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anonymous
 one year ago
Find the area bounded by the curve x=t1/t, y=t=1/t, y=65/8
anonymous
 one year ago
Find the area bounded by the curve x=t1/t, y=t=1/t, y=65/8

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Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.2Is that \[x= t  \frac{ 1 }{ t }~~~y=t\frac{ 1 }{ t }~~~y=\frac{ 65 }{ 8 }\]

ali2x2
 one year ago
Best ResponseYou've already chosen the best response.0@Astrophysics Yes it looks like it

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1y could be t+1/t since, + and = are on the same key of the keyboard

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.2I think you're right hartnn! So areas in parametric curves we have \[\int\limits_{a}^{b}g(t)f'(t) dt\]

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.2dw:1439044557140:dw now to see where the curve touches the line we set \[t+\frac{ 1 }{ t } = \frac{ 65 }{ 8 }\] solving for t will tell us at which time our curve will touch the line, then you can make a graph to make your curve. So we get our time to be \[t=\frac{ 1 }{ 8 } ~~~and ~~~ t = 8\]

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.2To find our values for x, you can make a graph as I suggested (just too keep your values and see what's going on), or you can just do when t = 1/8 \[x= t\frac{ 1 }{ t } \implies \frac{ 1 }{ 8 }  \frac{ 1 }{ \frac{ 1 }{ 8 } } = ...\] \[x= 8\frac{ 1 }{ 8 } = ...\] You'll then have your x,y,t values and you should be able to graph it, that's the major part, then setting up the integral shouldn't be too bad.

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.2I don't plan on doing this whole thing for you, so if you're there, please ask for help.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1Alternatively, if you don't like parametric curves, you may try eliminating the parameter easily by noticing that \[(a+b)^2(ab)^2 = 4ab\]

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1\[y^2  x^2 = \left(t+\frac{1}{t}\right)^2  \left(t\frac{1}{t}\right)^2=4*t*\frac{1}{t} = 4 \]

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1so the problem is equivalent to finding the area between curves : \(y^2x^2=4\) and \(y=65/8\)

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.2So much easier xD

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1Not really, looks both require almost same effort haha!

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.2Ah, I see, I just think it's easier to see the curve with your method...but yeah I think it's equal effort hehe.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0still not sure how to get the right answer.

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.2Ok well, doing it the method I suggested, what values did you get for x?

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.2\[x= t\frac{ 1 }{ t } \implies \frac{ 1 }{ 8 }  \frac{ 1 }{ \frac{ 1 }{ 8 } } = ...\] and \[x= 8\frac{ 1 }{ 8 } = ...\]

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.2We'll go over this step by step, so just find what x's are and we can continue :)
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