2mVL2lMtK6Mj0dYEbTd7TYWzA5EH9al7w1pEtq5glhngcOAHHmFr8xqKz3I/duQtIBSwhhQA2b4ERinnDP6LQW6nIH8truNbgOpWIn592hHcjGX1RtO5tS6Bt2seDwxg8IpmFHL+mPu1A6KJ9KGArsbljtUrJ9M= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:mime-version:content-type:content-transfer-encoding:content-disposition; b=UPZzHdb587uxY5XqPfzqL/7AF0naaXfG17qWN3+dNZpTdfTlSq0joJofTWcnkotmNTw3CbfaoVPzpKv2tdCRijPmyJc6mnlt5uUqYyPqjDruBT+ViTzA6Yu+XodBWWy8BkgWw9G3LYUivCzX2WGmcYAiNOb5mpWnDRFeIrbVVKk= Received: by 10.151.148.2 with SMTP id a2mr714765ybo.186.1206618755214; Thu, 27 Mar 2008 04:52:35 -0700 (PDT) Received: by 10.150.144.4 with HTTP; Thu, 27 Mar 2008 04:52:35 -0700 (PDT) Message-ID: Date: Thu, 27 Mar 2008 08:52:35 -0300 From: "Paulo Santa Rita" To: obm-l@mat.puc-rio.br Subject: [obm-l] Exercicios de Analise 1 MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m2RBqsWA010535 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Paulo Santa Rita" X-Spam-Status: No, hits=4.6 required=5.0 tests=AWL,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** Ola Pessoal ! ( vou escrever sem acentos ) O Livro que tenho aqui na minha mesa e o "Curso de Analise, Vol 1, Elon Lages Lima, Projeto Euclides, IMPA, 11 edicao, segunda impressao". Considero-o excelente, em verdade, a melhor introducao a Analise feita por um brasileiro. O enunciado das questoes voces deverao encontrar nele. Nao sei se vou conseguir completar este trabalho. As questoes, voces verao, sao simples, mas eu tenho muitas outras ocupacoes que poderao criar dificuldades no prosseguindo da solucoes.As solucoes sao minhas, quero dizer, todos os erros que surgirem sao de minha inteira e exclusiva responsabilidade e voces podem ( e devem ) me corrigir. Nao vou abordar aqui os capitulos 1, 2 e 3. Eles sao muito importantes e vou usar sistematicamente o conhecimente neles transmitido, mas a Analise comeca realmente no capitulo 4, sequencias e series de numeros reais. Os primeiros exercicios, em geral, sao altamente triviais e, portanto, vou fazer mais de um numa mesma mensagem. Eu vou fazendo as questoes conforme vou lendo. Vou tentar publicar ao menos uma mensagem a cada 2 dias. Em geral, e facil ver mais de uma maneira de fazer cada questao, mas sempre vou optar por aquela que me parece mais facil de entender, mesmo que essa solucao mais facil nao seja a mais sintetica ou/e a mais bela. "Tornai-me a aparecer, entes imaginários, que me enchíeis outrora os olhos visionários ! Poder-vos-ei fixar ? ... Tenho inda coração capaz de se render à vossa sedução ? ... " ( FAUSTO, de Goeth ) ( EXERCICIO 4.1 ) Se lim Xn = a entao, dado um E > 0 qualquer, mesmo que muito pequeno, por definicao teremos que : Existe um natural N0 tal que para todo natural n > N0 => | Xn - a | < E. Como, devido a propriedade dos modulos, | |Xn| - |a| | =< | Xn - a | segue, com mais forte razao, que para todo n > N0 => | |Xn| - |a| | < E, isto e, para todo E > 0 dado, existe N0 tal para todo n > N0 teremos que | |Xn| - |a| | < E, vale dizer, lim | Xn | = | a |, como queriamos demonstrar. Para mostrar a falsidade da afirmacao reciproca, tomemos como contra-exemplo a sequencia definida por : Xn = (1 - N) / N Teremos, sucessivamente lim |Xn| = lim| (1 - N)/N | = lim| (N-1)/N | = lim (1-N)/N = -1 = | 1 |. Assim, lim | Xn | = | 1 |. Mas : lim Xn = lim (1-N)/N = -1. No caso em que a=0 vale a afirmacao reciproca, isto e, lim |Xn| = |0| => lim Xn = 0. Para ver isso claramente, seja lim |Xn| = | 0 |= 0. Entao, dado um E>0 qualquer, mesmo que muito pequeno : Existe um natural N0 tal que n > N0 => | |Xn| - |0| | < E . Daqui seque : | |Xn| - |0| | < E => | |Xn| - 0 | < E => || Xn|| < E => | Xn| < E => | Xn - 0 | < E => lim Xn = 0 ( EXERCICIO 4.2 ) Como lim Xn = 0 entao, dado E > 0 qualquer ; Existe um natural N0 tal que para todo n > N0 => | Xn - 0| < E, isto e, |Xn| < E. Mas, por definicao, Yn = min{ |X1|, |X2|, ..., |Xn| }, vale dizer, Yn e real nao negativo e Yn =< | Xn | para todo "n" natural, ou seja, | Yn | < | Xn | para todo "n" natural. Como |Xn| < E para todo n > N0 entao entao |Yn| < E para todo n > N0 => |Yn - 0 | < E para todo n > N0 => lim Yn = 0. ( EXERCICIO 4.3 ) Suponha que nao fosse lim Xn = a. O que significa dizer isso ? Significa o seguinte : Existe um E > 0 tal que para todo N0 fixado existe n > N0 tal que | Xn - a | >= E Tomemos um tal E > 0 e fixemo-nos nos indices n > N0 que sao pares. Isto significa que existe um E > 0 tal que para todo N0 fixado existe n par > N0 tal que |Xn - a| >= E. Isto significa que lim X2n nao e "a", isto e, lim X2n # a ... ABSURDO ! Assim, nao pode ser lim Xn # a, vale dizer, lim Xn = a como queriamos demonstrar. A todos, com os melhores votos de Paz Profunda, sou Paulo Santa Rita 5,0830,1B0308 ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Mar 27 10:09:55 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2RD7DWA013046 for ; Thu, 27 Mar 2008 10:07:13 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2RD7DFK013044 for obm-l-MllGbsmmN; Thu, 27 Mar 2008 10:07:13 -0300 Received: from el-out-1112.google.com (el-out-1112.google.com [209.85.162.176]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2RD7AWA013037 for ; Thu, 27 Mar 2008 10:07:11 -0300 Received: by el-out-1112.google.com with SMTP id n30so2584802elf.7 for ; Thu, 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<26fc77ef0803270606u7834707m7698f4c6ea81cafe@mail.gmail.com> Date: Thu, 27 Mar 2008 10:06:51 -0300 From: "Palmerim Soares" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Re: off topic: resumos analise real In-Reply-To: <000c01c88f8b$d14475d0$01fea8c0@microcf7b75528> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_21488_32295589.1206623211099" References: <000c01c88f8b$d14475d0$01fea8c0@microcf7b75528> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Palmerim Soares" X-Spam-Status: No, hits=3.1 required=5.0 tests=AWL,IN_REP_TO,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: *** ------=_Part_21488_32295589.1206623211099 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: base64 Content-Disposition: inline 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Mar 27 10:19:33 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2RDIWWA013859 for ; Thu, 27 Mar 2008 10:18:32 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2RDIWea013857 for obm-l-MllGbsmmN; Thu, 27 Mar 2008 10:18:32 -0300 Received: from fg-out-1718.google.com (fg-out-1718.google.com [72.14.220.157]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2RDITWA013843 for ; Thu, 27 Mar 2008 10:18:29 -0300 Received: by fg-out-1718.google.com with SMTP id e12so3688968fga.3 for ; Thu, 27 Mar 2008 06:18:11 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=yY4DAg6Dl6yf4Aud3tC8Tjg1ujGKUHLhDlqvfYutp/o=; b=t5pn4YXhXHzutM86nBPKPzRjEq9E+eNUs2TEiQq/uy8FaJxXCFsjE+GOi08lHPj61EiHk3VYMpXFFvMJ4C3P/nS/tbSsRWucn+YaIJfwGG/53eYW+HOuDvylj4/BlWRrBwUr/hRd9KPsCODGOQg6WS7UUvVfeYhdp6P0AjMomlE= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=KjVqwR5Ohf+Rxo33JNf2Oi/oe8k0I22bdS2FKIvCEoZYQ+VqQ1fjLPk+O0dH1achUkzmMxH4Pg5zxgd0alTO3PABNHP7InWkqGIhnp4uuBiHCi8sfDkimHRwSXxNAQfj7Ioji/0fyZ1L/S15aMLJUieh49/G0jUF/JF5rF6w5zQ= Received: by 10.82.187.2 with SMTP id k2mr3306122buf.26.1206622422921; Thu, 27 Mar 2008 05:53:42 -0700 (PDT) Received: by 10.82.170.15 with HTTP; Thu, 27 Mar 2008 05:53:42 -0700 (PDT) Message-ID: Date: Thu, 27 Mar 2008 09:53:42 -0300 From: "Tiago Machado" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Computaca Grafica!!! In-Reply-To: MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_29637_4282469.1206622422900" References: Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Tiago Machado" X-Spam-Status: No, hits=2.2 required=5.0 tests=AWL,IN_REP_TO,MAILTO_LINK,MIME_EXCESSIVE_QP,PLING_PLING, QUOTED_EMAIL_TEXT,REFERENCES,SPAM_PHRASE_00_01, X_MAILING_LIST version=2.44 X-Spam-Level: ** ------=_Part_29637_4282469.1206622422900 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline sim. estudei na disciplina de processamento gr=E1fico. 2008/3/27 Eike Santos : > Mas, vc tem estudado ou estudou Rendering? > > Ats, > Marcos Eike > > 2008/3/27 Tiago Machado : > > Atualmente estou trabalhando na area de computa=E7=E3o gr=E1fica e t=E9= cnicas > > interativas. > > > > 2008/3/26 Eike Santos : > > > > > > > Blz. Rapaz... Tem msn? > > > Trabalha em que =E1rea? Atualmente estou estudando Rendering! > > > > > > Ats, > > > Marcos Eike > > > > > > 2008/3/26 Tiago Machado : > > > > > > > > > > > > > Oi Eike, > > > > > > > > Fa=E7o IC na area de computa=E7=E3o gr=E1fica. > > > > > > > > > > > > > > > > On Wed, Mar 26, 2008 at 7:09 PM, Eike Santos > > wrote: > > > > > > > > > > > > > > > > > > > > Alguem esta trabalhando ou gosta de computacao gr=E1fica em geral > aqui > > > > > na lista? Vamos trocas info? D=FAvidas e coisas afim? > > > > > > > > > > Ats, > > > > > -- > > > > > Marcos Eike Tinen dos Santos > > > > > +559881176565 > > > > > > > > > > OpenSuse- Comunidade Open do Suse > > > > > www.opensuse.org > > > > > OpenSolaris- Comunidade Open do Solaris > > > > > www.opensolaris.org > > > > > > > > > > > > > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > > > > > Instru=E7=F5es para entrar na lista, sair da lista e usar a lista= em > > > > > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > > > > > > > > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > > > > > > > > > > > > > > > > > > > > > > > > > -- > > > > > > > > > > > > Marcos Eike Tinen dos Santos > > > +559881176565 > > > > > > OpenSuse- Comunidade Open do Suse > > > www.opensuse.org > > > OpenSolaris- Comunidade Open do Solaris > > > www.opensolaris.org > > > > > > > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > > > Instru=E7=F5es para entrar na lista, sair da lista e usar a lista em > > > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > > > > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > > > > > > > > > > > -- > Marcos Eike Tinen dos Santos > +559881176565 > > OpenSuse- Comunidade Open do Suse > www.opensuse.org > OpenSolaris- Comunidade Open do Solaris > www.opensolaris.org > > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > Instru=E7=F5es para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > ------=_Part_29637_4282469.1206622422900 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline sim. estudei na disciplina de processamento gr=E1fico.

2008/3/27 Eike Santos <eiketinen@gmail.com>:
Mas, vc tem estudado ou estudou Rendering?

Ats,
Marcos Eike

2008/3/27 Tiago Machado <jaspier@gm= ail.com>:
> Atualmente estou trabalhando na = area de computa=E7=E3o gr=E1fica e t=E9cnicas
> interativas.
>
> 2008/3/26 Eike Santos <eiket= inen@gmail.com>:
>
>
> > Blz. Rapaz... Tem msn?
> > Trabalha em que =E1rea? Atualmente estou estudando Rendering!
> >
> > Ats,
> > Marcos Eike
> >
> > 2008/3/26 Tiago Machado <= jaspier@gmail.com>:
> >
> >
> >
> > > Oi Eike,
> > >
> > > Fa=E7o IC na area de computa=E7=E3o gr=E1fica.
> > >
> > >
> > >
> > > On Wed, Mar 26, 2008 at 7:09 PM, Eike Santos <eiketinen@gmail.com>
> wrote:
> > > >
> > > >
> > > >
> > > > Alguem esta trabalhando ou gosta de computacao gr=E1fic= a em geral aqui
> > > > na lista? Vamos trocas info? D=FAvidas e coisas afim? > > > >
> > > > Ats,
> > > > --
> > > > Marcos Eike Tinen dos Santos
> > > > +559881176565
> > > >
> > > > OpenSuse- Comunidade Open do Suse
> > > > w= ww.opensuse.org
> > > > OpenSolaris- Comunidade Open do Solaris
> > > > www.opensolaris.org
> > > >
> > > >
> =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
> > > > Instru=E7=F5es para entrar na lista, sair da lista e us= ar a lista em
> > > > http://www.mat.puc-rio.br/~obmlistas/obm-l.html
> > > >
> =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
> > > >
> > >
> > >
> >
> >
> >
> > --
> >
> >
> >
> > Marcos Eike Tinen dos Santos
> > +559881176565
> >
> > OpenSuse- Comunidade Open do Suse
> > www.opensus= e.org
> > OpenSolaris- Comunidade Open do Solaris
> > www.open= solaris.org
> >
> > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D
> > Instru=E7=F5es para entrar na lista, sair da lista e usar a lista= em
> > http://www.mat.puc-rio.br/~obmlistas/obm-l.html
> > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D
> >
>
>



--
Marcos Eike Tinen dos Santos
+559881176565

OpenSuse- Comunidade Open do Suse
www.opensuse.org<= br> OpenSolaris- Comunidade Open do Solaris
www.opensolaris.or= g

=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D
Instru=E7=F5es para entrar na lista, sair da lista e usar a lista em
http://www.mat.puc-rio.br/~obmlistas/obm-l.html
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D

------=_Part_29637_4282469.1206622422900-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Mar 27 10:24:12 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2RDNGWA014366 for ; Thu, 27 Mar 2008 10:23:16 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2RDNFMn014364 for obm-l-MllGbsmmN; Thu, 27 Mar 2008 10:23:15 -0300 Received: from an-out-0708.google.com (an-out-0708.google.com [209.85.132.240]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2RDNCWA014358 for ; Thu, 27 Mar 2008 10:23:13 -0300 Received: by an-out-0708.google.com with SMTP id c31so103348ana.120 for ; Thu, 27 Mar 2008 06:22:55 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=6VDbkj/hkggZXUDQHWalSJqAWo+tO2ZdZwEshQmM+Ig=; b=H3nno70PnVGGqJncgu4DYEPaBox1ZOGDJgCvwN5ESDINVrnzk6KfMx99OTCjONAbuy/V5IC6kHMMskjpsHCQvaujjPkDRNEeDCx5OIZG+OUls7fFfGcDmQVDEqfvPhIXZnHPOxLmhu+0b2/JEUnMiQGQaT3E2sHvgTFZoD4OZ18= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=ahqL/4QiLNJbsfrea7jj0L5kZ+sCKsGpgLUge2V3gDCvl7h1dUeX8UvH/lNXYc3+nhFgJTRMKCMm3MXVp1kOIyqnjrzC72SA8lQGHwDn/gMwSrfGVGzgj2+gPfXQT6Mc8LnOvQglOujLLTFHlXtPeexupibIlDK7DD6fl3QvgTg= Received: by 10.100.12.1 with SMTP id 1mr3340251anl.43.1206624175449; Thu, 27 Mar 2008 06:22:55 -0700 (PDT) Received: by 10.100.135.4 with HTTP; Thu, 27 Mar 2008 06:22:55 -0700 (PDT) Message-ID: Date: Thu, 27 Mar 2008 10:22:55 -0300 From: "Thelio Gama" To: obm-l@mat.puc-rio.br Subject: [SPAM] Re: [obm-l] combinatoria dificil In-Reply-To: <3e7bcb580803201443r10149ad4n4a3c3d7710b3573@mail.gmail.com> MIME-Version: 1.0 Content-Type: text/plain References: <3e7bcb580803201443r10149ad4n4a3c3d7710b3573@mail.gmail.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Thelio Gama" X-Spam-Status: Yes, hits=5.5 required=5.0 tests=AWL,GAPPY_TEXT,IN_REP_TO,JAVASCRIPT_UNSAFE,MAILTO_LINK, MIME_EXCESSIVE_QP,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ***** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_Part_23995_9903530.1206624175445" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (5.50 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: REFERENCES (-0.5 points) Has a valid-looking References header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: GAPPY_TEXT (0.0 points) BODY: Contains 'G.a.p.p.y-T.e.x.t' SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: QUOTED_EMAIL_TEXT (-0.8 points) BODY: Contains what looks like a quoted email text SPAM: JAVASCRIPT_UNSAFE (0.3 points) BODY: Easily-executed JavaScript code SPAM: MAILTO_LINK (0.2 points) BODY: Includes a URL link to send an email SPAM: MIME_EXCESSIVE_QP (1.0 points) RAW: Excessive quoted-printable encoding in body SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 240.132.85.209.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 240.132.85.209.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (0.3 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- ------=_Part_23995_9903530.1206624175445 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Terei a resposta oficial somente semana que vem. A quest=E3o foi proposta p= elo Prof. Paulo Jorge Teixeira (UFF) na 1=AA avalia=E7=E3o formativa de um curs= o em andamento na PUC-RJ. Mas tudo indica que =E9 realmente 48 e, portanto, houv= e um erro nas alternativas. Em 20/03/08, Henrique Renn=F3 escreveu: > > Ol=E1 pessoal! > > Acredito que a solu=E7=E3o do Salhab est=E1 correta. Seja Di o dia i e Hj= o > hor=E1rio j. > > D1H1: 3 mat=E9rias > D1H2: 2 mat=E9rias (para n=E3o repetir a utilizada em D1H1) > D1: 6 possibilidades > > Para D2, se escolhermos uma j=E1 utilizada em D1 ent=E3o n=E3o poderemos > utilizar a outra mat=E9ria utilizada em D1, sen=E3o D3 teria as mesmas > mat=E9rias. Assim, para D2 ter=EDamos uma j=E1 utilizada (2 mat=E9rias) e= uma > n=E3o utilizada. Logo, 2*1 =3D 2. Como a ordem importa, temos 2*2 =3D 4. > > D3 s=F3 possui 2 formas, com as ordens das mat=E9rias trocadas. > > Total: 6*4*2 =3D 48. > > Essa =E9 uma forma mais l=F3gica de resolver o problema. Estive tentando > utilizar combinat=F3ria e tamb=E9m achei a resposta 48. > > Sejam A,B,C as mat=E9rias. Quantas permuta=E7=F5es diferentes existem ent= re > A,A,B,B,C,C? Cada posi=E7=E3o seria um hor=E1rio em um dia, ou seja, > D1H1_D1H2_D2H1_D2H2_D3H1_D3H2. Bastaria calcular o n=FAmero de > permuta=E7=F5es com repeti=E7=E3o, ou seja, 6!/(2!*2!*2!) =3D 720/8 =3D 9= 0. > > Sabemos que n=E3o podemos ter uma permuta=E7=E3o do tipo AABCBC, pois AA > representa a mesma mat=E9ria em D1H1 e D1H2. Ent=E3o sabemos que a > resposta =E9 menor que 90. > > As formas inv=E1lidas ser=E3o: > > Se as 3 mat=E9rias do mesmo tipo est=E3o juntas no mesmo dia, ex: AABBCC. > Existem 3! =3D 6 formas, considerando AA,BB,CC como 3 elementos > permutados entre si. > > N=E3o h=E1 necessidade de verificar quando 2 mat=E9rias est=E3o no mesmo = dia > pois cai no caso acima. > > Quando h=E1 apenas 1 mat=E9ria repetida em 1 dia, ex: AABCBC, ent=E3o tem= os > 12 formas para cada par da mesma mat=E9ria utilizada no mesmo dia. Se AA > est=E1 em D1 ent=E3o D2 pode ser BC ou CB e D3 pode ser BC ou CB, 2*2 =3D= 4. > AA pode estar em D1,D2,D3. Assim, 4*3 =3D 12. Para BB e CC seria o > mesmo, dando um total de 3*12 =3D 36 formas quando h=E1 apenas uma mat=E9= ria > que se repete no mesmo dia. > > Assim, o total seria 90 - (6+36) =3D 90 - 42 =3D 48 formas distintas de > compor o hor=E1rio > > Thelio, voc=EA poderia passar a fonte do problema e verificar se as > respostas s=E3o essas mesmo? > > On 3/13/08, Thelio Gama wrote: > > =C9 pessoal... > > > > Achei muito dif=EDcil esta quest=E3o. Agrade=E7o se algu=E9m puder expl= ic=E1-la. > > > > Thelio > > > > uma turma tem aulas =E0s 2=AA, 4=AA e 6=AA feiras, de 8-9 horas e de 11= -12 > horas. As > > mat=E9rias s=E3o portugues, matem=E1tica e ingles, cada uma com duas au= las > > semanais, em dias diferentes. De quantos modos pode ser feito o hor=E1r= io > > dessa turma? > > a)96 ; b) 144 ; c)192 ; d) 6! ; e) 120 > > > -- > Henrique > > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > Instru=E7=F5es para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > ------=_Part_23995_9903530.1206624175445 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Terei a resposta oficial somente semana que vem. A quest=E3o foi proposta p= elo Prof. Paulo Jorge Teixeira (UFF) na 1=AA avalia=E7=E3o formativa de um = curso em andamento na PUC-RJ. Mas tudo indica que =E9 realmente 48 e, porta= nto, houve um erro nas alternativas.

Em 20/03/08, Henrique Renn=F3 <henri= que.renno@gmail.com> escreveu:=20
Ol=E1 pessoal!

Acredito q= ue a solu=E7=E3o do Salhab est=E1 correta. Seja Di o dia i e Hj o hor=E1rio= j.

D1H1: 3 mat=E9rias
D1H2: 2 mat=E9rias (para n=E3o repetir a utilizada em= D1H1)
D1: 6 possibilidades

Para D2, se escolhermos uma j=E1 util= izada em D1 ent=E3o n=E3o poderemos
utilizar a outra mat=E9ria utilizada= em D1, sen=E3o D3 teria as mesmas
mat=E9rias. Assim, para D2 ter=EDamos uma j=E1 utilizada (2 mat=E9rias) e u= ma
n=E3o utilizada. Logo, 2*1 =3D 2. Como a ordem importa, temos 2*2 =3D= 4.

D3 s=F3 possui 2 formas, com as ordens das mat=E9rias trocadas.<= br>
Total: 6*4*2 =3D 48.

Essa =E9 uma forma mais l=F3gica de resolver o problema. Estive tentand= o
utilizar combinat=F3ria e tamb=E9m achei a resposta 48.

Sejam A= ,B,C as mat=E9rias. Quantas permuta=E7=F5es diferentes existem entre
A,A= ,B,B,C,C? Cada posi=E7=E3o seria um hor=E1rio em um dia, ou seja,
D1H1_D1H2_D2H1_D2H2_D3H1_D3H2. Bastaria calcular o n=FAmero de
permuta= =E7=F5es com repeti=E7=E3o, ou seja, 6!/(2!*2!*2!) =3D 720/8 =3D 90.
Sabemos que n=E3o podemos ter uma permuta=E7=E3o do tipo AABCBC, pois AArepresenta a mesma mat=E9ria em D1H1 e D1H2. Ent=E3o sabemos que a
resposta =E9 menor que 90.

As formas inv=E1lidas ser=E3o:

Se = as 3 mat=E9rias do mesmo tipo est=E3o juntas no mesmo dia, ex: AABBCC.
E= xistem 3! =3D 6 formas, considerando AA,BB,CC como 3 elementos
permutado= s entre si.

N=E3o h=E1 necessidade de verificar quando 2 mat=E9rias est=E3o no mesm= o dia
pois cai no caso acima.

Quando h=E1 apenas 1 mat=E9ria repe= tida em 1 dia, ex: AABCBC, ent=E3o temos
12 formas para cada par da mesm= a mat=E9ria utilizada no mesmo dia. Se AA
est=E1 em D1 ent=E3o D2 pode ser BC ou CB e D3 pode ser BC ou CB, 2*2 =3D 4= .
AA pode estar em D1,D2,D3. Assim, 4*3 =3D 12. Para BB e CC seria o
= mesmo, dando um total de 3*12 =3D 36 formas quando h=E1 apenas uma mat=E9ri= a
que se repete no mesmo dia.

Assim, o total seria 90 - (6+36) =3D 90 - 42 =3D 48 formas distintas de=
compor o hor=E1rio

Thelio, voc=EA poderia passar a fonte do prob= lema e verificar se as
respostas s=E3o essas mesmo?

On 3/13/08, T= helio Gama <teliogama@gmail.com> wrote:
> =C9 pessoal...
>
> Achei muito dif=EDcil esta quest=E3o. A= grade=E7o se algu=E9m puder explic=E1-la.
>
> Thelio
>> uma turma tem aulas =E0s 2=AA, 4=AA e 6=AA feiras, de 8-9 horas e de = 11-12 horas. As
> mat=E9rias s=E3o portugues, matem=E1tica e ingles, cada uma com duas a= ulas
> semanais, em dias diferentes. De quantos modos pode ser feito = o hor=E1rio
> dessa turma?
> a)96  ; b) 144 &nbs= p; ; c)192   ; d) 6!    ; e) 120


--
Henrique

=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D
Instru=E7=F5es para entrar na lista, sair da li= sta e usar a lista em
http://www.mat.puc-rio.br/~obmlistas/obm-l.html
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D

------=_Part_23995_9903530.1206624175445-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Mar 27 10:56:49 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2RDteWA017159 for ; Thu, 27 Mar 2008 10:55:40 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2RDtdqP017155 for obm-l-MllGbsmmN; Thu, 27 Mar 2008 10:55:39 -0300 Received: from web31704.mail.mud.yahoo.com (web31704.mail.mud.yahoo.com [68.142.201.184]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id m2RDtNWA017091 for ; Thu, 27 Mar 2008 10:55:31 -0300 Received: (qmail 73492 invoked by uid 60001); 27 Mar 2008 13:55:05 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:Date:From:Subject:To:MIME-Version:Content-Type:Content-Transfer-Encoding:Message-ID; b=m8x0vBJsKkt5ViP0jlejzKaG20NVt/d6SK4LtlcpIrDpX1JwxVvjSNKQXreZ/DQHDEwFxuQH2KiPTa+/4/oA7cNBzO4Tz/krmOPt/N/Rg77MbuF4qCMoyUD55Tl/W33y3DHThNmKleVglWsdj5rihIBv2Tv6JKSm6Ez8biE1VGY=; X-YMail-OSG: ScMuMeAVM1lmcfbS1HhkzbNJJtAoKCisaVf4q80DvjULMtKvKu00QOvvuy6nGQA85vJNj2KghePuLVAQU9L4QkVWbhFC9gpBLUIzxR0rIAzAmbFSsZuwSYDp3u5Jag-- Received: from [201.50.246.201] by web31704.mail.mud.yahoo.com via HTTP; Thu, 27 Mar 2008 10:55:04 ART Date: Thu, 27 Mar 2008 10:55:04 -0300 (ART) From: Eder Albuquerque Subject: [SPAM] [obm-l] mdc To: Lista OBM MIME-Version: 1.0 Content-Type: text/plain Content-Transfer-Encoding: 7bit Message-ID: <973167.73049.qm@web31704.mail.mud.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Eder Albuquerque X-Spam-Status: Yes, hits=7.6 required=5.0 tests=FORGED_YAHOO_RCVD,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, SPAM_PHRASE_00_01,SPAM_REDIRECTOR,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******* X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="0-2007270386-1206626104=:73049" X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (7.60 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: SPAM_REDIRECTOR (0.4 points) URI: Uses open redirection service SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 184.201.142.68.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 184.201.142.68.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- --0-2007270386-1206626104=:73049 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 8bit Pessoal, o problema a seguir caiu numa prova de teoria dos números que fiz ontem e foi a única dúvida... Provar: mdc(a,b)= 1 => mdc(a+b,a²-ab+b²) =1 ou 3 Agradeço se alguém mostrar como se prova. Eder --------------------------------- Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-2007270386-1206626104=:73049 Content-Type: text/html; charset=iso-8859-1 Content-Transfer-Encoding: 8bit
Pessoal, o problema a seguir caiu numa prova  de teoria dos números que fiz ontem e foi a única dúvida...
 
Provar:
 
mdc(a,b)= 1   =>  mdc(a+b,a²-ab+b²) =1 ou 3
 
Agradeço se alguém mostrar como se prova.
 
Eder

Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-2007270386-1206626104=:73049-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Mar 27 11:11:06 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2RE9JWA018212 for ; Thu, 27 Mar 2008 11:09:19 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2RE9IMe018209 for obm-l-MllGbsmmN; Thu, 27 Mar 2008 11:09:18 -0300 Received: from rn-out-0910.google.com (rn-out-0910.google.com [64.233.170.186]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2RE9EWA018200 for ; Thu, 27 Mar 2008 11:09:15 -0300 Received: by rn-out-0910.google.com with SMTP id a46so2793898rne.9 for ; Thu, 27 Mar 2008 07:08:57 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; bh=LyDF7VVdBcWekDeMn080jfkYvi0LIGGe1yOPOAhBjKc=; b=n64SwqBXWgQTt+QpNr0WewLe1zg/QTijySHVDGP12iaiD3phZf4jaaiy3KjzUFFTiWvcqwkS7w+Niy/MxGJsHb/ggy94vqyM5xWdMrCM9Kke2OYoPYsCRSFz8hBy0yHy51u/locMxtjQjCcPTcA6/bg/Rt7mdG3jZKApa6dCysM= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; b=O4IzdXDnoetYcx1f7fCTjt3PpzIiGbYNaqCl7KsvPzAr8qb57AF0abBHR2hgN3Jfes3hKgc5JgKQnT4m14DuIUzpl/wW1WjaVoHAFZpOSMIjNvrTQuWbX4R8X3ArMcXMbV/7S5hfkXCkQBltnYM1FrP+KE35Oe1mnGwf+ix/kVc= Received: by 10.142.187.2 with SMTP id k2mr1153168wff.25.1206626936976; Thu, 27 Mar 2008 07:08:56 -0700 (PDT) Received: by 10.143.5.12 with HTTP; Thu, 27 Mar 2008 07:08:56 -0700 (PDT) Message-ID: Date: Thu, 27 Mar 2008 11:08:56 -0300 From: "Eike Santos" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Computaca Grafica!!! In-Reply-To: MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline References: Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m2RE9HWA018205 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Eike Santos" X-Spam-Status: No, hits=4.9 required=5.0 tests=IN_REP_TO,PLING_PLING,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SIGNATURE_LONG_SPARSE, SPAM_PHRASE_00_01,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** Estudou sobre o modelo de Monte Carlo? e Photon Mapping? Ats, Marcos Eike 2008/3/27 Tiago Machado : > sim. estudei na disciplina de processamento gráfico. > > 2008/3/27 Eike Santos : > > > > Mas, vc tem estudado ou estudou Rendering? > > > > Ats, > > Marcos Eike > > > > 2008/3/27 Tiago Machado : > > > > > > > > > Atualmente estou trabalhando na area de computação gráfica e técnicas > > > interativas. > > > > > > 2008/3/26 Eike Santos : > > > > > > > > > > Blz. Rapaz... Tem msn? > > > > Trabalha em que área? Atualmente estou estudando Rendering! > > > > > > > > Ats, > > > > Marcos Eike > > > > > > > > 2008/3/26 Tiago Machado : > > > > > > > > > > > > > > > > > Oi Eike, > > > > > > > > > > Faço IC na area de computação gráfica. > > > > > > > > > > > > > > > > > > > > On Wed, Mar 26, 2008 at 7:09 PM, Eike Santos > > > wrote: > > > > > > > > > > > > > > > > > > > > > > > > Alguem esta trabalhando ou gosta de computacao gráfica em geral > aqui > > > > > > na lista? Vamos trocas info? Dúvidas e coisas afim? > > > > > > > > > > > > Ats, > > > > > > -- > > > > > > Marcos Eike Tinen dos Santos > > > > > > +559881176565 > > > > > > > > > > > > OpenSuse- Comunidade Open do Suse > > > > > > www.opensuse.org > > > > > > OpenSolaris- Comunidade Open do Solaris > > > > > > www.opensolaris.org > > > > > > > > > > > > > > > > ========================================================================= > > > > > > Instruções para entrar na lista, sair da lista e usar a lista em > > > > > > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > > > > > > > > > > ========================================================================= > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > -- > > > > > > > > > > > > > > > > Marcos Eike Tinen dos Santos > > > > +559881176565 > > > > > > > > OpenSuse- Comunidade Open do Suse > > > > www.opensuse.org > > > > OpenSolaris- Comunidade Open do Solaris > > > > www.opensolaris.org > > > > > > > > > ========================================================================= > > > > Instruções para entrar na lista, sair da lista e usar a lista em > > > > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > > > > > ========================================================================= > > > > > > > > > > > > > > > > > > -- > > > > > > > > Marcos Eike Tinen dos Santos > > +559881176565 > > > > OpenSuse- Comunidade Open do Suse > > www.opensuse.org > > OpenSolaris- Comunidade Open do Solaris > > www.opensolaris.org > > > > ========================================================================= > > Instruções para entrar na lista, sair da lista e usar a lista em > > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > > ========================================================================= > > > > -- Marcos Eike Tinen dos Santos +559881176565 OpenSuse- Comunidade Open do Suse www.opensuse.org OpenSolaris- Comunidade Open do Solaris www.opensolaris.org ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Mar 27 12:03:07 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2RF1uWA022706 for ; Thu, 27 Mar 2008 12:01:56 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2RF1upM022704 for obm-l-MllGbsmmN; Thu, 27 Mar 2008 12:01:56 -0300 Received: from hm171.locaweb.com.br (hm171-2.locaweb.com.br [200.234.205.179]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id m2RF1tWA022700 for ; Thu, 27 Mar 2008 12:01:55 -0300 Received: (qmail 19036 invoked from network); 27 Mar 2008 15:01:43 -0000 Received: from unknown (10.1.10.169) by hm171.locaweb.com.br with QMQP; 27 Mar 2008 15:01:43 -0000 Received: from unknown (HELO lattes) (paulo@uniredes.org@189.24.241.229) by hm169.locaweb.com.br with SMTP; 27 Mar 2008 15:01:47 -0000 From: "Paulo - Uniredes" To: Subject: [SPAM] [obm-l] =?iso-8859-1?Q?RES:_=5Bobm-l=5D_RES:_=5Bobm-l=5D_Indica=E7=E3o_de_livros_?= =?iso-8859-1?Q?=28C=E1lculo_num=E9rico_e_Equa=E7=F5es_diferenciais=29?= Date: Thu, 27 Mar 2008 12:02:01 -0300 Organization: Uniredes Message-ID: MIME-Version: 1.0 Content-Type: text/plain X-Mailer: Microsoft Office Outlook, Build 11.0.5510 Thread-Index: AciPOGGx8ImhUcaRQCWuOrTDDqKmvgA4o9Mg In-Reply-To: <5bb472220803260430r477d89f3ye1066bd076953c7d@mail.gmail.com> X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.3198 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Paulo - Uniredes" X-Spam-Status: Yes, hits=7.8 required=5.0 tests=HTML_FONT_COLOR_BLUE,IN_REP_TO,MISSING_OUTLOOK_NAME, MSGID_CHARS_SPAM,MSGID_CHARS_WEIRD,NOSPAM_INC,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******* X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_NextPart_000_0000_01C89002.5F251820" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (7.80 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: NOSPAM_INC (-0.2 points) Where are you working at? SPAM: MSGID_CHARS_WEIRD (1.6 points) Message-Id has characters often found in spam SPAM: MSGID_CHARS_SPAM (0.1 points) Message-Id has characters indicating spam SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: HTML_FONT_COLOR_BLUE (0.2 points) BODY: HTML font color is blue SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 179.205.234.200.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 179.205.234.200.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: MISSING_OUTLOOK_NAME (1.1 points) Message looks like Outlook, but isn't SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- This is a multi-part message in MIME format. ------=_NextPart_000_0000_01C89002.5F251820 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Oi mestre Jo=E3o, =20 Os pre=E7os est=E3o em http://uniredes.org/loja01 =20 Sinceramente, n=E3o sei se voc=EA ficar=E1 satisfeito com o Pacitti I. O = ideal seria o volume II. Vou ver se ainda tenho na casa de minha m=E3e. Se sua leitura de espanhol for boa, vou recomendar outro, o Gastinel.=20 =20 Divirta-se. =20 []s =20 Paulo. =20 _____ =20 De: owner-obm-l@mat.puc-rio.br [mailto:owner-obm-l@mat.puc-rio.br] Em = nome de Joao Victor Brasil Enviada em: quarta-feira, 26 de mar=E7o de 2008 08:31 Para: obm-l@mat.puc-rio.br Assunto: Re: [obm-l] RES: [obm-l] Indica=E7=E3o de livros (C=E1lculo = num=E9rico e Equa=E7=F5es diferenciais) Paulo,=20 =20 Quanto voc=EA quer neste livros? Os do Piskonov, Apostol e Pacitti. =20 Joao Victor =20 ------=_NextPart_000_0000_01C89002.5F251820 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable
Oi mestre Jo=E3o,
 
Os pre=E7os est=E3o em http://uniredes.org/loja01=
 
Sinceramente, n=E3o sei se voc=EA ficar=E1 = satisfeito com o=20 Pacitti I. O ideal seria o volume II. Vou ver se ainda tenho na casa de = minha=20 m=E3e. Se sua leitura de espanhol for boa, vou recomendar outro, o = Gastinel.=20
 
Divirta-se.
 
[]s
 
Paulo.
 

De: owner-obm-l@mat.puc-rio.br=20 [mailto:owner-obm-l@mat.puc-rio.br] Em nome de Joao Victor=20 Brasil
Enviada em: quarta-feira, 26 de mar=E7o de 2008=20 08:31
Para: obm-l@mat.puc-rio.br
Assunto: Re: = [obm-l] RES:=20 [obm-l] Indica=E7=E3o de livros (C=E1lculo num=E9rico e Equa=E7=F5es=20 diferenciais)

Paulo,
 
Quanto voc=EA quer neste livros? Os do Piskonov, Apostol e = Pacitti.
 
Joao Victor

 
------=_NextPart_000_0000_01C89002.5F251820-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Mar 27 12:17:34 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2RFGPWA023617 for ; Thu, 27 Mar 2008 12:16:25 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2RFGOWv023615 for obm-l-MllGbsmmN; Thu, 27 Mar 2008 12:16:24 -0300 Received: from ti-out-0910.google.com (ti-out-0910.google.com [209.85.142.184]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2RFGGWA023604 for ; Thu, 27 Mar 2008 12:16:21 -0300 Received: by ti-out-0910.google.com with SMTP id y6so1685930tia.13 for ; Thu, 27 Mar 2008 08:15:59 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:mime-version:content-type:content-transfer-encoding:content-disposition; bh=jRKDbBr4PsMjJrt//8doE7epFHeqH06zRkboimu0pD4=; b=kYTmYdo0ozy4irI83cb8YKSjWxe+Vbif1NC+sJGSRJiSUZ3e5jXWDYmtcFC9LQU4XjOCwdqXrpcvCWdEc6B28bwHqwyLG/SsUSs+/cizhMfhJOtP+yDkFMCT7SqAfKdqOU7ct+gJxdtLQuYiM38R3G75VIYYqTxbR+YxdN/rTts= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:mime-version:content-type:content-transfer-encoding:content-disposition; b=BWjwFqOEjtEWLuzbk62DEukF5RfAJLHBeku4jOAE8sWU3y3BcXLAO86mQCpqA38/qDzC97FnD6haDpwCBJU5tfThneNMtQ605G2k5fSQnQx9QbwwHqyBFFPUgRBTO85y3Cdbnp6rvPVAgYhGN86wzGUjX/zGgFepjBErsHf+/ck= Received: by 10.150.123.16 with SMTP id v16mr848505ybc.156.1206630957491; Thu, 27 Mar 2008 08:15:57 -0700 (PDT) Received: by 10.150.144.4 with HTTP; Thu, 27 Mar 2008 08:15:57 -0700 (PDT) Message-ID: Date: Thu, 27 Mar 2008 12:15:57 -0300 From: "Paulo Santa Rita" To: obm-l@mat.puc-rio.br Subject: [obm-l] Exercicios de Analise 2 MIME-Version: 1.0 Content-Type: text/plain; charset=WINDOWS-1252 Content-Disposition: inline Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m2RFGOWA023613 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Paulo Santa Rita" X-Spam-Status: No, hits=4.7 required=5.0 tests=AWL,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** Ola Pessoal, Seguem mais 3 exercicios ( EXERCICIO 4.3 ) Dado E > 0. Como lim X2n=a, existe um natural par N1 tal que para todo numero par "n" com n > N1 teremos | Xn – a | < E. Igualmente, como lim X2n-1=a, existe um natural impar N2 tal que para todo numero impar "n" com n > N2 teremos | Xn – a | < E. Seja N3=max{N1,N2}. Se n > N3, seja "n" par ou impar, | Xn – a | < E, isto e, para todo natural "n" tal que n > N3 => | Xn – a | < E => lim Xn = a ( EXERCICIO 4.4 ) Vou representar por Nij os naturais do conjunto Ni. Assim, exemplificando, os naturais pertencentes a N3 são N31, N32, ... Dado E > 0. 1) Como LIM Xn = a, n em N1, existe um N10 tal que para todo n em N1 e n > N10 teremos | Xn – a | < E 2) Como LIM Xn = a, n em N2, existe um N20 tal que para todo n em N2 e n > N20 teremos | Xn – a | < E ... K) Como LIM Xn = a, n em Nk, existe um Nk0 tal que para todo n em Nk e n > Nk0 teremos | Xn – a | < E Seja N0 = max{ N10, N20, ..., NK0 }. Seja n um natural qualquer tal que n > N0. Como n estara em algum Ni ( pois a uniao de todos os Ni e o conjunto de todos os naturais ) segue que n > N0 = max{ N10, N20, ..., NK0 } >= Ni0 => N > Ni0 => | Xn – a | < E. Assim, para todo E > 0 exibimos um natural N0 = max{ N10, N20, ..., Nk0 } tal que para todo n > N0 teremos | Xn – a | < E, isto e, LIM Xn = a ( EXERCICIO 4.5 ) O autor da uma SUGESTAO, vale dizer, da a SOLUCAO. Para que voces possam se enriquecer ainda mais, aqui vai uma solucao diferente, sem usar a sugestao do Autor. Para cada k natural, seja Pk o K-esimo numero primo. Assim, a titulo de exemplificacao, teriamos P1=2, P2=3, P3=5, ... Definimos agora a sequencia de conjuntos : Nk = { Pk } uniao { todos os naturais NAO-PRIMOS divisiveis por exatamente K primos } k = 1, 2, ... Assim, por exemplo : N1 = { 2 } uniao { 2^L, 3^L, 5^L, ..., (NUMERO PRIMO)^L, ... } , onde L > 1 N2 = { 3 } uniao { ( (P1)^L)*( (P2)^M ) onde P1 e P2 são primos }, L,M > 0 e assim sucessivamente. OBS : coloque o 1 em N1 E facil ver que N = N1 uniao N2 uniao ... uniao Nk uniao ... e que cada Nk e por si um conjunto infinito. Assim, decompomos N, conjunto dos numeros naturais, numa infinidade de conjuntos infinitos tal como o autor pede. Alias, fizemos mais que isso : decompomos N numa infinidade de conjuntos infinitos dois a dois disjuntos ! Agora, seja "a" um real fixo qualquer. Para cada n em Nk facamos : 1) Xn = Pk se n = Pk 2) Xn = ((N – 1) / N)*a se n # Pk Fazendo "n" variar dentro de Nk e facil ver que LIM Xn = a, bastando considerar os "n" de Nk tais que n > Pk, pois LIM Xn = a*LIM((N-1)/N) = a e este limite não se altera se retirarmos uma quantidade finita ( os "n" =< Pk ) de termos. Assim, em todo Nk temos que LIM Xn = a, "n" variando em Nk. Mas não ocorre que LIM Xn = a, "n" variando nos Naturais ... Para ver isso claramente, seja dado E > 0. Como "a" e fixo e o conjunto dos numeros primos e ilimitado, para todo natural N0 fixado existe um primo Pk > max{ N0, a+E}. Como, por definicao, Xpk = Pk => | Xpk – a | > E, ou seja, para todo No fixado e possivel encontrar um natural "n" tal que | Xn – a | > E, vale dizer, LIM Xn # a, como queriamos demonstrar. Um Abraco a Todos ! Paulo Santa Rita 5,0C0D,1B0308 ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Mar 27 12:46:15 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2RFjFWA028202 for ; Thu, 27 Mar 2008 12:45:15 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2RFjEl7028197 for obm-l-MllGbsmmN; Thu, 27 Mar 2008 12:45:14 -0300 Received: from py-out-1112.google.com (py-out-1112.google.com [64.233.166.180]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2RFjBWA028142 for ; Thu, 27 Mar 2008 12:45:12 -0300 Received: by py-out-1112.google.com with SMTP id f47so4494846pye.14 for ; Thu, 27 Mar 2008 08:44:55 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:reply-to:to:subject:mime-version:content-type; bh=chIHQASxfh0rGPQa/JtrDExnjTAIyxhK95VqRzut8CE=; b=myHwpnzr6dNNb7rVo3EVZUDrmE4deMIs8TftSKxEvFfu0k6JpqM8UB2/uSLvkStgNoJ/iwVWRnfsOls3IlhGkcghoVbFhlAbk92lMTwTqohNIzeFl5j19qcqWDy529AZAfwXksIMSH+wVt5BhbBFgvsJtekKEul3Yz22oZcJ6vM= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:reply-to:to:subject:mime-version:content-type; b=VnTheLjfdtQL5kBhVEcr+SnnwUZ0Gsg6SYYxNsYfAsjBeWYNLtkl62eawgjeni/MQ2XiyF5Y7Rv6vwDi7wR+8h7TW95WAkiEm19qKNPvm5W7E6j40cI4PjduqBwR+PmVooSnEGMYR2KuKLRYjlToMVqYFmBYdsYJazHU+ODGL3Y= Received: by 10.65.105.3 with SMTP id h3mr3528064qbm.43.1206632694696; Thu, 27 Mar 2008 08:44:54 -0700 (PDT) Received: by 10.65.122.4 with HTTP; Thu, 27 Mar 2008 08:44:54 -0700 (PDT) Message-ID: Date: Thu, 27 Mar 2008 12:44:54 -0300 From: "=?ISO-8859-1?Q?Vin=EDcius_Almeida?=" To: obm-l@mat.puc-rio.br Subject: [SPAM] [obm-l] =?ISO-8859-1?Q?D=FAvida?= MIME-Version: 1.0 Content-Type: text/plain Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "=?ISO-8859-1?Q?Vin=EDcius_Almeida?=" X-Spam-Status: Yes, hits=5.1 required=5.0 tests=AWL,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ***** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_Part_12343_30213105.1206632694690" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (5.10 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 180.166.233.64.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 180.166.233.64.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-0.7 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- ------=_Part_12343_30213105.1206632694690 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Seja um tri=E2ngulo ABC aonde =C2 =3D 100=BA e existe um ponto D, sobre o l= ado AC tal que AC =3D BD. Sabe-se ainda que AD =3D AB. Qual o valor do =C2ngulo C? Se algu=E9m puder me ajudar seria bom, eu to quebrando a cabe=E7a a um temp= o. aquele abra=E7o ------=_Part_12343_30213105.1206632694690 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline
Seja um tri=E2ngulo ABC aonde =C2 =3D 100=BA e existe um ponto D, sobr= e o lado AC
tal que AC =3D BD. Sabe-se ainda que AD =3D AB. Qual o valor= do =C2ngulo C?
 
