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[SPAM] [obm-l] RES: [obm-l] Probabilidade do triāngulo

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Ol=E1 Cl=E1udio, entendi sua resolu=E7=E3o, por=E9m voc=EA n=E3o =
considerou que para o
ponto C n=E3o cair exatamente no centro do segmento AB ele deve cair na
primeira metade de AB ou na segunda metade de AB e para isso temos 50% =
de
chances.=20

=20

Att., carry_bit

  _____ =20

De: owner-obm-l@mat.puc-rio.br [mailto:owner-obm-l@mat.puc-rio.br] Em =
nome
de Claudio Gustavo
Enviada em: s=E1bado, 19 de maio de 2007 22:50
Para: obm-l@mat.puc-rio.br
Assunto: Re: [obm-l] Probabilidade do tri=E2ngulo

=20

  Sabe-se que o valor do lado do tri=E2ngulo n=E3o pode alcan=E7ar a =
metade do
per=EDmetro (basta aplicar a desigualdade triangular). Olhando para o =
segmento
AB, de comprimento fixo, o =FAnico local que n=E3o podemos colocar o =
primeiro
ponto C =E9 no centro de AB. Depois de colocado o ponto C, devemos =
colocar o
ponto D em locais de AB que distem menos de AB/2 de C, de A e de B, ou =
seja,
o ponto D deve estar sobre a parte maior que foi formada ap=F3s =
colocarmos C.
Portanto a probabilidade =E9 de 50%.

=20

  Abra=E7o,

Claudio Gustavo.


carry_bit <carry_bit@yahoo.com.br> escreveu:

Ol=E1 integrantes da obm-l,

=20

Eu me deparei com o seguinte problema e n=E3o consegui resolver!=20

=20

*  Dado um segmento de reta AB qualquer, dois pontos (C e D) s=E3o =
marcados ao
acaso nesse segmento. Qual =E9 a probabilidade de os tr=EAs segmentos =
assim
formados poderem constituir um tri=E2ngulo?

=20

=20

Agrade=E7o, Carry_bit

=20

 __________________________________________________
Fale com seus amigos de gra=E7a com o novo Yahoo! Messenger=20
http://br.messenger.yahoo.com/=20


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<p class=3DMsoNormal><font size=3D2 color=3Dgreen face=3DArial><span =
style=3D'font-size:
10.0pt;font-family:Arial;color:green'>Ol=E1 Cl=E1udio, entendi sua =
resolu=E7=E3o, por=E9m
voc=EA n=E3o considerou que para o ponto C n=E3o cair exatamente no =
centro do
segmento AB ele deve cair na primeira metade de AB ou na segunda metade =
de AB e
para isso temos 50% de chances. <o:p></o:p></span></font></p>

<p class=3DMsoNormal><font size=3D2 color=3Dgreen face=3DArial><span =
style=3D'font-size:
10.0pt;font-family:Arial;color:green'><o:p>&nbsp;</o:p></span></font></p>=


<p class=3DMsoNormal><font size=3D2 color=3Dgreen face=3DArial><span =
style=3D'font-size:
10.0pt;font-family:Arial;color:green'>Att., =
carry_bit<o:p></o:p></span></font></p>

<div>

<div class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><font =
size=3D3
face=3D"Times New Roman"><span style=3D'font-size:12.0pt'>

<hr size=3D2 width=3D"100%" align=3Dcenter tabindex=3D-1>

</span></font></div>

<p class=3DMsoNormal><b><font size=3D2 face=3DTahoma><span =
style=3D'font-size:10.0pt;
font-family:Tahoma;font-weight:bold'>De:</span></font></b><font size=3D2
face=3DTahoma><span style=3D'font-size:10.0pt;font-family:Tahoma'>
owner-obm-l@mat.puc-rio.br [mailto:owner-obm-l@mat.puc-rio.br] <b><span
style=3D'font-weight:bold'>Em nome de </span></b>Claudio Gustavo<br>
<b><span style=3D'font-weight:bold'>Enviada em:</span></b> s=E1bado, 19 =
de maio de
2007 22:50<br>
<b><span style=3D'font-weight:bold'>Para:</span></b> =
obm-l@mat.puc-rio.br<br>
<b><span style=3D'font-weight:bold'>Assunto:</span></b> Re: [obm-l] =
Probabilidade
do tri=E2ngulo</span></font><o:p></o:p></p>

</div>

<p class=3DMsoNormal><font size=3D3 face=3D"Times New Roman"><span =
style=3D'font-size:
12.0pt'><o:p>&nbsp;</o:p></span></font></p>

<div>

<p class=3DMsoNormal><font size=3D3 face=3D"Times New Roman"><span =
style=3D'font-size:
12.0pt'>&nbsp; Sabe-se que o valor do lado do tri=E2ngulo n=E3o pode =
alcan=E7ar a
metade do per=EDmetro (basta aplicar a desigualdade triangular). Olhando =
para o
segmento AB, de comprimento fixo, o =FAnico local que n=E3o podemos =
colocar o
primeiro ponto C =E9 no centro de AB. Depois de colocado o ponto C, =
devemos
colocar o ponto D em locais de AB que distem menos de AB/2 de C, de A e =
de B,
ou seja,&nbsp;o ponto D deve estar sobre a parte maior que foi formada =
ap=F3s
colocarmos C. Portanto a probabilidade =E9 de =
50%.<o:p></o:p></span></font></p>

