[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]
[SPAM] RE: [obm-l] trigonometria
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: 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: RCVD_IN_ORBS (2.2 points) RBL: Received via a relay in orbs.dorkslayers.com
SPAM: [RBL check: found 123.168.54.65.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 123.168.54.65.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 ---------------------
--_77f585c7-9b8e-4ee2-984a-f47d4575466b_
Content-Type: text/plain; charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable
Ol=E1!
Acredito que existam solu=E7=F5es mais elegantes, por=E9m no mome=
nto s=F3 disponho da que segue.
Para resolver a equa=E7=E3o proposta, recorreremos =E0s identidad=
es a seguir:
cos2x =3D 2cos=B2x -1
cos3x =3D 4cos=B3x - 3cosx
V=E1lidas para qualquer x real.
Temos, ent=E3o, a equa=E7=E3o:
cos=B2x + (2cos=B2x - 1)=B2 + (4cos=B3x - 3cosx)=B2 =3D 1
Fa=E7amos, ent=E3o, y =3D cosx. A nova equa=E7=E3o tem a forma:=20
y=B2 + (2y=B2 - 1)=B2 + y=B2(4y=B2 - 3)=B2 =3D 1
Ap=F3s algumas transforma=E7=F5es alg=E9bricas simples, n=F3s che=
gamos =E0 presente equa=E7=E3o equivalente:
y=B2[8(y=B2)=B2 - 10y=B2 + 3] =3D 0
cujas ra=EDzes s=E3o y =3D 0, y =3D sqrt{1/2}, y =3D -sqrt{1/2}, =
y =3D sqrt{3/4} e y =3D -sqrt{3/4}.
Basta, ent=E3o, voc=EA resolver a cole=E7=E3o de equa=E7=F5es obt=
idas, lembrando-se de que y =3D cosx.
Resposta: S =3D {x real | x=3D pi/6 + kpi ou x =3D -pi/6 + kpi ou=
x =3D pi/3 + kpi ou x =3D -pi/3 + kpi ou x =3D pi/2 + kpi, com k inteiro}
Acho que seja isso.
Abra=E7os!
Date: Mon, 19 Nov 2007 19:07:16 -0300
From: bissa_damazo@xxxxxxxxxxxx
Subject: [obm-l] trigonometria
To: obm-l@xxxxxxxxxxxxxx
Galera estou enroscado nessa questao. 1) (cosx)^2 + (cos2x)^2 + (cos3x)=
^2 =3D 1 agrade=E7o desde j=E1=20
Abra sua conta no Yahoo! Mail, o =FAnico sem limite de espa=E7o para =
armazenamento!=20
_________________________________________________________________
Conhe=E7a o Windows Live Spaces, a rede de relacionamentos conectada ao Mes=
senger!
http://spaces.live.com/signup.aspx=
--_77f585c7-9b8e-4ee2-984a-f47d4575466b_
Content-Type: text/html; charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable
<html>
<head>
<style>
.hmmessage P
{
margin:0px;
padding:0px
}
body.hmmessage
{
FONT-SIZE: 10pt;
FONT-FAMILY:Tahoma
}
</style>
</head>
<body class=3D'hmmessage'>
Ol=E1!<br><br> =
Acredito que existam solu=
=E7=F5es mais elegantes, por=E9m no momento s=F3 disponho da que segue.<br>=
<br> Para resolver a =
equa=E7=E3o proposta, recorreremos =E0s identidades a seguir:<br><br> =
cos2x =3D 2cos=B2x -1<br><=
br> cos3x =3D 4cos=B3=
x - 3cosx<br><br> V=
=E1lidas para qualquer x real.<br><br> &=
nbsp; Temos, ent=E3o, a equa=E7=E3o:<br><br> &=
nbsp; cos=B2x + (2cos=B2x - 1)=B2 + (4cos=B3x=
- 3cosx)=B2 =3D 1<br><br> &=
nbsp; Fa=E7amos, ent=E3o, y =3D cosx. A nova equa=E7=E3o tem a forma: <br><=
br> y=B2 + (2y=B2 - 1=
)=B2 + y=B2(4y=B2 - 3)=B2 =3D 1<br><br> =
Ap=F3s algumas transforma=E7=F5es alg=E9bricas simples, =
n=F3s chegamos =E0 presente equa=E7=E3o equivalente:<br><br> &nb=
sp; y=B2[8(y=B2)=B2 - 10y=B2 + 3] =3D 0=
<br><br> cujas ra=EDz=
es s=E3o y =3D 0, y =3D sqrt{1/2}, y =3D -sqrt{1/2}, y =3D sqrt{3/4} e y =
=3D -sqrt{3/4}.<br><br> &nbs=
p; Basta, ent=E3o, voc=EA resolver a cole=E7=E3o de equa=E7=F5es obtidas, l=
embrando-se de que y =3D cosx.<br><br> &=
nbsp; Resposta: S =3D {x real | x=3D pi/6 + kpi ou x =3D -pi/6 =
+ kpi ou x =3D pi/3 + kpi ou x =3D -pi/3 + kpi ou x =3D pi/2 + kpi, com k i=
nteiro}<br><br> Acho =
que seja isso.<br><br>  =
; Abra=E7os!<br><blockquote><hr>Date: Mon, 19 Nov 2007 19:07:16 -0300<br>Fr=
om: bissa_damazo@xxxxxxxxxxxx<br>Subject: [obm-l] trigonometria<br>To: obm-=
l@xxxxxxxxxxxxxx<br><br><div>Galera estou enroscado nessa questao.</div> <=
div> </div> <div>1) (cosx)^2 + (cos2x)^2 + (cos3x)^2 =3D 1</div> <di=
v> </div> <div>agrade=E7o desde j=E1</div>=20
<BR><hr size=3D"1">Abra sua conta no <a href=3D"http://br.rd.yahoo.co=
m/mail/taglines/mail/*http://br.mail.yahoo.com/"; target=3D"_blank">Yahoo! M=
ail</a>, o =FAnico sem limite de espa=E7o para armazenamento!=20
</blockquote><br /><hr />Conhe=E7a o Windows Live Spaces, o site de relacio=
namentos do Messenger! <a href=3D'http://spaces.live.com/signup.aspx' targe=
t=3D'_new'>Crie j=E1 o seu!</a></body>
</html>=
--_77f585c7-9b8e-4ee2-984a-f47d4575466b_--
=========================================================================
Instruções para entrar na lista, sair da lista e usar a lista em
http://www.mat.puc-rio.br/~obmlistas/obm-l.html
=========================================================================