Se algu=E9m puder me ajudar seria bom, eu to quebrando a cabe=E7a a um= tempo.
aquele abra=E7o
------=_Part_12343_30213105.1206632694690-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Mar 27 12:52:43 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2RFpcWA030687 for ; Thu, 27 Mar 2008 12:51:38 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2RFpceR030685 for obm-l-MllGbsmmN; Thu, 27 Mar 2008 12:51:38 -0300 Received: from smtp.uol.com.br (smtps.uol.com.br [200.221.4.131]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2RFpZWA030641 for ; Thu, 27 Mar 2008 12:51:35 -0300 Received: from localhost (localhost [127.0.0.1]) by socom4.uol.com.br (Postfix) with ESMTP id 8982FE0115E1 for ; Thu, 27 Mar 2008 12:51:19 -0300 (BRT) Received: from MARTE (unknown [200.128.35.134]) by socom4.uol.com.br (Postfix) with ESMTP id 4E8BDE002BA4 for ; Thu, 27 Mar 2008 12:51:18 -0300 (BRT) Message-ID: <98D269A7986D488F868969A11534ED51@MARTE> From: "Ojesed Mirror" To: References: In-Reply-To: Subject: [SPAM] Re: [obm-l] Computaca Grafica!!! 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O moderador vai "puxar as orelhas" de vocês. Troquem logo seus emails pessoais e caiam fora numa boa. Ojesed. ----- Original Message ----- From: "Eike Santos" To: Sent: Thursday, March 27, 2008 11:08 AM Subject: Re: [obm-l] Computaca Grafica!!! Estudou sobre o modelo de Monte Carlo? e Photon Mapping? Ats, Marcos Eike 2008/3/27 Tiago Machado : > sim. estudei na disciplina de processamento gráfico. > > 2008/3/27 Eike Santos : > > > > Mas, vc tem estudado ou estudou Rendering? > > > > Ats, > > Marcos Eike > > > > 2008/3/27 Tiago Machado : > > > > > > > > > Atualmente estou trabalhando na area de computação gráfica e técnicas > > > interativas. > > > > > > 2008/3/26 Eike Santos : > > > > > > > > > > Blz. Rapaz... Tem msn? > > > > Trabalha em que área? Atualmente estou estudando Rendering! > > > > > > > > Ats, > > > > Marcos Eike > > > > > > > > 2008/3/26 Tiago Machado : > > > > > > > > > > > > > > > > > Oi Eike, > > > > > > > > > > Faço IC na area de computação gráfica. > > > > > > > > > > > > > > > > > > > > On Wed, Mar 26, 2008 at 7:09 PM, Eike Santos > > > wrote: > > > > > > > > > > > > > > > > > > > > > > > > Alguem esta trabalhando ou gosta de computacao gráfica em geral > aqui > > > > > > na lista? Vamos trocas info? Dúvidas e coisas afim? > > > > > > > > > > > > Ats, > > > > > > -- > > > > > > Marcos Eike Tinen dos Santos > > > > > > +559881176565 > > > > > > > > > > > > OpenSuse- Comunidade Open do Suse > > > > > > www.opensuse.org > > > > > > OpenSolaris- Comunidade Open do Solaris > > > > > > www.opensolaris.org > > > > > > > > > > > > > > > > ========================================================================= > > > > > > Instruções para entrar na lista, sair da lista e usar a lista em > > > > > > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > > > > > > > > > > ========================================================================= > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > -- > > > > > > > > > > > > > > > > Marcos Eike Tinen dos Santos > > > > +559881176565 > > > > > > > > OpenSuse- Comunidade Open do Suse > > > > www.opensuse.org > > > > OpenSolaris- Comunidade Open do Solaris > > > > www.opensolaris.org > > > > > > > > > ========================================================================= > > > > Instruções para entrar na lista, sair da lista e usar a lista em > > > > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > > > > > ========================================================================= > > > > > > > > > > > > > > > > > > -- > > > > > > > > Marcos Eike Tinen dos Santos > > +559881176565 > > > > OpenSuse- Comunidade Open do Suse > > www.opensuse.org > > OpenSolaris- Comunidade Open do Solaris > > www.opensolaris.org > > > > ========================================================================= > > Instruções para entrar na lista, sair da lista e usar a lista em > > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > > ========================================================================= > > > > -- Marcos Eike Tinen dos Santos +559881176565 OpenSuse- Comunidade Open do Suse www.opensuse.org OpenSolaris- Comunidade Open do Solaris www.opensolaris.org ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Mar 27 13:03:57 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2RG2rWA002485 for ; Thu, 27 Mar 2008 13:02:53 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2RG2r0j002480 for obm-l-MllGbsmmN; Thu, 27 Mar 2008 13:02:53 -0300 Received: from mu-out-0910.google.com (mu-out-0910.google.com [209.85.134.187]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2RG2iWA002406 for ; Thu, 27 Mar 2008 13:02:50 -0300 Received: by mu-out-0910.google.com with SMTP id w8so5642095mue.1 for ; Thu, 27 Mar 2008 09:02:26 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; bh=6ubydtuurGgy8WKGbk4aFmoAwiv2dqua3IiAis6oRTw=; b=oP1GoCyovmG99DihCXg5vfHunJQ+2TWIvaKC8LuwqRPIxJqcW0urGFC09Pm9DJritU9oZu1O02nzhBd8VF+dbQNT4nJGUQoF1gmaE+JXVzVc8wyVzWjsk9TGpfS09NDHSa7YkmdIhj3VQujjBH9hPLUdFsP4Lg5YlL3o2ph/U0g= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; b=lZeN7PFX2L9rS/jOjyz+pokdmYV5wVEeo4lplNM3raBWpGlGWcuokUo7k6fj7aXcx6XgtcoJPIK/MoCErNKBJIO+U67bhKLH0NlQ0U3muLq9WZ6Fgmdr88hGgnPDdnr5/0qpxnOFrNGctS0XL5xhxIURiBvCpkGegtxHAEgy5jI= Received: by 10.82.170.3 with SMTP id s3mr2542447bue.18.1206633746113; Thu, 27 Mar 2008 09:02:26 -0700 (PDT) Received: by 10.82.127.13 with HTTP; Thu, 27 Mar 2008 09:02:26 -0700 (PDT) Message-ID: Date: Thu, 27 Mar 2008 13:02:26 -0300 From: "Johann Peter Gustav Lejeune Dirichlet" To: obm-l@mat.puc-rio.br Subject: =?ISO-8859-1?Q?Re:_[obm-l]_Problema_Combinat=F3ria?= In-Reply-To: MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline References: Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m2RG2qWA002471 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Johann Peter Gustav Lejeune Dirichlet" X-Spam-Status: No, hits=2.7 required=5.0 tests=AWL,FROM_ENDS_IN_NUMS,IN_REP_TO,QUOTED_EMAIL_TEXT, RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,REFERENCES, SIGNATURE_LONG_SPARSE,SPAM_PHRASE_00_01,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: ** São 24 livros de assuntos distintos? E os livros estão grudados na estante (se o de Teoria da Computação está do lado de Linguagens Formais, eles sempre estarão lado a lado?) Bem, seria algo como escolher cinco números não-consecutivos do conjunto {1,2,3,4\ldots,24}. Acho que dá pra usar alguma recursão. Vou pensar um pouco antes de continuar... Em 26/03/08, MauZ escreveu: > Olá a todos! > > Numa estante com 24 livros, de quantas maneiras posso retirar 5 livros sem > ter nenhum consecutivo? E no caso de n livros, quantas maneiras retiro p > livros sem ter nenhum consecutivo? > > > > Pra completar vou colocar parte da minha tentativa de solução, preciso de > ajuda pra saber se está certo até onde fiz e como finalizar pois empaquei. > > Fiz dessa forma: Todas Combinações - Combinações c/ Consecutivos > > Todas: 24!/5!19! > Consecutivos: 23!/4!19! + 22!/3!19! + 21!/2!19! + 20!/1!19! > > Fiz uma formula geral com n e p e deu o seguinte: > > n!/p!(n-p!) - [(n-1)!/(p-1)!(n-p)! + > (n-2)!/(p-2)!(n-p)!+...+(n-p+1)!/(n-p)!] > > Fatorando deu: > > (1/(n-p)!)[n!/p!-(n-1)!/(p-1)!-(n-2)!/(p-2)-...-(n-p+1)!/(n-p)!] > > Dae empaquei de vez... Não consegui continuar! > Quem souber fazer por favor me dê a luz! Ou simplesmente indique o erro no > meu raciocínio. > > Agradeço antecipadamente, > Maurizio > > -- Ideas are bulletproof. V ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Mar 27 15:46:52 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2RIjEWA020819 for ; Thu, 27 Mar 2008 15:45:14 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2RIjEni020817 for obm-l-MllGbsmmN; Thu, 27 Mar 2008 15:45:14 -0300 Received: from hm171.locaweb.com.br (hm171-2.locaweb.com.br [200.234.205.179]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id m2RIj2WA020799 for ; Thu, 27 Mar 2008 15:45:03 -0300 Message-Id: <200803271845.m2RIj2WA020799@saci.mat.puc-rio.br> Received: (qmail 24242 invoked from network); 27 Mar 2008 18:44:51 -0000 Received: from unknown (10.1.10.169) by hm171.locaweb.com.br with QMQP; 27 Mar 2008 18:44:51 -0000 Received: from unknown (HELO lattes) (paulo@uniredes.org@189.24.241.229) by hm169.locaweb.com.br with SMTP; 27 Mar 2008 18:44:58 -0000 From: "Paulo - Uniredes" To: Subject: [SPAM] [obm-l] =?iso-8859-1?Q?Conjuntos_num=E9ricos_na_Reta...?= Date: Thu, 27 Mar 2008 15:45:12 -0300 Organization: Uniredes MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" X-Mailer: Microsoft Office Outlook, Build 11.0.5510 Thread-Index: AciQLYBFDny6V/elRtm3JEV/gZGI4gADH0qw In-Reply-To: X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.3198 Content-Transfer-Encoding: 7bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m2RIj7WA020813 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Paulo - Uniredes" X-Spam-Status: Yes, hits=6.9 required=5.0 tests=AWL,IN_REP_TO,MISSING_OUTLOOK_NAME,MSG_ID_ADDED_BY_MTA_2, NOSPAM_INC,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, SPAM_PHRASE_00_01,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ****** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (6.90 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: NOSPAM_INC (-0.2 points) Where are you working at? SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: MSG_ID_ADDED_BY_MTA_2 (0.1 points) 'Message-Id' was added by a relay (2) SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 179.205.234.200.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 179.205.234.200.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: MISSING_OUTLOOK_NAME (1.1 points) Message looks like Outlook, but isn't SPAM: AWL (0.9 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- Como é que sabemos que os conjuntos já conhecidos são suficientes para representar números da Reta Real ? Existe alguma prova de que eles são necessários e sufucientes ? Explico: Temos os naturais Depois estendemos o conceito para os inteiros... Depois os racionais... Depois os irracionais... Bom, que me garante que não há número, na reta, que não se enquadre em qualquer desses conjuntos ? Há algum teorema "mágico" que diga isso, como existe o maravilhoso Teorema de Gödel sobre a inconsistência da lógica ? []s --- Paulo C. Santos (PC) e-mail: paulo@uniredes.org Homepage: http://uniredes.org Tel.: (21) 2510.8783 - Cel.: (21) 8753-0729 -------------------------------------------- MS-Messenger: Uniredes_Br@hotmail.Com ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Mar 27 16:31:53 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2RJUiWA023428 for ; Thu, 27 Mar 2008 16:30:44 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2RJUibg023425 for obm-l-MllGbsmmN; Thu, 27 Mar 2008 16:30:44 -0300 Received: from yw-out-2324.google.com (yw-out-2324.google.com [74.125.46.29]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2RJUgWA023417 for ; Thu, 27 Mar 2008 16:30:42 -0300 Received: by yw-out-2324.google.com with SMTP id 3so80869ywj.9 for ; Thu, 27 Mar 2008 12:30:25 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; bh=h9g+OSvW+Q9hfEbLpPFbyd5kCfoww91t8wmPWVU5dsw=; b=Yx8FoADuZpQdJ/NqIWYNNlgBXH+159dxf7Thkw/v4Kve1O6aXvg0m2p7UEXDh/jP2UwEX39S6bTF6AlmL15m9uy7oxjOsK3DiOTLu/gDji8LXkSk4wJXM+eNtjHUoaGKJ0fkP0FSbo1IN4AM+RWNOreZBrYbnyyJXrWOZ1ska7A= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; b=l/WQotLK26MevfBneLmaAKlUH5kAqAtjM9u99s7Z2baV8iaHVydfYHnvSVkNtnXtEAcqdN8iw57K5W5MdvXyxis2fCWLo/mexZ3X/5pvvy9T/sjijLHv5B048dridLIL831h0wN2Ub2k/X1mIraZ58HL6p8AR20H2N3TW6KjG7M= Received: by 10.150.192.7 with SMTP id p7mr1024648ybf.159.1206646224425; Thu, 27 Mar 2008 12:30:24 -0700 (PDT) Received: by 10.150.152.11 with HTTP; Thu, 27 Mar 2008 12:30:24 -0700 (PDT) Message-ID: <2d483c770803271230tc8e3041vfda8ab9cfcbfe8bb@mail.gmail.com> Date: Thu, 27 Mar 2008 16:30:24 -0300 From: "Ralph Teixeira" To: obm-l@mat.puc-rio.br Subject: =?ISO-8859-1?Q?Re:_[obm-l]_Conjuntos_num=E9ricos_na_Reta...?= In-Reply-To: <200803271845.m2RIj2WA020799@saci.mat.puc-rio.br> MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline References: <200803271845.m2RIj2WA020799@saci.mat.puc-rio.br> Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m2RJUhWA023422 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Ralph Teixeira" X-Spam-Status: No, hits=-1.6 required=5.0 tests=IN_REP_TO,QUOTED_EMAIL_TEXT,REFERENCES,SPAM_PHRASE_00_01, X_MAILING_LIST version=2.44 X-Spam-Level: Bom, a resposta à sua pergunta depende do que se entende por "números na reta". Se não há definição precisa de "reta numérica", não dá para discutir se todos os números "dela" (ela? que ela?) estão nos reais ou não. Uma solução rápida, limpa, simples e sem graça é **DEFINIR** a reta numérica como o conjunto dos números reais. Rápido, limpo e simples (mas sem graça). :) :) A boa notícia é que deste jeito a reta numérica herda todas as propriedades dos números reais, inclusive aquela de que "todo conjunto numérico limitado tem um supremo". Assim, a resposta usual é "garantimos que não há número, na reta, que não se enquadre no conjunto dos reais pois definimos a "reta numérica" como o conjunto dos reais". :P Abraço, Ralph P.S.: Por outro lado, dá para definir números "surreais" (veja http://en.wikipedia.org/wiki/Surreal_numbers). Para trabalhar com eles, algumas propriedades antigas têm de ser descartadas (por exemplo, neles a<=b e b<=a não implica a=b), mas eles são bem bacanas, são uma extensão dos reais que não tem nada a ver com os complexos e o pessoal tenta pensar neles ainda numa espécie de "reta", usando "nuvens" ao invés de "pontos", incluindo uns "pontos no infinito" e fazendo várias outras barbáries. Por incrível que pareça, no final, tudo funciona, as construções são justificadas formalmente e estes objetos têm aplicações. 2008/3/27 Paulo - Uniredes : > Como é que sabemos que os conjuntos já conhecidos são suficientes para > representar números da Reta Real ? Existe alguma prova de que eles são > necessários e sufucientes ? > > Explico: > > Temos os naturais > Depois estendemos o conceito para os inteiros... > Depois os racionais... > Depois os irracionais... > > Bom, que me garante que não há número, na reta, que não se enquadre em > qualquer desses conjuntos ? > > Há algum teorema "mágico" que diga isso, como existe o maravilhoso Teorema > de Gödel sobre a inconsistência da lógica ? > > > []s > > --- > Paulo C. Santos (PC) > e-mail: paulo@uniredes.org > Homepage: http://uniredes.org > Tel.: (21) 2510.8783 - Cel.: (21) 8753-0729 > -------------------------------------------- > MS-Messenger: Uniredes_Br@hotmail.Com > > > ========================================================================= > Instruções para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > ========================================================================= > ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Mar 27 17:15:47 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2RKEYWA026845 for ; Thu, 27 Mar 2008 17:14:34 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2RKEXBR026842 for obm-l-MllGbsmmN; Thu, 27 Mar 2008 17:14:33 -0300 Received: from fk-out-0910.google.com (fk-out-0910.google.com [209.85.128.190]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2RKERWA026786 for ; Thu, 27 Mar 2008 17:14:29 -0300 Received: by fk-out-0910.google.com with SMTP id 22so5450685fkq.13 for ; Thu, 27 Mar 2008 13:14:10 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=Rtek/bG47SSeJP2UkDvn4Ro9iXUfC6Clc+Obs1BtTjA=; b=NLPf7hOEJ/zwAv99vRyBnJKXoTIs3SjcU7beeHZK/4khj1V/ALMeIGAZSy2KxYzwVcdFIO8Ha56+5nAnz01zZr41z/ivEILOXDi6zw4aRTQAtfR7I1/UoVz/dJsF0puS6LRl4HSaCLK0vU11GSomc5oA5LUGbzkuqz5D0hroIqM= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=rahNZqsCSfhsS1DG52juJwoZkLwUyZxkSp39z0F0uegtCh8iQ+ZTA/CCSqVF4wBUEH2EW9g2KtnCYhj22QMFSqZ7+IKO7Al3cEa8Dma44D1UxwReVRwBOVkQdsEKQ8whUCNV0VdZ/4CaBo8nkD3GZQJytN3AnX7tjS96sk1xJR8= Received: by 10.82.136.8 with SMTP id j8mr3110557bud.31.1206648850226; Thu, 27 Mar 2008 13:14:10 -0700 (PDT) Received: by 10.86.57.15 with HTTP; Thu, 27 Mar 2008 13:14:10 -0700 (PDT) Message-ID: Date: Thu, 27 Mar 2008 17:14:10 -0300 From: "saulo nilson" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] mdc In-Reply-To: <973167.73049.qm@web31704.mail.mud.yahoo.com> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_25005_25318945.1206648850227" References: <973167.73049.qm@web31704.mail.mud.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "saulo nilson" X-Spam-Status: No, hits=1.5 required=5.0 tests=AWL,IN_REP_TO,MAILTO_LINK,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_01_02, SPAM_REDIRECTOR,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: * ------=_Part_25005_25318945.1206648850227 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline (a^2+b^2-ab)/(a+b)=3D((a+b)^2-3ab)/(a+b) o maximo divisor comum e o maior numero que nos podemos por em evidencia no numerador e no denominador da divisao acima. a+b=3Dpode ser multiplo 3 entao mdc(a+b,a=B2-ab+b=B2) =3D1 ou 3 2008/3/27 Eder Albuquerque : > Pessoal, o problema a seguir caiu numa prova de teoria dos n=FAmeros que > fiz ontem e foi a =FAnica d=FAvida... > > Provar: > > mdc(a,b)=3D 1 =3D> mdc(a+b,a=B2-ab+b=B2) =3D1 ou 3 > > Agrade=E7o se algu=E9m mostrar como se prova. > > Eder > > ------------------------------ > Abra sua conta no Yahoo! Mail, > o =FAnico sem limite de espa=E7o para armazenamento! > > ------=_Part_25005_25318945.1206648850227 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline
(a^2+b^2-ab)/(a+b)=3D((a+b)^2-3ab)/(a+b)
o maximo divisor comum e o maior numero que nos podemos por em evidenc= ia no numerador e no denominador da divisao acima.
a+b=3Dpode ser multiplo 3
entao mdc(a+b,a=B2-ab+b=B2) =3D1 ou 3
 
2008/3/27 Eder Albuquerque <eder_mat@yahoo.com.br>:
Pessoal, o problema a seguir caiu numa prova  de teoria dos n=FAm= eros que fiz ontem e foi a =FAnica d=FAvida...
 
Provar:
 
mdc(a,b)=3D 1   =3D>  mdc(a+b,a=B2-ab+b=B2) =3D1 ou = 3
 
Agrade=E7o se algu=E9m mostrar como se prova.
 
Eder

Abra sua conta no Yahoo! Mail= , o =FAnico sem limite de espa=E7o para armazenamento!


------=_Part_25005_25318945.1206648850227-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Mar 27 17:53:11 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2RKpvWA032132 for ; Thu, 27 Mar 2008 17:51:57 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2RKpure032123 for obm-l-MllGbsmmN; Thu, 27 Mar 2008 17:51:56 -0300 Received: from rn-out-0910.google.com (rn-out-0910.google.com [64.233.170.187]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2RKppWA032043 for ; Thu, 27 Mar 2008 17:51:52 -0300 Received: by rn-out-0910.google.com with SMTP id a46so3120763rne.9 for ; Thu, 27 Mar 2008 13:51:34 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; bh=JV1CimhZ7Bq/RgvTlJLOWAtOlxYfMpiytGzNjm10nV4=; b=plsFd/uCNFtyZjIXB2TKaB419gr7dPMFMU4ccYKBm+IGuyppsJWU4ZwqUKLyKBrLZ+0tV48Boo/qOz4C7FXUgOXuMUg/5dZ84AP3jFU7eFK636DYX+cQ13SDaDNlwVUGhlsZxnDQetpdzQ05znYXBzanPBFioYE0cECgBfL74eA= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; b=Rjxgu3viYmVvtiULa3vF44HPUdP9SHnLGcPjciKqZtk+00orD/HVdX9mY/9H7NwHHR9zA9HxOMSZldKoj2PjDVnB/DuFdfGVAFk9licvFhPKw3FHFVH6QdUSBlVVvB2yZfdupNXMtMm8/9JKNaqRAT2EfJhd5UnpqFfW6yq7nNE= Received: by 10.143.36.15 with SMTP id o15mr1769021wfj.182.1206651093603; Thu, 27 Mar 2008 13:51:33 -0700 (PDT) Received: by 10.143.5.12 with HTTP; Thu, 27 Mar 2008 13:51:33 -0700 (PDT) Message-ID: Date: Thu, 27 Mar 2008 17:51:33 -0300 From: "Eike Santos" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Computaca Grafica!!! In-Reply-To: <98D269A7986D488F868969A11534ED51@MARTE> MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline References: <98D269A7986D488F868969A11534ED51@MARTE> Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m2RKpsWA032103 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Eike Santos" X-Spam-Status: No, hits=4.9 required=5.0 tests=IN_REP_TO,PLING_PLING,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SIGNATURE_LONG_SPARSE, SPAM_PHRASE_00_01,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** Vamos discutir assuntos relacionados a matematica aplicada. Ats, Marcos Eike 2008/3/27 Ojesed Mirror : > O assunto é interessante, mas não é para ser discutido nesta lista, que é de > matemática olímpica. > O moderador vai "puxar as orelhas" de vocês. > > Troquem logo seus emails pessoais e caiam fora numa boa. > > Ojesed. > > > > ----- Original Message ----- > From: "Eike Santos" > To: > Sent: Thursday, March 27, 2008 11:08 AM > Subject: Re: [obm-l] Computaca Grafica!!! > > > Estudou sobre o modelo de Monte Carlo? e Photon Mapping? > > Ats, > Marcos Eike > > 2008/3/27 Tiago Machado : > > sim. estudei na disciplina de processamento gráfico. > > > > 2008/3/27 Eike Santos : > > > > > > > Mas, vc tem estudado ou estudou Rendering? > > > > > > Ats, > > > Marcos Eike > > > > > > 2008/3/27 Tiago Machado : > > > > > > > > > > > > > Atualmente estou trabalhando na area de computação gráfica e técnicas > > > > interativas. > > > > > > > > 2008/3/26 Eike Santos : > > > > > > > > > > > > > Blz. Rapaz... Tem msn? > > > > > Trabalha em que área? Atualmente estou estudando Rendering! > > > > > > > > > > Ats, > > > > > Marcos Eike > > > > > > > > > > 2008/3/26 Tiago Machado : > > > > > > > > > > > > > > > > > > > > > Oi Eike, > > > > > > > > > > > > Faço IC na area de computação gráfica. > > > > > > > > > > > > > > > > > > > > > > > > On Wed, Mar 26, 2008 at 7:09 PM, Eike Santos > > > > wrote: > > > > > > > > > > > > > > > > > > > > > > > > > > > > Alguem esta trabalhando ou gosta de computacao gráfica em geral > > aqui > > > > > > > na lista? Vamos trocas info? Dúvidas e coisas afim? > > > > > > > > > > > > > > Ats, > > > > > > > -- > > > > > > > Marcos Eike Tinen dos Santos > > > > > > > +559881176565 > > > > > > > > > > > > > > OpenSuse- Comunidade Open do Suse > > > > > > > www.opensuse.org > > > > > > > OpenSolaris- Comunidade Open do Solaris > > > > > > > www.opensolaris.org > > > > > > > > > > > > > > > > > > > > ========================================================================= > > > > > > > Instruções para entrar na lista, sair da lista e usar a lista em > > > > > > > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > > > > > > > > > > > > > ========================================================================= > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > -- > > > > > > > > > > > > > > > > > > > > Marcos Eike Tinen dos Santos > > > > > +559881176565 > > > > > > > > > > OpenSuse- Comunidade Open do Suse > > > > > www.opensuse.org > > > > > OpenSolaris- Comunidade Open do Solaris > > > > > www.opensolaris.org > > > > > > > > > > > > ========================================================================= > > > > > Instruções para entrar na lista, sair da lista e usar a lista em > > > > > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > > > > > > > ========================================================================= > > > > > > > > > > > > > > > > > > > > > > > > > -- > > > > > > > > > > > > Marcos Eike Tinen dos Santos > > > +559881176565 > > > > > > OpenSuse- Comunidade Open do Suse > > > www.opensuse.org > > > OpenSolaris- Comunidade Open do Solaris > > > www.opensolaris.org > > > > > > ========================================================================= > > > Instruções para entrar na lista, sair da lista e usar a lista em > > > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > > > ========================================================================= > > > > > > > > > > > -- > Marcos Eike Tinen dos Santos > +559881176565 > > OpenSuse- Comunidade Open do Suse > www.opensuse.org > OpenSolaris- Comunidade Open do Solaris > www.opensolaris.org > > ========================================================================= > Instruções para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > ========================================================================= > > ========================================================================= > Instruções para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > ========================================================================= > -- Marcos Eike Tinen dos Santos +559881176565 OpenSuse- Comunidade Open do Suse www.opensuse.org OpenSolaris- Comunidade Open do Solaris www.opensolaris.org ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Mar 27 18:04:10 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2RL2fWA000726 for ; Thu, 27 Mar 2008 18:02:43 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2RL2bCJ000719 for obm-l-MllGbsmmN; Thu, 27 Mar 2008 18:02:37 -0300 Received: from gv-out-0910.google.com (gv-out-0910.google.com [216.239.58.186]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2RL1vWA000691 for ; Thu, 27 Mar 2008 18:02:05 -0300 Received: by gv-out-0910.google.com with SMTP id u5so998657gve.25 for ; Thu, 27 Mar 2008 14:01:40 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; bh=PD1NkVcnft58tKD9TWc0KXb+/exbis4ESJRlOacJ3nQ=; b=XeWPAG2bSUrukYn8Wy+VyuwtS87QvYRysPEh8LHCYnDpcFC7X414TkLlEmxgIxqJQqLL3Gzlpa0sXvres3VOB9yJhUN2bjJG9nj0rGTJcVQBnDJY7XfVJjdoa5+bN5NEu0OseMr53e6iDguSxK8HA42mZPF8qp9drEaj6LaLWi4= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; b=fz4TF8Hd4goDKUaZvXEmcCdDZJV89JIdpvtQaAgN/6UFecpZ8vETSFXRzQZGO7Naf8zrRRmunfaYPYjgI5v/SHxSK0HqVFrPLfE2zwJpTv1t9xPyx9u6dyV+AEkJ97uVWo6LO4XK8LYAJexxatYATHZ/1lR1cpBC7NCSQE8hhkQ= Received: by 10.150.158.8 with SMTP id g8mr1111805ybe.25.1206651699400; Thu, 27 Mar 2008 14:01:39 -0700 (PDT) Received: by 10.150.152.11 with HTTP; Thu, 27 Mar 2008 14:01:39 -0700 (PDT) Message-ID: <2d483c770803271401h64bc32f4t5b2bce603c8fec@mail.gmail.com> Date: Thu, 27 Mar 2008 18:01:39 -0300 From: "Ralph Teixeira" To: obm-l@mat.puc-rio.br Subject: =?ISO-8859-1?Q?Re:_[obm-l]_Problema_Combinat=F3ria?= In-Reply-To: MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline References: Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m2RL2IWA000702 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Ralph Teixeira" X-Spam-Status: No, hits=1.4 required=5.0 tests=AWL,IN_REP_TO,MAILTO_TO_SPAM_ADDR,QUOTED_EMAIL_TEXT, RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,REFERENCES, SPAM_PHRASE_00_01,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: * Seja G(m,n) o número de maneiras de escolher m livros não consecutivos a partir de um conjunto com n livros (supomos que eles são todos diferentes e estão em fila na estante). onde m,n>=1. Condições de contorno: G(1,n)=n (pois há n maneiras de escolher 1 livro dentre n deles); por outro lado, para m>1, temos G(m,1)=G(m,2)=0 (não dá para escolher 2 ou mais livros não-consecutivos num conjunto com apenas 1 ou 2 livros). A partir daí, tenho uma recorrência: para escolher m livros de n, você tem duas opções: a) Incluir o livro 1; então você não pode incluir o livro 2, e, assim, ainda tem que escolher m-1 dos n-2 livros restantes. Assim, há aqui G(m-1,n-2) maneiras de fazer isto. b) Não incluir o livro 1; então você tem que escolher m dos n-1 restantes; há G(m,n-1) maneiras de fazer isto. Como as maneiras em (a) e (b) são disjuntas, temos a recorrência: G(m,n)=G(m,n-1)+G(m-1,n-2) Então juntando tudo: G(m,n)=G(m,n-1)+G(m-1,n-2) para m>=2 e n>=3 G(1,n)=n para n>=1 G(m,1)=G(m,2)=0 para m>=1 Bom, joguei isto no Calc do OpenOffice... e estou vendo uma espécie de Triângulo de Pascal deformado... Hmmmm... Ah, já sei. Seja f(x,y)=G(m,n) onde m=x-y e n=2x-y-1 (ou, se você preferir, x=n-m+1 e y=n-2m+1). A recorrência e as condiçõaes de contorno acima tranformam-se em condições em f que são idênticas àquelas que definem o triângulo de Pascal, isto é, f(x,y)=C(x,y). Então a resposta é que G(m,n)=C(n-m+1,n-2m+1). Ou, se você preferir, mostre por indução que esta última fórmula vale... Desculpa o final curto e meio grosso, mas acabou meu tempo. :) Eu ainda queria ver se tinha alguma solução verdadeiramente combinatória que levasse à reposta, mas fica para depois. Ah, e, se eu não errei nada, a resposta à pergunta original é G(5,24)=C(20,15)=15504 -- há 15504 maneiras de escolher 5 livros não consecutivos a partir de uma fila com 24. Perdão, sem tempo de checar tudo, espero não ter escrito besteiras homéricas. Abraço, Ralph 2008/3/27 Johann Peter Gustav Lejeune Dirichlet : > São 24 livros de assuntos distintos? E os livros estão grudados na > estante (se o de Teoria da Computação está do lado de Linguagens > Formais, eles sempre estarão lado a lado?) > Bem, seria algo como escolher cinco números não-consecutivos do conjunto > {1,2,3,4\ldots,24}. > Acho que dá pra usar alguma recursão. > Vou pensar um pouco antes de continuar... > > Em 26/03/08, MauZ escreveu: > > Olá a todos! > > > > Numa estante com 24 livros, de quantas maneiras posso retirar 5 livros sem > > ter nenhum consecutivo? E no caso de n livros, quantas maneiras retiro p > > livros sem ter nenhum consecutivo? > > > > > > > > Pra completar vou colocar parte da minha tentativa de solução, preciso de > > ajuda pra saber se está certo até onde fiz e como finalizar pois empaquei. > > > > Fiz dessa forma: Todas Combinações - Combinações c/ Consecutivos > > > > Todas: 24!/5!19! > > Consecutivos: 23!/4!19! + 22!/3!19! + 21!/2!19! + 20!/1!19! > > > > Fiz uma formula geral com n e p e deu o seguinte: > > > > n!/p!(n-p!) - [(n-1)!/(p-1)!(n-p)! + > > (n-2)!/(p-2)!(n-p)!+...+(n-p+1)!/(n-p)!] > > > > Fatorando deu: > > > > (1/(n-p)!)[n!/p!-(n-1)!/(p-1)!-(n-2)!/(p-2)-...-(n-p+1)!/(n-p)!] > > > > Dae empaquei de vez... Não consegui continuar! > > Quem souber fazer por favor me dê a luz! Ou simplesmente indique o erro no > > meu raciocínio. > > > > Agradeço antecipadamente, > > Maurizio > > > > > > > -- > Ideas are bulletproof. > > V > > ========================================================================= > Instruções para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > ========================================================================= > ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Mar 27 18:08:39 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2RL7IWA001052 for ; Thu, 27 Mar 2008 18:07:18 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2RL7D3I001048 for obm-l-MllGbsmmN; Thu, 27 Mar 2008 18:07:13 -0300 Received: from wf-out-1314.google.com (wf-out-1314.google.com [209.85.200.169]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2RL6nWA001030 for ; Thu, 27 Mar 2008 18:06:50 -0300 Received: by wf-out-1314.google.com with SMTP id 27so3683545wfd.18 for ; Thu, 27 Mar 2008 14:06:32 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:from:to:subject:date:mime-version:content-type:x-priority:x-msmail-priority:x-mailer:x-mimeole; bh=IP7ErNYI2RIR0rK1QTPbhupFs2pdGGfCzH3sqNbMNJw=; b=KboVy/TtTIfCMgLUp9qKgCbD2htaBiJ23A7iBiMFpXTyQNrO/hBbtkGBqFh9J8H9+3aJIZCj+Y8RqJIWaRUEYu3VpRAJGJUoyi/ZPo0tC4O0+aMS1Z0DQYVnOHZ5/aVQ1v3FP34DNsc3gnLb8orTuwUgPZPautLrgXjprcqQoNc= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:from:to:subject:date:mime-version:content-type:x-priority:x-msmail-priority:x-mailer:x-mimeole; b=VZwAJhoHA9EHThwhMtIEFCzGus3pyfepOkRKwe+VIGH9iXmsxekTG8Iu8rJTNGtl7z1n8HrUQGKeBUjXRSMD3T1NhsdICBJP0cw+cahPX1SOatGfDCDOd4qrPk/1IIgrf9vr7TPxhANt11wdFRcxOMlIN06r9EiMx3dHeTQrq/I= Received: by 10.142.114.15 with SMTP id m15mr1770953wfc.235.1206651992253; Thu, 27 Mar 2008 14:06:32 -0700 (PDT) Received: from claudia8e76cd2 ( [201.53.135.153]) by mx.google.com with ESMTPS id a13sm410656rnc.6.2008.03.27.14.06.29 (version=SSLv3 cipher=RC4-MD5); Thu, 27 Mar 2008 14:06:30 -0700 (PDT) Message-ID: <002301c8904e$6ba89bc0$0801a8c0@claudia8e76cd2> From: "Anna Luisa C." To: "OBM" Subject: [SPAM] [obm-l] Ajuda em geometria Date: Thu, 27 Mar 2008 18:06:20 -0300 MIME-Version: 1.0 Content-Type: text/plain X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2900.3138 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.3198 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Anna Luisa C." X-Spam-Status: Yes, hits=6.6 required=5.0 tests=RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,RCVD_IN_RELAYS_ORDB_ORG, SPAM_PHRASE_00_01,SUPERLONG_LINE,USER_AGENT_OE, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ****** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_NextPart_000_0020_01C89035.42A1B720" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (6.60 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: USER_AGENT_OE (0.2 points) X-Mailer header indicates a non-spam MUA (Outlook Express) SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: SUPERLONG_LINE (0.0 points) BODY: Contains a line >=199 characters long SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 169.200.85.209.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 169.200.85.209.relays.osirusoft.com.] SPAM: RCVD_IN_RELAYS_ORDB_ORG (0.6 points) RBL: Received via a relay in relays.ordb.org SPAM: [RBL check: found 153.135.53.201.relays.ordb.org.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- This is a multi-part message in MIME format. ------=_NextPart_000_0020_01C89035.42A1B720 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Por favor algu=E9m pode me ajudar nessas duas quest=F5es. 1) Num trap=E9zio ret=E2ngulo, o lado obl=EDquo BC =E9 o dobro da base = menor AB e M =E9 o ponto m=E9dio de BC. Se o =E2ngulo DMB =3D 120, quais = os =E2ngulos do trap=E9zio? 2) Considere um quadrado ABCD e sobre o lado AB constr=F3i-se um = tri=E2ngulo equil=E1tero APB. Seja I o ponto de encontro das diagonais = do quadrado e M o ponto m=E9dio de PB. Calcule a medida do =E2ngulo AIM. Desde j=E1 agrade=E7o a aten=E7=E3o. Anninha. ------=_NextPart_000_0020_01C89035.42A1B720 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable
Por favor algu=E9m pode me ajudar = nessas duas=20 quest=F5es.
 
1) Num trap=E9zio ret=E2ngulo, o lado = obl=EDquo BC =E9 o=20 dobro da base menor AB e M =E9 o ponto m=E9dio de BC. Se o =E2ngulo DMB = =3D 120, quais=20 os =E2ngulos do trap=E9zio?
 
2) Considere um quadrado ABCD e sobre o = lado AB=20 constr=F3i-se um tri=E2ngulo equil=E1tero APB. Seja I o ponto de = encontro das=20 diagonais do quadrado e M o ponto m=E9dio de PB. Calcule a medida do = =E2ngulo=20 AIM.
 