</div>

<div>

<p class=3DMsoNormal><font size=3D3 face=3D"Times New Roman"><span =
style=3D'font-size:
12.0pt'>&nbsp;<o:p></o:p></span></font></p>

</div>

<div>

<p class=3DMsoNormal><font size=3D3 face=3D"Times New Roman"><span =
style=3D'font-size:
12.0pt'>&nbsp; Abra=E7o,<o:p></o:p></span></font></p>

</div>

<div>

<p class=3DMsoNormal><font size=3D3 face=3D"Times New Roman"><span =
style=3D'font-size:
12.0pt'>Claudio Gustavo.<o:p></o:p></span></font></p>

</div>

<div>

<p class=3DMsoNormal><font size=3D3 face=3D"Times New Roman"><span =
style=3D'font-size:
12.0pt'><br>
<b><i><span style=3D'font-weight:bold;font-style:italic'>carry_bit
&lt;carry_bit@yahoo.com.br&gt;</span></i></b> =
escreveu:<o:p></o:p></span></font></p>

</div>

<blockquote style=3D'border:none;border-left:solid #1010FF =
1.5pt;padding:0cm 0cm 0cm 4.0pt;
margin-left:3.75pt;margin-top:5.0pt;margin-bottom:5.0pt'>

<div>

<p class=3DMsoNormal><font size=3D2 color=3Dgreen face=3DArial><span =
style=3D'font-size:
10.0pt;font-family:Arial;color:green'>Ol=E1 integrantes da =
obm-l,<o:p></o:p></span></font></p>

</div>

<div>

<p class=3DMsoNormal><font size=3D2 color=3Dgreen face=3DArial><span =
style=3D'font-size:
10.0pt;font-family:Arial;color:green'><o:p>&nbsp;</o:p></span></font></p>=


</div>

<div>

<p class=3DMsoNormal><font size=3D2 color=3Dgreen face=3DArial><span =
style=3D'font-size:
10.0pt;font-family:Arial;color:green'>Eu me deparei com o seguinte =
problema e
n=E3o consegui resolver! <o:p></o:p></span></font></p>

</div>

<div>

<p class=3DMsoNormal><font size=3D2 color=3Dgreen face=3DArial><span =
style=3D'font-size:
10.0pt;font-family:Arial;color:green'><o:p>&nbsp;</o:p></span></font></p>=


</div>

<div style=3D'margin-left:71.25pt'>

<p class=3DMsoNormal =
style=3D'margin-left:71.25pt;text-indent:-18.0pt;mso-list:
l0 level1 lfo2'><![if !supportLists]><font size=3D2 color=3Dgreen =
face=3DSymbol><span
style=3D'font-size:10.0pt;font-family:Symbol;color:green'><span =
style=3D'mso-list:
Ignore'>=B7<font size=3D1 face=3D"Times New Roman"><span =
style=3D'font:7.0pt "Times New Roman"'>&nbsp;
</span></font></span></span></font><![endif]><font size=3D2 =
color=3Dgreen
face=3DArial><span =
style=3D'font-size:10.0pt;font-family:Arial;color:green'>Dado um
segmento de reta AB qualquer, dois pontos (C e D) s=E3o marcados ao =
acaso nesse
segmento. Qual =E9 a probabilidade de os tr=EAs segmentos assim formados =
poderem constituir
um tri=E2ngulo?<o:p></o:p></span></font></p>

</div>

<div>

<p class=3DMsoNormal><font size=3D2 color=3Dgreen face=3DArial><span =
style=3D'font-size:
10.0pt;font-family:Arial;color:green'><o:p>&nbsp;</o:p></span></font></p>=


</div>

<div>

<p class=3DMsoNormal><font size=3D2 color=3Dgreen face=3DArial><span =
style=3D'font-size:
10.0pt;font-family:Arial;color:green'><o:p>&nbsp;</o:p></span></font></p>=


</div>

<div>

<p class=3DMsoNormal><font size=3D2 color=3Dgreen face=3DArial><span =
style=3D'font-size:
10.0pt;font-family:Arial;color:green'>Agrade=E7o, =
Carry_bit<o:p></o:p></span></font></p>

</div>

</blockquote>

<p class=3DMsoNormal><font size=3D3 face=3D"Times New Roman"><span =
style=3D'font-size:
12.0pt'><o:p>&nbsp;</o:p></span></font></p>

<p><font size=3D3 face=3D"Times New Roman"><span =
style=3D'font-size:12.0pt'>=A0___________________________________________=
_______<br>
Fale com seus amigos de gra=E7a com o novo Yahoo! Messenger <br>
http://br.messenger.yahoo.com/ <o:p></o:p></span></font></p>

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