Desde j=E1 agrade=E7o a = aten=E7=E3o.
Anninha.
------=_NextPart_000_0020_01C89035.42A1B720-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Mar 27 19:49:21 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2RMlpWA016389 for ; Thu, 27 Mar 2008 19:47:51 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2RMloP1016381 for obm-l-MllGbsmmN; Thu, 27 Mar 2008 19:47:50 -0300 Received: from ug-out-1314.google.com (ug-out-1314.google.com [66.249.92.174]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2RMlkWA016325 for ; Thu, 27 Mar 2008 19:47:47 -0300 Received: by ug-out-1314.google.com with SMTP id q7so577299uge.0 for ; Thu, 27 Mar 2008 15:47:29 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; bh=gNYcIym12HmaEJEvUwNNl3XsLMHcjFTcORqp9U6baGI=; b=X6yLlKX0SEGuFC7Lelk7Za/wlGN1febIyBDc/izMqXLE3qylGbaHXSNj6LzSKTlv+fb9jBTWcvXUkFo9u4VjRQP5I9gAFICk2SjgPkZAzQ6fjVEjyIjxCyH5+l+iTJNZj0Ra8Y1kJSmkmFYKtT3HepiBYEKMXDT23NS0OeWnDO4= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; b=ta+OKW128ew5IBVvUaApxsQP8Ef06dbHFmh3BKRyDteD306GY0aIoZqtXs+R1qUS8W34UY+ZYUKnZLje8IHbPuR8NHtJwc20fx7hsLGgjPOBhZPJClIvPZz5Pg7k21rq+eqM1UI7bICQo0uyZtBFEiIblZjj75VtFO1G2ZYizyY= Received: by 10.67.20.3 with SMTP id x3mr2665198ugi.3.1206658049060; Thu, 27 Mar 2008 15:47:29 -0700 (PDT) Received: by 10.66.237.17 with HTTP; Thu, 27 Mar 2008 15:47:28 -0700 (PDT) Message-ID: <2b5739960803271547h7584b608kb1dbc59171ca9fad@mail.gmail.com> Date: Thu, 27 Mar 2008 19:47:28 -0300 From: "Rogerio Ponce" To: obm-l@mat.puc-rio.br Subject: =?ISO-8859-1?Q?Re:_[obm-l]_Problema_Combinat=F3ria?= In-Reply-To: MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline References: Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m2RMlmWA016372 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Rogerio Ponce" X-Spam-Status: No, hits=3.7 required=5.0 tests=IN_REP_TO,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: *** Ola' Mauricio e colegas da lista, os 5 livros retirados determinam 6 intervalos , dos quais o mais 'a esquerda e o mais 'a direita podem ter o valor minimo de 0, e os outros quatro valem no minimo 1. Para uniformizar tudo, podemos imaginar que exista um livro a mais do lado direito, e outro do lado esquerdo da estante, de forma que agora precisamos determinar 6 intervalos, todos maiores que zero, somando um total de 24+2-5 = 21. Em outras palavras, o que procuramos e' o numero de solucoes inteiras positivas para a+b+c+d+e+f=21 que vale C(21-1, 6-1) = C(20,5) Ou seja, (20*19*18*17*16) / (5*4*3*2*1) = 15504 []'s Rogerio Ponce Em 26/03/08, MauZ escreveu: > Olá a todos! > > Numa estante com 24 livros, de quantas maneiras posso retirar 5 livros sem > ter nenhum consecutivo? E no caso de n livros, quantas maneiras retiro p > livros sem ter nenhum consecutivo? > > > > Pra completar vou colocar parte da minha tentativa de solução, preciso de > ajuda pra saber se está certo até onde fiz e como finalizar pois empaquei. > > Fiz dessa forma: Todas Combinações - Combinações c/ Consecutivos > > Todas: 24!/5!19! > Consecutivos: 23!/4!19! + 22!/3!19! + 21!/2!19! + 20!/1!19! > > Fiz uma formula geral com n e p e deu o seguinte: > > n!/p!(n-p!) - [(n-1)!/(p-1)!(n-p)! + > (n-2)!/(p-2)!(n-p)!+...+(n-p+1)!/(n-p)!] > > Fatorando deu: > > (1/(n-p)!)[n!/p!-(n-1)!/(p-1)!-(n-2)!/(p-2)-...-(n-p+1)!/(n-p)!] > > Dae empaquei de vez... Não consegui continuar! > Quem souber fazer por favor me dê a luz! Ou simplesmente indique o erro no > meu raciocínio. > > Agradeço antecipadamente, > Maurizio > > ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Thu Mar 27 23:20:40 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2S2IuWA002307 for ; Thu, 27 Mar 2008 23:18:56 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2S2ItYA002305 for obm-l-MllGbsmmN; Thu, 27 Mar 2008 23:18:55 -0300 Received: from sc2.he.tucows.com (smtpout2050.sc2.he.tucows.com [64.97.155.50]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2S2IsWA002283 for ; Thu, 27 Mar 2008 23:18:54 -0300 Received: from sc2-out05.emaildefenseservice.com (64.97.201.175) by sc2.he.tucows.com (7.3.127) id 47E4F0770051AEE4 for obm-l@mat.puc-rio.br; Fri, 28 Mar 2008 02:18:37 +0000 X-SpamScore: 2 X-Spamcatcher-Summary: 2,0,0,60e5e8fd28907b30,e78590c924dafc7c,cauchy@globo.com,-,RULES_HIT:355:379:541:582:988:989:1152:1260:1277:1311:1313:1314:1345:1513:1515:1516:1518:1521:1534:1536:1559:1593:1594:1711:1714:1730:1747:1766:1792:2393:2559:2562:2828:3165:3869:3876:3877:5007:6114:6312:7652:7904,0,RBL:none,CacheIP:none,Bayesian:0.5,0.5,0.5,Netcheck:none,DomainCache:0,MSF:not bulk,SPF:,MSBL:none,DNSBL:none,TSO:0 X-Spamcatcher-Explanation: Received: from sc2.he.tucows.com (mail11.sc2.he.tucows.com [64.97.154.89]) by sc2-out05.emaildefenseservice.com (Postfix) with ESMTP for ; Fri, 28 Mar 2008 02:18:37 +0000 (UTC) Received: from [189.81.73.113] by sc2.he.tucows.com with HTTP; Fri, 28 Mar 2008 02:18:36 +0000 Date: Thu, 27 Mar 2008 23:18:36 -0300 Message-ID: <47C429A7000A55B1@mail11.sc2.he.tucows.com> From: cauchy@globo.com Subject: [SPAM] [obm-l] teoria dos inteiros-ajuda To: obm-l@mat.puc-rio.br MIME-Version: 1.0 Content-Type: text/plain; charset="ISO-8859-15" X-Mailer: GloboMail X-Originating-IP: 189.81.73.113 Content-Transfer-Encoding: 7bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m2S2ItWA002303 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: cauchy@globo.com X-Spam-Status: Yes, hits=7.7 required=5.0 tests=NO_REAL_NAME,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, RCVD_IN_RELAYS_ORDB_ORG,SPAM_PHRASE_00_01,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******* X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (7.70 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: NO_REAL_NAME (1.3 points) From: does not include a real name SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 89.154.97.64.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 89.154.97.64.relays.osirusoft.com.] SPAM: RCVD_IN_RELAYS_ORDB_ORG (0.6 points) RBL: Received via a relay in relays.ordb.org SPAM: [RBL check: found 113.73.81.189.relays.ordb.org.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- a é inteiro, b inteiro não nulo, tais que (2^n).a + b é um quadrado perfeito para todo n natural. Prove que a=0. ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Fri Mar 28 00:48:37 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2S3lLWA010133 for ; Fri, 28 Mar 2008 00:47:22 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2S3lKIS010129 for obm-l-MllGbsmmN; Fri, 28 Mar 2008 00:47:20 -0300 Received: from smtpi03s.infolink.com.br (smtpi03s.infolink.com.br [200.187.64.122]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2S3lGWA010063 for ; Fri, 28 Mar 2008 00:47:16 -0300 Received: from smtpi03s.infolink.com.br (localhost [127.0.0.1]) by smtpi03s.infolink.com.br (Postfix) with ESMTP id 5BD6C71267D for ; Fri, 28 Mar 2008 00:47:00 -0300 (EST) Received: from [127.0.0.1] (unknown [189.60.112.176]) by smtpi03s.infolink.com.br (Postfix) with ESMTP id 39C827015C2 for ; Fri, 28 Mar 2008 00:47:00 -0300 (EST) Message-ID: <47EC69EE.9060900@infolink.com.br> Date: Fri, 28 Mar 2008 00:45:50 -0300 From: Carlos Nehab User-Agent: Thunderbird 2.0.0.12 (Windows/20080213) MIME-Version: 1.0 To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Conjuntos =?ISO-8859-1?Q?num=E9ricos_na_Reta=2E=2E?= =?ISO-8859-1?Q?=2E?= References: <200803271845.m2RIj2WA020799@saci.mat.puc-rio.br> <2d483c770803271230tc8e3041vfda8ab9cfcbfe8bb@mail.gmail.com> In-Reply-To: <2d483c770803271230tc8e3041vfda8ab9cfcbfe8bb@mail.gmail.com> Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: 7bit X-Antivirus: avast! (VPS 080327-0, 27/03/2008), Outbound message X-Antivirus-Status: Clean Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Carlos Nehab X-Spam-Status: No, hits=4.6 required=5.0 tests=AWL,CTYPE_JUST_HTML,IN_REP_TO,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, USER_AGENT,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** Oi, Ralph (e Paulo),

Apenas matando as suadades...um rápido comentário:

Para os aficcionados, o livro "Surreal Numbers" é "quase" novelesco (com fundo matemático, é claro) do Knuth (um verdadeiro mago) e já foi traduzido para o português (a edição original tem mais de 30 anos - eu era quase um "pirralho" na época  :-)       e  ainda dava aula no IME...- ah... que saudades Ralph me lembrou...). 
É  um belo, pequeno e imperdível livro para a maioria dos participantes desta lista.  Quem ainda não leu em inglês, aproveite: eu comprei no começo do ano uma cópia em português na livraria da Travessa (acho que foi uns 40 reais - mas pela Amazon em inglês é naturalmente mais barato).

E aproveitando a deixa do Ralph, quem for curioso também pode e deve dar estudar Fuzzy Sets, Fuzzy Numbers (Numeros Nebulosos, etc). Os de Engenharia Elétrica ou Computação, certamente terão contato com isto, bem como com Algoritmos Genéticos...

Ou seja, há muito mais coisa para se aprender do que supõe a vã flosofia, ou mesmo a reta (sur)real...

Abraços,
Nehab

Ralph Teixeira escreveu: 
.......
P.S.: Por outro lado, dá para definir números "surreais" (veja
http://en.wikipedia.org/wiki/Surreal_numbers). Para trabalhar com
eles, algumas propriedades antigas têm de ser descartadas (por
exemplo, neles a<=b e b<=a não implica a=b), mas eles são bem bacanas,
são uma extensão dos reais que não tem nada a ver com os complexos e o
pessoal tenta pensar neles ainda numa espécie de "reta", usando
"nuvens" ao invés de "pontos", incluindo uns "pontos no infinito" e
fazendo várias outras barbáries. Por incrível que pareça, no final,
tudo funciona, as construções são justificadas formalmente e estes
objetos têm aplicações.

========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Fri Mar 28 06:35:53 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2S9Y6WA031422 for ; Fri, 28 Mar 2008 06:34:06 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2S9Y6Db031420 for obm-l-MllGbsmmN; Fri, 28 Mar 2008 06:34:06 -0300 Received: from fg-out-1718.google.com (fg-out-1718.google.com [72.14.220.155]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2S9Y4WA031379 for ; Fri, 28 Mar 2008 06:34:05 -0300 Received: by fg-out-1718.google.com with SMTP id e12so142613fga.3 for ; Fri, 28 Mar 2008 02:33:47 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; bh=GbmFLYRMe5ZrwXHsmBs04zv1qbXcArImE+2e0vSbWtg=; b=J94WRBGKJqYydiHmM6WoyzMeSucFUJmTEqVAhrrDxxsOkUCm+/NbZXUmhB5nCHvWKpC6QOhBI7SNIAgWETym2NqByB05vrEykE391RuFAnXAKuIx50NbZfuOd6XC7WneSTSjtJUn0/AxaR8sKVZ15HcJf5zKeEKCd7N8j1TDP/w= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; b=GU19JYuoNEVChmQ4eCGV6dzNwL0+jxztCLEril7VTp7T6hnms2ybsViEQEsJ6vuG9CVShZh4LWO8UEvKcIvNDjaXZjau8U91W3gpl6ZHYCyT+ZofiIECX7WeRyj3D6URS6SBZnOFY9DNiK603M29oCc71JmK5xSo4eeIkyNsEmg= Received: by 10.82.175.17 with SMTP id x17mr4838357bue.23.1206696827376; Fri, 28 Mar 2008 02:33:47 -0700 (PDT) Received: by 10.82.127.13 with HTTP; Fri, 28 Mar 2008 02:33:47 -0700 (PDT) Message-ID: Date: Fri, 28 Mar 2008 06:33:47 -0300 From: "Johann Peter Gustav Lejeune Dirichlet" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] duvida In-Reply-To: <271113.55179.qm@web45705.mail.sp1.yahoo.com> MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline References: <271113.55179.qm@web45705.mail.sp1.yahoo.com> Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m2S9Y5WA031418 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Johann Peter Gustav Lejeune Dirichlet" X-Spam-Status: No, hits=0.2 required=5.0 tests=AWL,FROM_ENDS_IN_NUMS,IN_REP_TO,QUOTED_EMAIL_TEXT, REFERENCES,SIGNATURE_LONG_SPARSE,SPAM_PHRASE_00_01, X_MAILING_LIST version=2.44 X-Spam-Level: Este é o segundo e-mail com o cabeçalho duvidoso que encontro... Enfim, Para n=1 não há o que fazer. Podemos dizer que X={1,2,3,4,...,n} Seja então X!=X U {n+1}. Seja F(t) o cara com quem associamos t no conjunto X!. Assim sendo, se F(n+1)=n+1 podemos arrancar os dois do cenário, e temos os n! de antes. Mas e se não for? Isso não muda quase nada: se F(n+1)=k, podemos arrancar o k e rearranjar a função F. Assim, digamos: 1 2 3 4 4 2 3 1 Tirando o par (4,1), temos 1 2 3 4 2 3 Trocamos o menor elemento por 1, o segundo menor por 2, o terceiro menor por 3, etc: 1 2 3 3 1 2 E pronto! O valor de F(n+1) pode ser qualquer um dos elementos de X, o que dá n+1 posssibilidades. Junto com os n! da indução, estamos OK! Em 16/03/08, José de Jesus Rosa escreveu: > Por favor, me ajudem nessa questão: > > Seja X um conjunto finito de cardinalidade n. Use a indução para mostrar que > o conjunto das bijeções f: X---X tem cadnalidade n! > > > > ________________________________ > Abra sua conta no Yahoo! Mail, o único sem limite de espaço para > armazenamento! > > ________________________________ > Abra sua conta no Yahoo! Mail, o único sem limite de espaço para > armazenamento! > > > > -- Ideas are bulletproof. V ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Fri Mar 28 06:45:33 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2S9iWWA002217 for ; Fri, 28 Mar 2008 06:44:32 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2S9iV3o002211 for obm-l-MllGbsmmN; Fri, 28 Mar 2008 06:44:31 -0300 Received: from wr-out-0506.google.com (wr-out-0506.google.com [64.233.184.235]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2S9iRWA002147 for ; Fri, 28 Mar 2008 06:44:27 -0300 Received: by wr-out-0506.google.com with SMTP id c46so116987wra.18 for ; Fri, 28 Mar 2008 02:44:11 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; bh=HqP8Ssmc9nR85sIUfmctHOb+lKvRZVu7fT+BMdEQv1c=; b=YSRTuWlCVbo/6f5//UGcU93jwm1D0bOACfHBZJfEY8BLk1itVhApsyAoekiMH52nGVzaWSdYaDz598NMyW01XnLLXPxuzbAaJ0SjdfV4BR7iPIn7HYKzdfR4QkiAGLL2kb+8qCgH7thbl2UV1VPxKamHNpUvh/6iIrupSCMEQng= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; b=Hdmhy4cmMKl1q/FIYvvyu5b6NG1aBmZ3lem2E292pdUlNqgJQLTU2pd4U6IcF4W8FcQ42ijuqLjWw1u0mzT16+1FJYBXURMDnLgOyoQcbVAvtYW0/Uhf+N1WSEnm9z1pfuCF2hSusXioZYC+oT1iH0QC26NaExY82KQD+bqxbcU= Received: by 10.114.202.15 with SMTP id z15mr3239157waf.72.1206697450631; Fri, 28 Mar 2008 02:44:10 -0700 (PDT) Received: by 10.114.176.17 with HTTP; Fri, 28 Mar 2008 02:44:10 -0700 (PDT) Message-ID: <1bcd8af0803280244r72f5fda7r66448598d5c33598@mail.gmail.com> Date: Fri, 28 Mar 2008 10:44:10 +0100 From: "Bernardo Freitas Paulo da Costa" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] mdc In-Reply-To: MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline References: <973167.73049.qm@web31704.mail.mud.yahoo.com> Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m2S9iTWA002195 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Bernardo Freitas Paulo da Costa" X-Spam-Status: No, hits=3.6 required=5.0 tests=AWL,IN_REP_TO,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: *** A idéia é exatamente esso, mas tem um detalhe sórdido : como você mesmo mostrou, o mdc tem que dividir 3ab e (a+b) ao mesmo tempo (já que se ele divide a+b ele vai dividir também o resto, que é (a+b)^2). Se a+b for múltiplo de 3, então o mdc é *no mínimo* 3. O que faltou foi ver que não pode ser maior do que isso, e é aí que entra a parte de "a e b são primos entre si". Vejamos : se o mdc tiver algum outro fator, m por exemplo, como ele divide 3ab (é ótimo ter uma parcela fatorada pra calcular mdcs!) ele divide 3, a, ou b (não necessariamente exclusivo). Bom, como o "3" já foi contado, ele divide a ou b. Podemos supor que divide a (o outro caso é simétrico!). Como é mdc, ele divide também, a+b. Como m divide a e m divide a+b, m divide (a+b) - a = b (esse truque é ótimo, e ajuda a simplificar as contas, e foi bem o que o Saulo fez). Mas daí m divide a e b, e como eles são primos entre si, m = 1. A gente provou então que se tem um fator que divide 3ab e a+b ao mesmo tempo, ele não divide nem a nem b. Então, ele divide 3, e é 1 ou 3. Daí, a gente prova uma coisa um tiquinho mais forte : o mdc é 3 se e somente se a+b é múltiplo de 3 ! Abraços, -- Bernardo Freitas Paulo da Costa 2008/3/27 saulo nilson : > (a^2+b^2-ab)/(a+b)=((a+b)^2-3ab)/(a+b) > o maximo divisor comum e o maior numero que nos podemos por em evidencia no > numerador e no denominador da divisao acima. > a+b=pode ser multiplo 3 > entao mdc(a+b,a²-ab+b²) =1 ou 3 > > 2008/3/27 Eder Albuquerque : > > > > > > > Pessoal, o problema a seguir caiu numa prova de teoria dos números que > fiz ontem e foi a única dúvida... > > > > Provar: > > > > mdc(a,b)= 1 => mdc(a+b,a²-ab+b²) =1 ou 3 > > > > Agradeço se alguém mostrar como se prova. > > > > Eder > > > > ________________________________ > > > Abra sua conta no Yahoo! Mail, o único sem limite de espaço para > armazenamento! ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Fri Mar 28 10:19:29 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2SDH8WA012130 for ; Fri, 28 Mar 2008 10:17:08 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2SDH3ms012126 for obm-l-MllGbsmmN; Fri, 28 Mar 2008 10:17:03 -0300 Received: from fk-out-0910.google.com (fk-out-0910.google.com [209.85.128.186]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2SDGnWA012111 for ; Fri, 28 Mar 2008 10:16:50 -0300 Received: by fk-out-0910.google.com with SMTP id 22so399132fkq.13 for ; Fri, 28 Mar 2008 06:16:33 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:mime-version:content-type:content-transfer-encoding:content-disposition; bh=/ji6yMWZsPuuFUN0kUZCXN5FzX5vQ1b4LZcrMAzLkcU=; b=jpN7xbewGQ6LtTErg3shB13qWkqY0OqVo/KjglgsgLPUL4NpEk8qQtfqWUtMVFOLP/W98Q/Myukg4lOEkYi0Opr7nO4AAj5GA6p4rIXEGVZhyvmP7MqdeFs4Lc0DFnFJzLwVriwNtmLwnCTZ6A+/Gy0plyq5bapD+j83asvrHto= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:mime-version:content-type:content-transfer-encoding:content-disposition; b=UetX7/AAuvcLldDtRWQB+dusbxj5cP0s/aDTmp3hx7nx7W20SSDn72DP9lvZZQmIYMzUS3vwt7QYNGJfA4NPvAEDwa0yH42NGV8gH0VPw7DcAE+ZdXUWhBc4ngIzarpubTlPwvZHrg7xXKTFIN+POVHBRUaHyoC9e1a2WyVut68= Received: by 10.82.120.18 with SMTP id s18mr5499581buc.3.1206710192964; Fri, 28 Mar 2008 06:16:32 -0700 (PDT) Received: by 10.82.114.8 with HTTP; Fri, 28 Mar 2008 06:16:32 -0700 (PDT) Message-ID: <70bb75a50803280616i1f554269q1ede36e9cda122b0@mail.gmail.com> Date: Fri, 28 Mar 2008 10:16:32 -0300 From: "Emanuel Valente" To: obm-l@mat.puc-rio.br Subject: [obm-l] Pintores MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m2SDGvWA012114 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Emanuel Valente" X-Spam-Status: No, hits=4.7 required=5.0 tests=AWL,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** Não consegui montar algebricamente o seguinte problema. Ficarei grato se me ajudarem! Duas pessoas, A e B, pintam separadamente 1m^2 de um muro em tempos que diferem de 1 minuto. Trabalhando juntas, elas pintam 27m^2 por hora. Quanto tempo cada uma leva pra pintar 1 m^2 ? ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Fri Mar 28 11:05:57 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2SE4YWA015587 for ; Fri, 28 Mar 2008 11:04:38 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2SE4T5R015584 for obm-l-MllGbsmmN; Fri, 28 Mar 2008 11:04:29 -0300 Received: from mail.fazenda.ms.gov.br (mail.fazenda.ms.gov.br [200.181.116.25]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2SE4GWA015565 for ; Fri, 28 Mar 2008 11:04:17 -0300 Received: by mail.fazenda.ms.gov.br (Postfix, from userid 115) id A60F17B5C004; Fri, 28 Mar 2008 10:04:00 -0400 (AMT) Received: from mail.fazenda.ms.gov.br (localhost [127.0.0.1]) by mail.fazenda.ms.gov.br (Postfix) with ESMTP id 7F62C7B5C002 for ; Fri, 28 Mar 2008 10:04:00 -0400 (AMT) Received: from 10.5.119.29 by mail.fazenda.ms.gov.br with HTTP; Fri, 28 Mar 2008 10:04:00 -0400 (VET) Message-ID: <1343.10.5.119.29.1206713040.squirrel@mail.fazenda.ms.gov.br> In-Reply-To: <70bb75a50803280616i1f554269q1ede36e9cda122b0@mail.gmail.com> References: <70bb75a50803280616i1f554269q1ede36e9cda122b0@mail.gmail.com> Date: Fri, 28 Mar 2008 10:04:00 -0400 (VET) Subject: [SPAM] Re: [obm-l] Pintores From: jjunior@fazenda.ms.gov.br To: obm-l@mat.puc-rio.br User-Agent: Webmail MS MIME-Version: 1.0 Content-Type: text/plain;charset=iso-8859-1 Content-Transfer-Encoding: 7bit X-Priority: 3 (Normal) Importance: Normal Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: jjunior@fazenda.ms.gov.br X-Spam-Status: Yes, hits=5.9 required=5.0 tests=AWL,IN_REP_TO,NO_REAL_NAME,PRIORITY_NO_NAME, QUOTED_EMAIL_TEXT,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, REFERENCES,SPAM_PHRASE_00_01,USER_AGENT,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ***** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. 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Em 27 metros, 27r + 27l = 60. Logo, 27(l-1) + 27l = 60 -> 54l = 60 + 27 -> l = 87/54 = 1min 36,67seg. r = 36,67 seg. > Não consegui montar algebricamente o seguinte problema. Ficarei grato > se me ajudarem! > > Duas pessoas, A e B, pintam separadamente 1m^2 de um muro em tempos > que diferem de 1 minuto. Trabalhando juntas, elas pintam 27m^2 por > hora. Quanto tempo cada uma leva pra pintar 1 m^2 ? > > ========================================================================= > Instruções para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > ========================================================================= > ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Fri Mar 28 11:08:07 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2SE79WA015678 for ; Fri, 28 Mar 2008 11:07:09 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2SE79I9015675 for obm-l-MllGbsmmN; Fri, 28 Mar 2008 11:07:09 -0300 Received: from rn-out-0910.google.com (rn-out-0910.google.com [64.233.170.189]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2SE76WA015670 for ; Fri, 28 Mar 2008 11:07:07 -0300 Received: by rn-out-0910.google.com with SMTP id a46so112965rne.9 for ; Fri, 28 Mar 2008 07:06:50 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; bh=e8d2kxrQd6HGXZEO7laaAfj7imqwwsnNQWxza8tnu+8=; b=MA9bVGYHPB8vPnyX7RsirTawv74ef859SgFWW9+b1v7FDbDFsdum0LBb0nqas4JxFmNgsk22L4/F3ryD0XVS2bblpwAd/REv0YKlHxTry9YJJZWz5jj6JHLgh1ObnEwX/2SLyu372hzCWE+WLKadxTboSbxaKgawQHv2IAQggTk= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; b=WsGINRnZrJM1mVur/7I4w6/X1m0oyFddV+Nh1xwEm9j6mrfzNLDzy2oRBOpxAXC+Qnh7ygHqDytLe4EGX2upjb5guEni1XJlYBoqOqaYC5TilOlYkbB0+rikCplrkTqQM8ABeB5Jc0yBDjMCTBB+tA1thTRJzLz9jCCG+EUOWmU= Received: by 10.114.135.1 with SMTP id i1mr3759378wad.88.1206713208738; Fri, 28 Mar 2008 07:06:48 -0700 (PDT) Received: by 10.114.176.17 with HTTP; Fri, 28 Mar 2008 07:06:48 -0700 (PDT) Message-ID: <1bcd8af0803280706n4202cafcn692743bcdaabf525@mail.gmail.com> Date: Fri, 28 Mar 2008 15:06:48 +0100 From: "Bernardo Freitas Paulo da Costa" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Pintores In-Reply-To: <70bb75a50803280616i1f554269q1ede36e9cda122b0@mail.gmail.com> MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline References: <70bb75a50803280616i1f554269q1ede36e9cda122b0@mail.gmail.com> Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m2SE78WA015673 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Bernardo Freitas Paulo da Costa" X-Spam-Status: No, hits=3.5 required=5.0 tests=AWL,IN_REP_TO,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SIGNATURE_LONG_SPARSE, SPAM_PHRASE_00_01,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: *** Uma boa técnica para esse tipo de problemas é criar novas quantidades no problema, introduzindo algo como "trabalho realizado", que é o produto de uma "velocidade de trabalho" por "tempo trabalhado". Isso permite somar quantidades coerentes (paredes pintadas, aqui) e principalmente melhor visualizar o problema. Isso servirá também para problemas do tipo "Duas torneiras enchem um tanque em tanto tempo ; se retirarmos uma delas, o tempo passa a ser sei lá quantas vezes maior. Quanto tempo seriam gastos se tivéssemos duas torneiras iguais à que foi retirada?" Para a solução : sejam va, vb as "velocidades" de cada um deles. Juntos eles pintam 27 em 60 minutos te diz que 27 m^2 = 60 min * (va + vb) => veja que va, vb estão em "m^2 por minuto", então tá certinho (se você, além das variáveis, prestar atenção no que elas querem dizer, vai ver que muitas vezes só tem um jeito de montar a equação pra somar coisas do mesmo tipo e multiplicar quantidades coerentes!) os tempos de pintar 1m^2 diferem de 1 minuto 1 m^2 = Ta * va = Tb * vb e Ta - Tb = 1 min => aqui tanto faz qual é o mais rápido, e além disso, o problema não disse quem é, então eu posso pensar que tem uma chance de não ser importante ! agora é só fazer as substituições (e você pode inclusive ser apressado e dizer, "bom, eu quero Ta e Tb, então vou tentar escrever tudo só com eles") va = 1 / Ta vb = 1 / Tb = 1 / (Ta - 1) jogue na primeira equação 27 = 60 * (1/ Ta + 1/(Ta - 1)) = 60 * (Ta - 1 + Ta)/( Ta(Ta - 1) ) e daí é só partir pro abraço : (vou dividir por 3 pra diminuir os números) 9 Ta^2 - 9 Ta = 20 * (2Ta - 1) = 40 Ta - 20 9 x^2 - 49 x + 20 = 0 x = 49 +- raiz(49^2 - 720) / 18 = (49 +- 41) / 18 = 90/18 ou 8/18 = 5 ou 4/9 Agora a gente volta : se Ta = 5, Tb = 4, um pinta 12 m^2 / hora, o outro 15 m^2 /hora, somou, bateu ! se Ta = 4/9, Tb = -5/9, enquanto um pinta, o outro... despinta ? bom, acho que essa solução não dá ; repare que se você fizer as contas sem se preocupar, vai dar certo também, porque dá uma velocidade final de 9/4 - 9/5 = 9/20 m^2 / minuto (que é exatamente a outra, que é 1/5 + 1/4) e tudo vai coincidir. Abraços, -- Bernardo Freitas Paulo da Costa On Fri, Mar 28, 2008 at 2:16 PM, Emanuel Valente wrote: > Não consegui montar algebricamente o seguinte problema. Ficarei grato > se me ajudarem! > > Duas pessoas, A e B, pintam separadamente 1m^2 de um muro em tempos > que diferem de 1 minuto. Trabalhando juntas, elas pintam 27m^2 por > hora. Quanto tempo cada uma leva pra pintar 1 m^2 ? ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Fri Mar 28 11:21:43 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2SEKIWA016495 for ; Fri, 28 Mar 2008 11:20:18 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2SEKH84016493 for obm-l-MllGbsmmN; Fri, 28 Mar 2008 11:20:17 -0300 Received: from web56611.mail.re3.yahoo.com (web56611.mail.re3.yahoo.com [66.196.97.55]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id m2SEKFWA016486 for ; Fri, 28 Mar 2008 11:20:15 -0300 Received: (qmail 91591 invoked by uid 60001); 28 Mar 2008 14:19:58 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:Date:From:Subject:To:MIME-Version:Content-Type:Content-Transfer-Encoding:Message-ID; b=PR089tX6PpvdhaTycADiu5Q1MFDbIA1iowaydLI+r9brZDZGgKS5DhOCTe8WRBtD/IuUCveCgeKCiu9VKwCuWhFHFBjMfbd5+uuumNAQ0XTnNCMnRe+fvTmyZkuA2O+CvfBEIodrUefksqGjSpsZJFAIKh5zxY7kWIKHuINMOf4=; X-YMail-OSG: CLEIZisVM1kyYnw9TQO4YNtIKHkg3X.mptSehT6wmq.2wCiwJbKBZF0GeK0w_grVJ.346z3gwinplf8Zqbv3LKa69zvFdfogrmRLMBaMzGB7gD3yL5mByW57kKl9A5tWyPa.6jNpDDVSQ85oeyhrxuHa Received: from [201.20.206.79] by web56611.mail.re3.yahoo.com via HTTP; Fri, 28 Mar 2008 11:19:58 ART Date: Fri, 28 Mar 2008 11:19:58 -0300 (ART) From: Gustavo Souza Subject: [SPAM] [obm-l] Geometria Plana / Algebra To: obm-l@mat.puc-rio.br MIME-Version: 1.0 Content-Type: text/plain Content-Transfer-Encoding: 7bit Message-ID: <346017.91402.qm@web56611.mail.re3.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Gustavo Souza X-Spam-Status: Yes, hits=8.4 required=5.0 tests=AWL,FORGED_YAHOO_RCVD,MIME_BOUND_DIGITS_5,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,RCVD_IN_RELAYS_ORDB_ORG, SPAM_PHRASE_00_01,SPAM_REDIRECTOR,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="0-848668211-1206713998=:91402" X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. 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SPAM: SPAM: Content analysis details: (8.40 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: MIME_BOUND_DIGITS_5 (1.7 points) Spam tool pattern in MIME boundary SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: SPAM_REDIRECTOR (0.4 points) URI: Uses open redirection service SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 55.97.196.66.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 55.97.196.66.relays.osirusoft.com.] SPAM: RCVD_IN_RELAYS_ORDB_ORG (0.6 points) RBL: Received via a relay in relays.ordb.org SPAM: [RBL check: found 79.206.20.201.relays.ordb.org.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-1.5 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- --0-848668211-1206713998=:91402 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 8bit Se alguem puder me ajudar com esses 2 exercicios>> O de geometria tem um desenho, então hospedei o mesmo nesse link http://img148.imageshack.us/img148/5118/exercicioyi6.gif Resposta: a²(2.3^0,5 - 1) / 44 O de algebra é: Fatore x+1, para x>=0 Resposta: (x^0,5 + 2^0,5.x^0,25 + 1) . (x^0,5 - 2^0,5.x^0,25 + 1) Esse exercicio de algebra me parece estranho, pois a variavel fica dentro da raiz, alguem poderia me explicar por favor? Abraço a Todos e Obrigado --------------------------------- Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-848668211-1206713998=:91402 Content-Type: text/html; charset=iso-8859-1 Content-Transfer-Encoding: 8bit
Se alguem puder me ajudar com esses 2 exercicios>>
 
O de geometria tem um desenho, então hospedei o mesmo nesse link
 
 
Resposta: a²(2.3^0,5 - 1) / 44
 
O de algebra é:
 
Fatore x+1, para x>=0
 
Resposta: (x^0,5 + 2^0,5.x^0,25 + 1) . (x^0,5 - 2^0,5.x^0,25 + 1)
 
 
Esse exercicio de algebra me parece estranho, pois a variavel fica dentro da raiz, alguem poderia me explicar por favor?
 
 
Abraço a Todos e Obrigado

Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-848668211-1206713998=:91402-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Fri Mar 28 11:36:55 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2SEZvWA017765 for ; Fri, 28 Mar 2008 11:35:57 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2SEZvDI017763 for obm-l-MllGbsmmN; Fri, 28 Mar 2008 11:35:57 -0300 Received: from el-out-1112.google.com (el-out-1112.google.com [209.85.162.179]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2SEZtWA017758 for ; Fri, 28 Mar 2008 11:35:55 -0300 Received: by el-out-1112.google.com with SMTP id o28so114261ele.3 for ; Fri, 28 Mar 2008 07:35:39 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; bh=DclhMLPIFQTnKUd6KnXtkP+vGXFvpHqL5PM9jluXNmE=; b=iD510LNh1HXks/prhegPec1chnntkU4HUTU8tweAkbzjGiQHaHD8AgF4meTEodu+7VbCYJroQ8RPcDPoTVXYk6vkdhHTNldxlto6WGydF8DIkSUVHV9WC1WA3w2ts7Etht+BPpcp2b8mb9yd+pboWci2ykJDaG/ZVaIK0+VKFKk= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; b=kEdByFB0H8UVJoVWtGBxZzeq8OaVTCvwvGDQiU8deE9XQTfIqk/AWlGBqd/AoNPCQWYhrd5qGt6fJkMJXUaECXIAiQgrBH+G34UE7cB+vXAnfb+6sgOfqia2iOXrn/nkc0MiPCUBaNZr1OfhOur7jTd6Wtki70PpHBujhChyab0= Received: by 10.141.185.3 with SMTP id m3mr1442188rvp.40.1206714938751; Fri, 28 Mar 2008 07:35:38 -0700 (PDT) Received: by 10.141.160.14 with HTTP; Fri, 28 Mar 2008 07:35:38 -0700 (PDT) Message-ID: <2b5739960803280735y1f787f86w92700523971a70f8@mail.gmail.com> Date: Fri, 28 Mar 2008 11:35:38 -0300 From: "Rogerio Ponce" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Pintores In-Reply-To: <70bb75a50803280616i1f554269q1ede36e9cda122b0@mail.gmail.com> MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline References: <70bb75a50803280616i1f554269q1ede36e9cda122b0@mail.gmail.com> Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m2SEZuWA017761 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Rogerio Ponce" X-Spam-Status: No, hits=3.7 required=5.0 tests=AWL,IN_REP_TO,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: *** Ola' Emanuel, digamos que a pessoa A pinte R m2 de muro por minuto , e B pinte S m2 / minuto. Entao, A e B pintam 1m2 de muro em 1/R minutos e 1/S minutos , respectivamente. Portanto, conforme o enunciado, 1/R - 1/S = 1 E trabalhando juntas, pintam (R+S) m2 por minuto, que e' o mesmo que 60*(R+S) m2 por hora, e que, segundo o enunciado, vale 27. Entao, temos as seguintes equacoes: 1/R - 1/S = 1 60*(R+S) = 27 E daqui em diante, voce sabe completar... []'s Rogerio Ponce 2008/3/28, Emanuel Valente : > Não consegui montar algebricamente o seguinte problema. Ficarei grato > se me ajudarem! > > Duas pessoas, A e B, pintam separadamente 1m^2 de um muro em tempos > que diferem de 1 minuto. Trabalhando juntas, elas pintam 27m^2 por > hora. Quanto tempo cada uma leva pra pintar 1 m^2 ? > ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Fri Mar 28 12:14:30 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2SFDRWA031715 for ; Fri, 28 Mar 2008 12:13:27 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2SFDQ12031711 for obm-l-MllGbsmmN; Fri, 28 Mar 2008 12:13:26 -0300 Received: from wa-out-1112.google.com (wa-out-1112.google.com [209.85.146.177]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2SFDMWA031657 for ; Fri, 28 Mar 2008 12:13:23 -0300 Received: by wa-out-1112.google.com with SMTP id m28so349293wag.13 for ; Fri, 28 Mar 2008 08:13:06 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; bh=2o1JtjpMg3HZVhYKzBfvECBCNR78Logd5SLhF98dwCc=; b=Ble9lsvo8tblHibHhj0rzm0S80mYqFrzV+AHyAxW35FRN3yhttO+6MXFMOYcjMy7PCJ14WUiGZVCnQ5zTFF+PRX+MGaaMqWIoDkiEpKjI4covLfJwrER5I5QQniTs2aLJjxL62+3cC1UWA3xAxA9vo6O8t53+XFCXpWQfjUkrMY= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; b=UZnOuC/Rm/io8nCpSZpj449sEgQgR+sDt35WOapex3KkaWR6N0En/b4zdJK6ACgdZ7awW7i6uu+DF5Xb0WyW6b2+JDNzyNxqwsA+SlFEX8/W/bYAFry1mpoTnaqDS34FARI+M8vU7lCQn3YiIrTcthmivLivzFmXUq7Zu4Cpjpg= Received: by 10.115.18.1 with SMTP id v1mr3953800wai.15.1206716737238; Fri, 28 Mar 2008 08:05:37 -0700 (PDT) Received: by 10.114.176.17 with HTTP; Fri, 28 Mar 2008 08:05:37 -0700 (PDT) Message-ID: <1bcd8af0803280805m1c430e73lb7c9c4bc0c1d046f@mail.gmail.com> Date: Fri, 28 Mar 2008 16:05:37 +0100 From: "Bernardo Freitas Paulo da Costa" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Geometria Plana / Algebra In-Reply-To: <346017.91402.qm@web56611.mail.re3.yahoo.com> MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline References: <346017.91402.qm@web56611.mail.re3.yahoo.com> Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m2SFDOWA031696 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Bernardo Freitas Paulo da Costa" X-Spam-Status: No, hits=2.6 required=5.0 tests=AWL,IN_REP_TO,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SIGNATURE_SHORT_SPARSE, SPAM_PHRASE_00_01,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: ** Só uma ajuda então (pro de geometria, o de álgebra, como você falou, é pouco claro...) Esse exercício mostra bem como é importante usar vários lados da geometria juntos... a área do triângulo hachurado é (base * altura) / 2 Pegue a base no lado do quadrado, que essa é fácil de calcular. Agora, é achar a altura. Bom, aqui, você bota tudo "nos eixos", um dos jeitos é você botar o ponto de contato como origem, daí uma reta é y = x raiz(3) e a outra y = a/2 - x/2 (pra achar o a/2 e o x/2, basta você ver quanto vale "em cima da origem" (0,a/2) e depois num outro ponto qualquer - como (a,0) ou (-a,a) - pra achar o 1/2 * x). Você quer achar a altura, que é medida pelo x : substitua e seja feliz. On Fri, Mar 28, 2008 at 3:19 PM, Gustavo Souza wrote: > Se alguem puder me ajudar com esses 2 exercicios>> > > O de geometria tem um desenho, então hospedei o mesmo nesse link > > http://img148.imageshack.us/img148/5118/exercicioyi6.gif > > Resposta: a²(2.3^0,5 - 1) / 44 > > O de algebra é: > > Fatore x+1, para x>=0 > > Resposta: (x^0,5 + 2^0,5.x^0,25 + 1) . (x^0,5 - 2^0,5.x^0,25 + 1) > > > Esse exercicio de algebra me parece estranho, pois a variavel fica dentro da > raiz, alguem poderia me explicar por favor? > > > Abraço a Todos e Obrigado > > ________________________________ > > Abra sua conta no Yahoo! Mail, o único sem limite de espaço para > armazenamento! -- Bernardo Freitas Paulo da Costa ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Fri Mar 28 13:26:48 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2SGNvWA007773 for ; Fri, 28 Mar 2008 13:23:57 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2SGNuMe007771 for obm-l-MllGbsmmN; Fri, 28 Mar 2008 13:23:56 -0300 Received: from fk-out-0910.google.com (fk-out-0910.google.com [209.85.128.190]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2SGNsWA007758 for ; Fri, 28 Mar 2008 13:23:55 -0300 Received: by fk-out-0910.google.com with SMTP id 22so478743fkq.13 for ; Fri, 28 Mar 2008 09:23:38 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; bh=5SivC89tvKujNT9WfLmEBf4nVt0z9XSm0bM0PlegcfM=; b=exIQpxkRGSBMXdmyPBscfoj29lp4i8ob632N5dio0g9WUzzdeVZR/GxW7zpV2Ey1v06KJOAeJizJFwrvjh2kpJMNXy22Y8C7Ss049jABCvIHbQ3PWxN6o86qRfU3ydRVzNQRxdRQSnqSoA9+e7WIgDTleOj9Uwr0R35sTuS5bBs= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; b=lwISEcpLReYAZ1k/YBTNu0fG+IwfbJ4yb7TuQieTKBdwrByINYlPmFFFsKhDwckQRNPq8/4fL4C9+OISJX5s2SGu5BwtmJZ824LyFiaZ+aLnVwKUpC/XTFtMacGU6HCqFT7PML1k/psE39vWoz/wc+RtuvBCth8Kt4/1rHd7dx8= Received: by 10.82.188.14 with SMTP id l14mr6016938buf.37.1206721417396; Fri, 28 Mar 2008 09:23:37 -0700 (PDT) Received: by 10.82.114.8 with HTTP; Fri, 28 Mar 2008 09:23:37 -0700 (PDT) Message-ID: <70bb75a50803280923x54297a1axb1b203fe36db9d52@mail.gmail.com> Date: Fri, 28 Mar 2008 13:23:37 -0300 From: "Emanuel Valente" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Pintores In-Reply-To: <2b5739960803280735y1f787f86w92700523971a70f8@mail.gmail.com> MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline References: <70bb75a50803280616i1f554269q1ede36e9cda122b0@mail.gmail.com> <2b5739960803280735y1f787f86w92700523971a70f8@mail.gmail.com> Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m2SGNuWA007769 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Emanuel Valente" X-Spam-Status: No, hits=3.7 required=5.0 tests=AWL,IN_REP_TO,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: *** Olá, a resposta do Bernardo bateu com o gabarito (4 min e 5 min). Pra dizer a verdade estava no caminho certo, mas tinha assustado com um valor de delta alto num problema relativamente simples. Pelo que vi a equação do Rogério saiu com variáveis trocadas em relação a do Bernardo, fiz a conta e deu valor quebrado. Junior, não entendi seu raciocínio quando você escreveu: 27r + 27l = 60. Obrigado a todos dede já! -- Emanuel Valente On Fri, Mar 28, 2008 at 11:35 AM, Rogerio Ponce wrote: > Ola' Emanuel, > digamos que a pessoa A pinte R m2 de muro por minuto , e B pinte S m2 / minuto. > Entao, A e B pintam 1m2 de muro em 1/R minutos e 1/S minutos , respectivamente. > > Portanto, conforme o enunciado, > 1/R - 1/S = 1 > > E trabalhando juntas, pintam (R+S) m2 por minuto, que e' o mesmo que > 60*(R+S) m2 por hora, e que, segundo o enunciado, vale 27. > > Entao, temos as seguintes equacoes: > 1/R - 1/S = 1 > 60*(R+S) = 27 > > E daqui em diante, voce sabe completar... > []'s > Rogerio Ponce > > > 2008/3/28, Emanuel Valente : > > > > Não consegui montar algebricamente o seguinte problema. Ficarei grato > > se me ajudarem! > > > > Duas pessoas, A e B, pintam separadamente 1m^2 de um muro em tempos > > que diferem de 1 minuto. Trabalhando juntas, elas pintam 27m^2 por > > hora. Quanto tempo cada uma leva pra pintar 1 m^2 ? > > > > > > ========================================================================= > Instruções para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > ========================================================================= > ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Fri Mar 28 14:19:14 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2SHHSWA012216 for ; Fri, 28 Mar 2008 14:17:28 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2SHHSIh012214 for obm-l-MllGbsmmN; Fri, 28 Mar 2008 14:17:28 -0300 Received: from web52401.mail.re2.yahoo.com (web52401.mail.re2.yahoo.com [206.190.48.164]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id m2SHHQWA012203 for ; Fri, 28 Mar 2008 14:17:27 -0300 Received: (qmail 1777 invoked by uid 60001); 28 Mar 2008 17:17:00 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:Date:From:Subject:To:In-Reply-To:MIME-Version:Content-Type:Content-Transfer-Encoding:Message-ID; b=YYJlz342etahuqlacKjwRF5kHnuzTUI6QjNBYrZhZNYDyXYs9gs+SQR/IJRS9afz0fIkTjXlAUVop/xCCNNBw0JCp4xJWR5na5Ra9kH57z1dbisLwScVhORaNQkOVRN2Yamwp2p1O1LkIJ94zX5N4LtvPE/bGly0LfljfquDBC4=; X-YMail-OSG: pJsm.4EVM1k4ZMN5cblERoBPf2aDRpZVeSP2JWImGvvRu9VfJ8WA.yRNRhJ0NGhGqMEIzEuodiA5HkkNEKzNi8ax08hFv4yKztu5sFafncELiLwVOsqpr8VPRFCi3g-- Received: from [200.136.239.126] by web52401.mail.re2.yahoo.com via HTTP; Fri, 28 Mar 2008 14:16:59 ART Date: Fri, 28 Mar 2008 14:16:59 -0300 (ART) From: Thais Oliveira Subject: [SPAM] [obm-l] Objetos de \Aprendizagem virtual To: obm-l@mat.puc-rio.br In-Reply-To: <47EC69EE.9060900@infolink.com.br> MIME-Version: 1.0 Content-Type: text/plain Content-Transfer-Encoding: 7bit Message-ID: <101832.1746.qm@web52401.mail.re2.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Thais Oliveira X-Spam-Status: Yes, hits=7.4 required=5.0 tests=FORGED_YAHOO_RCVD,IN_REP_TO,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,RCVD_IN_RELAYS_ORDB_ORG, SPAM_PHRASE_00_01,SPAM_REDIRECTOR,SUPERLONG_LINE, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******* X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="0-1419566842-1206724619=:1746" X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (7.40 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: SUPERLONG_LINE (0.0 points) BODY: Contains a line >=199 characters long SPAM: SPAM_REDIRECTOR (0.4 points) URI: Uses open redirection service SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 164.48.190.206.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 164.48.190.206.relays.osirusoft.com.] SPAM: RCVD_IN_RELAYS_ORDB_ORG (0.6 points) RBL: Received via a relay in relays.ordb.org SPAM: [RBL check: found 126.239.136.200.relays.ordb.org.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- --0-1419566842-1206724619=:1746 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 8bit Ola pessoal, tudo bem? Estou a procura de qualquer tipo de objeto de aprendizagem virtual que facilite o ensino de matemática. Se vcs conherem sites interessantes com video, jogos, arquivo em flsh ou coisa do genero me mandem poe favor. Muito obrigada Thais --------------------------------- Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-1419566842-1206724619=:1746 Content-Type: text/html; charset=iso-8859-1 Content-Transfer-Encoding: 8bit Ola pessoal, tudo bem?

Estou a procura de qualquer tipo de objeto de aprendizagem virtual que facilite o ensino de matemática. Se vcs conherem sites interessantes com video, jogos, arquivo em flsh ou coisa do genero me mandem poe favor.

Muito obrigada

Thais

Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-1419566842-1206724619=:1746-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Fri Mar 28 14:53:25 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2SHqCWA018460 for ; Fri, 28 Mar 2008 14:52:12 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2SHqBmh018456 for obm-l-MllGbsmmN; Fri, 28 Mar 2008 14:52:11 -0300 Received: from nf-out-0910.google.com (nf-out-0910.google.com [64.233.182.190]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2SHq8WA018419 for ; Fri, 28 Mar 2008 14:52:09 -0300 Received: by nf-out-0910.google.com with SMTP id k4so275534nfd.19 for ; Fri, 28 Mar 2008 10:51:51 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=BicJggM2f6BiZIBAFBtolo0Jk5DsncKJ89k5JEPoHXk=; b=MXLZ4KcnccnZWp1k2ITuH2qVy7X3A0zhDt8PbYRJ7rl/00jFyOAPDyf/qHuK8gGvTzKNmMTM7dLIY5rb13zsPI5wmlW75co2z7NGCRmYF9KcEakHSVfm+WF3Si5X7O3NHQTzFDj1UwvdM5AngPNU73M2bt0TFhXSOsujpNZpz4I= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=hoybg4qlJvz5FelNs3jfuXo6WDm/gqfdLm86GHbUxRTCq086uX8n55Vg9A3vnZqnOjZc8+OYDUkl4nDTe3FJ2h7YgoT8KGFHGwUINdgA1nb6riOjF2jolcREUNvgaJyoX8IKJYJLTDFV9ob7KynyMgnJPO4yuHtlkfPVrJve/vc= Received: by 10.78.20.13 with SMTP id 13mr8634205hut.47.1206726708036; Fri, 28 Mar 2008 10:51:48 -0700 (PDT) Received: by 10.78.172.14 with HTTP; Fri, 28 Mar 2008 10:51:47 -0700 (PDT) Message-ID: <92295ee80803281051w374ff1dbxaa7d7a30001b6576@mail.gmail.com> Date: Fri, 28 Mar 2008 14:51:47 -0300 From: "Fernando Lukas Miglorancia" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Objetos de \Aprendizagem virtual In-Reply-To: <101832.1746.qm@web52401.mail.re2.yahoo.com> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_26320_15871336.1206726707936" References: <47EC69EE.9060900@infolink.com.br> <101832.1746.qm@web52401.mail.re2.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Fernando Lukas Miglorancia" X-Spam-Status: No, hits=3.7 required=5.0 tests=AWL,IN_REP_TO,JAVASCRIPT_UNSAFE,MAILTO_LINK, QUOTED_EMAIL_TEXT,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, REFERENCES,SPAM_PHRASE_01_02,SPAM_REDIRECTOR, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: *** ------=_Part_26320_15871336.1206726707936 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Ol=E1, Thais, Se eu descobrir algo, te mando sim. Abra=E7=E3o, Fernando 2008/3/28, Thais Oliveira : > > Ola pessoal, tudo bem? > > Estou a procura de qualquer tipo de objeto de aprendizagem virtual que > facilite o ensino de matem=E1tica. Se vcs conherem sites interessantes co= m > video, jogos, arquivo em flsh ou coisa do genero me mandem poe favor. > > Muito obrigada > > Thais > > ------------------------------ > Abra sua conta no Yahoo! Mail, > o =FAnico sem limite de espa=E7o para armazenamento! > > ------=_Part_26320_15871336.1206726707936 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline
 Ol=E1, Thais,
 
 
  Se eu descobrir algo, te  mando sim.
 
  Abra=E7=E3o,
 
  Fernando

 
2008/3/28, Thais Oliveira <tha_unicamp@yahoo.com.br>:
Ola pessoal, tudo bem?

Es= tou a procura de qualquer tipo de objeto de aprendizagem virtual que facili= te o ensino de matem=E1tica. Se vcs conherem sites interessantes com video,= jogos, arquivo em flsh ou coisa do genero me mandem poe favor.

Muito obrigada

Thais

Abra sua conta no Yahoo! Mail, o =FAnico sem limite de espa=E7o p= ara armazenamento!=20


------=_Part_26320_15871336.1206726707936-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Fri Mar 28 16:35:42 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2SJXqWA004416 for ; Fri, 28 Mar 2008 16:33:52 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2SJXq4Y004414 for obm-l-MllGbsmmN; Fri, 28 Mar 2008 16:33:52 -0300 Received: from web52402.mail.re2.yahoo.com (web52402.mail.re2.yahoo.com [206.190.48.165]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id m2SJXoWA004410 for ; Fri, 28 Mar 2008 16:33:51 -0300 Received: (qmail 77908 invoked by uid 60001); 28 Mar 2008 19:33:30 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:Date:From:Subject:To:In-Reply-To:MIME-Version:Content-Type:Content-Transfer-Encoding:Message-ID; b=EaMZAOh0mhGN1eSNpqyzSagKOTTAodClsutKXCKvXRBTkUGPK1QeMb4tMwL2boVcqn49DPu7nZLdIEYpNc9vivRGF4vBUG+4t2wV2G1ao/8G+aUXtceG8N27cRFMzEpI4s+gLuDDoiRXKfSBb2uppplnAl5+Kj2ce0SGk877Urw=; X-YMail-OSG: 03m6NZkVM1m8RAe3GWKsKNUe3s2kWzd4s2ayDohQX6fyU1VPPI4z0iIasRqMQc7HenHLlQUqENbh2PMFRUxJcIPEj0QNrcAL2wlk0TOix8S6LoITk1hRsY4ufbO54g-- Received: from [200.136.239.24] by web52402.mail.re2.yahoo.com via HTTP; Fri, 28 Mar 2008 16:33:30 ART Date: Fri, 28 Mar 2008 16:33:30 -0300 (ART) From: Thais Oliveira Subject: [SPAM] Re: [obm-l] Objetos de \Aprendizagem virtual To: obm-l@mat.puc-rio.br In-Reply-To: <92295ee80803281051w374ff1dbxaa7d7a30001b6576@mail.gmail.com> MIME-Version: 1.0 Content-Type: text/plain Content-Transfer-Encoding: 7bit Message-ID: <341065.77668.qm@web52402.mail.re2.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Thais Oliveira X-Spam-Status: Yes, hits=8.3 required=5.0 tests=AWL,FORGED_YAHOO_RCVD,IN_REP_TO,JAVASCRIPT_UNSAFE, MAILTO_LINK,MIME_BOUND_DIGITS_5,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,RCVD_IN_RELAYS_ORDB_ORG, SPAM_PHRASE_01_02,SPAM_REDIRECTOR,SUPERLONG_LINE, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="0-436183384-1206732810=:77668" X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (8.30 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: MIME_BOUND_DIGITS_5 (1.7 points) Spam tool pattern in MIME boundary SPAM: SPAM_PHRASE_01_02 (0.5 points) BODY: Spam phrases score is 01 to 02 (low) SPAM: [score: 1] SPAM: JAVASCRIPT_UNSAFE (0.3 points) BODY: Easily-executed JavaScript code SPAM: MAILTO_LINK (0.2 points) BODY: Includes a URL link to send an email SPAM: SUPERLONG_LINE (0.0 points) BODY: Contains a line >=199 characters long SPAM: SPAM_REDIRECTOR (0.4 points) URI: Uses open redirection service SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 165.48.190.206.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 165.48.190.206.relays.osirusoft.com.] SPAM: RCVD_IN_RELAYS_ORDB_ORG (0.6 points) RBL: Received via a relay in relays.ordb.org SPAM: [RBL check: found 24.239.136.200.relays.ordb.org.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-1.0 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- --0-436183384-1206732810=:77668 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 8bit Obrigada Fernando! Fernando Lukas Miglorancia escreveu: Olá, Thais, Se eu descobrir algo, te mando sim. Abração, Fernando 2008/3/28, Thais Oliveira : Ola pessoal, tudo bem? Estou a procura de qualquer tipo de objeto de aprendizagem virtual que facilite o ensino de matemática. Se vcs conherem sites interessantes com video, jogos, arquivo em flsh ou coisa do genero me mandem poe favor. Muito obrigada Thais --------------------------------- Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --------------------------------- Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-436183384-1206732810=:77668 Content-Type: text/html; charset=iso-8859-1 Content-Transfer-Encoding: 8bit Obrigada Fernando!

Fernando Lukas Miglorancia <fernandomiglorancia@gmail.com> escreveu:
 Olá, Thais,
 
 
  Se eu descobrir algo, te  mando sim.
 
  Abração,
 
  Fernando

 
2008/3/28, Thais Oliveira <tha_unicamp@yahoo.com.br>:
Ola pessoal, tudo bem?

Estou a procura de qualquer tipo de objeto de aprendizagem virtual que facilite o ensino de matemática. Se vcs conherem sites interessantes com video, jogos, arquivo em flsh ou coisa do genero me mandem poe favor.

Muito obrigada

Thais
Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento!


Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-436183384-1206732810=:77668-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Fri Mar 28 18:55:13 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2SLrHWA019912 for ; Fri, 28 Mar 2008 18:53:17 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2SLrGBL019909 for obm-l-MllGbsmmN; Fri, 28 Mar 2008 18:53:16 -0300 Received: from rv-out-0910.google.com (rv-out-0910.google.com [209.85.198.190]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2SLhkWA016547 for ; Fri, 28 Mar 2008 18:46:21 -0300 Received: by rv-out-0910.google.com with SMTP id c27so253567rvf.9 for ; Fri, 28 Mar 2008 14:43:20 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=NpZ84nQw7TZFXv9IwbbSHPUnyPU7Dt22pG4tJFki2pQ=; b=ek+VewUhTeG2HUfRoAQ7NSoOxCcKADd5XqyEKlzxv/xvTLf/k+w0V4JuL+IhMVZJ7Klb/K3UvwXEHocoakw/qW5s3qzvxlxgi/6bWr9dp4WG6pZiR7UHwP2DmL5kTAUKC4XHn0oMtzN9Db0rif0MJoKIyM2QnYQHdDsozw7pzJw= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=sZCLIINT1/0w9xQ8n0Md9hbKbSnmjTKPyvDInSptlrMLgHp1Detfga4Np/kVA2ORgk3N+ELB/bBQj5mGhMYQHMb/B6pL4Ea8p0Du1iXNISQzBAMt+52KwMKg2jAEnIelAOy921mheIyfVT/u0ROJgtDUBlWIe932wYMtRSs9bxE= Received: by 10.141.198.9 with SMTP id a9mr1822316rvq.219.1206740600905; Fri, 28 Mar 2008 14:43:20 -0700 (PDT) Received: by 10.140.132.5 with HTTP; Fri, 28 Mar 2008 14:43:20 -0700 (PDT) Message-ID: <49b5b5d60803281443q2268d45cs2cd6aad3e7c02c17@mail.gmail.com> Date: Fri, 28 Mar 2008 18:43:20 -0300 From: "Fernando A Candeias" To: obm-l@mat.puc-rio.br Subject: =?ISO-8859-1?Q?Re:_[obm-l]_Conjuntos_num=E9ricos_na_Reta...?= In-Reply-To: <47EC69EE.9060900@infolink.com.br> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_22125_14635968.1206740600901" References: <200803271845.m2RIj2WA020799@saci.mat.puc-rio.br> <2d483c770803271230tc8e3041vfda8ab9cfcbfe8bb@mail.gmail.com> <47EC69EE.9060900@infolink.com.br> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Fernando A Candeias" X-Spam-Status: No, hits=4.2 required=5.0 tests=IN_REP_TO,JAVASCRIPT_UNSAFE,MAILTO_LINK,QUOTED_EMAIL_TEXT, RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,REFERENCES, SPAM_PHRASE_00_01,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** ------=_Part_22125_14635968.1206740600901 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Caros colegas de lista Uma outra maneira de responder ao questionamento do Paulo, mais trabalhosa por=E9m mais intuitiva, est=E1 descrita em Foundations of Geometry, de Hilb= ert. Ele desenvolve a geometria de maneira puramente axiom=E1tica, e no # 8 trat= a dos axiomas de continuiidade, que s=E3o o de Arquimedes V.1 e o da Completu= de da Reta, V.2. A partir do que, juntamente com os axiomas que dizem respeit= o =E0 ordem, =E9 poss=EDvel demonstrar a equival=EAncia entre os pontos da r= eta e do conjunto dos reais. Em outro livro que tenho, de G. Verrier, uma introdu=E7=E3o =E0s geometrias= n=E3o euclidianas por m=E9todos elementares, o autor substitui os dois postulados citados pelo axioma de Dedekind, o que imediatamente identifica a reta geom=E9trica com os reais, como dito pelo Ralph. O livro baseia-se na obra = de Hilbert. Trata de todos axiomas comuns =E0s tr=EAs geomertrias, e posterior= mente introduz novos postulados e/ou suprime alguns, a partir do que desenvolve = o assunto. Tudo por m=E9todos elementares. =C9 muito interessante. Est=E1 esc= rito em franc=EAs, adquiri em 1951, creio que esta esgotado. Mas se algu=E9m ti= ver interesse, posso do=E1-lo juntamente com o de Hilbert. Sobre os surreais conhe=E7o pouco, mas parece muito interessante a id=E9ia = de que os numeros infinitesimais passem a ter exist=EAncia efetiva, o que dispensaria em parte os complicados =E9psilons e deltas da defini=E7=E3o us= ual de continuidade de uma fun=E7=E3o em um ponto. (Weierstrasse). Vou ver se enco= ntro o livro mencionado pelo Nehab. Gostaria de saber como os problemas geom=E9ricos s=E3o abordados, se fazendo corresponder a cada segmento de re= ta a parte Re do surreal, ou o n=FAmero completo, incluindo um infinitesimal. Ne= ssa hip=F3tese lembraria Leibntz com suas m=F4nadas, ou o sonho pitag=F3rico do= "tudo =E9 n=FAmero". Fernando A Candeias 2008/3/28, Carlos Nehab : > > Oi, Ralph (e Paulo), > > Apenas matando as suadades...um r=E1pido coment=E1rio: > > Para os aficcionados, o livro "Surreal Numbers" =E9 "quase" novelesco (co= m > fundo matem=E1tico, =E9 claro) do Knuth (um verdadeiro mago) e j=E1 foi t= raduzido > para o portugu=EAs (a edi=E7=E3o original tem mais de 30 anos - eu era qu= ase um > "pirralho" na =E9poca :-) e ainda dava aula no IME...- ah... que > saudades Ralph me lembrou...). > =C9 um belo, pequeno e imperd=EDvel livro para a maioria dos participant= es > desta lista. Quem ainda n=E3o leu em ingl=EAs, aproveite: eu comprei no = come=E7o > do ano uma c=F3pia em portugu=EAs na livraria da Travessa (acho que foi u= ns 40 > reais - mas pela Amazon em ingl=EAs =E9 naturalmente mais barato). > > E aproveitando a deixa do Ralph, quem for curioso tamb=E9m pode e deve da= r > estudar Fuzzy Sets, Fuzzy Numbers (Numeros Nebulosos, etc). Os de Engenha= ria > El=E9trica ou Computa=E7=E3o, certamente ter=E3o contato com isto, bem co= mo com > Algoritmos Gen=E9ticos... > > Ou seja, h=E1 muito mais coisa para se aprender do que sup=F5e a v=E3 flo= sofia, > ou mesmo a reta (sur)real... > > Abra=E7os, > Nehab > > Ralph Teixeira escreveu: > > .......P.S.: Por outro lado, d=E1 para definir n=FAmeros "surreais" (veja= http://en.wikipedia.org/wiki/Surreal_numbers). Para trabalhar com > eles, algumas propriedades antigas t=EAm de ser descartadas (por > exemplo, neles a<=3Db e b<=3Da n=E3o implica a=3Db), mas eles s=E3o bem b= acanas, > s=E3o uma extens=E3o dos reais que n=E3o tem nada a ver com os complexos = e o > pessoal tenta pensar neles ainda numa esp=E9cie de "reta", usando > "nuvens" ao inv=E9s de "pontos", incluindo uns "pontos no infinito" e > fazendo v=E1rias outras barb=E1ries. Por incr=EDvel que pare=E7a, no fina= l, > tudo funciona, as constru=E7=F5es s=E3o justificadas formalmente e estes > objetos t=EAm aplica=E7=F5es. > > > > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > Instru=E7=F5es para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D --=20 Fernando A Candeias ------=_Part_22125_14635968.1206740600901 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline
Caros colegas de lista
 
Uma outra maneira de responder ao questionamento do Paulo, mais trabal= hosa por=E9m mais intuitiva, est=E1 descrita em Foundations of Geometry, de= Hilbert. Ele desenvolve a geometria de maneira puramente axiom=E1tica, e n= o # 8 trata dos axiomas de continuiidade, que s=E3o o de Arquimedes V.1 e o= da Completude da Reta,  V.2. A partir do que, juntamente com os = axiomas que dizem respeito =E0 ordem, =E9 poss=EDvel demonstrar  = a equival=EAncia entre os pontos da reta e do conjunto dos reais.=
Em outro livro que tenho, de G. Verrier, uma introdu=E7=E3o =E0s geome= trias n=E3o euclidianas por m=E9todos elementares, o autor substitui os doi= s postulados citados pelo axioma de Dedekind, o que imediatamente identific= a a reta geom=E9trica com os reais, como dito pelo Ralph. O livro base= ia-se na obra de Hilbert. Trata de todos axiomas comuns =E0s tr=EAs geomert= rias, e posteriormente introduz novos postulados e/ou suprime alguns, = a partir do que desenvolve o assunto. Tudo por m=E9todos elementares.= =C9 muito interessante. Est=E1 escrito  em franc=EAs, adqui= ri em 1951, creio que esta esgotado. Mas se algu=E9m tiver interesse, posso= do=E1-lo juntamente com o de Hilbert.
Sobre os surreais conhe=E7o pouco, mas parece muito interessante a id= =E9ia de que os numeros infinitesimais passem a ter exist=EAncia efetiva, o= que dispensaria em parte os complicados =E9psilons e deltas da defini=E7= =E3o usual de continuidade de uma fun=E7=E3o em um ponto. (Weierstrasse).&n= bsp;Vou ver se encontro o livro mencionado pelo Nehab. Gostaria de saber co= mo os problemas geom=E9ricos s=E3o abordados, se fazendo corresponder&= nbsp;a cada segmento de reta a parte Re do surreal, ou o n=FAmero=  completo, incluindo um infinitesimal. Nessa hip=F3tese lembraria= Leibntz com suas m=F4nadas, ou o sonho pitag=F3rico do "tudo =E9= n=FAmero".
 
Fernando A Candeias
 
2008/3/28, Carlos Nehab <nehab@infolink.com.br>:
Oi, Ralph (e= Paulo),

Apenas matando as suadades...um r=E1pido coment=E1rio:
<= br>Para os aficcionados, o livro "Surreal Numbers" =E9 "quas= e" novelesco (com fundo matem=E1tico, =E9 claro) do Knuth (um verdadei= ro mago) e j=E1 foi traduzido para o portugu=EAs (a edi=E7=E3o original tem= mais de 30 anos - eu era quase um "pirralho" na =E9poca  :-)       e  ain= da dava aula no IME...- ah... que saudades Ralph me lembrou...). 
=C9  um belo, pequeno e imperd=EDvel livro para a maioria dos particip= antes desta lista.  Quem ainda n=E3o leu em ingl=EAs, aproveite: eu co= mprei no come=E7o do ano uma c=F3pia em portugu=EAs na livraria da Travessa= (acho que foi uns 40 reais - mas pela Amazon em ingl=EAs =E9 naturalmente = mais barato).

E aproveitando a deixa do Ralph, quem for curioso tamb=E9m pode e deve = dar estudar Fuzzy Sets, Fuzzy Numbers (Numeros Nebulosos, etc). Os de Engen= haria El=E9trica ou Computa=E7=E3o, certamente ter=E3o contato com isto, be= m como com Algoritmos Gen=E9ticos...

Ou seja, h=E1 muito mais coisa para se aprender do que sup=F5e a v=E3 f= losofia, ou mesmo a reta (sur)real...

Abra=E7os,
Nehab

Ralph Teixeira escreveu:=20 
.......
P.S.: Por outro lado, d=E1 para definir n=FAmeros "s=
urreais" (veja
http://en.wikipedi=
a.org/wiki/Surreal_numbers). Para trabalhar com
eles, algumas propriedades antigas t=EAm de ser descartadas (por
exemplo, neles a<=3Db e b<=3Da n=E3o implica a=3Db), mas eles s=E3o b=
em bacanas,
s=E3o uma extens=E3o dos reais que n=E3o tem nada a ver com os complexos e =
o
pessoal tenta pensar neles ainda numa esp=E9cie de "reta", usando
"nuvens" ao inv=E9s de "pontos", incluindo uns "po=
ntos no infinito" e
fazendo v=E1rias outras barb=E1ries. Por incr=EDvel que pare=E7a, no final,
tudo funciona, as constru=E7=F5es s=E3o justificadas formalmente e estes
objetos t=EAm aplica=E7=F5es.

 
=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D Instru= =E7=F5es para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br= /~obmlistas/obm-l.html =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D



--
Fernando A Candeias=20 ------=_Part_22125_14635968.1206740600901-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Fri Mar 28 18:57:21 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2SLuRWA020959 for ; Fri, 28 Mar 2008 18:56:27 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2SLuRo7020956 for obm-l-MllGbsmmN; Fri, 28 Mar 2008 18:56:27 -0300 Received: from rv-out-0910.google.com (rv-out-0910.google.com [209.85.198.187]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2SLoWWA018832 for ; Fri, 28 Mar 2008 18:51:50 -0300 Received: by rv-out-0910.google.com with SMTP id c27so255188rvf.9 for ; Fri, 28 Mar 2008 14:50:07 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=NpZ84nQw7TZFXv9IwbbSHPUnyPU7Dt22pG4tJFki2pQ=; b=ek+VewUhTeG2HUfRoAQ7NSoOxCcKADd5XqyEKlzxv/xvTLf/k+w0V4JuL+IhMVZJ7Klb/K3UvwXEHocoakw/qW5s3qzvxlxgi/6bWr9dp4WG6pZiR7UHwP2DmL5kTAUKC4XHn0oMtzN9Db0rif0MJoKIyM2QnYQHdDsozw7pzJw= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=sZCLIINT1/0w9xQ8n0Md9hbKbSnmjTKPyvDInSptlrMLgHp1Detfga4Np/kVA2ORgk3N+ELB/bBQj5mGhMYQHMb/B6pL4Ea8p0Du1iXNISQzBAMt+52KwMKg2jAEnIelAOy921mheIyfVT/u0ROJgtDUBlWIe932wYMtRSs9bxE= Received: by 10.141.198.9 with SMTP id a9mr1822316rvq.219.1206740600905; Fri, 28 Mar 2008 14:43:20 -0700 (PDT) Received: by 10.140.132.5 with HTTP; Fri, 28 Mar 2008 14:43:20 -0700 (PDT) Message-ID: <49b5b5d60803281443q2268d45cs2cd6aad3e7c02c17@mail.gmail.com> Date: Fri, 28 Mar 2008 18:43:20 -0300 From: "Fernando A Candeias" To: obm-l@mat.puc-rio.br Subject: =?ISO-8859-1?Q?Re:_[obm-l]_Conjuntos_num=E9ricos_na_Reta...?= In-Reply-To: <47EC69EE.9060900@infolink.com.br> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_22125_14635968.1206740600901" References: <200803271845.m2RIj2WA020799@saci.mat.puc-rio.br> <2d483c770803271230tc8e3041vfda8ab9cfcbfe8bb@mail.gmail.com> <47EC69EE.9060900@infolink.com.br> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Fernando A Candeias" X-Spam-Status: No, hits=4.2 required=5.0 tests=IN_REP_TO,JAVASCRIPT_UNSAFE,MAILTO_LINK,QUOTED_EMAIL_TEXT, RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,REFERENCES, SPAM_PHRASE_00_01,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** ------=_Part_22125_14635968.1206740600901 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Caros colegas de lista Uma outra maneira de responder ao questionamento do Paulo, mais trabalhosa por=E9m mais intuitiva, est=E1 descrita em Foundations of Geometry, de Hilb= ert. Ele desenvolve a geometria de maneira puramente axiom=E1tica, e no # 8 trat= a dos axiomas de continuiidade, que s=E3o o de Arquimedes V.1 e o da Completu= de da Reta, V.2. A partir do que, juntamente com os axiomas que dizem respeit= o =E0 ordem, =E9 poss=EDvel demonstrar a equival=EAncia entre os pontos da r= eta e do conjunto dos reais. Em outro livro que tenho, de G. Verrier, uma introdu=E7=E3o =E0s geometrias= n=E3o euclidianas por m=E9todos elementares, o autor substitui os dois postulados citados pelo axioma de Dedekind, o que imediatamente identifica a reta geom=E9trica com os reais, como dito pelo Ralph. O livro baseia-se na obra = de Hilbert. Trata de todos axiomas comuns =E0s tr=EAs geomertrias, e posterior= mente introduz novos postulados e/ou suprime alguns, a partir do que desenvolve = o assunto. Tudo por m=E9todos elementares. =C9 muito interessante. Est=E1 esc= rito em franc=EAs, adquiri em 1951, creio que esta esgotado. Mas se algu=E9m ti= ver interesse, posso do=E1-lo juntamente com o de Hilbert. Sobre os surreais conhe=E7o pouco, mas parece muito interessante a id=E9ia = de que os numeros infinitesimais passem a ter exist=EAncia efetiva, o que dispensaria em parte os complicados =E9psilons e deltas da defini=E7=E3o us= ual de continuidade de uma fun=E7=E3o em um ponto. (Weierstrasse). Vou ver se enco= ntro o livro mencionado pelo Nehab. Gostaria de saber como os problemas geom=E9ricos s=E3o abordados, se fazendo corresponder a cada segmento de re= ta a parte Re do surreal, ou o n=FAmero completo, incluindo um infinitesimal. Ne= ssa hip=F3tese lembraria Leibntz com suas m=F4nadas, ou o sonho pitag=F3rico do= "tudo =E9 n=FAmero". Fernando A Candeias 2008/3/28, Carlos Nehab : > > Oi, Ralph (e Paulo), > > Apenas matando as suadades...um r=E1pido coment=E1rio: > > Para os aficcionados, o livro "Surreal Numbers" =E9 "quase" novelesco (co= m > fundo matem=E1tico, =E9 claro) do Knuth (um verdadeiro mago) e j=E1 foi t= raduzido > para o portugu=EAs (a edi=E7=E3o original tem mais de 30 anos - eu era qu= ase um > "pirralho" na =E9poca :-) e ainda dava aula no IME...- ah... que > saudades Ralph me lembrou...). > =C9 um belo, pequeno e imperd=EDvel livro para a maioria dos participant= es > desta lista. Quem ainda n=E3o leu em ingl=EAs, aproveite: eu comprei no = come=E7o > do ano uma c=F3pia em portugu=EAs na livraria da Travessa (acho que foi u= ns 40 > reais - mas pela Amazon em ingl=EAs =E9 naturalmente mais barato). > > E aproveitando a deixa do Ralph, quem for curioso tamb=E9m pode e deve da= r > estudar Fuzzy Sets, Fuzzy Numbers (Numeros Nebulosos, etc). Os de Engenha= ria > El=E9trica ou Computa=E7=E3o, certamente ter=E3o contato com isto, bem co= mo com > Algoritmos Gen=E9ticos... > > Ou seja, h=E1 muito mais coisa para se aprender do que sup=F5e a v=E3 flo= sofia, > ou mesmo a reta (sur)real... > > Abra=E7os, > Nehab > > Ralph Teixeira escreveu: > > .......P.S.: Por outro lado, d=E1 para definir n=FAmeros "surreais" (veja= http://en.wikipedia.org/wiki/Surreal_numbers). Para trabalhar com > eles, algumas propriedades antigas t=EAm de ser descartadas (por > exemplo, neles a<=3Db e b<=3Da n=E3o implica a=3Db), mas eles s=E3o bem b= acanas, > s=E3o uma extens=E3o dos reais que n=E3o tem nada a ver com os complexos = e o > pessoal tenta pensar neles ainda numa esp=E9cie de "reta", usando > "nuvens" ao inv=E9s de "pontos", incluindo uns "pontos no infinito" e > fazendo v=E1rias outras barb=E1ries. Por incr=EDvel que pare=E7a, no fina= l, > tudo funciona, as constru=E7=F5es s=E3o justificadas formalmente e estes > objetos t=EAm aplica=E7=F5es. > > > > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > Instru=E7=F5es para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D --=20 Fernando A Candeias ------=_Part_22125_14635968.1206740600901 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline
Caros colegas de lista
 
Uma outra maneira de responder ao questionamento do Paulo, mais trabal= hosa por=E9m mais intuitiva, est=E1 descrita em Foundations of Geometry, de= Hilbert. Ele desenvolve a geometria de maneira puramente axiom=E1tica, e n= o # 8 trata dos axiomas de continuiidade, que s=E3o o de Arquimedes V.1 e o= da Completude da Reta,  V.2. A partir do que, juntamente com os = axiomas que dizem respeito =E0 ordem, =E9 poss=EDvel demonstrar  = a equival=EAncia entre os pontos da reta e do conjunto dos reais.=
Em outro livro que tenho, de G. Verrier, uma introdu=E7=E3o =E0s geome= trias n=E3o euclidianas por m=E9todos elementares, o autor substitui os doi= s postulados citados pelo axioma de Dedekind, o que imediatamente identific= a a reta geom=E9trica com os reais, como dito pelo Ralph. O livro base= ia-se na obra de Hilbert. Trata de todos axiomas comuns =E0s tr=EAs geomert= rias, e posteriormente introduz novos postulados e/ou suprime alguns, = a partir do que desenvolve o assunto. Tudo por m=E9todos elementares.= =C9 muito interessante. Est=E1 escrito  em franc=EAs, adqui= ri em 1951, creio que esta esgotado. Mas se algu=E9m tiver interesse, posso= do=E1-lo juntamente com o de Hilbert.
Sobre os surreais conhe=E7o pouco, mas parece muito interessante a id= =E9ia de que os numeros infinitesimais passem a ter exist=EAncia efetiva, o= que dispensaria em parte os complicados =E9psilons e deltas da defini=E7= =E3o usual de continuidade de uma fun=E7=E3o em um ponto. (Weierstrasse).&n= bsp;Vou ver se encontro o livro mencionado pelo Nehab. Gostaria de saber co= mo os problemas geom=E9ricos s=E3o abordados, se fazendo corresponder&= nbsp;a cada segmento de reta a parte Re do surreal, ou o n=FAmero=  completo, incluindo um infinitesimal. Nessa hip=F3tese lembraria= Leibntz com suas m=F4nadas, ou o sonho pitag=F3rico do "tudo =E9= n=FAmero".
 
Fernando A Candeias
 
2008/3/28, Carlos Nehab <nehab@infolink.com.br>:
Oi, Ralph (e= Paulo),

Apenas matando as suadades...um r=E1pido coment=E1rio:
<= br>Para os aficcionados, o livro "Surreal Numbers" =E9 "quas= e" novelesco (com fundo matem=E1tico, =E9 claro) do Knuth (um verdadei= ro mago) e j=E1 foi traduzido para o portugu=EAs (a edi=E7=E3o original tem= mais de 30 anos - eu era quase um "pirralho" na =E9poca  :-)       e  ain= da dava aula no IME...- ah... que saudades Ralph me lembrou...). 
=C9  um belo, pequeno e imperd=EDvel livro para a maioria dos particip= antes desta lista.  Quem ainda n=E3o leu em ingl=EAs, aproveite: eu co= mprei no come=E7o do ano uma c=F3pia em portugu=EAs na livraria da Travessa= (acho que foi uns 40 reais - mas pela Amazon em ingl=EAs =E9 naturalmente = mais barato).

E aproveitando a deixa do Ralph, quem for curioso tamb=E9m pode e deve = dar estudar Fuzzy Sets, Fuzzy Numbers (Numeros Nebulosos, etc). Os de Engen= haria El=E9trica ou Computa=E7=E3o, certamente ter=E3o contato com isto, be= m como com Algoritmos Gen=E9ticos...

Ou seja, h=E1 muito mais coisa para se aprender do que sup=F5e a v=E3 f= losofia, ou mesmo a reta (sur)real...

Abra=E7os,
Nehab

Ralph Teixeira escreveu:=20 
.......
P.S.: Por outro lado, d=E1 para definir n=FAmeros "s=
urreais" (veja
http://en.wikipedi=
a.org/wiki/Surreal_numbers). Para trabalhar com
eles, algumas propriedades antigas t=EAm de ser descartadas (por
exemplo, neles a<=3Db e b<=3Da n=E3o implica a=3Db), mas eles s=E3o b=
em bacanas,
s=E3o uma extens=E3o dos reais que n=E3o tem nada a ver com os complexos e =
o
pessoal tenta pensar neles ainda numa esp=E9cie de "reta", usando
"nuvens" ao inv=E9s de "pontos", incluindo uns "po=
ntos no infinito" e
fazendo v=E1rias outras barb=E1ries. Por incr=EDvel que pare=E7a, no final,
tudo funciona, as constru=E7=F5es s=E3o justificadas formalmente e estes
objetos t=EAm aplica=E7=F5es.

 
=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D Instru= =E7=F5es para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br= /~obmlistas/obm-l.html =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D



--
Fernando A Candeias=20 ------=_Part_22125_14635968.1206740600901-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Fri Mar 28 19:00:42 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2SLxfWA022161 for ; Fri, 28 Mar 2008 18:59:42 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2SLxfAq022156 for obm-l-MllGbsmmN; Fri, 28 Mar 2008 18:59:41 -0300 Received: from rv-out-0910.google.com (rv-out-0910.google.com [209.85.198.190]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2SLhkWB016547 for ; Fri, 28 Mar 2008 18:59:36 -0300 Received: by rv-out-0910.google.com with SMTP id c27so253567rvf.9 for ; Fri, 28 Mar 2008 14:53:20 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=NpZ84nQw7TZFXv9IwbbSHPUnyPU7Dt22pG4tJFki2pQ=; b=ek+VewUhTeG2HUfRoAQ7NSoOxCcKADd5XqyEKlzxv/xvTLf/k+w0V4JuL+IhMVZJ7Klb/K3UvwXEHocoakw/qW5s3qzvxlxgi/6bWr9dp4WG6pZiR7UHwP2DmL5kTAUKC4XHn0oMtzN9Db0rif0MJoKIyM2QnYQHdDsozw7pzJw= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=sZCLIINT1/0w9xQ8n0Md9hbKbSnmjTKPyvDInSptlrMLgHp1Detfga4Np/kVA2ORgk3N+ELB/bBQj5mGhMYQHMb/B6pL4Ea8p0Du1iXNISQzBAMt+52KwMKg2jAEnIelAOy921mheIyfVT/u0ROJgtDUBlWIe932wYMtRSs9bxE= Received: by 10.141.198.9 with SMTP id a9mr1822316rvq.219.1206740600905; Fri, 28 Mar 2008 14:43:20 -0700 (PDT) Received: by 10.140.132.5 with HTTP; Fri, 28 Mar 2008 14:43:20 -0700 (PDT) Message-ID: <49b5b5d60803281443q2268d45cs2cd6aad3e7c02c17@mail.gmail.com> Date: Fri, 28 Mar 2008 18:43:20 -0300 From: "Fernando A Candeias" To: obm-l@mat.puc-rio.br Subject: =?ISO-8859-1?Q?Re:_[obm-l]_Conjuntos_num=E9ricos_na_Reta...?= In-Reply-To: <47EC69EE.9060900@infolink.com.br> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_22125_14635968.1206740600901" References: <200803271845.m2RIj2WA020799@saci.mat.puc-rio.br> <2d483c770803271230tc8e3041vfda8ab9cfcbfe8bb@mail.gmail.com> <47EC69EE.9060900@infolink.com.br> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Fernando A Candeias" X-Spam-Status: No, hits=4.2 required=5.0 tests=IN_REP_TO,JAVASCRIPT_UNSAFE,MAILTO_LINK,QUOTED_EMAIL_TEXT, RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,REFERENCES, SPAM_PHRASE_00_01,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** ------=_Part_22125_14635968.1206740600901 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Caros colegas de lista Uma outra maneira de responder ao questionamento do Paulo, mais trabalhosa por=E9m mais intuitiva, est=E1 descrita em Foundations of Geometry, de Hilb= ert. Ele desenvolve a geometria de maneira puramente axiom=E1tica, e no # 8 trat= a dos axiomas de continuiidade, que s=E3o o de Arquimedes V.1 e o da Completu= de da Reta, V.2. A partir do que, juntamente com os axiomas que dizem respeit= o =E0 ordem, =E9 poss=EDvel demonstrar a equival=EAncia entre os pontos da r= eta e do conjunto dos reais. Em outro livro que tenho, de G. Verrier, uma introdu=E7=E3o =E0s geometrias= n=E3o euclidianas por m=E9todos elementares, o autor substitui os dois postulados citados pelo axioma de Dedekind, o que imediatamente identifica a reta geom=E9trica com os reais, como dito pelo Ralph. O livro baseia-se na obra = de Hilbert. Trata de todos axiomas comuns =E0s tr=EAs geomertrias, e posterior= mente introduz novos postulados e/ou suprime alguns, a partir do que desenvolve = o assunto. Tudo por m=E9todos elementares. =C9 muito interessante. Est=E1 esc= rito em franc=EAs, adquiri em 1951, creio que esta esgotado. Mas se algu=E9m ti= ver interesse, posso do=E1-lo juntamente com o de Hilbert. Sobre os surreais conhe=E7o pouco, mas parece muito interessante a id=E9ia = de que os numeros infinitesimais passem a ter exist=EAncia efetiva, o que dispensaria em parte os complicados =E9psilons e deltas da defini=E7=E3o us= ual de continuidade de uma fun=E7=E3o em um ponto. (Weierstrasse). Vou ver se enco= ntro o livro mencionado pelo Nehab. Gostaria de saber como os problemas geom=E9ricos s=E3o abordados, se fazendo corresponder a cada segmento de re= ta a parte Re do surreal, ou o n=FAmero completo, incluindo um infinitesimal. Ne= ssa hip=F3tese lembraria Leibntz com suas m=F4nadas, ou o sonho pitag=F3rico do= "tudo =E9 n=FAmero". Fernando A Candeias 2008/3/28, Carlos Nehab : > > Oi, Ralph (e Paulo), > > Apenas matando as suadades...um r=E1pido coment=E1rio: > > Para os aficcionados, o livro "Surreal Numbers" =E9 "quase" novelesco (co= m > fundo matem=E1tico, =E9 claro) do Knuth (um verdadeiro mago) e j=E1 foi t= raduzido > para o portugu=EAs (a edi=E7=E3o original tem mais de 30 anos - eu era qu= ase um > "pirralho" na =E9poca :-) e ainda dava aula no IME...- ah... que > saudades Ralph me lembrou...). > =C9 um belo, pequeno e imperd=EDvel livro para a maioria dos participant= es > desta lista. Quem ainda n=E3o leu em ingl=EAs, aproveite: eu comprei no = come=E7o > do ano uma c=F3pia em portugu=EAs na livraria da Travessa (acho que foi u= ns 40 > reais - mas pela Amazon em ingl=EAs =E9 naturalmente mais barato). > > E aproveitando a deixa do Ralph, quem for curioso tamb=E9m pode e deve da= r > estudar Fuzzy Sets, Fuzzy Numbers (Numeros Nebulosos, etc). Os de Engenha= ria > El=E9trica ou Computa=E7=E3o, certamente ter=E3o contato com isto, bem co= mo com > Algoritmos Gen=E9ticos... > > Ou seja, h=E1 muito mais coisa para se aprender do que sup=F5e a v=E3 flo= sofia, > ou mesmo a reta (sur)real... > > Abra=E7os, > Nehab > > Ralph Teixeira escreveu: > > .......P.S.: Por outro lado, d=E1 para definir n=FAmeros "surreais" (veja= http://en.wikipedia.org/wiki/Surreal_numbers). Para trabalhar com > eles, algumas propriedades antigas t=EAm de ser descartadas (por > exemplo, neles a<=3Db e b<=3Da n=E3o implica a=3Db), mas eles s=E3o bem b= acanas, > s=E3o uma extens=E3o dos reais que n=E3o tem nada a ver com os complexos = e o > pessoal tenta pensar neles ainda numa esp=E9cie de "reta", usando > "nuvens" ao inv=E9s de "pontos", incluindo uns "pontos no infinito" e > fazendo v=E1rias outras barb=E1ries. Por incr=EDvel que pare=E7a, no fina= l, > tudo funciona, as constru=E7=F5es s=E3o justificadas formalmente e estes > objetos t=EAm aplica=E7=F5es. > > > > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > Instru=E7=F5es para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D --=20 Fernando A Candeias ------=_Part_22125_14635968.1206740600901 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline
Caros colegas de lista
 
Uma outra maneira de responder ao questionamento do Paulo, mais trabal= hosa por=E9m mais intuitiva, est=E1 descrita em Foundations of Geometry, de= Hilbert. Ele desenvolve a geometria de maneira puramente axiom=E1tica, e n= o # 8 trata dos axiomas de continuiidade, que s=E3o o de Arquimedes V.1 e o= da Completude da Reta,  V.2. A partir do que, juntamente com os = axiomas que dizem respeito =E0 ordem, =E9 poss=EDvel demonstrar  = a equival=EAncia entre os pontos da reta e do conjunto dos reais.=
Em outro livro que tenho, de G. Verrier, uma introdu=E7=E3o =E0s geome= trias n=E3o euclidianas por m=E9todos elementares, o autor substitui os doi= s postulados citados pelo axioma de Dedekind, o que imediatamente identific= a a reta geom=E9trica com os reais, como dito pelo Ralph. O livro base= ia-se na obra de Hilbert. Trata de todos axiomas comuns =E0s tr=EAs geomert= rias, e posteriormente introduz novos postulados e/ou suprime alguns, = a partir do que desenvolve o assunto. Tudo por m=E9todos elementares.= =C9 muito interessante. Est=E1 escrito  em franc=EAs, adqui= ri em 1951, creio que esta esgotado. Mas se algu=E9m tiver interesse, posso= do=E1-lo juntamente com o de Hilbert.
Sobre os surreais conhe=E7o pouco, mas parece muito interessante a id= =E9ia de que os numeros infinitesimais passem a ter exist=EAncia efetiva, o= que dispensaria em parte os complicados =E9psilons e deltas da defini=E7= =E3o usual de continuidade de uma fun=E7=E3o em um ponto. (Weierstrasse).&n= bsp;Vou ver se encontro o livro mencionado pelo Nehab. Gostaria de saber co= mo os problemas geom=E9ricos s=E3o abordados, se fazendo corresponder&= nbsp;a cada segmento de reta a parte Re do surreal, ou o n=FAmero=  completo, incluindo um infinitesimal. Nessa hip=F3tese lembraria= Leibntz com suas m=F4nadas, ou o sonho pitag=F3rico do "tudo =E9= n=FAmero".
 
Fernando A Candeias
 
2008/3/28, Carlos Nehab <nehab@infolink.com.br>:
Oi, Ralph (e= Paulo),

Apenas matando as suadades...um r=E1pido coment=E1rio:
<= br>Para os aficcionados, o livro "Surreal Numbers" =E9 "quas= e" novelesco (com fundo matem=E1tico, =E9 claro) do Knuth (um verdadei= ro mago) e j=E1 foi traduzido para o portugu=EAs (a edi=E7=E3o original tem= mais de 30 anos - eu era quase um "pirralho" na =E9poca  :-)       e  ain= da dava aula no IME...- ah... que saudades Ralph me lembrou...). 
=C9  um belo, pequeno e imperd=EDvel livro para a maioria dos particip= antes desta lista.  Quem ainda n=E3o leu em ingl=EAs, aproveite: eu co= mprei no come=E7o do ano uma c=F3pia em portugu=EAs na livraria da Travessa= (acho que foi uns 40 reais - mas pela Amazon em ingl=EAs =E9 naturalmente = mais barato).

E aproveitando a deixa do Ralph, quem for curioso tamb=E9m pode e deve = dar estudar Fuzzy Sets, Fuzzy Numbers (Numeros Nebulosos, etc). Os de Engen= haria El=E9trica ou Computa=E7=E3o, certamente ter=E3o contato com isto, be= m como com Algoritmos Gen=E9ticos...

Ou seja, h=E1 muito mais coisa para se aprender do que sup=F5e a v=E3 f= losofia, ou mesmo a reta (sur)real...

Abra=E7os,
Nehab

Ralph Teixeira escreveu:=20 
.......
P.S.: Por outro lado, d=E1 para definir n=FAmeros "s=
urreais" (veja
http://en.wikipedi=
a.org/wiki/Surreal_numbers). Para trabalhar com
eles, algumas propriedades antigas t=EAm de ser descartadas (por
exemplo, neles a<=3Db e b<=3Da n=E3o implica a=3Db), mas eles s=E3o b=
em bacanas,
s=E3o uma extens=E3o dos reais que n=E3o tem nada a ver com os complexos e =
o
pessoal tenta pensar neles ainda numa esp=E9cie de "reta", usando
"nuvens" ao inv=E9s de "pontos", incluindo uns "po=
ntos no infinito" e
fazendo v=E1rias outras barb=E1ries. Por incr=EDvel que pare=E7a, no final,
tudo funciona, as constru=E7=F5es s=E3o justificadas formalmente e estes
objetos t=EAm aplica=E7=F5es.

 
=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D Instru= =E7=F5es para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br= /~obmlistas/obm-l.html =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D



--
Fernando A Candeias=20 ------=_Part_22125_14635968.1206740600901-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Fri Mar 28 19:47:52 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2SMkcWA007102 for ; Fri, 28 Mar 2008 19:46:38 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2SMkbTV007096 for obm-l-MllGbsmmN; Fri, 28 Mar 2008 19:46:38 -0300 Received: from wa-out-1112.google.com (wa-out-1112.google.com [209.85.146.177]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2SMkWWA007029 for ; Fri, 28 Mar 2008 19:46:33 -0300 Received: by wa-out-1112.google.com with SMTP id m28so528197wag.13 for ; Fri, 28 Mar 2008 15:46:17 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=0olvI0nGofDcGUWULt6JnHfhFBVTp4iw5+lSg7fwvlc=; b=l8WINL2TyzkYAkFnXzmsMAC384/ZW9/tR+HTgicgRzd26EdbZCyBktG6nL1Iqb4vcrX5tTOqgtDfrX4ineLEolYf/+ktPjZIhAY7PbWSfoQHyBzOh3WAZJkpbgO8yDkdVAtJEuvlDxDKnikyg2/AKoOlZN/1pMvXueVgN0OsNCc= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=EXLK8xCuheuCetD4cfppg1N9UGz91UruCrqx6TiVRZfACLS5yr59I/ig9umlMsEdhBXFMtmqCEDNDMDRDwrOlCKWv/xN8HWZR9EIjlU8CR/+WgCjgIz35kGd+FcoGKQg4wUINvo68L+9YjS1pWB/U7m73Z/Lz4dSVfByZyrwTU0= Received: by 10.115.73.20 with SMTP id a20mr4896184wal.32.1206743971128; Fri, 28 Mar 2008 15:39:31 -0700 (PDT) Received: by 10.114.134.8 with HTTP; Fri, 28 Mar 2008 15:39:31 -0700 (PDT) Message-ID: <3bd00efc0803281539h42a7a848gcc44e39be3f30990@mail.gmail.com> Date: Fri, 28 Mar 2008 19:39:31 -0300 From: "Marcelo Salhab Brogliato" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] T. dos Numeros, olimpico! In-Reply-To: <99886d920803261733m20957fdcwead8e048e725b6fe@mail.gmail.com> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_20984_13513714.1206743971111" References: <99886d920803261733m20957fdcwead8e048e725b6fe@mail.gmail.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Marcelo Salhab Brogliato" X-Spam-Status: No, hits=4.3 required=5.0 tests=AWL,HTML_FONT_COLOR_GRAY,HTML_FONT_COLOR_UNSAFE,IN_REP_TO, MAILTO_LINK,MAILTO_TO_SPAM_ADDR,QUOTED_EMAIL_TEXT, RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,REFERENCES, SPAM_PHRASE_00_01,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** ------=_Part_20984_13513714.1206743971111 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Ol=E1 Bruno, suponha que exista K, tal que: (K+j)! =3D=3D j (mod 10), j =3D 1, ..., 9 vejamos: (K+1)! =3D=3D 1 (mod 10) (K+2)! =3D=3D 2 (mod 10), mas (K+2)! =3D (K+2)(K+1)! =3D=3D K+2 (mod 10) portanto, K+2 =3D=3D 2 (mod 10) .... e: K =3D=3D 0 (mod 10) (K+3)! =3D=3D 3 (mod 10), mas (K+3)! =3D (K+3)(K+2)! =3D=3D 2(K+3) (mod 10) portanto, 2(K+3) =3D 2K+6 =3D=3D 3 (mod 10) mas, K =3D=3D 0 (mod 10), e, obtemos: 6 =3D=3D 3 (mod 10) ABSURDO! portanto, est=E1 provado que n=E3o existe. um abra=E7o, Salhab 2008/3/26 Bruno Fran=E7a dos Reis : > Problema: > > Prove que n=E3o existem numeros fatoriais consecutivos com primeiros digi= tos > iguais a 1, 2, ..., 9. > Em outras palavras: prove que n=E3o existe K tal que (K+j)! comece pelo > algarismo j, para todo j =3D 1, ..., 9. > > Abra=E7o > Bruno > > -- > Bruno FRAN=C7A DOS REIS > > msn: brunoreis666@hotmail.com > skype: brunoreis666 > tel: +33 (0)6 28 43 42 16 > > e^(pi*i)+1=3D0 ------=_Part_20984_13513714.1206743971111 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Ol=E1 Bruno,

suponha que exista K, tal que:
(K+j)! =3D=3D j (mod = 10), j =3D 1, ..., 9

vejamos:
(K+1)! =3D=3D 1 (mod 10)

(K+= 2)! =3D=3D 2 (mod 10), mas (K+2)! =3D (K+2)(K+1)! =3D=3D K+2 (mod 10)
po= rtanto, K+2 =3D=3D 2 (mod 10) .... e: K =3D=3D 0 (mod 10)

(K+3)! =3D=3D 3 (mod 10), mas (K+3)! =3D (K+3)(K+2)! =3D=3D 2(K+3) (mod= 10)
portanto, 2(K+3) =3D 2K+6 =3D=3D 3 (mod 10)
mas, K =3D=3D 0 (mod= 10), e, obtemos: 6 =3D=3D 3 (mod 10)
ABSURDO!

portanto, est=E1 p= rovado que n=E3o existe.

um abra=E7o,
Salhab



2008/3= /26 Bruno Fran=E7a dos Reis <bfreis@= gmail.com>:
Problema:

Prove que n=E3o existem numeros fatoriais consecutivos com= primeiros digitos iguais a 1, 2, ..., 9.
Em outras palavras: prove que = n=E3o existe K tal que (K+j)! comece pelo algarismo j, para todo j =3D 1, .= .., 9.

Abra=E7o
Bruno

--
B= runo FRAN=C7A DOS REIS

msn: brunoreis666@hotmail.com
skype: brunoreis666tel: +33 (0)6 28 43 42 16

e^(pi*i)+1=3D0

------=_Part_20984_13513714.1206743971111-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Fri Mar 28 19:52:10 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2SMpDWA008993 for ; Fri, 28 Mar 2008 19:51:13 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2SMpCe4008983 for obm-l-MllGbsmmN; Fri, 28 Mar 2008 19:51:12 -0300 Received: from wx-out-0506.google.com (wx-out-0506.google.com [66.249.82.231]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2SMp3WA008899 for ; Fri, 28 Mar 2008 19:51:05 -0300 Received: by wx-out-0506.google.com with SMTP id t4so616273wxc.18 for ; Fri, 28 Mar 2008 15:50:47 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=PB3KatMHzPIeeCh1cZzV2OdofdC83tJEDQNH+O87ZSk=; b=DD0qxoyPMuC+WKNJ+4DeZ33U0tMSJkxajecivzUYk7Xjz3STITGYRIwt92RMsyB3ZG7CHFd9emMbuZt64pmoIngDL9xAGvl9gfKmD2ii8XfJa+RCMYEuLQ3HfZUgDG0mCBWkRjLXQDSXZ5f0FzrdnvWX1huuNhH+1tPYkddj3QM= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=i+6P88NptXTBw6TzWET1zgLrMZUSTpNNDqHm5HjzGTVOUacpD1mBvAsxgmDMKftBCvy9WhN6cETyyrqVvkaqoV0nKcuKuYBKS2BK6WIhJodr/rm30Mtb5U8Y72j+jy2CsMLWubqEGh3yRcAglcikysJNp6PUS3KFUJBXZQRTd74= Received: by 10.114.110.1 with SMTP id i1mr4836799wac.112.1206744646166; Fri, 28 Mar 2008 15:50:46 -0700 (PDT) Received: by 10.114.134.8 with HTTP; Fri, 28 Mar 2008 15:50:46 -0700 (PDT) Message-ID: <3bd00efc0803281550g5a4a12dcgf091c31a4cbf6cc7@mail.gmail.com> Date: Fri, 28 Mar 2008 19:50:46 -0300 From: "Marcelo Salhab Brogliato" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] combinatoria dificil In-Reply-To: MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_21001_19321718.1206744646159" References: <3e7bcb580803201443r10149ad4n4a3c3d7710b3573@mail.gmail.com> <5bb472220803240629k4f430aa9v765f20fdbd0bdad2@mail.gmail.com> <001b01c88dc5$3863fdd0$d400a8c0@AMD> <5bb472220803240908y48701b01y7b8cfeae9d66eeed@mail.gmail.com> <000b01c88dce$d8e27bc0$d400a8c0@AMD> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Marcelo Salhab Brogliato" X-Spam-Status: No, hits=4.3 required=5.0 tests=ASCII_FORM_ENTRY,AWL,GAPPY_TEXT,HTML_FONT_COLOR_GRAY, HTML_FONT_COLOR_UNSAFE,IN_REP_TO,MAILTO_LINK, MAILTO_TO_SPAM_ADDR,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** ------=_Part_21001_19321718.1206744646159 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Ol=E1 Johann, observando sua solu=E7=E3o, vi que H =3D=3D -2 (mod 13) mas, -2 =3D=3D 11 (mod 13) logo: H =3D 13x - 2 =3D 13(x-1) + 11 nao analisei sua solucao desta parte para baixo.. um abra=E7o, Salhab 2008/3/26 Johann Peter Gustav Lejeune Dirichlet < peterdirichlet2003@gmail.com>: > N=E3o =E9 t=E3o escabroso quanto parece: > > 19H + 13M =3D 1000 > > M=F3dulo 13, temos > 19H=3D1000 > 7H=3D1000=3D-14 > H=3D-2=3D(mod 13) > > Entao H=3D13x+2 > > Substitui: > > 19(13x+2) + 13M =3D 1000 > 247x+13M=3D962 > 19x+M=3D74 > > M=3D74-19x > H=3D13x+2 > > Agora que parametrizou, faz com que ambos sejam positivos, ou 74-19x>0 > > 74>19x > x<74/19<4 > > Bem, da=ED =E9 s=F3 testar! > > Em 24/03/08, Fernando escreveu: > > > > > > Oi Jo=E3o Victor, a quest=E3o =E9 que eu j=E1 havia escrito esta equa= =E7=E3o. > Acontece > > que ela =E9 "diofantina", admitindo infinitas solu=E7=F5es. Claro que, = de > acordo > > com as condi=E7=F5es do exerc=EDcio proposto deve-se conseguir restring= ir a > > quantidade delas para um n=FAmero bem menos (eu creio). > > > > P.S.: Nem toda diofantiona tem infinitas solu=E7=F5es. > > Diofantina significa somente `resolva em Z=3D{0,1,-1,2,-2,3,-3,...}=B4 > Ou seja, at=E9 mesmo x=3D2 pode ser diofantina, bem como x^3=3D5 > > > Amplexo. > > Fernando > > > > ________________________________ > > ________________________________ > > > > > > ----- Original Message ----- > > From: Joao Victor Brasil > > To: obm-l@mat.puc-rio.br > > Sent: Monday, March 24, 2008 1:08 PM > > Subject: Re: [obm-l] combinatoria dificil > > > > > > Fernando, > > > > Infelizmente n=E3o tenho, mas tenta ver algo nesse sentido: > > 19H + 13M =3D 1000, H=3D Homem e M=3DMulher > > > > Joao Victor > > > > > > On 3/24/08, Fernando wrote: > > > > > > > > > Ol=E1 Jo=E3o Victor, boa tarde! > > > > > > Voc=EA possui a solu=E7=E3o do problema abaixo? > > > Se SIM, poderia envi=E1-la para mim? > > > > > > > > > > > > Sociedade Brasileira de Matem=E1tica > > > > > > EUREKA! N=B014, 2002 > > > > > > VIII OLIMP=CDADA DE MAIO > > > > > > Enunciados e Resultado Brasileiro > > > > > > PRIMEIRO N=CDVEL > > > > > > 11/05/2002 > > > > > > PROBLEMA 1 > > > > > > Um grupo de homens, alguns dos quais acompanhados pelas esposas, > gastaram > > 1000 > > > > > > d=F3lares num hotel. Cada homem gastou 19 d=F3lares e cada mulher, 13 > d=F3lares. > > > > > > Determine quantas mulheres e quantos homens estavam no hotel. > > > > > > > > > > > > http://www.obm.org.br/eureka/eureka14.pdf > > > > > > acesso em 23/03/2008 > > > > > > > > > Agrade=E7o sua aten=E7=E3o. > > > > > > Amplexo. > > > Fernando Pinto > > > > > > ________________________________ > > ________________________________ > > > > > > > > ----- Original Message ----- > > > From: Joao Victor Brasil > > > To: obm-l@mat.puc-rio.br > > > Sent: Monday, March 24, 2008 10:29 AM > > > Subject: Re: [obm-l] combinatoria dificil > > > > > > > > > > > > =C9 verdade pessoal. Errei e muito na minha resolu=E7=E3o. > > > > > > Mas olha s=F3, concordo plenamente com a resposta do Henrique, 48 > > possibilidades. > > > > > > Usando o princ=EDpio multiplicativo D1H1_D1H2_D2H1_D2H2_D3H1_D3H2 ach= ei > 72 > > possibilidades, me alertaram sobre as repeti=E7=F5es e analisei um modo= de > > retir=E1-las. > > > D1H1:3 disc > > > D1H2: 2 disc > > > D2H1: 2 disc (repetir as mesmas disciplinas do dia 1) > > > D2H2: 1 disc > > > D3H1: 2 disc (apesar de sobrar somente uma disc, temos duas aulas) > > > D3H2: 1 disc > > > > > > 3*2*2*1*2*1 =3D 24. 72 - 24 =3D 48 poss. > > > > > > Joao Victor > > > > > > > > > On 3/20/08, Henrique Renn=F3 wrote: > > > > Ol=E1 pessoal! > > > > > > > > Acredito que a solu=E7=E3o do Salhab est=E1 correta. Seja Di o dia = i e Hj > o > > hor=E1rio j. > > > > > > > > D1H1: 3 mat=E9rias > > > > D1H2: 2 mat=E9rias (para n=E3o repetir a utilizada em D1H1) > > > > D1: 6 possibilidades > > > > > > > > Para D2, se escolhermos uma j=E1 utilizada em D1 ent=E3o n=E3o pode= remos > > > > utilizar a outra mat=E9ria utilizada em D1, sen=E3o D3 teria as mes= mas > > > > mat=E9rias. Assim, para D2 ter=EDamos uma j=E1 utilizada (2 mat=E9r= ias) e > uma > > > > n=E3o utilizada. Logo, 2*1 =3D 2. Como a ordem importa, temos 2*2 = =3D 4. > > > > > > > > D3 s=F3 possui 2 formas, com as ordens das mat=E9rias trocadas. > > > > > > > > Total: 6*4*2 =3D 48. > > > > > > > > Essa =E9 uma forma mais l=F3gica de resolver o problema. Estive ten= tando > > > > utilizar combinat=F3ria e tamb=E9m achei a resposta 48. > > > > > > > > Sejam A,B,C as mat=E9rias. Quantas permuta=E7=F5es diferentes exist= em > entre > > > > A,A,B,B,C,C? Cada posi=E7=E3o seria um hor=E1rio em um dia, ou seja= , > > > > D1H1_D1H2_D2H1_D2H2_D3H1_D3H2. Bastaria calcular o n=FAmero de > > > > permuta=E7=F5es com repeti=E7=E3o, ou seja, 6!/(2!*2!*2!) =3D 720/8= =3D 90. > > > > > > > > Sabemos que n=E3o podemos ter uma permuta=E7=E3o do tipo AABCBC, po= is AA > > > > representa a mesma mat=E9ria em D1H1 e D1H2. Ent=E3o sabemos que a > > > > resposta =E9 menor que 90. > > > > > > > > As formas inv=E1lidas ser=E3o: > > > > > > > > Se as 3 mat=E9rias do mesmo tipo est=E3o juntas no mesmo dia, ex: > AABBCC. > > > > Existem 3! =3D 6 formas, considerando AA,BB,CC como 3 elementos > > > > permutados entre si. > > > > > > > > N=E3o h=E1 necessidade de verificar quando 2 mat=E9rias est=E3o no = mesmo dia > > > > pois cai no caso acima. > > > > > > > > Quando h=E1 apenas 1 mat=E9ria repetida em 1 dia, ex: AABCBC, ent= =E3o > temos > > > > 12 formas para cada par da mesma mat=E9ria utilizada no mesmo dia. = Se > AA > > > > est=E1 em D1 ent=E3o D2 pode ser BC ou CB e D3 pode ser BC ou CB, 2= *2 =3D > 4. > > > > AA pode estar em D1,D2,D3. Assim, 4*3 =3D 12. Para BB e CC seria o > > > > mesmo, dando um total de 3*12 =3D 36 formas quando h=E1 apenas uma > mat=E9ria > > > > que se repete no mesmo dia. > > > > > > > > Assim, o total seria 90 - (6+36) =3D 90 - 42 =3D 48 formas distinta= s de > > > > compor o hor=E1rio > > > > > > > > Thelio, voc=EA poderia passar a fonte do problema e verificar se as > > > > respostas s=E3o essas mesmo? > > > > > > > > On 3/13/08, Thelio Gama wrote: > > > > > =C9 pessoal... > > > > > > > > > > Achei muito dif=EDcil esta quest=E3o. Agrade=E7o se algu=E9m pude= r > explic=E1-la. > > > > > > > > > > Thelio > > > > > > > > > > uma turma tem aulas =E0s 2=AA, 4=AA e 6=AA feiras, de 8-9 horas e= de 11-12 > > horas. As > > > > > mat=E9rias s=E3o portugues, matem=E1tica e ingles, cada uma com d= uas > aulas > > > > > semanais, em dias diferentes. De quantos modos pode ser feito o > > hor=E1rio > > > > > dessa turma? > > > > > a)96 ; b) 144 ; c)192 ; d) 6! ; e) 120 > > > > > > > > > > > > -- > > > > Henrique > > > > > > > > > > > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > > > > Instru=E7=F5es para entrar na lista, sair da lista e usar a lista e= m > > > > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > > > > > > > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > > > > > > > > > > > > > > > > > -- > Ideas are bulletproof. > > V > > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > Instru=E7=F5es para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > ------=_Part_21001_19321718.1206744646159 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Ol=E1 Johann,

observando sua solu=E7=E3o, vi que H =3D=3D -2 (mod 13= )
mas, -2 =3D=3D 11 (mod 13)
logo: H =3D 13x - 2 =3D 13(x-1) + 11
=
nao analisei sua solucao desta parte para baixo..

um abra=E7o,Salhab


2008/3/26 Johann Peter Gustav Lejeune Dirichlet = <peterdirichlet2003@gmai= l.com>:
N=E3o =E9 t=E3o escabroso quanto parece:

19H + 13M =3D 1000

M=F3dulo 13, temos
19H=3D1000
7H=3D1000=3D-14
H=3D-2=3D(mod 13)

Entao H=3D13x+2

Substitui:

19(13x+2) + 13M =3D 1000
247x+13M=3D962
19x+M=3D74

M=3D74-19x
H=3D13x+2

Agora que parametrizou, faz com que ambos sejam positivos, ou 74-19x>0
74>19x
x<74/19<4

Bem, da=ED =E9 s=F3 testar!

Em 24/03/08, Fernando<artes= matematica@globo.com> escreveu:
>
>
> Oi Jo=E3o Victor, a quest=E3o =E9 que eu j=E1 havia escrito esta equa= =E7=E3o. Acontece
> que ela =E9 "diofantina", admitindo infinitas solu=E7=F5es. = Claro que, de acordo
> com as condi=E7=F5es do exerc=EDcio proposto deve-se conseguir restrin= gir a
> quantidade delas para um n=FAmero bem menos (eu creio).
>

P.S.: Nem toda diofantiona tem infinitas solu=E7=F5es.

Diofantina significa somente `resolva em Z=3D{0,1,-1,2,-2,3,-3,...}=B4
Ou seja, at=E9 mesmo x=3D2 pode ser diofantina, bem como x^3=3D5

> Amplexo.
> Fernando
>
>  ________________________________
>  ________________________________
>
>
> ----- Original Message -----
> From: Joao Victor Brasil
> To: obm-l@mat.puc-rio.br > Sent: Monday, March 24, 2008 1:08 PM
> Subject: Re: [obm-l] combinatoria dificil
>
>
> Fernando,
>
> Infelizmente n=E3o tenho, mas tenta ver algo nesse sentido:
> 19H + 13M =3D 1000, H=3D Homem  e M=3DMulher
>
> Joao Victor
>
>
> On 3/24/08, Fernando <= artesmatematica@globo.com> wrote:
> >
> >
> > Ol=E1 Jo=E3o Victor, boa tarde!
> >
> > Voc=EA possui a solu=E7=E3o do problema abaixo?
> > Se SIM, poderia envi=E1-la para mim?
> >
> >
> >
> > Sociedade Brasileira de Matem=E1tica
> >
> > EUREKA! N=B014, 2002
> >
> > VIII OLIMP=CDADA DE MAIO
> >
> > Enunciados e Resultado Brasileiro
> >
> > PRIMEIRO N=CDVEL
> >
> > 11/05/2002
> >
> > PROBLEMA 1
> >
> > Um grupo de homens, alguns dos quais acompanhados pelas esposas, = gastaram
> 1000
> >
> > d=F3lares num hotel. Cada homem gastou 19 d=F3lares e cada mulher= , 13 d=F3lares.
> >
> > Determine quantas mulheres e quantos homens estavam no hotel.
> >
> >
> >
> > http://www.obm.org.br/eureka/eureka14.pdf
> >
> > acesso em 23/03/2008
> >
> >
> > Agrade=E7o sua aten=E7=E3o.
> >
> > Amplexo.
> > Fernando Pinto
> >
> > ________________________________
>  ________________________________
>
> >
> > ----- Original Message -----
> > From: Joao Victor Brasil
> > To: obm-l@mat.puc-rio.br<= /a>
> > Sent: Monday, March 24, 2008 10:29 AM
> > Subject: Re: [obm-l] combinatoria dificil
> >
> >
> >
> > =C9 verdade pessoal. Errei e muito na minha resolu=E7=E3o.
> >
> > Mas olha s=F3, concordo plenamente com a resposta do Henrique, 48=
> possibilidades.
> >
> > Usando o princ=EDpio multiplicativo D1H1_D1H2_D2H1_D2H2_D3H1_D3H2= achei 72
> possibilidades, me alertaram sobre as repeti=E7=F5es e analisei um mod= o de
> retir=E1-las.
> > D1H1:3 disc
> > D1H2: 2 disc
> > D2H1: 2 disc (repetir as mesmas disciplinas do dia 1)
> > D2H2: 1 disc
> > D3H1: 2 disc (apesar de sobrar somente uma disc, temos duas aulas= )
> > D3H2: 1 disc
> >
> > 3*2*2*1*2*1 =3D 24.           72 - 24 = =3D 48 poss.
> >
> > Joao Victor
> >
> >
> > On 3/20/08, Henrique Renn=F3 <henrique.renno@gmail.com> wrote:
> > > Ol=E1 pessoal!
> > >
> > > Acredito que a solu=E7=E3o do Salhab est=E1 correta. Seja Di= o dia i e Hj o
> hor=E1rio j.
> > >
> > > D1H1: 3 mat=E9rias
> > > D1H2: 2 mat=E9rias (para n=E3o repetir a utilizada em D1H1)<= br> > > > D1: 6 possibilidades
> > >
> > > Para D2, se escolhermos uma j=E1 utilizada em D1 ent=E3o n= =E3o poderemos
> > > utilizar a outra mat=E9ria utilizada em D1, sen=E3o D3 teria= as mesmas
> > > mat=E9rias. Assim, para D2 ter=EDamos uma j=E1 utilizada (2 = mat=E9rias) e uma
> > > n=E3o utilizada. Logo, 2*1 =3D 2. Como a ordem importa, temo= s 2*2 =3D 4.
> > >
> > > D3 s=F3 possui 2 formas, com as ordens das mat=E9rias trocad= as.
> > >
> > > Total: 6*4*2 =3D 48.
> > >
> > > Essa =E9 uma forma mais l=F3gica de resolver o problema. Est= ive tentando
> > > utilizar combinat=F3ria e tamb=E9m achei a resposta 48.
> > >
> > > Sejam A,B,C as mat=E9rias. Quantas permuta=E7=F5es diferente= s existem entre
> > > A,A,B,B,C,C? Cada posi=E7=E3o seria um hor=E1rio em um dia, = ou seja,
> > > D1H1_D1H2_D2H1_D2H2_D3H1_D3H2. Bastaria calcular o n=FAmero = de
> > > permuta=E7=F5es com repeti=E7=E3o, ou seja, 6!/(2!*2!*2!) = =3D 720/8 =3D 90.
> > >
> > > Sabemos que n=E3o podemos ter uma permuta=E7=E3o do tipo AAB= CBC, pois AA
> > > representa a mesma mat=E9ria em D1H1 e D1H2. Ent=E3o sabemos= que a
> > > resposta =E9 menor que 90.
> > >
> > > As formas inv=E1lidas ser=E3o:
> > >
> > > Se as 3 mat=E9rias do mesmo tipo est=E3o juntas no mesmo dia= , ex: AABBCC.
> > > Existem 3! =3D 6 formas, considerando AA,BB,CC como 3 elemen= tos
> > > permutados entre si.
> > >
> > > N=E3o h=E1 necessidade de verificar quando 2 mat=E9rias est= =E3o no mesmo dia
> > > pois cai no caso acima.
> > >
> > > Quando h=E1 apenas 1 mat=E9ria repetida em 1 dia, ex: AABCBC= , ent=E3o temos
> > > 12 formas para cada par da mesma mat=E9ria utilizada no mesm= o dia. Se AA
> > > est=E1 em D1 ent=E3o D2 pode ser BC ou CB e D3 pode ser BC o= u CB, 2*2 =3D 4.
> > > AA pode estar em D1,D2,D3. Assim, 4*3 =3D 12. Para BB e CC s= eria o
> > > mesmo, dando um total de 3*12 =3D 36 formas quando h=E1 apen= as uma mat=E9ria
> > > que se repete no mesmo dia.
> > >
> > > Assim, o total seria 90 - (6+36) =3D 90 - 42 =3D 48 formas d= istintas de
> > > compor o hor=E1rio
> > >
> > > Thelio, voc=EA poderia passar a fonte do problema e verifica= r se as
> > > respostas s=E3o essas mesmo?
> > >
> > > On 3/13/08, Thelio Gama <teliogama@gmail.com> wrote:
> > > > =C9 pessoal...
> > > >
> > > > Achei muito dif=EDcil esta quest=E3o. Agrade=E7o se alg= u=E9m puder explic=E1-la.
> > > >
> > > > Thelio
> > > >
> > > > uma turma tem aulas =E0s 2=AA, 4=AA e 6=AA feiras, de 8= -9 horas e de 11-12
> horas. As
> > > > mat=E9rias s=E3o portugues, matem=E1tica e ingles, cada= uma com duas aulas
> > > > semanais, em dias diferentes. De quantos modos pode ser= feito o
> hor=E1rio
> > > > dessa turma?
> > > > a)96  ; b) 144   ; c)192   ; d) 6!  = ;  ; e) 120
> > >
> > >
> > > --
> > > Henrique
> > >
> > >
> =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
> > > Instru=E7=F5es para entrar na lista, sair da lista e usar a = lista em
> > > http://www.mat.puc-rio.br/~obmlistas/obm-l.html
> > >
> =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
> > >
> >
> >
>
>


--
Ideas are bulletproof.

V

=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D
Instru=E7=F5es para entrar na lista, sair da lista e usar a lista em
http://www.mat.puc-rio.br/~obmlistas/obm-l.html
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D

------=_Part_21001_19321718.1206744646159-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Fri Mar 28 20:13:20 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2SNCCWA017544 for ; Fri, 28 Mar 2008 20:12:13 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2SNCCcB017538 for obm-l-MllGbsmmN; Fri, 28 Mar 2008 20:12:12 -0300 Received: from wa-out-1112.google.com (wa-out-1112.google.com [209.85.146.179]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2SNC7WA017471 for ; Fri, 28 Mar 2008 20:12:08 -0300 Received: by wa-out-1112.google.com with SMTP id m28so538012wag.13 for ; Fri, 28 Mar 2008 16:11:51 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; bh=rwOcO7cMMq+DfuluQWZiDcZHpUsyxANpBF/CvGhlI9w=; b=h1rB+VKjUZ/ZlHLL4Xq4ahYyxD177P94glktUAnaRWIielHbm50NBpQgpho29S4lmluS354Ie4n8qNH0sMM5X2wCRbZH9M5fa6SGaGZi9oRVgYr9RFCm/UEbig2MidJd9/TpIymSjI3acosvSy9YJeIzEtPBqCiWB76X+uu5ovo= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; b=FmrYRaBtZeZ2n9jZguxYj0Q3N9/2OXyLIjGGJ5X3M25hy+zaiMGShyCkzZ/tx/bYKMntsJTKSffaU2EGMy4FnFogetYvSekWB/TuXsoNqnXb/stg5EGle/bhLEI+IDZPCjOmvhV+iwzo9fRPp/q5P5dCd77uvGB3IdLqKDuz/Bg= Received: by 10.114.59.1 with SMTP id h1mr4928081waa.39.1206745911780; Fri, 28 Mar 2008 16:11:51 -0700 (PDT) Received: by 10.114.58.13 with HTTP; Fri, 28 Mar 2008 16:11:51 -0700 (PDT) Message-ID: <3e7bcb580803281611h42a02089pfdc9b8cc63ab260a@mail.gmail.com> Date: Fri, 28 Mar 2008 20:11:51 -0300 From: "=?ISO-8859-1?Q?Henrique_Renn=F3?=" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] combinatoria dificil In-Reply-To: <3bd00efc0803281550g5a4a12dcgf091c31a4cbf6cc7@mail.gmail.com> MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline References: <3e7bcb580803201443r10149ad4n4a3c3d7710b3573@mail.gmail.com> <5bb472220803240629k4f430aa9v765f20fdbd0bdad2@mail.gmail.com> <001b01c88dc5$3863fdd0$d400a8c0@AMD> <5bb472220803240908y48701b01y7b8cfeae9d66eeed@mail.gmail.com> <000b01c88dce$d8e27bc0$d400a8c0@AMD> <3bd00efc0803281550g5a4a12dcgf091c31a4cbf6cc7@mail.gmail.com> Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m2SNCAWA017523 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "=?ISO-8859-1?Q?Henrique_Renn=F3?=" X-Spam-Status: No, hits=1.5 required=5.0 tests=AWL,IN_REP_TO,MAILTO_TO_SPAM_ADDR,QUOTED_EMAIL_TEXT, RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,REFERENCES, SIGNATURE_SHORT_SPARSE,SPAM_PHRASE_00_01,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: * Por que seria -2 ? 19H + 13M = 1000 Aplicando (mod 13) em ambos os lados. 6H = 12 H = 2 H = 13x + 2, x >= 0 2008/3/28 Marcelo Salhab Brogliato : > Olá Johann, > > observando sua solução, vi que H == -2 (mod 13) > mas, -2 == 11 (mod 13) > logo: H = 13x - 2 = 13(x-1) + 11 > > nao analisei sua solucao desta parte para baixo.. > > um abraço, > Salhab > > > > 2008/3/26 Johann Peter Gustav Lejeune Dirichlet > : > > > > Não é tão escabroso quanto parece: > > > > 19H + 13M = 1000 > > > > Módulo 13, temos > > 19H=1000 > > 7H=1000=-14 > > H=-2=(mod 13) > > > > Entao H=13x+2 > > > > Substitui: > > > > 19(13x+2) + 13M = 1000 > > 247x+13M=962 > > 19x+M=74 > > > > M=74-19x > > H=13x+2 > > > > Agora que parametrizou, faz com que ambos sejam positivos, ou 74-19x>0 > > > > 74>19x > > x<74/19<4 > > > > Bem, daí é só testar! > > -- Henrique ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Fri Mar 28 22:16:42 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2T1FLWA019385 for ; Fri, 28 Mar 2008 22:15:21 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2T1FLTL019383 for obm-l-MllGbsmmN; Fri, 28 Mar 2008 22:15:21 -0300 Received: from wa-out-1112.google.com (wa-out-1112.google.com [209.85.146.178]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2T1FIWA019380 for ; Fri, 28 Mar 2008 22:15:19 -0300 Received: by wa-out-1112.google.com with SMTP id m28so586311wag.13 for ; Fri, 28 Mar 2008 18:15:02 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; bh=myZjSEzo4NGese5IKNyO4njGv9nUCcDWnyVWsUVbCMo=; b=kg9D71mcyWnAzTDsdqPUEvbTjQvOWOQLzJ1INZIUSGqJNrXSzT3BRM3JGORekwe1vpaAwrt5jNVKwiyhE54bfkazw2T6FB2x43Px+CFRePeWIXHn5st5KDWWw32++pb15JtcMB16emyDH7pwe1tsDmVeuJKSb9qAKsj6Hh1gKLc= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; b=ZwZ1T/oLpsJ2A0Se1TD7BeuwIXsgT92/M/NPMMnjIr+PQbZ6G7BmYJlTBxcqMy3yQIPV4rtZRMjpEX098gQZJ0HQipbspPCI/3AZ9FXNzUuL0dqCUcSZV3Yo05f8oah8uuG5NR3DcLBhR7xiOlpOuQUbIOvfLUbxuKv0yV7o6mk= Received: by 10.114.169.2 with SMTP id r2mr5018966wae.118.1206753302434; Fri, 28 Mar 2008 18:15:02 -0700 (PDT) Received: by 10.114.58.13 with HTTP; Fri, 28 Mar 2008 18:15:02 -0700 (PDT) Message-ID: <3e7bcb580803281815q25213a50pc71773f79e9f970@mail.gmail.com> Date: Fri, 28 Mar 2008 22:15:02 -0300 From: "=?ISO-8859-1?Q?Henrique_Renn=F3?=" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] T. dos Numeros, olimpico! In-Reply-To: <3bd00efc0803281539h42a7a848gcc44e39be3f30990@mail.gmail.com> MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline References: <99886d920803261733m20957fdcwead8e048e725b6fe@mail.gmail.com> <3bd00efc0803281539h42a7a848gcc44e39be3f30990@mail.gmail.com> Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m2T1FKWA019381 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "=?ISO-8859-1?Q?Henrique_Renn=F3?=" X-Spam-Status: No, hits=1.5 required=5.0 tests=AWL,IN_REP_TO,MAILTO_TO_SPAM_ADDR,QUOTED_EMAIL_TEXT, RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,REFERENCES, SIGNATURE_SHORT_SPARSE,SPAM_PHRASE_00_01,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: * Olá Marcelo! Muito legal sua demonstração, mas eu tenho dúvidas se essa seria a demonstração válida para o problema. Aquele "comece" não seria o primeiro algarismo da esquerda para a direita? Por exemplo, 5! = 120, começa com 1, já que todo fatorial de um número natural a partir do 5 tem como "último" algarismo o 0, pois sempre haverá um 5*2 na multiplicação. Assim, pela sua demonstração (mod 10) todo número >= 5 tem o 0 como "último" algarismo de seu fatorial. Outra pergunta. Você participa do TopCoder? Abraços e bom fim de semana! 2008/3/28 Marcelo Salhab Brogliato : > Olá Bruno, > > suponha que exista K, tal que: > (K+j)! == j (mod 10), j = 1, ..., 9 > > vejamos: > (K+1)! == 1 (mod 10) > > (K+2)! == 2 (mod 10), mas (K+2)! = (K+2)(K+1)! == K+2 (mod 10) > portanto, K+2 == 2 (mod 10) .... e: K == 0 (mod 10) > > (K+3)! == 3 (mod 10), mas (K+3)! = (K+3)(K+2)! == 2(K+3) (mod 10) > portanto, 2(K+3) = 2K+6 == 3 (mod 10) > mas, K == 0 (mod 10), e, obtemos: 6 == 3 (mod 10) > ABSURDO! > > portanto, está provado que não existe. > > um abraço, > Salhab > > > > 2008/3/26 Bruno França dos Reis : > > > > Problema: > > > > Prove que não existem numeros fatoriais consecutivos com primeiros digitos > iguais a 1, 2, ..., 9. > > Em outras palavras: prove que não existe K tal que (K+j)! comece pelo > algarismo j, para todo j = 1, ..., 9. > > > > Abraço > > Bruno > > > > -- > > Bruno FRANÇA DOS REIS > > > > msn: brunoreis666@hotmail.com > > skype: brunoreis666 > > tel: +33 (0)6 28 43 42 16 > > > > e^(pi*i)+1=0 > > -- Henrique ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Fri Mar 28 23:09:59 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2T28nWA022302 for ; Fri, 28 Mar 2008 23:08:49 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2T28nnm022300 for obm-l-MllGbsmmN; Fri, 28 Mar 2008 23:08:49 -0300 Received: from smtp.uol.com.br (smtps.uol.com.br [200.221.4.131]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2T28lWA022288 for ; Fri, 28 Mar 2008 23:08:47 -0300 Received: from localhost (localhost [127.0.0.1]) by socom2.uol.com.br (Postfix) with ESMTP id 05A0A8E3 for ; Fri, 28 Mar 2008 23:08:32 -0300 (BRT) Received: from PreturlanPC (unknown [201.82.21.15]) by socom2.uol.com.br (Postfix) with ESMTP id 4BE8E5E8 for ; Fri, 28 Mar 2008 23:08:31 -0300 (BRT) From: =?iso-8859-1?Q?Jo=E3o_Gabriel_Preturlan?= To: Subject: [SPAM] [obm-l] =?iso-8859-1?B?RnVu5+Nv?= Date: Fri, 28 Mar 2008 23:08:35 -0300 Message-ID: <000001c89141$cbe9ad50$63bd07f0$@com.br> MIME-Version: 1.0 Content-Type: text/plain X-Mailer: Microsoft Office Outlook 12.0 Thread-Index: AciRQct5arsdQ3xGSYWxZ+Ds+9Q8Tg== Content-Language: pt-br X-SIG5: a01bca8ba2f607d3aebf4023a5b8ed45 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: =?iso-8859-1?Q?Jo=E3o_Gabriel_Preturlan?= X-Spam-Status: Yes, hits=6.4 required=5.0 tests=AWL,HTML_70_90,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, SPAM_PHRASE_00_01,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ****** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_NextPart_000_0001_01C89128.A69C7550" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (6.40 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: HTML_70_90 (0.9 points) BODY: Message is 70-90% HTML tags SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 15.21.82.201.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 15.21.82.201.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-0.3 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- Esta é uma mensagem em várias partes no formato MIME. ------=_NextPart_000_0001_01C89128.A69C7550 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Pe=E7o ajuda com esta quest=E3o: =20 =93Seja h : R - R uma fun=E7=E3o real que satisfaz as seguintes = condi=E7=F5es: i) h(x) + h(y) =3D h(xy), para todo x; y pertencente ao conjunto R. ii) h (Max([m/2^p.3^q],[n/2^p]) + min([m/2^p],[n/2^p.3^q]))=3D log(base = 2)(q + 1), para todos m; n pertencente a Z e para todos p; q pertencente a N. Mostre que se x pertence a Q, ent=E3o h(x) =3D 0.=94 =20 OBS.: L=EA-se [m/2^p.3^q] como M sobre o produto de dois elevado a p e = tr=EAs elevado a q. L=EA-se tamb=E9m log(base 2)(q + 1) como logaritmo de (q+1) na base 2. =20 Desde J=E1 Agrade=E7o Muito pela ajuda. =20 JG. No virus found in this outgoing message. Checked by AVG.=20 Version: 7.5.519 / Virus Database: 269.22.1/1348 - Release Date: = 28/03/2008 10:58 =20 ------=_NextPart_000_0001_01C89128.A69C7550 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable

Pe=E7o ajuda com esta = quest=E3o:

 

“Seja h : R - R uma fun=E7=E3o = real que satisfaz as seguintes condi=E7=F5es:

i) h(x) + h(y) =3D h(xy), para todo x; y pertencente ao conjunto R.

ii) h (Max([m/2^p.3^q],[n/2^p]) + = min([m/2^p],[n/2^p.3^q]))=3D log(base 2)(q + 1), para todos m; n pertencente a Z e para todos = p; q pertencente a = N.

Mostre que se x = pertence a = Q, ent=E3o h(x) =3D 0.”

 

=

OBS.: L=EA-se [m/2^p.3^q] como M sobre o produto de dois elevado a p e tr=EAs elevado a = q.

L=EA-se tamb=E9m log(base 2)(q + 1) como logaritmo de (q+1) na base 2.

 

=

Desde J=E1 Agrade=E7o Muito pela ajuda.

 

=

JG.


No virus found in this outgoing message.
Checked by AVG.
Version: 7.5.519 / Virus Database: 269.22.1/1348 - Release Date: = 28/03/2008 10:58

------=_NextPart_000_0001_01C89128.A69C7550-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Fri Mar 28 23:36:37 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2T2ZMWA023375 for ; Fri, 28 Mar 2008 23:35:23 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2T2ZMnm023372 for obm-l-MllGbsmmN; Fri, 28 Mar 2008 23:35:22 -0300 Received: from n10.bullet.re3.yahoo.com (n10.bullet.re3.yahoo.com [68.142.237.123]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id m2T2Z6WA023358 for ; Fri, 28 Mar 2008 23:35:07 -0300 Received: from [68.142.237.87] by n10.bullet.re3.yahoo.com with NNFMP; 29 Mar 2008 02:34:50 -0000 Received: from [69.147.75.190] by t3.bullet.re3.yahoo.com with NNFMP; 29 Mar 2008 02:34:49 -0000 Received: from [127.0.0.1] by omp106.mail.re1.yahoo.com with NNFMP; 29 Mar 2008 02:34:49 -0000 X-Yahoo-Newman-Id: 953415.28000.bm@omp106.mail.re1.yahoo.com Received: (qmail 24529 invoked from network); 29 Mar 2008 02:34:49 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=Received:X-Yahoo-Newman-Property:Message-ID:Date:From:User-Agent:MIME-Version:To:Subject:References:In-Reply-To:Content-Type:Content-Transfer-Encoding; b=u9zUuWVFVXQPtln/G5BF72OtqqMY8Eb/Nx1yBpjCyYeIJX1IZX/TxlB8rlDydrlWVUI+NgD8o3+2Zyglo2SSRsLYHuzZbrdN8sfqYyiWJpy/a3VUrkCAXgQZkxbuZ8a05zU19ejYdsmNvH57Wf4uJn1ZHvF0CojNrLqCXPRoPwM= ; Received: from unknown (HELO ?192.168.254.4?) (eduardoam1978@201.51.6.120 with plain) by smtp105.mail.mud.yahoo.com with SMTP; 29 Mar 2008 02:34:48 -0000 X-Yahoo-Newman-Property: ymail-3 Message-ID: <47EDC698.5090701@yahoo.com.br> Date: Fri, 28 Mar 2008 23:33:28 -0500 From: Eduardo AM User-Agent: Thunderbird 2.0.0.12 (Windows/20080213) MIME-Version: 1.0 To: obm-l@mat.puc-rio.br Subject: [SPAM] [obm-l] Livro "Desenvolvendo a =?ISO-8859-1?Q?matem=E1tica=2E=2E=2E=22?= References: <3e7bcb580803201443r10149ad4n4a3c3d7710b3573@mail.gmail.com> <5bb472220803240629k4f430aa9v765f20fdbd0bdad2@mail.gmail.com> <001b01c88dc5$3863fdd0$d400a8c0@AMD> <5bb472220803240908y48701b01y7b8cfeae9d66eeed@mail.gmail.com> <000b01c88dce$d8e27bc0$d400a8c0@AMD> In-Reply-To: Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Eduardo AM X-Spam-Status: Yes, hits=6.3 required=5.0 tests=FORGED_YAHOO_RCVD,FROM_ENDS_IN_NUMS,IN_REP_TO,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, USER_AGENT,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ****** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (6.30 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: REFERENCES (-0.5 points) Has a valid-looking References header SPAM: USER_AGENT (-0.5 points) Found a User-Agent header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: FROM_ENDS_IN_NUMS (0.9 points) From: ends in numbers SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 190.75.147.69.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 190.75.147.69.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- Apareceu esse livro la na faculdade: "Desenvolvendo a Matematica 1500 Exercicios resolvidos Prof Marcus Vinicius Reis Ferreira" e parece ser uma coleção... alguem tem alguma opnião sobre eles? Ou ate mesmo a editora pois procurando pelo google pouca coisa aparece. Obrigado, Eduardo AM// ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sat Mar 29 09:35:54 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2TCYMWA031878 for ; Sat, 29 Mar 2008 09:34:22 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2TCYMkw031876 for obm-l-MllGbsmmN; Sat, 29 Mar 2008 09:34:22 -0300 Received: from web56915.mail.re3.yahoo.com (web56915.mail.re3.yahoo.com [66.196.97.104]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id m2TCYJWA031863 for ; Sat, 29 Mar 2008 09:34:20 -0300 Received: (qmail 19672 invoked by uid 60001); 29 Mar 2008 12:34:04 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:Date:From:Subject:To:In-Reply-To:MIME-Version:Content-Type:Content-Transfer-Encoding:Message-ID; b=Xm1/sDvhiWWQEnAcVXO+SJIU3kieWF1BsZQ4+U7kAAH9bRAPHF/WaLQm+jXONLCSXiVsDTT+6FRfxMDYSlsfHzTJL9HTbnLEu8asjZe0ZQdC0oSQcyv3wONd8pTWGFL/nxS0PvE6XgsmFCLzeHJp8jIoOpv8BNokhT4ITf6ovAw=; X-YMail-OSG: XbRLtIEVM1ne.6k8lbjPmDWo7_87n9qnpzxPLbRNP6XaTGOaqVbN6zlJiFeq6eq.I2QusfTn4FycKKhTbtZ.r6qw5akrUO7EtlrwIPQ4UnGj4OXhZpTX4oTIAZFziw-- Received: from [189.62.141.221] by web56915.mail.re3.yahoo.com via HTTP; Sat, 29 Mar 2008 09:34:03 ART Date: Sat, 29 Mar 2008 09:34:03 -0300 (ART) From: cleber vieira Subject: [SPAM] [obm-l] =?iso-8859-1?q?Amigos=20gostaria=20da=20ajuda=20de=20vcs.=20Estou=20h=E1?= =?iso-8859-1?q?=20algum=20tempo=20tentando=20e=20nada...?= To: obm-l@mat.puc-rio.br In-Reply-To: <206410.11049.qm@web56902.mail.re3.yahoo.com> MIME-Version: 1.0 Content-Type: text/plain Content-Transfer-Encoding: 7bit Message-ID: <981050.18848.qm@web56915.mail.re3.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: cleber vieira X-Spam-Status: Yes, hits=8.1 required=5.0 tests=AWL,FORGED_YAHOO_RCVD,HTML_FONT_COLOR_BLUE,IN_REP_TO, RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,RCVD_IN_RELAYS_ORDB_ORG, SPAM_PHRASE_00_01,SPAM_REDIRECTOR,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="0-1885895764-1206794043=:18848" X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (8.10 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: HTML_FONT_COLOR_BLUE (0.2 points) BODY: HTML font color is blue SPAM: SPAM_REDIRECTOR (0.4 points) URI: Uses open redirection service SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 104.97.196.66.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 104.97.196.66.relays.osirusoft.com.] SPAM: RCVD_IN_RELAYS_ORDB_ORG (0.6 points) RBL: Received via a relay in relays.ordb.org SPAM: [RBL check: found 221.141.62.189.relays.ordb.org.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (0.5 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- --0-1885895764-1206794043=:18848 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 8bit O triângulo ABC, retângulo em A, é tal que o < ABC é maior que < ACB. A bissetriz interna de
O triângulo ABC, retângulo em A, é tal que o < ABC é maior que < ACB.
A bissetriz interna de <A, intercepta o lado BC em D. Seja HD perpendicular a BC ( H entre A e C). Nestas condições podemos afirmar que o ângulo <HBD mede, em graus:
a) 25
b) 65
c) 35
d) 45
 
Obrigado!!!
 

Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-1885895764-1206794043=:18848-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sat Mar 29 11:35:33 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2TEYEWA009670 for ; Sat, 29 Mar 2008 11:34:14 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2TEYDQ8009666 for obm-l-MllGbsmmN; Sat, 29 Mar 2008 11:34:13 -0300 Received: from wa-out-1112.google.com (wa-out-1112.google.com [209.85.146.177]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2TEY7WA009596 for ; Sat, 29 Mar 2008 11:34:10 -0300 Received: by wa-out-1112.google.com with SMTP id m28so903951wag.13 for ; Sat, 29 Mar 2008 07:33:52 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=AWvsNHjeLRmJelcxmFw2X1b5tMLRPTlVJfiKHPg2wrY=; b=e9MDl0HxNdO+TL7spIEfqU6HTMMFieVU3rWwLY0Sw1laA2imgwDKX7bnHGGJ0gU6EDNoxy/74tSYXpI1FO5BmT9fYPeB9h7+hS3/jeM1pngWB3QGcCqWqaMLB5rDTtkK0XTSNDxasQRAFqrfpBa5znzLTCMGodc/BfEj8zSBjXo= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=gBNKNPuPK7d6JDvuPcijQr8V535M2GZ6KTuO8gei4mEU7OkEexfgFXLWuxK2itN3kKYvqwiyGmwtI0Ez10xWfLp+12GY2BQZsMditv46q46H0GcZ/aNfz1VpYgoReWc4rpJoKE5SkQ3YXOAlItcFrycxLPNER0iq66Wx2+OyTZ8= Received: by 10.114.157.1 with SMTP id f1mr6097034wae.10.1206801227350; Sat, 29 Mar 2008 07:33:47 -0700 (PDT) Received: by 10.114.161.8 with HTTP; Sat, 29 Mar 2008 07:33:47 -0700 (PDT) Message-ID: Date: Sat, 29 Mar 2008 11:33:47 -0300 From: MauZ To: obm-l@mat.puc-rio.br Subject: =?ISO-8859-1?Q?Re:_[obm-l]_Problema_Combinat=F3ria?= In-Reply-To: <2b5739960803271547h7584b608kb1dbc59171ca9fad@mail.gmail.com> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_321_10815680.1206801227333" References: <2b5739960803271547h7584b608kb1dbc59171ca9fad@mail.gmail.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: MauZ X-Spam-Status: No, hits=4.8 required=5.0 tests=AWL,IN_REP_TO,JAVASCRIPT_UNSAFE,MAILTO_LINK, QUOTED_EMAIL_TEXT,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, REFERENCES,SPAM_PHRASE_00_01,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** ------=_Part_321_10815680.1206801227333 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Ol=E1 pessoal eu montei um esquema usando binomio de newton. Ficou da seguinte forma a resposta: Vou usar (a//b) como binomio a!/b!(a-b)! temos todas as combina=E7=F5es como: (n//p) e as que tem consecutivos como: (n-1//p-1)+(n-2//p-2)...(n-p+1//n-p), somando pela regra da diagonal: (n//p-1)-1 (sendo o primeiro binomio como pelo menos 2 consecutivos, o segundo com pel= o menos 3, etc... Da segunte forma. a primeira escolha pego 1 livro e imediatamente o seu da direita. Num grupo de 24 livros por ex, tenho 23 maneiras de fazer isso, pelo fato do ultimo livro nao ter nada =E0 sua direita) logo a solu=E7=E3o =E9: (n//p)-(n//p-1) + 1 testei para alguns valores e t=E1 OK,, O que voc=EAs acham? []'s Maurizio Em 27/03/08, Rogerio Ponce escreveu: > > Ola' Mauricio e colegas da lista, > os 5 livros retirados determinam 6 intervalos , dos quais o mais 'a > esquerda e o mais 'a direita podem ter o valor minimo de 0, e os > outros quatro valem no minimo 1. > > Para uniformizar tudo, podemos imaginar que exista um livro a mais do > lado direito, e outro do lado esquerdo da estante, de forma que agora > precisamos determinar 6 intervalos, todos maiores que zero, somando um > total de 24+2-5 =3D 21. > > Em outras palavras, o que procuramos e' o numero de solucoes inteiras > positivas para > a+b+c+d+e+f=3D21 > que vale C(21-1, 6-1) =3D C(20,5) > Ou seja, (20*19*18*17*16) / (5*4*3*2*1) =3D 15504 > > []'s > > Rogerio Ponce > > > > > Em 26/03/08, MauZ escreveu: > > > Ol=E1 a todos! > > > > Numa estante com 24 livros, de quantas maneiras posso retirar 5 livros > sem > > ter nenhum consecutivo? E no caso de n livros, quantas maneiras retiro = p > > livros sem ter nenhum consecutivo? > > > > > > > > Pra completar vou colocar parte da minha tentativa de solu=E7=E3o, prec= iso > de > > ajuda pra saber se est=E1 certo at=E9 onde fiz e como finalizar pois > empaquei. > > > > Fiz dessa forma: Todas Combina=E7=F5es - Combina=E7=F5es c/ Consecutivo= s > > > > Todas: 24!/5!19! > > Consecutivos: 23!/4!19! + 22!/3!19! + 21!/2!19! + 20!/1!19! > > > > Fiz uma formula geral com n e p e deu o seguinte: > > > > n!/p!(n-p!) - [(n-1)!/(p-1)!(n-p)! + > > (n-2)!/(p-2)!(n-p)!+...+(n-p+1)!/(n-p)!] > > > > Fatorando deu: > > > > (1/(n-p)!)[n!/p!-(n-1)!/(p-1)!-(n-2)!/(p-2)-...-(n-p+1)!/(n-p)!] > > > > Dae empaquei de vez... N=E3o consegui continuar! > > Quem souber fazer por favor me d=EA a luz! Ou simplesmente indique o e= rro > no > > meu racioc=EDnio. > > > > Agrade=E7o antecipadamente, > > Maurizio > > > > > > > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > Instru=E7=F5es para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > ------=_Part_321_10815680.1206801227333 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Ol=E1 pessoal

eu montei um esquema usando binomio de newton.

= Ficou da seguinte forma a resposta:
Vou usar (a//b) como binomio a!/b!(a= -b)!

temos todas as combina=E7=F5es como: (n//p)
e as que tem con= secutivos como: (n-1//p-1)+(n-2//p-2)...(n-p+1//n-p), somando pela regra da= diagonal: (n//p-1)-1
(sendo o primeiro binomio como pelo menos 2 consecutivos, o segundo com pel= o menos 3, etc... Da segunte forma. a primeira escolha pego 1 livro e imedi= atamente o seu da direita. Num grupo de 24 livros por ex, tenho 23 maneiras= de fazer isso, pelo fato do ultimo livro nao ter nada =E0 sua direita)

logo a solu=E7=E3o =E9:

(n//p)-(n//p-1) + 1

testei para a= lguns valores e t=E1 OK,,

O que voc=EAs acham?

[]'s
Ma= urizio

Em 27/03/08, Rogerio Ponce <= abrlwsky@gmail.com> escreveu:
Ola' Mauricio e colegas da lista,
os 5 livros retirados determinam = 6 intervalos , dos quais o mais 'a
esquerda e o mais 'a direita= podem ter o valor minimo de 0, e os
outros quatro valem no minimo 1.
Para uniformizar tudo, podemos imaginar que exista um livro a mais do=
lado direito, e outro do lado esquerdo da estante, de forma que agora<= br> precisamos determinar 6 intervalos, todos maiores que zero, somando um<= br> total de 24+2-5 =3D 21.

Em outras palavras, o que procuramos e= 9; o numero de solucoes inteiras
positivas para
  a+b+c+d+= e+f=3D21
que vale C(21-1, 6-1) =3D C(20,5)
Ou seja, (20*19*18*17*16= ) /  (5*4*3*2*1) =3D  15504

[]'s

Rogerio Ponce




Em 26/03/08, Ma= uZ<mauz.matematica@gmail.co= m> escreveu:

> Ol=E1 a todos!
>
> Numa estante com 24 livros, de q= uantas maneiras posso retirar 5 livros sem
> ter nenhum consecutivo? E no caso de n livros, quantas maneiras retir= o p
> livros sem ter nenhum consecutivo?
>
>
><= br> > Pra completar vou colocar parte da minha tentativa de solu=E7=E3o,= preciso de
> ajuda pra saber se est=E1 certo at=E9 onde fiz e como finalizar pois = empaquei.
>
> Fiz dessa forma: Todas Combina=E7=F5es - Combin= a=E7=F5es c/ Consecutivos
>
> Todas: 24!/5!19!
> Conse= cutivos: 23!/4!19! + 22!/3!19! + 21!/2!19! + 20!/1!19!
>
> Fiz uma formula geral com n e p e deu o seguinte:
> >  n!/p!(n-p!) - [(n-1)!/(p-1)!(n-p)! +
> (n-2)!/(p-= 2)!(n-p)!+...+(n-p+1)!/(n-p)!]
>
> Fatorando deu:
> > (1/(n-p)!)[n!/p!-(n-1)!/(p-1)!-(n-2)!/(p-2)-...-(n-p+1)!/(n-p)!]
>
> Dae empaquei de vez... N=E3o consegui continuar!
>&nb= sp; Quem souber fazer por favor me d=EA a luz! Ou simplesmente indique= o erro no
> meu racioc=EDnio.
>
> Agrade=E7o antecipa= damente,
> Maurizio
>
>


=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D
Instru=E7=F5es para entrar na lista, sair da l= ista e usar a lista em
http://www.mat.puc-rio.br/~obmlistas/obm-l.html
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D

------=_Part_321_10815680.1206801227333-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sat Mar 29 12:24:19 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2TFMjWA014505 for ; Sat, 29 Mar 2008 12:22:45 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2TFMj0s014503 for obm-l-MllGbsmmN; Sat, 29 Mar 2008 12:22:45 -0300 Received: from hm171.locaweb.com.br (hm171-2.locaweb.com.br [200.234.205.179]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id m2TFMiWA014485 for ; Sat, 29 Mar 2008 12:22:44 -0300 Message-Id: <200803291522.m2TFMiWA014485@saci.mat.puc-rio.br> Received: (qmail 3444 invoked from network); 29 Mar 2008 15:22:34 -0000 Received: from unknown (10.1.10.169) by hm171.locaweb.com.br with QMQP; 29 Mar 2008 15:22:34 -0000 Received: from unknown (HELO lattes) (paulo@uniredes.org@189.24.248.165) by hm169.locaweb.com.br with SMTP; 29 Mar 2008 15:22:38 -0000 From: "Paulo - Uniredes" To: Subject: [SPAM] [obm-l] =?iso-8859-1?Q?RES:_=5Bobm-l=5D_Conjuntos_num=E9ricos_na_Reta...?= Date: Sat, 29 Mar 2008 12:22:32 -0300 Organization: Uniredes MIME-Version: 1.0 Content-Type: text/plain X-Mailer: Microsoft Office Outlook, Build 11.0.5510 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.3198 Thread-Index: AciRIe8DQkxeDS7WSeOF0zDUa1elOgAjlv8g In-Reply-To: <49b5b5d60803281443q2268d45cs2cd6aad3e7c02c17@mail.gmail.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Paulo - Uniredes" X-Spam-Status: Yes, hits=6.6 required=5.0 tests=AWL,HTML_FONT_COLOR_BLUE,IN_REP_TO,MISSING_OUTLOOK_NAME, MSG_ID_ADDED_BY_MTA_2,NOSPAM_INC,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ****** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_NextPart_000_0052_01C89197.9098A070" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (6.60 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: NOSPAM_INC (-0.2 points) Where are you working at? SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: HTML_FONT_COLOR_BLUE (0.2 points) BODY: HTML font color is blue SPAM: MSG_ID_ADDED_BY_MTA_2 (0.1 points) 'Message-Id' was added by a relay (2) SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 179.205.234.200.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 179.205.234.200.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: MISSING_OUTLOOK_NAME (1.1 points) Message looks like Outlook, but isn't SPAM: AWL (0.4 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- This is a multi-part message in MIME format. ------=_NextPart_000_0052_01C89197.9098A070 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Parece que essa quest=E3o n=E3o tem correla=E7=E3o com a matem=E1tica = ol=EDmpica. Mas imaginem uma banca que lembre de n=FAmeros "diferentes" e consiga fazer quest=F5es abordando o assunto. Isso pegaria nossos "atletas" = desprevenidos... =20 =20 []s =20 --- Paulo C. Santos (PC) e-mail: paulo@uniredes.org Homepage: http://uniredes.org =20 Tel.: (21) 2510.8783 - Cel.: (21) 8753-0729 -------------------------------------------- MS-Messenger: Uniredes_Br@hotmail.Com=20 _____ =20 De: owner-obm-l@mat.puc-rio.br [mailto:owner-obm-l@mat.puc-rio.br] Em = nome de Fernando A Candeias Enviada em: sexta-feira, 28 de mar=E7o de 2008 18:43 Para: obm-l@mat.puc-rio.br Assunto: Re: [obm-l] Conjuntos num=E9ricos na Reta... Caros colegas de lista =20 Uma outra maneira de responder ao questionamento do Paulo, mais = trabalhosa por=E9m mais intuitiva, est=E1 descrita em Foundations of Geometry, de = Hilbert. Ele desenvolve a geometria de maneira puramente axiom=E1tica, e no # 8 = trata dos axiomas de continuiidade, que s=E3o o de Arquimedes V.1 e o da = Completude da Reta, V.2. A partir do que, juntamente com os axiomas que dizem = respeito =E0 ordem, =E9 poss=EDvel demonstrar a equival=EAncia entre os pontos = da reta e do conjunto dos reais.=20 Em outro livro que tenho, de G. Verrier, uma introdu=E7=E3o =E0s = geometrias n=E3o euclidianas por m=E9todos elementares, o autor substitui os dois = postulados citados pelo axioma de Dedekind, o que imediatamente identifica a reta geom=E9trica com os reais, como dito pelo Ralph. O livro baseia-se na = obra de Hilbert. Trata de todos axiomas comuns =E0s tr=EAs geomertrias, e = posteriormente introduz novos postulados e/ou suprime alguns, a partir do que = desenvolve o assunto. Tudo por m=E9todos elementares. =C9 muito interessante. Est=E1 = escrito em franc=EAs, adquiri em 1951, creio que esta esgotado. Mas se algu=E9m = tiver interesse, posso do=E1-lo juntamente com o de Hilbert. Sobre os surreais conhe=E7o pouco, mas parece muito interessante a = id=E9ia de que os numeros infinitesimais passem a ter exist=EAncia efetiva, o que dispensaria em parte os complicados =E9psilons e deltas da defini=E7=E3o = usual de continuidade de uma fun=E7=E3o em um ponto. (Weierstrasse). Vou ver se = encontro o livro mencionado pelo Nehab. Gostaria de saber como os problemas geom=E9ricos s=E3o abordados, se fazendo corresponder a cada segmento de = reta a parte Re do surreal, ou o n=FAmero completo, incluindo um infinitesimal. = Nessa hip=F3tese lembraria Leibntz com suas m=F4nadas, ou o sonho pitag=F3rico = do "tudo =E9 n=FAmero". =20 Fernando A Candeias ------=_NextPart_000_0052_01C89197.9098A070 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable
Parece que essa quest=E3o n=E3o tem = correla=E7=E3o com a matem=E1tica=20 ol=EDmpica. Mas imaginem uma banca que lembre de n=FAmeros "diferentes" = e consiga=20 fazer quest=F5es abordando o assunto. Isso pegaria nossos "atletas"=20 desprevenidos...
 
 
[]s
 

---
Paulo C. Santos (PC)
e-mail:=20 paulo@uniredes.org
Homepage: http://uniredes.org
Tel.: (21) = 2510.8783 -=20 Cel.: (21)=20 8753-0729
--------------------------------------------
MS-Messenger= :=20 Uniredes_Br@hotmail.Com


De: owner-obm-l@mat.puc-rio.br=20 [mailto:owner-obm-l@mat.puc-rio.br] Em nome de Fernando A=20 Candeias
Enviada em: sexta-feira, 28 de mar=E7o de 2008=20 18:43
Para: obm-l@mat.puc-rio.br
Assunto: Re: = [obm-l]=20 Conjuntos num=E9ricos na Reta...

Caros colegas de lista
 
Uma outra maneira de responder ao questionamento do Paulo, mais = trabalhosa=20 por=E9m mais intuitiva, est=E1 descrita em Foundations of Geometry, de = Hilbert. Ele=20 desenvolve a geometria de maneira puramente axiom=E1tica, e no # 8 trata = dos=20 axiomas de continuiidade, que s=E3o o de Arquimedes V.1 e o da = Completude da Reta,=20  V.2. A partir do que, juntamente com os axiomas que dizem = respeito =E0=20 ordem, =E9 poss=EDvel demonstrar  a equival=EAncia entre = os pontos=20 da reta e do conjunto dos reais.
Em outro livro que tenho, de G. Verrier, uma introdu=E7=E3o =E0s = geometrias n=E3o=20 euclidianas por m=E9todos elementares, o autor substitui os dois = postulados=20 citados pelo axioma de Dedekind, o que imediatamente identifica a reta=20 geom=E9trica com os reais, como dito pelo Ralph. O livro baseia-se = na obra de=20 Hilbert. Trata de todos axiomas comuns =E0s tr=EAs geomertrias, e = posteriormente=20 introduz novos postulados e/ou suprime alguns,  a partir do que = desenvolve=20 o assunto. Tudo por m=E9todos elementares. =C9 muito=20 interessante. Est=E1 escrito  em franc=EAs, adquiri em = 1951, creio=20 que esta esgotado. Mas se algu=E9m tiver interesse, posso do=E1-lo = juntamente com=20 o de Hilbert.
Sobre os surreais conhe=E7o pouco, mas parece muito interessante a = id=E9ia de=20 que os numeros infinitesimais passem a ter exist=EAncia efetiva, o que = dispensaria=20 em parte os complicados =E9psilons e deltas da defini=E7=E3o usual de = continuidade de=20 uma fun=E7=E3o em um ponto. (Weierstrasse). Vou ver se encontro o = livro=20 mencionado pelo Nehab. Gostaria de saber como os problemas geom=E9ricos = s=E3o=20 abordados, se fazendo corresponder a cada segmento de = reta a=20 parte Re do surreal, ou o n=FAmero completo, incluindo um=20 infinitesimal. Nessa hip=F3tese lembraria Leibntz com suas = m=F4nadas, ou o=20 sonho pitag=F3rico do "tudo =E9 n=FAmero".
 
Fernando A Candeias
------=_NextPart_000_0052_01C89197.9098A070-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sat Mar 29 12:29:36 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2TFSYWA014971 for ; Sat, 29 Mar 2008 12:28:34 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2TFSYjl014969 for obm-l-MllGbsmmN; Sat, 29 Mar 2008 12:28:34 -0300 Received: from hm171.locaweb.com.br (hm171-2.locaweb.com.br [200.234.205.179]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id m2TFSWWA014964 for ; Sat, 29 Mar 2008 12:28:32 -0300 Message-Id: <200803291528.m2TFSWWA014964@saci.mat.puc-rio.br> Received: (qmail 5030 invoked from network); 29 Mar 2008 15:28:22 -0000 Received: from unknown (10.1.10.169) by hm171.locaweb.com.br with QMQP; 29 Mar 2008 15:28:22 -0000 Received: from unknown (HELO lattes) (paulo@uniredes.org@189.24.248.165) by hm169.locaweb.com.br with SMTP; 29 Mar 2008 15:28:26 -0000 From: "Paulo - Uniredes" To: Subject: [SPAM] RES: [obm-l] Objetos de \Aprendizagem virtual Date: Sat, 29 Mar 2008 12:28:21 -0300 Organization: Uniredes MIME-Version: 1.0 Content-Type: text/plain X-Mailer: Microsoft Office Outlook, Build 11.0.5510 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.3198 Thread-Index: AciRn2MwG6PYT4YPQoyifgwSWvHsegAEZLOw In-Reply-To: <92295ee80803281051w374ff1dbxaa7d7a30001b6576@mail.gmail.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Paulo - Uniredes" X-Spam-Status: Yes, hits=6.8 required=5.0 tests=AWL,IN_REP_TO,JAVASCRIPT_UNSAFE,MAILTO_LINK, MISSING_OUTLOOK_NAME,MSG_ID_ADDED_BY_MTA_2,NOSPAM_INC, RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01, SPAM_REDIRECTOR,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ****** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_NextPart_000_0056_01C89198.6029FC80" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (6.80 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: NOSPAM_INC (-0.2 points) Where are you working at? SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: JAVASCRIPT_UNSAFE (0.3 points) BODY: Easily-executed JavaScript code SPAM: MAILTO_LINK (0.2 points) BODY: Includes a URL link to send an email SPAM: SPAM_REDIRECTOR (0.4 points) URI: Uses open redirection service SPAM: MSG_ID_ADDED_BY_MTA_2 (0.1 points) 'Message-Id' was added by a relay (2) SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 179.205.234.200.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 179.205.234.200.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: MISSING_OUTLOOK_NAME (1.1 points) Message looks like Outlook, but isn't SPAM: AWL (-0.1 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- This is a multi-part message in MIME format. ------=_NextPart_000_0056_01C89198.6029FC80 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Oi pessoal. =20 N=E3o =E9 exatamente a resposta desejada, mas ajuda muito comprar o CD = "Revista do professor de matem=E1tica", =E0 venda no = www.IMPA.BR . O pessoal l=E1 =E9 muito legal e te atende bem. =20 Vejam tamb=E9m : DVDs do Programa de Aperfei=E7oamento para Professores = de Matem=E1tica do Ensino M=E9dio em http://www.impa.br/opencms/pt/publicacoes/publicacoes_dvds_papmem.html . =20 =20 S=E3o apenas alternativas... =20 []s =20 --- Paulo C. Santos (PC) e-mail: paulo@uniredes.org Homepage: http://uniredes.org =20 Tel.: (21) 2510.8783 - Cel.: (21) 8753-0729 -------------------------------------------- MS-Messenger: Uniredes_Br@hotmail.Com=20 =20 _____ =20 De: owner-obm-l@mat.puc-rio.br [mailto:owner-obm-l@mat.puc-rio.br] Em = nome de Fernando Lukas Miglorancia Enviada em: sexta-feira, 28 de mar=E7o de 2008 14:52 Para: obm-l@mat.puc-rio.br Assunto: Re: [obm-l] Objetos de \Aprendizagem virtual Ol=E1, Thais, =20 =20 Se eu descobrir algo, te mando sim. =20 Abra=E7=E3o, =20 Fernando =20 2008/3/28, Thais Oliveira :=20 Ola pessoal, tudo bem? Estou a procura de qualquer tipo de objeto de aprendizagem virtual que facilite o ensino de matem=E1tica. Se vcs conherem sites interessantes = com video, jogos, arquivo em flsh ou coisa do genero me mandem poe favor. Muito obrigada Thais _____ =20 Abra sua conta no Yahoo! Mail , = o =FAnico sem limite de espa=E7o para armazenamento!=20 ------=_NextPart_000_0056_01C89198.6029FC80 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable
Oi pessoal.
 
N=E3o =E9 exatamente a resposta desejada, mas ajuda muito = comprar o CD=20 "Revista do professor de matem=E1tica", =E0 venda no www.IMPA.BR . O = pessoal l=E1 =E9=20 muito legal e te atende bem.
 
Vejam tamb=E9m : DVDs do Programa de Aperfei=E7oamento para = Professores=20 de Matem=E1tica do Ensino M=E9dio em http://www.impa.br/opencms/pt/publicacoes/publicacoes_dvd= s_papmem.html .
 
 
S=E3o apenas alternativas...
 
[]s
 

---
Paulo C. Santos (PC)
e-mail:=20 paulo@uniredes.org
Homepage: http://uniredes.org
Tel.: (21) = 2510.8783 -=20 Cel.: (21)=20 8753-0729
--------------------------------------------
MS-Messenger= :=20 Uniredes_Br@hotmail.Com

 

De: owner-obm-l@mat.puc-rio.br=20 [mailto:owner-obm-l@mat.puc-rio.br] Em nome de Fernando Lukas=20 Miglorancia
Enviada em: sexta-feira, 28 de mar=E7o de 2008=20 14:52
Para: obm-l@mat.puc-rio.br
Assunto: Re: = [obm-l]=20 Objetos de \Aprendizagem virtual

 Ol=E1, Thais,
 
 
  Se eu descobrir algo, te  mando sim.
 
  Abra=E7=E3o,
 
  Fernando

 
2008/3/28, Thais Oliveira <tha_unicamp@yahoo.com.br>= :=20
Ola=20 pessoal, tudo bem?

Estou a procura de qualquer tipo de objeto = de=20 aprendizagem virtual que facilite o ensino de matem=E1tica. Se vcs = conherem=20 sites interessantes com video, jogos, arquivo em flsh ou coisa do = genero me=20 mandem poe favor.

Muito obrigada

Thais

Abra sua conta no Yahoo! Mail, o =FAnico sem limite de espa=E7o para = armazenamento!=20


------=_NextPart_000_0056_01C89198.6029FC80-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sat Mar 29 14:33:19 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2THVoWA023545 for ; Sat, 29 Mar 2008 14:31:50 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2THVouO023543 for obm-l-MllGbsmmN; Sat, 29 Mar 2008 14:31:50 -0300 Received: from smtp2.oi.com.br (smtp5.oi.com.br [200.222.115.129]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2THVnWA023538 for ; Sat, 29 Mar 2008 14:31:49 -0300 Received: from smtp2.oi.com.br (localhost.localdomain [127.0.0.1]) by smtp2.oi.com.br (Postfix) with ESMTP id 91FDF7001FE2 for ; Sat, 29 Mar 2008 14:31:35 -0300 (BRT) Received: from pessoal2b51d2e (unknown [189.71.125.181]) by smtp2.oi.com.br (Postfix) with SMTP id 1F91070020B3 for ; Sat, 29 Mar 2008 14:31:35 -0300 (BRT) Message-ID: <000801c16281$01f262d0$b57d47bd@pessoal2b51d2e> From: "Pedro " To: Subject: [SPAM] [obm-l] =?iso-8859-1?Q?=E1lgebra?= Date: Thu, 1 Nov 2001 00:57:55 -0200 MIME-Version: 1.0 Content-Type: text/plain X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2900.2180 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.2180 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Pedro " X-Spam-Status: Yes, hits=8.3 required=5.0 tests=AWL,DATE_IN_PAST_96_XX,FROM_ENDS_IN_NUMS,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01,USER_AGENT_OE, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_NextPart_000_0005_01C16270.3DDB5C90" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (8.30 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: FROM_ENDS_IN_NUMS (0.9 points) From: ends in numbers SPAM: USER_AGENT_OE (0.2 points) X-Mailer header indicates a non-spam MUA (Outlook Express) SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: DATE_IN_PAST_96_XX (1.5 points) Date: is 96 hours or more before Received: date SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 181.125.71.189.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 181.125.71.189.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-0.1 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- This is a multi-part message in MIME format. ------=_NextPart_000_0005_01C16270.3DDB5C90 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Amigos da lista me uma ajuda nas seguintes quest=F5es: 1) Se x =3D 1+ raiz quadrada(2004), ent=E3o 4x^3 - 2007x - 2005 =E9 = igual a : a) 0 b) 1 c) -1 d) 2 = e) -2 2) Dado x^1 + x^ -1 =3D {1 + raiz qradrada(5)}/2. O valor de x^2000 + = x^ -2000 =E9 igual a : =20 a)1 b)2 c){1 + raiz = qradrada(5)}/2 d)20 3)Simplifique : { x^7 + y^7 + z^7}/xyz(x^4 + y^4 + z^4) ------=_NextPart_000_0005_01C16270.3DDB5C90 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable
 Amigos da lista me uma ajuda nas = seguintes=20 quest=F5es:
 
  1) Se x =3D 1+ raiz = quadrada(2004), ent=E3o 4x^3=20 - 2007x - 2005 =E9 igual a :
 
       =20 a) 0          &nbs= p;           =20 b) 1           =20 c) -1       d)=20 2            e)=20 -2
 
 2) Dado x^1 + x^ -1 =3D {1 + raiz = qradrada(5)}/2. O valor de x^2000 + x^ -2000 =E9 igual a :
 
 a)1         &= nbsp;           &n= bsp;  =20  b)2          &nbs= p;            = ;=20  c){1 + raiz=20 qradrada(5)}/2          = ;         =20    d)20
 
 
 3)Simplifique : { x^7 + y^7 + = z^7}/xyz(x^4 +=20 y^4 + z^4)
------=_NextPart_000_0005_01C16270.3DDB5C90-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sat Mar 29 16:08:51 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2TJ7dWA031372 for ; Sat, 29 Mar 2008 16:07:39 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2TJ7cOr031370 for obm-l-MllGbsmmN; Sat, 29 Mar 2008 16:07:38 -0300 Received: from zeus.hotlink.com.br (zeus.hotlink.com.br [189.1.1.250]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2TJ7bWA031356 for ; Sat, 29 Mar 2008 16:07:37 -0300 Received: by zeus.hotlink.com.br (Postfix, from userid 1002) id 2EBDAE28219; Sat, 29 Mar 2008 15:45:38 -0300 (BRT) Received: from windows5095252 (veloz-1-2-22.hotlink.com.br [189.1.2.22]) by zeus.hotlink.com.br (Postfix) with SMTP id D3CB6E28215 for ; Sat, 29 Mar 2008 15:45:37 -0300 (BRT) Message-ID: <001101c891cc$9cde9d50$5700a8c0@windows5095252> From: "Gustavo Duarte" To: =?iso-8859-1?Q?Olimp=EDada?= Subject: [SPAM] [obm-l] =?iso-8859-1?Q?M=E9idas?= Date: Sat, 29 Mar 2008 15:42:16 -0300 MIME-Version: 1.0 Content-Type: text/plain X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2900.3138 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.3198 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Gustavo Duarte" X-Spam-Status: Yes, hits=6.3 required=5.0 tests=AWL,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, RCVD_IN_RELAYS_ORDB_ORG,SPAM_PHRASE_00_01,USER_AGENT_OE, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ****** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_NextPart_000_000E_01C891B3.775CE7D0" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (6.30 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: USER_AGENT_OE (0.2 points) X-Mailer header indicates a non-spam MUA (Outlook Express) SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 250.1.1.189.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 250.1.1.189.relays.osirusoft.com.] SPAM: RCVD_IN_RELAYS_ORDB_ORG (0.6 points) RBL: Received via a relay in relays.ordb.org SPAM: [RBL check: found 22.2.1.189.relays.ordb.org.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-0.3 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- This is a multi-part message in MIME format. ------=_NextPart_000_000E_01C891B3.775CE7D0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable 1)Em m=E9idas =E9 f=E1cil mostrar que para 2 valores positivos ,o = quadrado da m=E9dia geom=E9trica =E9 igual ao produto das m=E9dias = harm=F4nicas e aritm=E9tica, par=E9m essa rela=E7=E3o vale tb para 3 ou = mais n=FAmeros ?=20 2) faz sentido m=E9dia ponderada com alguns pesos negativos ? desde j=E1 obrigado. ------=_NextPart_000_000E_01C891B3.775CE7D0 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable
 1)Em m=E9idas =E9 f=E1cil mostrar = que para=20 2 valores positivos ,o quadrado da m=E9dia geom=E9trica = =E9 igual ao=20 produto das m=E9dias harm=F4nicas e aritm=E9tica, par=E9m essa = rela=E7=E3o vale tb para=20 3 ou mais n=FAmeros ?
 2) faz sentido m=E9dia ponderada = com alguns=20 pesos negativos ?
desde j=E1 = obrigado.
------=_NextPart_000_000E_01C891B3.775CE7D0-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sat Mar 29 16:59:42 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2TJvtWA008889 for ; Sat, 29 Mar 2008 16:57:55 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2TJvshM008882 for obm-l-MllGbsmmN; Sat, 29 Mar 2008 16:57:54 -0300 Received: from fk-out-0910.google.com (fk-out-0910.google.com [209.85.128.189]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2TJvCWA008851 for ; Sat, 29 Mar 2008 16:57:18 -0300 Received: by fk-out-0910.google.com with SMTP id 22so1355093fkq.13 for ; Sat, 29 Mar 2008 12:56:56 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=dnuJhb3cmguorrGwtGbmTORn/c5f+oTusvH29PvXjYs=; b=HbCrLTa9cSq4pM35u6gwkhncRxdKI2e/CgoP2gmGqRJ1JE8RW4my7RnELlH7W0FjAtG4MTiFGXC2z2FS8cwlEM47WuwUmL/kLSXwR1KPUKkKc+67RbYIgAAxvYDSjl1V52prNarTtgfHIEZHdG5CySRE5ZP8003y+qCV69+tQZU= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=c7r5xK/8AFhfyO741mEr1yMCDX5qwR/4LOqmN7k5LML6EO68/DOCQgrQ74/6D/8YmmAMpKxPbqwVF2fiXClvXAv1Z852NsfBZIdOcZ9hiLTFrxvGsFpWc+y2mnV9bE8UfvIOIpHKLUMMvbrIMcEqZTZXahFMjiSQNKMpL1pUysg= Received: by 10.78.200.20 with SMTP id x20mr14650402huf.55.1206820616607; Sat, 29 Mar 2008 12:56:56 -0700 (PDT) Received: by 10.78.172.14 with HTTP; Sat, 29 Mar 2008 12:56:56 -0700 (PDT) Message-ID: <92295ee80803291256j35db3255t6b9913c233760e7a@mail.gmail.com> Date: Sat, 29 Mar 2008 12:56:56 -0700 From: "Fernando Lukas Miglorancia" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Objetos de \Aprendizagem virtual In-Reply-To: <341065.77668.qm@web52402.mail.re2.yahoo.com> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_28907_22960809.1206820616600" References: <92295ee80803281051w374ff1dbxaa7d7a30001b6576@mail.gmail.com> <341065.77668.qm@web52402.mail.re2.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Fernando Lukas Miglorancia" X-Spam-Status: No, hits=3.9 required=5.0 tests=AWL,IN_REP_TO,JAVASCRIPT_UNSAFE,MAILTO_LINK, QUOTED_EMAIL_TEXT,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, REFERENCES,SPAM_PHRASE_01_02,SPAM_REDIRECTOR, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: *** ------=_Part_28907_22960809.1206820616600 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline De nada, Thais ! Em 28/03/08, Thais Oliveira escreveu: > > Obrigada Fernando! > > *Fernando Lukas Miglorancia * escreveu: > > Ol=E1, Thais, > > > Se eu descobrir algo, te mando sim. > > Abra=E7=E3o, > > Fernando > > > 2008/3/28, Thais Oliveira : > > > > Ola pessoal, tudo bem? > > > > Estou a procura de qualquer tipo de objeto de aprendizagem virtual que > > facilite o ensino de matem=E1tica. Se vcs conherem sites interessantes = com > > video, jogos, arquivo em flsh ou coisa do genero me mandem poe favor. > > > > Muito obrigada > > > > Thais > > ------------------------------ > > Abra sua conta no Yahoo! Mail, > > o =FAnico sem limite de espa=E7o para armazenamento! > > > > > ------------------------------ > Abra sua conta no Yahoo! Mail, > o =FAnico sem limite de espa=E7o para armazenamento! > > ------=_Part_28907_22960809.1206820616600 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline De nada, Thais !

Em 28/03/08, Thais Oliveira <tha_uni= camp@yahoo.com.br> escreveu:
Obrigada Fernando!

= Fernando Lukas Miglorancia <fernandomiglorancia@gmail.com> escreveu:=20
 Ol=E1, Thais,
 
 
  Se eu descobrir algo, te  mando sim.
 
  Abra=E7=E3o,
 
  Fernando

 
2008/3/28, Thais Oliveira <tha_unicamp@yahoo.com.br>:= =20
Ola pessoal, tudo bem?

Es= tou a procura de qualquer tipo de objeto de aprendizagem virtual que facili= te o ensino de matem=E1tica. Se vcs conherem sites interessantes com video,= jogos, arquivo em flsh ou coisa do genero me mandem poe favor.

Muito obrigada

Thais
Abra sua conta no Yahoo! Mail, o =FAnico sem limite de espa=E7o p= ara armazenamento!=20


Abra sua conta no Yahoo! Mail, o =FAnico sem limite de espa=E7o p= ara armazenamento!=20


------=_Part_28907_22960809.1206820616600-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sat Mar 29 17:27:52 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2TKQpWA011355 for ; Sat, 29 Mar 2008 17:26:51 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2TKQpDF011350 for obm-l-MllGbsmmN; Sat, 29 Mar 2008 17:26:51 -0300 Received: from relay1.uol.com.br (relay1.uol.com.br [200.221.4.108]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2TKQlWA011287 for ; Sat, 29 Mar 2008 17:26:47 -0300 Received: from localhost (localhost [127.0.0.1]) by sniper1.uol.com.br (Postfix) with ESMTP id C6BEDF03E59D for ; Sat, 29 Mar 2008 17:26:32 -0300 (BRT) Received: from uol.com.br (whisky3.mail.sys.intranet [172.26.5.87]) by sniper1.uol.com.br (Postfix) with ESMTP id 89EA2F03EE1C for ; Sat, 29 Mar 2008 17:26:32 -0300 (BRT) Date: Sat, 29 Mar 2008 17:26:32 -0300 Message-Id: Subject: [obm-l] Iteano- TCU MIME-Version: 1.0 X-Sensitivity: 3 Content-Type: multipart/alternative; boundary="_=__=_XaM3_.1206822392.2A.430497.42.25528.52.42.007.1456972148" From: "vitoriogauss" To: "obm-l" X-XaM3-API-Version: 4.3(R1) (B10) X-SenderIP: 201.36.92.190 X-SIG5: 71c5c67d32aa5b8c5b2ec3f80c72a24d Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "vitoriogauss" X-Spam-Status: No, hits=0.9 required=5.0 tests=AWL,LINES_OF_YELLING,SPAM_PHRASE_00_01, TO_LOCALPART_EQ_REAL,UPPERCASE_25_50,X_MAILING_LIST version=2.44 X-Spam-Level: --_=__=_XaM3_.1206822392.2A.430497.42.25528.52.42.007.1456972148 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable COLEGA, VC SE FORMOU NO ITA? APENAS CURIOSIDADE, POIS UM AMIGO MEU SE FORMOU L=C1 E RECENTEMENTE FOI O= 1=BA COLOCADO NO TCU: Davi Ferreira Gomes Barreto. Sou cearense e atualmente ensino em Recife. abra=E7os. --_=__=_XaM3_.1206822392.2A.430497.42.25528.52.42.007.1456972148 Content-Type: text/html; charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable
COLEGA, VC SE FORMOU NO ITA?
 
APENAS CURIOSIDADE, POIS UM AMIGO MEU SE FORMOU L=C1 E RECENTEMENTE = FOI O 1=BA COLOCADO NO TCU: Davi Ferreira Gomes Barreto.=
 
Sou cearense e atualmente ensino em Recife.
 
abra=E7os.
--_=__=_XaM3_.1206822392.2A.430497.42.25528.52.42.007.1456972148-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sat Mar 29 21:16:29 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2U0EZWA000478 for ; Sat, 29 Mar 2008 21:14:35 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2U0EWcY000475 for obm-l-MllGbsmmN; Sat, 29 Mar 2008 21:14:32 -0300 Received: from smtpi01s.infolink.com.br (smtpi01s.infolink.com.br [200.187.64.121]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2U0EHWA000467 for ; Sat, 29 Mar 2008 21:14:17 -0300 Received: from smtpi01s.infolink.com.br (localhost [127.0.0.1]) by smtpi01s.infolink.com.br (Postfix) with ESMTP id C841C1A7816 for ; Sat, 29 Mar 2008 21:14:02 -0300 (EST) Received: from [127.0.0.1] (unknown [189.60.112.176]) by smtpi01s.infolink.com.br (Postfix) with ESMTP id 750791ADFF8 for ; Sat, 29 Mar 2008 21:14:02 -0300 (EST) Message-ID: <47EEDB04.7080107@infolink.com.br> Date: Sat, 29 Mar 2008 21:12:52 -0300 From: Carlos Nehab User-Agent: Thunderbird 2.0.0.12 (Windows/20080213) MIME-Version: 1.0 To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Objetos de \Aprendizagem virtual References: <101832.1746.qm@web52401.mail.re2.yahoo.com> In-Reply-To: <101832.1746.qm@web52401.mail.re2.yahoo.com> Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: 7bit X-Antivirus: avast! (VPS 080328-0, 28/03/2008), Outbound message X-Antivirus-Status: Clean Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Carlos Nehab X-Spam-Status: No, hits=4.8 required=5.0 tests=AWL,CTYPE_JUST_HTML,IN_REP_TO,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, SPAM_REDIRECTOR,USER_AGENT,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** Oi, Thais,

Não sei se é exatamenteo o que você procura, mas eu de cara indicaria 3 sites que acho ótimos (pois não sei em qual "série" de ensino você atua):
1) http://nrich.maths.org/public/       (muita coisa interessante)
2) http://www.cut-the-knot.org/geometry.shtml  ou http://www.cut-the-knot.org/index.shtml
(muito, mas muito bom)   e
3) http://math.rice.edu/~lanius/Lessons/  (pouco atualizado, mas muito bom).

Abraços,
Nehab

Thais Oliveira escreveu:
Ola pessoal, tudo bem?

Estou a procura de qualquer tipo de objeto de aprendizagem virtual que facilite o ensino de matemática. Se vcs conherem sites interessantes com video, jogos, arquivo em flsh ou coisa do genero me mandem poe favor.

Muito obrigada

Thais

Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento!
========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sun Mar 30 09:27:35 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2UCPlWA002816 for ; Sun, 30 Mar 2008 09:25:47 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2UCPleX002814 for obm-l-MllGbsmmN; Sun, 30 Mar 2008 09:25:47 -0300 Received: from fk-out-0910.google.com (fk-out-0910.google.com [209.85.128.188]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2UCPjWA002807 for ; Sun, 30 Mar 2008 09:25:45 -0300 Received: by fk-out-0910.google.com with SMTP id 22so1875273fkq.13 for ; Sun, 30 Mar 2008 05:25:30 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=7K7o6jm2M2pEotksuDI82hIpcZNmOrhQUGhO219E2Mo=; b=nSJ91l6YWIfoOFW0ChmE70N36angyuk15z6rJ4vfx7es7nZtgO7THkwEobhP787YJ+CWOf2Xi5FReHMdKdyyu/IFtNaB5m1Yln634WkmOmPEfoH5wT1Eom0AGKlnspYO4vxBkhMx78r/J7hkcZ9y4HI9WtPxSZjLDCpLMCcgeMw= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=fGzWbaGbq6FShQq02RGrDK15FVGi0p/xKKIP6tEwGvc0xU1IwFGa354Rx31cv+IB5leu1IlPPJFRZhhDZo6LPXZZ0cNUNjv2OkF0GKXK8xAgChA/b5nRxKL+mTjX6SswkseWJs+uw7F2hsoni3zuGVKSpw6+L+My72UGZuZEPyk= Received: by 10.78.189.5 with SMTP id m5mr17149534huf.77.1206879930369; Sun, 30 Mar 2008 05:25:30 -0700 (PDT) Received: by 10.78.129.14 with HTTP; Sun, 30 Mar 2008 05:25:30 -0700 (PDT) Message-ID: Date: Sun, 30 Mar 2008 09:25:30 -0300 From: "=?ISO-8859-1?Q?J=F4natas?=" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Objetos de \Aprendizagem virtual In-Reply-To: <101832.1746.qm@web52401.mail.re2.yahoo.com> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_7497_20071434.1206879930321" References: <47EC69EE.9060900@infolink.com.br> <101832.1746.qm@web52401.mail.re2.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "=?ISO-8859-1?Q?J=F4natas?=" X-Spam-Status: No, hits=4.4 required=5.0 tests=AWL,IN_REP_TO,JAVASCRIPT_UNSAFE,MAILTO_LINK, QUOTED_EMAIL_TEXT,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, REFERENCES,SPAM_PHRASE_00_01,SPAM_REDIRECTOR, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** ------=_Part_7497_20071434.1206879930321 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Quando eu estudava Geometria Plana, aprendi muito com esse site: http://agutie.homestead.com/ acho ele muito bom. http://www.mathlinks.ro/Forum/ (Nesse tem um mund=E3o de quest=F5es, tb muito bom) J=F4natas. 2008/3/28, Thais Oliveira : > > Ola pessoal, tudo bem? > > Estou a procura de qualquer tipo de objeto de aprendizagem virtual que > facilite o ensino de matem=E1tica. Se vcs conherem sites interessantes co= m > video, jogos, arquivo em flsh ou coisa do genero me mandem poe favor. > > Muito obrigada > > Thais > > ------------------------------ > Abra sua conta no Yahoo! Mail, > o =FAnico sem limite de espa=E7o para armazenamento! > > ------=_Part_7497_20071434.1206879930321 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Quando eu estudava Geometria Plana, aprendi muito com esse site: http://agutie.homestead.com/
acho ele= muito bom.
http://www.mathl= inks.ro/Forum/
(Nesse tem um mund=E3o de quest=F5es, tb muito bom)

J=F4natas.

2008/3/28, Thais Oliveira <tha_unicamp@yahoo.com.br>:
Ola pessoal, tudo bem?

Estou a procura de qualquer tipo de objeto de= aprendizagem virtual que facilite o ensino de matem=E1tica. Se vcs conhere= m sites interessantes com video, jogos, arquivo em flsh ou coisa do genero = me mandem poe favor.

Muito obrigada

Thais

=20

Abra sua conta no Yahoo! Mail, o =FAnic= o sem limite de espa=E7o para armazenamento!=20


------=_Part_7497_20071434.1206879930321-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sun Mar 30 15:40:46 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2UId7WA011188 for ; Sun, 30 Mar 2008 15:39:09 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2UId7Hg011180 for obm-l-MllGbsmmN; Sun, 30 Mar 2008 15:39:07 -0300 Received: from relay1.bol.com.br (relay1.bol.com.br [200.221.4.105]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2UIcwWA011077 for ; Sun, 30 Mar 2008 15:38:59 -0300 Received: from localhost (localhost [127.0.0.1]) by salsa1.bol.com.br (Postfix) with ESMTP id 12C9718EDF for ; Sun, 30 Mar 2008 15:38:44 -0300 (BRT) Received: from bol.com.br (whisper3.mail.sys.intranet [172.26.5.138]) by salsa1.bol.com.br (Postfix) with ESMTP id E619818EA5 for ; Sun, 30 Mar 2008 15:38:43 -0300 (BRT) Date: Sun, 30 Mar 2008 15:38:43 -0300 Message-Id: Subject: [obm-l] =?iso-8859-1?b?UmU6IFtvYm0tbF0gUHJvYmxlbWEgQ29tYmluYXTzcmlh?= MIME-Version: 1.0 X-Sensitivity: 3 Content-Type: text/plain; charset=iso-8859-1 From: "fernandobarcel" To: "obm-l" X-XaM3-API-Version: 4.3(R1) (B10) X-SenderIP: 201.37.255.159 X-SIG5: bb29fdb59ddb1212693bc5fbda7b15dc Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m2UId3WA011139 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "fernandobarcel" X-Spam-Status: No, hits=0.0 required=5.0 tests=AWL,SPAM_PHRASE_00_01,TO_LOCALPART_EQ_REAL,X_MAILING_LIST version=2.44 X-Spam-Level: > (sendo o primeiro binomio como pelo menos 2 consecutivos, o segundo com pelo > menos 3, etc... Não entendi o que você fez, mas acho que isso aí tá errado, pois PELO MENOS 2 CONSECUTIVOS engloba o PELO MENOS 3 CONSECUTIVOS. No problema original (tirar 5 de 24 livros), quanto valem N e P na sua fórmula? E que valor você conseguiu pra resposta? ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sun Mar 30 16:36:17 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2UJZ4WA014445 for ; Sun, 30 Mar 2008 16:35:05 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2UJZ1Z3014443 for obm-l-MllGbsmmN; Sun, 30 Mar 2008 16:35:01 -0300 Received: from fg-out-1718.google.com (fg-out-1718.google.com [72.14.220.156]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2UJYjWA014427 for ; Sun, 30 Mar 2008 16:34:46 -0300 Received: by fg-out-1718.google.com with SMTP id e12so1156438fga.3 for ; Sun, 30 Mar 2008 12:34:31 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=IIyGqLoBNM+LVavmEskcbs33pf6GjKqjcy1NtlDAj10=; b=a8SbBqwZtCsRDDv5dr/XICQKhHFwiKwFNBRPSzdAo+5yhrm9g6487b01MrWxJ4m+6+7R/gSOlGf5qRgkeqls5MB/jATAbst1qvfjNBJjcgCA9+9j7RGcT9A5bLmmbh+Fy1Mnl8Oh4Vsl4MS2+ClT+gEXgNixFC3IzQR51cFNEvc= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=q5WdFiAagZyAgMhqi+gwZPlCHhqKr/QLXXI860OFKve52voNkQaLfN0kPrbM6qsbsESpD4HGpAW8pKNGubYfHPYoGVEupgmEJLcClIvnVwzBXpvs6TAubOpRiQVxWkBnnpfWRNsLr9gvJWKQa4ykAgoyOuKDmQaFSlrVVSMjSFY= Received: by 10.86.26.11 with SMTP id 11mr3835507fgz.17.1206905671152; Sun, 30 Mar 2008 12:34:31 -0700 (PDT) Received: by 10.86.73.20 with HTTP; Sun, 30 Mar 2008 12:34:31 -0700 (PDT) Message-ID: Date: Sun, 30 Mar 2008 16:34:31 -0300 From: "saulo nilson" To: obm-l@mat.puc-rio.br Subject: =?ISO-8859-1?Q?Re:_[obm-l]_=E1lgebra?= In-Reply-To: <000801c16281$01f262d0$b57d47bd@pessoal2b51d2e> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_4998_22741741.1206905671130" References: <000801c16281$01f262d0$b57d47bd@pessoal2b51d2e> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "saulo nilson" X-Spam-Status: No, hits=-1.5 required=5.0 tests=AWL,EMAIL_ATTRIBUTION,IN_REP_TO,MAILTO_LINK, MAILTO_TO_SPAM_ADDR,QUOTED_EMAIL_TEXT,REFERENCES, SPAM_PHRASE_00_01,X_MAILING_LIST version=2.44 X-Spam-Level: ------=_Part_4998_22741741.1206905671130 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline 2) (1+rq5)/2=3D2cos36 fazendo x=3Dcosa+isena x+1/x=3D2cosa=3D2cos36 a=3D36 x^2000+1/x^2000=3D2cos2000*36=3D2 On Wed, Oct 31, 2001 at 11:57 PM, Pedro wrote: > Amigos da lista me uma ajuda nas seguintes quest=F5es: > > 1) Se x =3D 1+ raiz quadrada(2004), ent=E3o 4x^3 - 2007x - 2005 =E9 igu= al a : > > a) 0 b) 1 c) -1 d) > 2 e) -2 > > 2) Dado x^1 + x^ -1 =3D {1 + raiz qradrada(5)}/2. O valor de x^2000 + x^ > -2000 =E9 igual a : > > a)1 b)2 c){1 + raiz > qradrada(5)}/2 d)20 > > > 3)Simplifique : { x^7 + y^7 + z^7}/xyz(x^4 + y^4 + z^4) > ------=_Part_4998_22741741.1206905671130 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline
2)
(1+rq5)/2=3D2cos36
fazendo x=3Dcosa+isena
x+1/x=3D2cosa=3D2cos36
a=3D36
x^2000+1/x^2000=3D2cos2000*36=3D2

On Wed, Oct 31, 2001 at 11:57 PM, Pedro <npc1972@oi.com.br> wrote:
 Amigos da lista me uma ajuda nas= seguintes quest=F5es:
 
  1) Se x =3D 1+ raiz quadrada(20= 04), ent=E3o 4x^3 - 2007x - 2005 =E9 igual a :
 
      &n= bsp; a) 0          &= nbsp;            b) = 1            c) = ;-1       d) 2     &= nbsp;      e) -2
 
 2) Dado x^1 + x^ -1 =3D {1 + rai= z qradrada(5)}/2. O valor de x^2000 + x^ -2000 =E9 igual a :
 
 a)1     = ;            &n= bsp;        b)2    &= nbsp;           &nbs= p;        c){1 + raiz qradrada(5)}/2&nbs= p;            &= nbsp;         d)20
 
 
 3)Simplifique : { x^7 + y^7 + z^= 7}/xyz(x^4 + y^4 + z^4)

------=_Part_4998_22741741.1206905671130-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sun Mar 30 19:28:03 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2UMQFWA016023 for ; Sun, 30 Mar 2008 19:26:15 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2UMQFhc016021 for obm-l-MllGbsmmN; Sun, 30 Mar 2008 19:26:15 -0300 Received: from wa-out-1112.google.com (wa-out-1112.google.com [209.85.146.183]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2UMQCWA015983 for ; Sun, 30 Mar 2008 19:26:13 -0300 Received: by wa-out-1112.google.com with SMTP id m28so1687683wag.13 for ; Sun, 30 Mar 2008 15:25:59 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=FczLzhEgq77f1aBcitNmCNLIU6FG5oFjAJL/690Yhuw=; b=KwPOCveMHqgOHIs1ZiB+e764HJq3gAhMVR3e4SfSsOhC4PoqFCQq9adZHZR+K90GAYr7LJGpN41gl9HHKe+KW2elY02Z1/EJ5pgZQnpE/ljjx7XsInIr4jc8jXBSz86ccfgmYRHPMe+my1Kew9C4zkXTreL84J6anRiCR92S7OI= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=cdFwj0hpciGwAYPWG+iGH6DzoYf2i45KBOgC7wgaVFWGKM274TA2+7N6DtlofopgGL0GdoQsVY/Ij4uqcPPTItOgpO/DFobny1YdDAAjaNCQdUyrI55fqjGIXq+9jdxC1XpH8nN6GRD7YH2UjwWFruweFwPspqk+dZBYNKf6+PA= Received: by 10.114.88.1 with SMTP id l1mr8630925wab.126.1206915958497; Sun, 30 Mar 2008 15:25:58 -0700 (PDT) Received: by 10.114.161.8 with HTTP; Sun, 30 Mar 2008 15:25:58 -0700 (PDT) Message-ID: Date: Sun, 30 Mar 2008 19:25:58 -0300 From: MauZ To: obm-l@mat.puc-rio.br Subject: [SPAM] =?ISO-8859-1?Q?Re:_[obm-l]_Re:_[obm-l]_Problema_Combinat=F3ria?= In-Reply-To: MIME-Version: 1.0 Content-Type: text/plain References: Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: MauZ X-Spam-Status: Yes, hits=5.1 required=5.0 tests=AWL,IN_REP_TO,MAILTO_LINK,MIME_EXCESSIVE_QP, QUOTED_EMAIL_TEXT,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, REFERENCES,SPAM_PHRASE_00_01,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ***** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_Part_5029_19318355.1206915958491" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (5.10 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: REFERENCES (-0.5 points) Has a valid-looking References header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: QUOTED_EMAIL_TEXT (-0.8 points) BODY: Contains what looks like a quoted email text SPAM: MAILTO_LINK (0.2 points) BODY: Includes a URL link to send an email SPAM: MIME_EXCESSIVE_QP (1.0 points) RAW: Excessive quoted-printable encoding in body SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 183.146.85.209.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 183.146.85.209.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (0.2 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- ------=_Part_5029_19318355.1206915958491 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Ent=E3o Fernando, eu concordo com voc=EA nesse aspecto, mas a quest=E3o =E9 que a formula funcionou para os casos pequenos que test= ei no caso de 24 e 5 livros seriam n=3D24 e p=3D5 No caso de 5 livros e 3 para escolher a formula traz resposta =3D 1, o que = =E9 verdade. Testei alguns outros e deu OK. Mas justamente tem essa falha q vc enunciou. Abra=E7os Em 30/03/08, fernandobarcel escreveu: > > > > (sendo o primeiro binomio como pelo menos 2 consecutivos, o segundo com > pelo > > menos 3, etc... > > > > N=E3o entendi o que voc=EA fez, mas acho que isso a=ED t=E1 errado, pois = PELO > MENOS 2 CONSECUTIVOS engloba o > PELO MENOS 3 CONSECUTIVOS. > > No problema original (tirar 5 de 24 livros), quanto valem N e P na sua > f=F3rmula? > E que valor voc=EA conseguiu pra resposta? > > > > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > Instru=E7=F5es para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > ------=_Part_5029_19318355.1206915958491 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Ent=E3o Fernando,

eu concordo com voc=EA nesse aspecto,
mas a que= st=E3o =E9 que a formula funcionou para os casos pequenos que testei
no caso de 24 e 5 livros seriam n=3D24 e p=3D5
No caso de 5 livros e 3 = para escolher a formula traz resposta =3D 1, o que =E9 verdade.
Testei alguns outros e deu OK.

Mas justamente tem essa falha q vc en= unciou.

Abra=E7os

Em 30/03/0= 8, fernandobarcel <fernandobarcel@bol.com.br> escreveu:

> (sendo o primeiro binomio como pelo menos 2 consecutivos, o segun= do com pelo
> menos 3, etc...



N=E3o entendi o que = voc=EA fez, mas acho que isso a=ED t=E1 errado, pois PELO MENOS 2 CONSECUTI= VOS engloba o
PELO MENOS 3 CONSECUTIVOS.

No problema original (tirar 5 de 24 li= vros), quanto valem N e P na sua f=F3rmula?
E que valor voc=EA consegui= u pra resposta?



=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D
Instru=E7=F5es para entrar na lista, sair da lista e usar a lista em
<= a href=3D"http://www.mat.puc-rio.br/~obmlistas/obm-l.html">http://www.mat.p= uc-rio.br/~obmlistas/obm-l.html
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D

------=_Part_5029_19318355.1206915958491-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sun Mar 30 20:23:12 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2UNM5WA021239 for ; Sun, 30 Mar 2008 20:22:05 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2UNM4CE021227 for obm-l-MllGbsmmN; Sun, 30 Mar 2008 20:22:04 -0300 Received: from fg-out-1718.google.com (fg-out-1718.google.com [72.14.220.157]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2UNLwWA021196 for ; Sun, 30 Mar 2008 20:21:59 -0300 Received: by fg-out-1718.google.com with SMTP id e12so1223354fga.3 for ; Sun, 30 Mar 2008 16:21:43 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=hveRT1teGGbSTu53+W9YsgfphVfd1JNvIF2/3C/L6FE=; b=WMPCkWbgnW3rPGNNylaA2GUGsnazLlVMkqo9fCOfX68StY44DT1DCVQipllCiGj1cXdQg52ez0bnIzu9xrLJ+1hyfHGattCTdQ+qvtmTxH3CO5DQ1pZaaFACkwqJB/X7YR9FAfzs4vZJUURG18HCtnlVJwH6vjTF22mE2NyfqFo= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=YYpEOBol7Ra0FtXtGio8wtIwykwPlx2O25fTowaf0OtLYH6DLakT8ibE2OImLJcGE2sgP6CA/WScofPvW3cmuWea1y6Z+ANp2BoHeoTi2le8IKTgLmJppIU8EAoJboimDFbMqtsTpZNY4KzBhBzGwpCqLxhnHfaAHWP0zw6rnAw= Received: by 10.82.118.1 with SMTP id q1mr13746631buc.13.1206919303404; Sun, 30 Mar 2008 16:21:43 -0700 (PDT) Received: by 10.82.170.19 with HTTP; Sun, 30 Mar 2008 16:21:43 -0700 (PDT) Message-ID: Date: Sun, 30 Mar 2008 20:21:43 -0300 From: "Tiago Machado" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Objetos de \Aprendizagem virtual In-Reply-To: MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_3562_32799013.1206919303387" References: <47EC69EE.9060900@infolink.com.br> <101832.1746.qm@web52401.mail.re2.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Tiago Machado" X-Spam-Status: No, hits=1.2 required=5.0 tests=AWL,HTML_FONT_COLOR_GRAY,HTML_FONT_COLOR_UNSAFE,IN_REP_TO, MAILTO_LINK,QUOTED_EMAIL_TEXT,REFERENCES,SPAM_PHRASE_00_01, SPAM_REDIRECTOR,X_MAILING_LIST version=2.44 X-Spam-Level: * ------=_Part_3562_32799013.1206919303387 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline http://www.wolfram.com/ 2008/3/30 J=F4natas : > Quando eu estudava Geometria Plana, aprendi muito com esse site: > http://agutie.homestead.com/ > acho ele muito bom. > http://www.mathlinks.ro/Forum/ > (Nesse tem um mund=E3o de quest=F5es, tb muito bom) > > J=F4natas. > > > 2008/3/28, Thais Oliveira : > > > Ola pessoal, tudo bem? > > > > Estou a procura de qualquer tipo de objeto de aprendizagem virtual que > > facilite o ensino de matem=E1tica. Se vcs conherem sites interessantes = com > > video, jogos, arquivo em flsh ou coisa do genero me mandem poe favor. > > > > Muito obrigada > > > > Thais > > > > ------------------------------ > > Abra sua conta no Yahoo! Mail, > > o =FAnico sem limite de espa=E7o para armazenamento! > > > > > ------=_Part_3562_32799013.1206919303387 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline
http://www.wolfram.com/

=
2008/3/30 J=F4natas <jssouza1@gmail.com>:
Quando eu estudava Geometria Plana, aprendi muito com esse site: http://agutie.homestead.co= m/
acho ele muito bom.
http://www.mathlinks.ro/Forum/
(Nesse tem um mund=E3o de quest=F5es, tb muito bom)

J=F4natas.


2008/3/28, Thais Oliveira <tha_unicamp@yahoo.com.br>:<= /div>
Ola pessoal, tudo bem?

Estou a procura de qualquer tipo de objeto de= aprendizagem virtual que facilite o ensino de matem=E1tica. Se vcs conhere= m sites interessantes com video, jogos, arquivo em flsh ou coisa do genero = me mandem poe favor.

Muito obrigada

Thais

=20

Abra sua conta no Yahoo! M= ail, o =FAnico sem limite de espa=E7o para armazenamento!=20



------=_Part_3562_32799013.1206919303387-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Sun Mar 30 22:53:28 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2V1pgWA029071 for ; Sun, 30 Mar 2008 22:51:42 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2V1pgc5029069 for obm-l-MllGbsmmN; Sun, 30 Mar 2008 22:51:42 -0300 Received: from wa-out-1112.google.com (wa-out-1112.google.com [209.85.146.180]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2V1peWA029066 for ; Sun, 30 Mar 2008 22:51:41 -0300 Received: by wa-out-1112.google.com with SMTP id m28so1772927wag.13 for ; Sun, 30 Mar 2008 18:51:26 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:mime-version:content-type; bh=7wwFtf3/tdqTmruAb/AGEb9kN9TrgkWEO13XE43CKTI=; b=M+LlxRpXPjS7Piv6+95CdFdrAlIgk8BxcXPXtzzGM0ujn++vYUnqSwhpVO8Pu5XBYOAhdfbTLss/YZmGZNnQpNLXul/Ar0Em1PjPsYUAJzGSLZAFO9FRpl0OAm3WYtXdjbfGWh0K9SyGyITLdbokjauWUMVJ663jGkmXK4k4UAw= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:mime-version:content-type; b=eF2xxdXufihfZtbuDO1CU56g5LMyjj98bQBQBWwHfWdFvMu+UD+IkeBThViE3SjT/CQJOoASxaQQLTXf1bVeduAvnLXwthg151drZmea5RIXK66cQ12g675p6Up0JNzbGXMkxoopJnpLv3DWqdj7jugD7OU0t5d1DH1ONTVSR4M= Received: by 10.114.110.12 with SMTP id i12mr8969046wac.73.1206928286839; Sun, 30 Mar 2008 18:51:26 -0700 (PDT) Received: by 10.114.161.8 with HTTP; Sun, 30 Mar 2008 18:51:26 -0700 (PDT) Message-ID: Date: Sun, 30 Mar 2008 22:51:26 -0300 From: MauZ To: obm-l@mat.puc-rio.br Subject: [SPAM] [obm-l] =?ISO-8859-1?Q?Inequa=E7=E3o_3=BA_grau_-_N=E3o_t=E1_saindo!?= MIME-Version: 1.0 Content-Type: text/plain Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: MauZ X-Spam-Status: Yes, hits=5.5 required=5.0 tests=AWL,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ***** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_Part_5501_6065615.1206928286826" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (5.50 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 180.146.85.209.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 180.146.85.209.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-0.3 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- ------=_Part_5501_6065615.1206928286826 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Ol=E1 pessoal! Abs =E9 MODULO abs(x^2-a)+abs(1-3x) <=3D 2+abs(3/x+1) Obrigado! ------=_Part_5501_6065615.1206928286826 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Ol=E1 pessoal!

Abs =E9 MODULO

abs(x^2-a)+abs(1-3x) <=3D 2+= abs(3/x+1)


Obrigado!
------=_Part_5501_6065615.1206928286826-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Mon Mar 31 08:50:51 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2VBn1WA021168 for ; Mon, 31 Mar 2008 08:49:01 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2VBn1u1021165 for obm-l-MllGbsmmN; Mon, 31 Mar 2008 08:49:01 -0300 Received: from mail.fazenda.ms.gov.br (mail.fazenda.ms.gov.br [200.181.116.25]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2VBmxWA021158 for ; Mon, 31 Mar 2008 08:49:00 -0300 Received: by mail.fazenda.ms.gov.br (Postfix, from userid 115) id 60B987B5C002; Mon, 31 Mar 2008 07:48:46 -0400 (AMT) Received: from mail.fazenda.ms.gov.br (localhost [127.0.0.1]) by mail.fazenda.ms.gov.br (Postfix) with ESMTP id D3F3B7B5C001 for ; Mon, 31 Mar 2008 07:48:45 -0400 (AMT) Received: from 10.5.119.29 by mail.fazenda.ms.gov.br with HTTP; Mon, 31 Mar 2008 07:48:45 -0400 (VET) Message-ID: <1119.10.5.119.29.1206964125.squirrel@mail.fazenda.ms.gov.br> In-Reply-To: <70bb75a50803280923x54297a1axb1b203fe36db9d52@mail.gmail.com> References: <70bb75a50803280616i1f554269q1ede36e9cda122b0@mail.gmail.com> <2b5739960803280735y1f787f86w92700523971a70f8@mail.gmail.com> <70bb75a50803280923x54297a1axb1b203fe36db9d52@mail.gmail.com> Date: Mon, 31 Mar 2008 07:48:45 -0400 (VET) Subject: [SPAM] Re: [obm-l] Pintores From: jjunior@fazenda.ms.gov.br To: obm-l@mat.puc-rio.br User-Agent: Webmail MS MIME-Version: 1.0 Content-Type: text/plain;charset=iso-8859-1 Content-Transfer-Encoding: 7bit X-Priority: 3 (Normal) Importance: Normal Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: jjunior@fazenda.ms.gov.br X-Spam-Status: Yes, hits=5.7 required=5.0 tests=AWL,IN_REP_TO,NO_REAL_NAME,PRIORITY_NO_NAME, QUOTED_EMAIL_TEXT,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, REFERENCES,SPAM_PHRASE_00_01,USER_AGENT,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ***** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (5.70 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: REFERENCES (-0.5 points) Has a valid-looking References header SPAM: USER_AGENT (-0.5 points) Found a User-Agent header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: NO_REAL_NAME (1.3 points) From: does not include a real name SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: QUOTED_EMAIL_TEXT (-0.8 points) BODY: Contains what looks like a quoted email text SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 25.116.181.200.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 25.116.181.200.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: PRIORITY_NO_NAME (1.0 points) Message has priority setting, but no X-Mailer SPAM: AWL (0.2 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- Emanuel, tinha erro no que escrevi. Eis aí o que segue: r = l - 1. r é o tempo do rápido pintar 1m2; l, o do lento. É dito que eles levam 60 minutos na pintura de 27m2, logo levam juntos 60/27 em 1m2. Mas 1/(1/r+1/l) é outra forma de calcular o tempo na pintura da unidade de área. Assim, 1/r + 1/l = 9/20 -> 20(l+r)=9rl -> 20(2l-1) = 9l(l-1) -> 40l – 20 = 9l^2 – 9l -> 9l^2 - 49l + 20 = 0. Mas alguém, antes de nós, chegou à resposta 5 para o lento, ratificada pelo gabarito, conforme informas. Basta, então, verificar se 5 é raiz da equação acima, e é, de fato. Júnior. > Olá, a resposta do Bernardo bateu com o gabarito (4 min e 5 min). Pra > dizer a verdade estava no caminho certo, mas tinha assustado com um > valor de delta alto num problema relativamente simples. Pelo que vi a > equação do Rogério saiu com variáveis trocadas em relação a do > Bernardo, fiz a conta e deu valor quebrado. > > Junior, não entendi seu raciocínio quando você escreveu: > 27r + 27l = 60. > > Obrigado a todos dede já! > > -- > Emanuel Valente > > On Fri, Mar 28, 2008 at 11:35 AM, Rogerio Ponce > wrote: >> Ola' Emanuel, >> digamos que a pessoa A pinte R m2 de muro por minuto , e B pinte S m2 >> / minuto. >> Entao, A e B pintam 1m2 de muro em 1/R minutos e 1/S minutos , >> respectivamente. >> >> Portanto, conforme o enunciado, >> 1/R - 1/S = 1 >> >> E trabalhando juntas, pintam (R+S) m2 por minuto, que e' o mesmo que >> 60*(R+S) m2 por hora, e que, segundo o enunciado, vale 27. >> >> Entao, temos as seguintes equacoes: >> 1/R - 1/S = 1 >> 60*(R+S) = 27 >> >> E daqui em diante, voce sabe completar... >> []'s >> Rogerio Ponce >> >> >> 2008/3/28, Emanuel Valente : >> >> >> > Não consegui montar algebricamente o seguinte problema. Ficarei grato >> > se me ajudarem! >> > >> > Duas pessoas, A e B, pintam separadamente 1m^2 de um muro em tempos >> > que diferem de 1 minuto. Trabalhando juntas, elas pintam 27m^2 por >> > hora. Quanto tempo cada uma leva pra pintar 1 m^2 ? >> > >> >> >> >> ========================================================================= >> Instruções para entrar na lista, sair da lista e usar a lista em >> http://www.mat.puc-rio.br/~obmlistas/obm-l.html >> ========================================================================= >> > > ========================================================================= > Instruções para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > ========================================================================= > ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Mon Mar 31 09:46:36 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2VCj2WA024770 for ; Mon, 31 Mar 2008 09:45:02 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2VCj2NB024768 for obm-l-MllGbsmmN; Mon, 31 Mar 2008 09:45:02 -0300 Received: from fg-out-1718.google.com (fg-out-1718.google.com [72.14.220.156]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2VCixWA024761 for ; Mon, 31 Mar 2008 09:45:00 -0300 Received: by fg-out-1718.google.com with SMTP id e12so1479918fga.3 for ; Mon, 31 Mar 2008 05:44:46 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; bh=v74vu0nRATfxT/LIZwIJym5NzBfA0snXmKiroLH6yGc=; b=pfZY7SBLoyh3mAPXhOEAROPVOW3SDHxx/fEwtUKmQ6Qwx1pNUqKeVgiBRbuaPv/ylX+DiyONYHLffMyu12GsS7DFj9Yb44tHnvMF8wkL75WljqZtlQo3cRiwQkBARJup6LZ/H/JQuGufxvCuw6WlsVqmeJM0n9+wUDkKPn3j/O8= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; b=In3W9V2+XeNk6khsKNaNWuKoHS4aGCz2jAHyM08i7jQESbBPraQ0PJncaO5f6ppqspgZPGZuyL9ChsEVMhgIlq1FXMZX0P4jbQKPbXP6KzmGCN61pNiP71UdpToL15CMZIRYZ7gA1Eue+YoOOUdkIEHnyOnKHLTd9/Otj9Jemdw= Received: by 10.82.170.3 with SMTP id s3mr15730890bue.18.1206967485927; Mon, 31 Mar 2008 05:44:45 -0700 (PDT) Received: by 10.82.127.13 with HTTP; Mon, 31 Mar 2008 05:44:45 -0700 (PDT) Message-ID: Date: Mon, 31 Mar 2008 09:44:45 -0300 From: "Johann Peter Gustav Lejeune Dirichlet" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] T. dos Numeros, olimpico! In-Reply-To: <3e7bcb580803281815q25213a50pc71773f79e9f970@mail.gmail.com> MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline References: <99886d920803261733m20957fdcwead8e048e725b6fe@mail.gmail.com> <3bd00efc0803281539h42a7a848gcc44e39be3f30990@mail.gmail.com> <3e7bcb580803281815q25213a50pc71773f79e9f970@mail.gmail.com> Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m2VCj1WA024766 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Johann Peter Gustav Lejeune Dirichlet" X-Spam-Status: No, hits=0.4 required=5.0 tests=AWL,FROM_ENDS_IN_NUMS,IN_REP_TO,MAILTO_TO_SPAM_ADDR, QUOTED_EMAIL_TEXT,REFERENCES,SIGNATURE_LONG_SPARSE, SPAM_PHRASE_00_01,X_MAILING_LIST version=2.44 X-Spam-Level: Banco da IMO, 2000. Na verdade era `começa´ mesmo do jeito que foi escrito. Em 28/03/08, Henrique Rennó escreveu: > Olá Marcelo! > > Muito legal sua demonstração, mas eu tenho dúvidas se essa seria a > demonstração válida para o problema. Aquele "comece" não seria o > primeiro algarismo da esquerda para a direita? Por exemplo, 5! = 120, > começa com 1, já que todo fatorial de um número natural a partir do 5 > tem como "último" algarismo o 0, pois sempre haverá um 5*2 na > multiplicação. Assim, pela sua demonstração (mod 10) todo número >= 5 > tem o 0 como "último" algarismo de seu fatorial. > > Outra pergunta. Você participa do TopCoder? > > Abraços e bom fim de semana! > > 2008/3/28 Marcelo Salhab Brogliato : > > > Olá Bruno, > > > > suponha que exista K, tal que: > > (K+j)! == j (mod 10), j = 1, ..., 9 > > > > vejamos: > > (K+1)! == 1 (mod 10) > > > > (K+2)! == 2 (mod 10), mas (K+2)! = (K+2)(K+1)! == K+2 (mod 10) > > portanto, K+2 == 2 (mod 10) .... e: K == 0 (mod 10) > > > > (K+3)! == 3 (mod 10), mas (K+3)! = (K+3)(K+2)! == 2(K+3) (mod 10) > > portanto, 2(K+3) = 2K+6 == 3 (mod 10) > > mas, K == 0 (mod 10), e, obtemos: 6 == 3 (mod 10) > > ABSURDO! > > > > portanto, está provado que não existe. > > > > um abraço, > > Salhab > > > > > > > > 2008/3/26 Bruno França dos Reis : > > > > > > > Problema: > > > > > > Prove que não existem numeros fatoriais consecutivos com primeiros digitos > > iguais a 1, 2, ..., 9. > > > Em outras palavras: prove que não existe K tal que (K+j)! comece pelo > > algarismo j, para todo j = 1, ..., 9. > > > > > > Abraço > > > Bruno > > > > > > -- > > > Bruno FRANÇA DOS REIS > > > > > > msn: brunoreis666@hotmail.com > > > skype: brunoreis666 > > > tel: +33 (0)6 28 43 42 16 > > > > > > e^(pi*i)+1=0 > > > > > > > > > -- > Henrique > > ========================================================================= > Instruções para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > ========================================================================= > -- Ideas are bulletproof. V ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Mon Mar 31 11:36:38 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2VEYHWA030610 for ; Mon, 31 Mar 2008 11:34:17 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2VEYGd4030608 for obm-l-MllGbsmmN; Mon, 31 Mar 2008 11:34:16 -0300 Received: from smtpi03s.infolink.com.br (smtpi03s.infolink.com.br [200.187.64.122]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2VEYFWA030585 for ; Mon, 31 Mar 2008 11:34:15 -0300 Received: from smtpi03s.infolink.com.br (localhost [127.0.0.1]) by smtpi03s.infolink.com.br (Postfix) with ESMTP id C73EF713680 for ; Mon, 31 Mar 2008 11:34:02 -0300 (EST) Received: from metrical01 (20151166051.user.veloxzone.com.br [201.51.166.51]) by smtpi03s.infolink.com.br (Postfix) with ESMTP id 9BAEC704C4E for ; Mon, 31 Mar 2008 11:34:02 -0300 (EST) Message-ID: <05aa01c8933c$08c1f970$0200000a@metrical01> From: "Rejane" To: Subject: [SPAM] [obm-l] Sistema Date: Mon, 31 Mar 2008 11:32:23 -0300 MIME-Version: 1.0 Content-Type: text/plain X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2900.3138 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.3198 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Rejane" X-Spam-Status: Yes, hits=5.5 required=5.0 tests=AWL,BIG_FONT,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, SPAM_PHRASE_00_01,USER_AGENT_OE,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ***** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="----=_NextPart_000_05A7_01C89322.E3360AC0" SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (5.50 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: USER_AGENT_OE (0.2 points) X-Mailer header indicates a non-spam MUA (Outlook Express) SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: BIG_FONT (0.3 points) BODY: FONT Size +2 and up or 3 and up SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 51.166.51.201.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 51.166.51.201.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-0.8 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- This is a multi-part message in MIME format. ------=_NextPart_000_05A7_01C89322.E3360AC0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Ol=E1, algu=E9m poderia me ajudar com esse sistema: {x+y=3D1 {2x+by=3D2 ->calcular B de modo que o determinante da icognita X seja igual ao = proprio valor de X. ------=_NextPart_000_05A7_01C89322.E3360AC0 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable
 

Ol=E1,

algu=E9m poderia me ajudar com esse = sistema:

{x+y=3D1

{2x+by=3D2

->calcular B de modo que o determinante da = icognita X=20 seja igual ao proprio valor de X.

------=_NextPart_000_05A7_01C89322.E3360AC0-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Mon Mar 31 13:50:11 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2VGlRWA011928 for ; Mon, 31 Mar 2008 13:47:27 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2VGlPD2011925 for obm-l-MllGbsmmN; Mon, 31 Mar 2008 13:47:25 -0300 Received: from wx-out-0506.google.com (wx-out-0506.google.com [66.249.82.237]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2VGlNWA011922 for ; Mon, 31 Mar 2008 13:47:23 -0300 Received: by wx-out-0506.google.com with SMTP id t4so2087100wxc.18 for ; Mon, 31 Mar 2008 09:47:09 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:mime-version:content-type:content-transfer-encoding:content-disposition; bh=z5D84BVUURgg5yw5kCDOxuOucpn2vyZ0wqiMzrlC07o=; b=mesYcbsc2MBbVtG9s/8zZLTfXIBgI8VBklR0LbrpzO+qZwJv4l4344rC/KIeBwNNuizOovZxvhfxIZTWsuR5Ac+KFrf57w28rIZKRPXWfzj12NzkXPpwNyeqUCUFdn/qRu/MzH5wVg0Y7L2ex8r3ZkHIX6ZBL3aHYRGswMaiF78= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:mime-version:content-type:content-transfer-encoding:content-disposition; b=hwsNPzFUQETkIPOWdrEAKzq9RIxUsZxShPTJGj5Gv6HMuOFyrd1c7L6WPonqe8IdbjxJKK15TJOYH0pvsLi+B+ZHL84IanbUkHYmRR6RzhfRm+sMt1hXRytU3tOkGgoiWCmmZgHVEQ+mUgS5YpT7vhjxXYrNiB2GrKxIXOQ50UY= Received: by 10.70.54.2 with SMTP id c2mr8181795wxa.85.1206982029581; Mon, 31 Mar 2008 09:47:09 -0700 (PDT) Received: by 10.70.116.11 with HTTP; Mon, 31 Mar 2008 09:47:09 -0700 (PDT) Message-ID: <7e31215a0803310947j561b3c1euaa3901959474f2c7@mail.gmail.com> Date: Mon, 31 Mar 2008 13:47:09 -0300 From: "Rodrigo Renji" To: obm-l Subject: [SPAM] [obm-l] =?ISO-8859-1?Q?S=E9rie?= MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline Content-Transfer-Encoding: 7bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m2VGlOWA011923 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Rodrigo Renji" X-Spam-Status: Yes, hits=5.1 required=5.0 tests=AWL,RCVD_IN_MULTIHOP_DSBL,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01, TO_LOCALPART_EQ_REAL,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ***** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (5.10 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: TO_LOCALPART_EQ_REAL (-0.3 points) To: repeats local-part as real name SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: RCVD_IN_MULTIHOP_DSBL (0.8 points) RBL: Received via a relay in multihop.dsbl.org SPAM: [RBL check: found 237.82.249.66.multihop.dsbl.org] SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 237.82.249.66.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 237.82.249.66.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: AWL (-1.2 points) AWL: Auto-whitelist adjustment SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- Mostrar que somatório de n=1 até infinito de 1/(n)(n+k) =Hk/k onde Hk é o k-ésimo número harmônico, k>=1, k natural Hk= somatorio de p=1 até k de 1/p ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Mon Mar 31 14:06:09 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2VH4mWA012789 for ; Mon, 31 Mar 2008 14:04:48 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2VH4mDJ012787 for obm-l-MllGbsmmN; Mon, 31 Mar 2008 14:04:48 -0300 Received: from el-out-1112.google.com (el-out-1112.google.com [209.85.162.176]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2VH4kWA012781 for ; Mon, 31 Mar 2008 14:04:46 -0300 Received: by el-out-1112.google.com with SMTP id o28so497109ele.3 for ; Mon, 31 Mar 2008 10:04:32 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=imuIGv1VJZhjlL1rUdSBWFQZpstSF9onvbHOkJX8vhc=; b=RWdJLFxGv+Fnvq3A1EzWx1C5wAxzVa3YeuiYxZgtqe/6rI2vvsSZPWMJqowH4fqLgE4LO3OuCiwHYsQ84O4S9Kubw/z75RIMVMWE8vU+JTnTaZctU3EOKHrpQTCc4H48v9DRLPGSaQKt5L6rOPsKLO8XPI3dyAApU8R1rF1u/WI= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=kcsbokD829JvZlkZD9rzFZpp7mb2rogQHDAlBDyDflbzsAlUn9Lc0XCuNF/vSg7K/9E7GUclb4cyr/BbFx9NiAEV5mC1SWYdR0W4/oCkdzWPrpvB4Dxj4qdL1LS3RlFGk7h7RQmGaRQmCu5j7usThNNq+hIyMHpXlcNOrXJD/bU= Received: by 10.114.151.13 with SMTP id y13mr10307053wad.134.1206983071477; Mon, 31 Mar 2008 10:04:31 -0700 (PDT) Received: by 10.114.78.2 with HTTP; Mon, 31 Mar 2008 10:04:31 -0700 (PDT) Message-ID: <2eaf8c650803311004n52dc6f18na7f89e8412c6b180@mail.gmail.com> Date: Mon, 31 Mar 2008 11:04:31 -0600 From: colombo To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Sistema In-Reply-To: <05aa01c8933c$08c1f970$0200000a@metrical01> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_39679_16701002.1206983071481" References: <05aa01c8933c$08c1f970$0200000a@metrical01> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: colombo X-Spam-Status: No, hits=3.5 required=5.0 tests=AWL,BIG_FONT,EMAIL_ATTRIBUTION,IN_REP_TO,MAILTO_LINK, QUOTED_EMAIL_TEXT,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, REFERENCES,SPAM_PHRASE_00_01,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: *** ------=_Part_39679_16701002.1206983071481 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Regra de Cramer o valor de x =3D det M1/det M. Onde M=3D{{1,1},{2,b}} =E9 = a matrix com 1 1 na primeira linha e 2 b na segunda. =E9 a matriz do sistema = e M1=3D{{1,1},{2,1}} =E9 matrix obtida por substituir a primeira coluna (que = se refere a variavel x) pela coluna obtida considerando as os coeficientes constantes. Tem uma cara que b=3D1, n=E3o acha? A formula de Crammer =E9: se o sistema nas vari=E1veios x e y tem det{{a,b},{c,d}} diferente de zero. Seja o sistema ax+by=3Dr1 cx+dy=3Dr2 , ent=E3o pela regra de Crammer temos x=3D det{{r1,b},{r2,d}} / det{{a,b},{c,d}} e y=3Ddet{{a,r1},{b,r2}} /det{{a,b},{c,d}}. ok? On Mon, Mar 31, 2008 at 8:32 AM, Rejane wrote: > > > *Ol=E1,* > > *algu=E9m poderia me ajudar com esse sistema:* > > ** > > *{x+y=3D1* > > *{2x+by=3D2* > > ** > > *->calcular B de modo que o determinante da icognita X seja igual ao > proprio valor de X.* > > ** > ------=_Part_39679_16701002.1206983071481 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Regra de Cramer o valor de x =3D det M1/det M. Onde M=3D{{1,1},{2,b}} = =E9 a matrix com 1 1 na primeira linha e 2 b na segunda. =E9 a matriz do s= istema e M1=3D{{1,1},{2,1}} =E9 matrix obtida por substituir a primeira col= una (que se refere a variavel x) pela coluna obtida considerando as os coef= icientes constantes.

Tem uma cara que b=3D1, n=E3o acha?

A formula de Crammer =E9: se= o sistema nas vari=E1veios x e y tem det{{a,b},{c,d}} diferente de zero. S= eja o sistema

 ax+by=3Dr1
 cx+dy=3Dr2 ,
 ent= =E3o pela regra de Crammer temos
x=3D det{{r1,b},{r2,d}} / det{{a,b},{c,d}} e
y=3Ddet{{a,r1},{b,r2}} /de= t{{a,b},{c,d}}.

ok?

On Mon, Mar 31= , 2008 at 8:32 AM, Rejane <rejane@= rack.com.br> wrote:
 

Ol=E1,

algu=E9m poderia me ajudar com esse sistema:<= /i>

{x+y=3D1

{2x+by=3D2

->calcular B de modo que o determinante da icogni= ta X=20 seja igual ao proprio valor de X.


------=_Part_39679_16701002.1206983071481-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Mon Mar 31 14:52:29 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2VHojWA015922 for ; Mon, 31 Mar 2008 14:50:45 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2VHoj75015920 for obm-l-MllGbsmmN; Mon, 31 Mar 2008 14:50:45 -0300 Received: from an-out-0708.google.com (an-out-0708.google.com [209.85.132.251]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2VHohWA015895 for ; Mon, 31 Mar 2008 14:50:43 -0300 Received: by an-out-0708.google.com with SMTP id c31so405962ana.120 for ; Mon, 31 Mar 2008 10:50:29 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; bh=wOhWPCSy96JNNodioyp8HpF+8KYgpsGqINrD9VGMlCw=; b=LONOldOA5qpIOvhCpJlbFLLhAtMbZsHwoF3MuLJiWgP5ay9XGIfgNq4WLptHZtlNCF6J7SvCbcYDDPWJ29sDI032q3NM91C95JBvHeG65UaPJzXCI85X2adVLEyUdS7j15rgIrTeBJWXilnzA94rr7PZ/DGccR9TJWIefEfaJAw= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:references; b=tCdTsRDFqBlS/+5L/Cfj43yVYiUn+VFGd0eQLIYIFVaj2gAoDjayacNF7xYPpTmMaeAQ2nYjyf+DFXT6DSq6FvJbhn8NpNdX/gYkxPynaUtQpCPqqewglG7Y5X3WSv1WtMtvVyvchjzjAVcO7nAslC24Lvq8bRcxn7qzC2JBfz0= Received: by 10.100.144.11 with SMTP id r11mr16578206and.75.1206985829025; Mon, 31 Mar 2008 10:50:29 -0700 (PDT) Received: by 10.100.178.1 with HTTP; Mon, 31 Mar 2008 10:50:27 -0700 (PDT) Message-ID: <753eb5ac0803311050x304f875cq5dfa9ff0d0723743@mail.gmail.com> Date: Mon, 31 Mar 2008 14:50:27 -0300 From: "Gabriel Haeser" To: obm-l@mat.puc-rio.br Subject: =?ISO-8859-1?Q?Re:_[obm-l]_S=E9rie?= In-Reply-To: <7e31215a0803310947j561b3c1euaa3901959474f2c7@mail.gmail.com> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_7653_19756144.1206985828996" References: <7e31215a0803310947j561b3c1euaa3901959474f2c7@mail.gmail.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Gabriel Haeser" X-Spam-Status: No, hits=4.9 required=5.0 tests=IN_REP_TO,MAILTO_LINK,MIME_EXCESSIVE_QP,QUOTED_EMAIL_TEXT, RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,REFERENCES, SPAM_PHRASE_00_01,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** ------=_Part_7653_19756144.1206985828996 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline soma[1/(n)(n+k)]=3Dsoma[(1/k).(1/n-1/(n+k))]=3D1/k.(soma[1/n]-soma[1/(n+k)]= )=3DHk/k 2008/3/31, Rodrigo Renji : > > Mostrar que > > somat=F3rio de n=3D1 at=E9 infinito de 1/(n)(n+k) =3DHk/k > > onde Hk =E9 o k-=E9simo n=FAmero harm=F4nico, k>=3D1, k natural > > Hk=3D somatorio de p=3D1 at=E9 k de 1/p > > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > Instru=E7=F5es para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > ------=_Part_7653_19756144.1206985828996 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline soma[1/(n)(n+k)]=3Dsoma[(1/k).(1/n-1/(n+k))]=3D1/k.(soma[1/n]-soma[1/(n+k)]= )=3DHk/k

2008/3/31, Rodrigo Renji &= lt;rodrigo.uff.math@gmail.com= >:
Mostrar que

somat=F3rio de n=3D1 at=E9 infinito de 1/(n)(n+k) =3DH= k/k

onde Hk =E9 o k-=E9simo n=FAmero harm=F4nico, k>=3D1, k nat= ural

Hk=3D somatorio de p=3D1 at=E9 k de 1/p

=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D
Instru=E7=F5es para entrar na lista, sair da lista e usar a lista em
<= a href=3D"http://www.mat.puc-rio.br/~obmlistas/obm-l.html">http://www.mat.p= uc-rio.br/~obmlistas/obm-l.html
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D

------=_Part_7653_19756144.1206985828996-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html =========================================================================
On 3/24/08, Fernando <artesmatematica@globo.com&g= t;=20 wrote:=20
Ol=E1 Jo=E3o Victor, boa = tarde!
 
Voc=EA possui a solu=E7=E3o do = problema=20 abaixo?
Se SIM, poderia envi=E1-la para = mim?
 

Sociedade Brasileira de Matem=E1tica

EUREKA! N=B014,=20 2002

VIII OLIMP=CDADA DE=20 MAIO

Enunciados e Resultado=20 Brasileiro

PRIMEIRO = N=CDVEL

11/05/2002

PROBLEMA = 1

Um grupo de homens, alguns dos = quais=20 acompanhados pelas esposas, gastaram 1000

d=F3lares num hotel. Cada homem = gastou 19=20 d=F3lares e cada mulher, 13 d=F3lares.

Determine quantas mulheres e = quantos homens=20 estavam no hotel.

 

http://www.obm.org.br/eureka/eureka14.pdf

acesso em=20 23/03/2008

 
 
Agrade=E7o sua = aten=E7=E3o.
 
Amplexo.
Fernando Pinto
 
----- Original Message ----- =
From: = Joao Victor = Brasil=20
Sent: Monday, March 24, = 2008 10:29=20 AM
Subject: Re: [obm-l] = combinatoria=20 dificil

 
=C9 verdade pessoal. Errei e muito na minha = resolu=E7=E3o.
 
Mas olha s=F3, concordo plenamente com a resposta do = Henrique, 48=20 possibilidades.
 
Usando o princ=EDpio multiplicativo = D1H1_D1H2_D2H1_D2H2_D3H1_D3H2 achei=20 72 possibilidades, me alertaram sobre as repeti=E7=F5es e analisei = um modo de=20 retir=E1-las.
D1H1:3 disc
D1H2: 2 disc
D2H1: 2 disc (repetir as mesmas disciplinas do dia 1)
D2H2: 1 disc
D3H1: 2 disc (apesar de sobrar somente uma disc, temos duas=20 aulas)
D3H2: 1 disc
 
3*2*2*1*2*1 =3D=20 24.           72 = - 24 =3D=20 48 poss.
 
Joao Victor

 
On 3/20/08, Henrique Renn=F3 <henrique.renno@gmail.com> wrote:=20
Ol=E1=20 pessoal!

Acredito que a solu=E7=E3o do Salhab est=E1 = correta. Seja Di o=20 dia i e Hj o hor=E1rio j.

D1H1: 3 mat=E9rias
D1H2: 2 = mat=E9rias=20 (para n=E3o repetir a utilizada em D1H1)
D1: 6=20 possibilidades

Para D2, se escolhermos uma j=E1 utilizada = em D1=20 ent=E3o n=E3o poderemos
utilizar a outra mat=E9ria utilizada = em D1, sen=E3o=20 D3 teria as mesmas
mat=E9rias. Assim, para D2 ter=EDamos uma = j=E1 utilizada=20 (2 mat=E9rias) e uma
n=E3o utilizada. Logo, 2*1 =3D 2. Como a = ordem=20 importa, temos 2*2 =3D 4.

D3 s=F3 possui 2 formas, com as = ordens das=20 mat=E9rias trocadas.

Total: 6*4*2 =3D 48.

Essa =E9 = uma forma=20 mais l=F3gica de resolver o problema. Estive = tentando
utilizar=20 combinat=F3ria e tamb=E9m achei a resposta 48.

Sejam = A,B,C as=20 mat=E9rias. Quantas permuta=E7=F5es diferentes existem = entre
A,A,B,B,C,C?=20 Cada posi=E7=E3o seria um hor=E1rio em um dia, ou=20 seja,
D1H1_D1H2_D2H1_D2H2_D3H1_D3H2. Bastaria calcular o = n=FAmero=20 de
permuta=E7=F5es com repeti=E7=E3o, ou seja, 6!/(2!*2!*2!) = =3D 720/8 =3D=20 90.

Sabemos que n=E3o podemos ter uma permuta=E7=E3o do = tipo AABCBC,=20 pois AA
representa a mesma mat=E9ria em D1H1 e D1H2. Ent=E3o = sabemos que=20 a
resposta =E9 menor que 90.

As formas inv=E1lidas=20 ser=E3o:

Se as 3 mat=E9rias do mesmo tipo est=E3o juntas = no mesmo dia,=20 ex: AABBCC.
Existem 3! =3D 6 formas, considerando AA,BB,CC = como 3=20 elementos
permutados entre si.

N=E3o h=E1 necessidade = de verificar=20 quando 2 mat=E9rias est=E3o no mesmo dia
pois cai no caso=20 acima.

Quando h=E1 apenas 1 mat=E9ria repetida em 1 dia, = ex: AABCBC,=20 ent=E3o temos
12 formas para cada par da mesma mat=E9ria = utilizada no=20 mesmo dia. Se AA
est=E1 em D1 ent=E3o D2 pode ser BC ou CB e = D3 pode ser=20 BC ou CB, 2*2 =3D 4.
AA pode estar em D1,D2,D3. Assim, 4*3 = =3D 12. Para=20 BB e CC seria o
mesmo, dando um total de 3*12 =3D 36 formas = quando h=E1=20 apenas uma mat=E9ria
que se repete no mesmo = dia.

Assim, o total=20 seria 90 - (6+36) =3D 90 - 42 =3D 48 formas distintas = de
compor o=20 hor=E1rio

Thelio, voc=EA poderia passar a fonte do = problema e=20 verificar se as
respostas s=E3o essas mesmo?

On = 3/13/08, Thelio=20 Gama <teliogama@gmail.com> wrote:
> =C9=20 pessoal...
>
> Achei muito dif=EDcil esta quest=E3o. = Agrade=E7o se=20 algu=E9m puder explic=E1-la.
>
> = Thelio
>
> uma=20 turma tem aulas =E0s 2=AA, 4=AA e 6=AA feiras, de 8-9 horas e de = 11-12 horas.=20 As
> mat=E9rias s=E3o portugues, matem=E1tica e ingles, = cada uma com=20 duas aulas
> semanais, em dias diferentes. De quantos = modos pode=20 ser feito o hor=E1rio
> dessa turma?
> = a)96  ; b)=20 144   ; c)192   ; d) = 6!    ; e)=20 = 120


--
Henrique

=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D
Instru=E7=F5es=20 para entrar na lista, sair da lista e usar a lista em
http://www.mat.puc-rio.br/~obmlistas/obm-l.html
=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D

------=_NextPart_000_0008_01C88DB5.B07B5990-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Mon Mar 24 15:56:37 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2OIsXWA019103 for ; Mon, 24 Mar 2008 15:54:33 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2OIsWbO019101 for obm-l-MllGbsmmN; Mon, 24 Mar 2008 15:54:32 -0300 Received: from gama-rt.urisan.tche.br (smtp.san.uri.br [200.203.104.150]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2OIsRWA019095 for ; Mon, 24 Mar 2008 15:54:29 -0300 Received: from www.urisan.tche.br (localhost [127.0.0.1]) by gama-rt.urisan.tche.br (Postfix) with ESMTP id 023EA1743D3 for ; Mon, 24 Mar 2008 15:55:02 -0300 (BRT) Received: from 10.1.1.189 by www.urisan.tche.br with HTTP; Mon, 24 Mar 2008 15:55:02 -0300 (BRT) Message-ID: <1154.10.1.1.189.1206384902.squirrel@www.urisan.tche.br> In-Reply-To: <001c01c88c5f$12c5e500$6401a8c0@pai> References: <001c01c88c5f$12c5e500$6401a8c0@pai> Date: Mon, 24 Mar 2008 15:55:02 -0300 (BRT) Subject: [SPAM] Re: [obm-l] off topic: exercicios analise real From: rbdantas@urisan.tche.br To: obm-l@mat.puc-rio.br User-Agent: SquirrelMail/1.4.6 MIME-Version: 1.0 Content-Type: text/plain;charset=iso-8859-1 Content-Transfer-Encoding: 7bit X-Priority: 3 (Normal) Importance: Normal Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: rbdantas@urisan.tche.br X-Spam-Status: Yes, hits=5.5 required=5.0 tests=IN_REP_TO,NO_REAL_NAME,PRIORITY_NO_NAME,QUOTED_EMAIL_TEXT, RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,REFERENCES, SPAM_PHRASE_00_01,USER_AGENT,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ***** X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (5.50 hits, 5 required) SPAM: IN_REP_TO (-0.8 points) Found a In-Reply-To header SPAM: REFERENCES (-0.5 points) Has a valid-looking References header SPAM: USER_AGENT (-0.5 points) Found a User-Agent header SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: NO_REAL_NAME (1.3 points) From: does not include a real name SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: QUOTED_EMAIL_TEXT (-0.8 points) BODY: Contains what looks like a quoted email text SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 150.104.203.200.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 150.104.203.200.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: PRIORITY_NO_NAME (1.0 points) Message has priority setting, but no X-Mailer SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- > Ola Hermann. Eu tenho centenas de exercicios resolvidos de analise mas não estão em arquivos que possam ser enviados via net. No futuro pretendo escrever um livro com esse material. Uma dica que pode te ajudar a resolver esses exercicios é estudar por outros livros do elon, tipo Curso de analise vol 2 , espaços metricos , topologia geral, etc... Estude os exemplos com bastante atenção, isso podera ser de grande ajuda na solução dos exercicios. Abs. Rivaldo Senhores, boa tarde, sei que é off-topic desculpem-me, mas, tá difícil de > fazer sozinho, gostaria da ajuda do pessoal da lista. > Assunto: exercícios resolvidos do livro de análise do Elon > do pequeno ou do grande (volume 1). > Sei fazer alguns, outros não sei nem por onde começar. > Peço: > se você possui alguns resolvidos e puder me ceder agradeço muito. > meu e-mail: ilhadepaqueta@bol.com.br > Obrigado > Hermann Cabri > > ========================================================================= > Instruções para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > ========================================================================= > ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Mon Mar 24 17:14:05 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2OKC6WA024087 for ; Mon, 24 Mar 2008 17:12:11 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2OKBxg5024081 for obm-l-MllGbsmmN; Mon, 24 Mar 2008 17:11:59 -0300 Received: from mobius.impa.br (mobius.impa.br [147.65.1.81]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2OKBMWA024053; Mon, 24 Mar 2008 17:11:22 -0300 Received: from [147.65.2.170] (obm-01.impa.br [147.65.2.170]) (authenticated bits=0) by mobius.impa.br (8.13.8/8.13.8) with ESMTP id m2OKB38e030577 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=NO); Mon, 24 Mar 2008 17:11:03 -0300 Message-ID: <47E80B11.8010705@impa.br> Date: Mon, 24 Mar 2008 17:12:01 -0300 From: Olimpiada Brasileira de Matematica User-Agent: Thunderbird 1.5.0.14 (Windows/20071210) MIME-Version: 1.0 To: aobm-l@mat.puc-rio.br, Lista de discussao , socios.obm@impa.br, gugu@impa.br Subject: [obm-l] Informativo sobre evento. Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 8bit X-Greylist: Sender succeeded SMTP AUTH authentication, not delayed by milter-greylist-3.0 (mobius.impa.br [147.65.1.27]); Mon, 24 Mar 2008 17:11:03 -0300 (BRT) Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Olimpiada Brasileira de Matematica X-Spam-Status: No, hits=4.8 required=5.0 tests=AWL,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01, USER_AGENT,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** Caros(as) amigos(as) da OBM, A seguir enviamos, informações sobre a IV Semana da Matemática da UFF. outras informações e o programa de atividades no site: http://www.uff.br/semanadamatematica/home.html Cordialmente, Secretaria da OBM. ============================================================== IV Semana de Matemática da UFF 13 a 17 de maio de 2008 Niterói - Rio de Janeiro *APRESENTAÇÃO * A IV Semana de Matemática da UFF será realizada no Campus do Valonguinho da Universidade Federal Fluminense, no período de 13 a 17 de maio de 2008. O objetivo principal é o de se criar um ambiente onde pesquisadores, educadores e a comunidade em geral possam interagir, divulgando experiências, inovações e diagnosticando novas áreas de atuação em Matemática nas suas várias manifestações. Público-alvo: alunos e professores do curso de matemática da UFF, alunos e professores das escolas de ensino fundamental e médio da região. Atividades previstas: palestras , minicursos e oficinas , mesa redonda , grupos de pesquisa, comunicações e o museu interativo para o ensino da matemática . Atividades culturais: sessões de cinema. Secretária Regina Simplício de Souza Telefone: (021) 2629-2005 FAX: (021) 2629-2114 E-mail: semanadamatematica@vm.uff.br Horário de atendimento: das 14 h às 18 h. Endereço: Universidade Federal Fluminense Instituto de Matemática Rua Mário Santos Braga, S/N, Campus do Valonguinho CEP 24020-140, Niterói, RJ, Brasil *COMISSÃO ORGANIZADORA *Dirce Uesu Pesco (Coordenadora), Ana Maria Lima de Farias (Vice-Coordenadora), Anne Michelle Dysman Gomes, Gabriel Calsamiglia Mendlewicz, Humberto José Bortolossi, José Roberto Linhares de Mattos, Mario Olivero Marques da Silva, Ralph Costa Teixeira, Solimá Gomes Pimentel, Wanderley Moura Rezende. ------------------------------------------------------------------------ ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Mon Mar 24 17:45:50 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2OKijWA027010 for ; Mon, 24 Mar 2008 17:44:45 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2OKijKR027008 for obm-l-MllGbsmmN; Mon, 24 Mar 2008 17:44:45 -0300 Received: from web58211.mail.re3.yahoo.com (web58211.mail.re3.yahoo.com [68.142.236.149]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with SMTP id m2OKigWA026992 for ; Mon, 24 Mar 2008 17:44:43 -0300 Received: (qmail 82363 invoked by uid 60001); 24 Mar 2008 20:44:22 -0000 DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=s1024; d=yahoo.com.br; h=X-YMail-OSG:Received:Date:From:Subject:To:MIME-Version:Content-Type:Content-Transfer-Encoding:Message-ID; b=BShlctF2KONAOTf+LFf0b9eEX71mhYC7pVSHFjpBard50jWfb3NbkXcuuRwFPmn5LwDMizOYYUbwuxZ7xAf+zXpTJurVAKH89tjrshtIX5hzRVdX+QRh8n8aifWrv27UxWF27I4wF4jEb4MP6ZpRO51DVgcE38x4S9cnPtK9MfQ=; X-YMail-OSG: FWqCA9kVM1kWBm.E5U0Ecp5q7aQjhnabzYgxmZveF4ZOz_slp7l721jlGCid95sDhQ-- Received: from [200.159.32.85] by web58211.mail.re3.yahoo.com via HTTP; Mon, 24 Mar 2008 17:44:22 ART Date: Mon, 24 Mar 2008 17:44:22 -0300 (ART) From: Douglas Alexandre Subject: [SPAM] [obm-l] =?iso-8859-1?q?Fun=E7=F5es=20limitadas?= To: obm-l@mat.puc-rio.br MIME-Version: 1.0 Content-Type: text/plain Content-Transfer-Encoding: 7bit Message-ID: <657129.82325.qm@web58211.mail.re3.yahoo.com> Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Douglas Alexandre X-Spam-Status: Yes, hits=7.6 required=5.0 tests=FORGED_YAHOO_RCVD,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM, SPAM_PHRASE_00_01,SPAM_REDIRECTOR,X_MAILING_LIST, X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Flag: YES X-Spam-Level: ******* X-Spam-Checker-Version: SpamAssassin 2.44 (1.115.2.24-2003-01-30-exp) X-Spam-Prev-Content-Type: multipart/alternative; boundary="0-1645741501-1206391462=:82325" X-Spam-Prev-Content-Transfer-Encoding: 8bit SPAM: -------------------- Start SpamAssassin results ---------------------- SPAM: This mail is probably spam. The original message has been altered SPAM: so you can recognise or block similar unwanted mail in future. SPAM: See http://spamassassin.org/tag/ for more details. SPAM: SPAM: Content analysis details: (7.60 hits, 5 required) SPAM: X_MAILING_LIST (-0.3 points) Found a X-Mailing-List header SPAM: SPAM_PHRASE_00_01 (0.8 points) BODY: Spam phrases score is 00 to 01 (low) SPAM: [score: 0] SPAM: SPAM_REDIRECTOR (0.4 points) URI: Uses open redirection service SPAM: FORGED_YAHOO_RCVD (1.4 points) 'From' yahoo.com does not match 'Received' headers SPAM: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com SPAM: [RBL check: found 149.236.142.68.orbs.dorkslayers.com., type: 68.178.232.99] SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points) RBL: Received via a relay in relays.osirusoft.com SPAM: [RBL check: found 149.236.142.68.relays.osirusoft.com.] SPAM: X_OSIRU_OPEN_RELAY (2.7 points) RBL: DNSBL: sender is Confirmed Open Relay SPAM: SPAM: -------------------- End of SpamAssassin results --------------------- --0-1645741501-1206391462=:82325 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 8bit Como resolvo a seguinte questão: Sejam f,g : X->R^+, funções limitadas superiormente. Prove que sup(f.g)<= (menor ou igual)sup(f).sup(g) e que sup(f^2)=(sup(f))^2 --------------------------------- Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-1645741501-1206391462=:82325 Content-Type: text/html; charset=iso-8859-1 Content-Transfer-Encoding: 8bit
Como resolvo a seguinte questão: Sejam f,g : X->R^+, funções limitadas superiormente. Prove que sup(f.g)<= (menor ou igual)sup(f).sup(g) e que sup(f^2)=(sup(f))^2

Abra sua conta no Yahoo! Mail, o único sem limite de espaço para armazenamento! --0-1645741501-1206391462=:82325-- ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Mon Mar 24 19:05:36 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2OM45WA031936 for ; Mon, 24 Mar 2008 19:04:05 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2OM45KM031934 for obm-l-MllGbsmmN; Mon, 24 Mar 2008 19:04:05 -0300 Received: from ug-out-1314.google.com (ug-out-1314.google.com [66.249.92.172]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2OM42WA031924 for ; Mon, 24 Mar 2008 19:04:03 -0300 Received: by ug-out-1314.google.com with SMTP id q7so2265880uge.0 for ; Mon, 24 Mar 2008 15:03:43 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=beta; h=domainkey-signature:received:received:message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; bh=awUhsHejdq1WmGO+5Hzj2zkJegFByHA0luxLTwwYerc=; b=PYqlGeY1BkN/RlImlImJkxOlQLrhx/GH801Dlj02uOZrnogubaR7unJhgkUtxalXAPrm/s8/bGxdNkbr0gi8fNJEq9ysCUA0ryZd1fyvTEwzegAwBkYJ4mG74HDqPzHaKcr2N3miEJ6/PU7K9FvDtqx1BEK3z/6HrF6XaZyzzkg= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=beta; h=message-id:date:from:to:subject:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; b=Zto/gLKNJqLncK/I926/RBq0SO8lSW00wkH2eosTlYyVLlNhqWnGuXjxXiKW7Go7PHDwlGi6xVgvBtMVJu95hhK1GEAUa2lOZeZhL5puHRXojIdCpohCe//YKAmuRrEbiZdgJHfh0hvziaOZlJA6kryXVPIyqxbMXZTO1kcfIvU= Received: by 10.67.121.2 with SMTP id y2mr5049719ugm.78.1206396222740; Mon, 24 Mar 2008 15:03:42 -0700 (PDT) Received: by 10.66.219.5 with HTTP; Mon, 24 Mar 2008 15:03:42 -0700 (PDT) Message-ID: <2d483c770803241503x6d7de335l6bab8e9753d852c5@mail.gmail.com> Date: Mon, 24 Mar 2008 19:03:42 -0300 From: "Ralph Teixeira" To: obm-l@mat.puc-rio.br Subject: Re: [obm-l] Informativo sobre evento. In-Reply-To: <47E80B11.8010705@impa.br> MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline References: <47E80B11.8010705@impa.br> Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by saci.mat.puc-rio.br id m2OM44WA031931 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: "Ralph Teixeira" X-Spam-Status: No, hits=4.0 required=5.0 tests=AWL,IN_REP_TO,QUOTED_EMAIL_TEXT,RCVD_IN_ORBS, RCVD_IN_OSIRUSOFT_COM,REFERENCES,SPAM_PHRASE_00_01, X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** Ah, muito obrigado pela divulgacao. Melhor ainda, o endereco http://www.uff.br/semanadamatematica/ poe um menuzinho simpatico do lado esquerdo para facilitar a navegacao. Destaque para o cartaz, que NAO EH UM FILME. Abraco, Ralph (um dos membros da comissao organizadora) 2008/3/24 Olimpiada Brasileira de Matematica : > Caros(as) amigos(as) da OBM, > > A seguir enviamos, informações sobre a IV Semana da Matemática da UFF. > outras informações e o programa de atividades no site: > http://www.uff.br/semanadamatematica/home.html > > Cordialmente, > > Secretaria da OBM. > ============================================================== > IV Semana de Matemática da UFF > 13 a 17 de maio de 2008 > Niterói - Rio de Janeiro > > *APRESENTAÇÃO > * > A IV Semana de Matemática da UFF será realizada no Campus do Valonguinho > da Universidade Federal Fluminense, no período de 13 a 17 de maio de > 2008. O objetivo principal é o de se criar um ambiente onde > pesquisadores, educadores e a comunidade em geral possam interagir, > divulgando experiências, inovações e diagnosticando novas áreas de > atuação em Matemática nas suas várias manifestações. > Público-alvo: alunos e professores do curso de matemática da UFF, alunos > e professores das escolas de ensino fundamental e médio da região. > Atividades previstas: palestras , minicursos e oficinas > , mesa redonda , grupos de pesquisa, > comunicações e o museu interativo para o ensino da matemática . > Atividades culturais: sessões de cinema. > > Secretária Regina Simplício de Souza > Telefone: (021) 2629-2005 > FAX: (021) 2629-2114 > E-mail: semanadamatematica@vm.uff.br > Horário de atendimento: das 14 h às 18 h. > > Endereço: > Universidade Federal Fluminense > Instituto de Matemática > Rua Mário Santos Braga, S/N, Campus do Valonguinho > CEP 24020-140, Niterói, RJ, Brasil > > *COMISSÃO ORGANIZADORA > *Dirce Uesu Pesco (Coordenadora), > Ana Maria Lima de Farias (Vice-Coordenadora), > Anne Michelle Dysman Gomes, Gabriel Calsamiglia Mendlewicz, Humberto > José Bortolossi, > José Roberto Linhares de Mattos, Mario Olivero Marques da Silva, Ralph > Costa Teixeira, > Solimá Gomes Pimentel, Wanderley Moura Rezende. > > > > > > > > > ------------------------------------------------------------------------ > > ========================================================================= > Instruções para entrar na lista, sair da lista e usar a lista em > http://www.mat.puc-rio.br/~obmlistas/obm-l.html > ========================================================================= > ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Tue Mar 25 10:02:20 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2PD19WA028063 for ; Tue, 25 Mar 2008 10:01:09 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2PD19KR028061 for obm-l-MllGbsmmN; Tue, 25 Mar 2008 10:01:09 -0300 Received: from mobius.impa.br (mobius.impa.br [147.65.1.81]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2PD18WA028045; Tue, 25 Mar 2008 10:01:08 -0300 Received: from [147.65.2.170] (obm-01.impa.br [147.65.2.170]) (authenticated bits=0) by mobius.impa.br (8.13.8/8.13.8) with ESMTP id m2PD0o8S005547 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=NO); Tue, 25 Mar 2008 10:00:50 -0300 Message-ID: <47E8F7BC.1030802@impa.br> Date: Tue, 25 Mar 2008 10:01:48 -0300 From: Olimpiada Brasileira de Matematica User-Agent: Thunderbird 1.5.0.14 (Windows/20071210) MIME-Version: 1.0 To: aobm-l@mat.puc-rio.br, Lista de discussao Subject: [obm-l] Novo regulamento da OBM Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 8bit X-Greylist: Sender succeeded SMTP AUTH authentication, not delayed by milter-greylist-3.0 (mobius.impa.br [147.65.1.27]); Tue, 25 Mar 2008 10:00:50 -0300 (BRT) Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Olimpiada Brasileira de Matematica X-Spam-Status: No, hits=4.9 required=5.0 tests=AWL,RCVD_IN_ORBS,RCVD_IN_OSIRUSOFT_COM,SPAM_PHRASE_00_01, USER_AGENT,X_MAILING_LIST,X_OSIRU_OPEN_RELAY version=2.44 X-Spam-Level: **** Caros(as) amigos(as) da AOBM O regulamento da OBM foi modificado em 2008. Por favor, confira as atualizações no endereço: http://www.obm.org.br/frameset-regulament.htm Cordialmente, Secretaria da OBM ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~obmlistas/obm-l.html ========================================================================= From owner-obm-l@saci.mat.puc-rio.br Tue Mar 25 10:39:36 2008 Return-Path: Received: from saci.mat.puc-rio.br (localhost [127.0.0.1]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2PDcVWA030394 for ; Tue, 25 Mar 2008 10:38:31 -0300 Received: (from majordom@localhost) by saci.mat.puc-rio.br (8.12.8/8.12.8/Submit) id m2PDcVbf030392 for obm-l-MllGbsmmN; Tue, 25 Mar 2008 10:38:31 -0300 Received: from correio.mme.gov.br (correio.mme.gov.br [200.198.213.101]) by saci.mat.puc-rio.br (8.12.8/8.12.8) with ESMTP id m2PDcPWA030365 for ; Tue, 25 Mar 2008 10:38:28 -0300 Received: from VENUS.mme.gov.br ([172.16.1.53]) by srv017.mme.gov.br ([172.16.1.46]) with mapi; Tue, 25 Mar 2008 10:38:09 -0300 From: Artur Costa Steiner To: "obm-l@mat.puc-rio.br" Date: Tue, 25 Mar 2008 10:38:06 -0300 Subject: =?iso-8859-1?Q?RES:_[obm-l]_m=F3dulo?= Thread-Topic: =?iso-8859-1?Q?[obm-l]_m=F3dulo?= Thread-Index: AciOeX4IG89zbrUASMGsKzHdwwf39gAA1gXw Message-ID: In-Reply-To: <638971.61255.qm@web45906.mail.sp1.yahoo.com> Accept-Language: pt-BR, en-US Content-Language: pt-BR X-MS-Has-Attach: X-MS-TNEF-Correlator: acceptlanguage: pt-BR, en-US x-tm-as-product-ver: SMEX-8.0.0.1226-5.000.1023-15808.003 x-tm-as-result: No--30.010000-4.000000-31 x-tm-as-user-approved-sender: No x-tm-as-user-blocked-sender: No Content-Type: multipart/alternative; boundary="_000_E4C89EA639092445A78832509143CCB83908610AEEVENUSmmegovbr_" MIME-Version: 1.0 Sender: owner-obm-l@mat.puc-rio.br Precedence: bulk Reply-To: obm-l@mat.puc-rio.br X-mailing-list: obm-l@mat.puc-rio.br X-mailing-list-sender: Artur Costa Steiner X-Spam-Status: No, hits=1.7 required=5.0 tests=AWL,HTML_FONT_COLOR_BLUE,IN_REP_TO,SPAM_PHRASE_00_01, SPAM_REDIRECTOR,TO_ADDRESS_EQ_REAL,X_MAILING_LIST version=2.44 X-Spam-Level: * --_000_E4C89EA639092445A78832509143CCB83908610AEEVENUSmmegovbr_ Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Admitamos que | a- b | > 0. Ent=E3o |a-b|/2 >0 e temos que |a-b| > |a-b|/2 = > 0, o que (com r =3D |a- b|/2) contraria a hip=F3tese de que |a-b < r par= a todo r >0 . Segue-se que |a- b| =3D 0, o que equivale a dizer que a =3D b= .. Artur -----Mensagem original----- De: owner-obm-l@mat.puc-rio.br [mailto:owner-obm-l@mat.puc-rio.br]Em nome d= e Joel Castro Enviada em: ter=E7a-feira, 25 de mar=E7o de 2008 09:41 Para: obm-l@mat.puc-rio.br Assunto: [obm-l] m=F3dulo tenho pequena d=FAvida: prove: se para todo r maior que zero, o m=F3dulo da diferen=E7a de a e b = =E9 menor que r, ent=E3o a =E9 igual a b. valeu!!!!!! _____ Abra sua conta no Yahoo! Mail, o =FAnico sem limite de espa=E7o para armazenamen= to! --_000_E4C89EA639092445A78832509143CCB83908610AEEVENUSmmegovbr_ Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable
Admitamos que | a- b | > 0. Ent=E3o |a-b|/2 >0 e temos= que |a-b| > |a-b|/2 > 0, o que (com r =3D |a- b|/2)  contraria = a hip=F3tese de que |a-b < r para todo r >0 . Segue-se que |a- b| =3D 0, o que equivale a dizer que a =3D b..
 
Artur
  S=E3o 13 por membro (total de 4.13=3D52 dedos).

saulo n= ilson <saulo.nilson@gmail.com<= /a>> escreveu:
ou s= ao 13 em cada perna?

2008/3/8 saulo nil= son <saulo.nilson@gmail.com>:
vc passou para = base 13, mas como pode ter 4 pernas e 13 dedos? nao tem que ser simetrico?<= br>
2008/3/8 Claudio Gustavo <claudioggll@yahoo.com.br>:
<= div>

jvbrasil@gmail.com> escreveu:
Quando completamos 10= unidades transformamos em uma dezena. Como no sistema de base 10, usamos a= t=E9 o algarismo 9; o sistema marciano tolera o algarismo 5 como unidade&nb= sp;e n=E3o tolera o 8. Logo os marcianos devem ter 6 ou 7 dedos nas m=E3os.=  

On 3/5/08, Klaus Ferraz <klaus= ferraz@yahoo.com.br> wrote:
A primeira expedicao a Marte encontrou somente= as ruinas de uma civilizacao. Os exploradores concluiram dos artefatos e d= esenhos que as criaturas que produziram esta civilizacao tinham quatro= pernas, cada uma terminada em um conjunto de garras parecidas com dedos. A= p=F3s muito estudo foram capazes de traduzir a matematica marciana. Eles en= contraram a seguinte equacao:
5x^2-50x+125=3D0
Esta era uma matematica estranha. O val= or x=3D5 parecia correto, mas x=3D8 n=E3o. Entao os exploradores lembraram = a maneira como o nosso sistema de numeracao foi desenvolvido e encontraram = evidencias de que o sistema marciano teve uma historia analoga. Quantos dedos tinham os marcia= nos?

Abra sua conta no Yahoo!= Mail, o =FAnico sem limite de espa=E7o para armazenamento!


Abra sua = conta no Yahoo! Mail, o =FAnico sem limite de espa=E7o para armaz= enamento!
=