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blackstreet23
 one year ago
Let Vx and Vy represent the volumes of the solids that result
when the region enclosed by y=3x, y=0, x=1, x=b (b>1) is revolved about the x and y axis, respectively. Is there a value of b such that Vx=Vy?
blackstreet23
 one year ago
Let Vx and Vy represent the volumes of the solids that result when the region enclosed by y=3x, y=0, x=1, x=b (b>1) is revolved about the x and y axis, respectively. Is there a value of b such that Vx=Vy?

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Region of interest:dw:1433735228846:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0The solid we get upon revolving about the \(y\) axis: dw:1433735322750:dw and the solid we get upon revolving about the \(x\) axis: dw:1433735432439:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0The volumes of each are given by the integrals \[V_y=2\pi\int_1^bx\times3x\,dx=6\pi\int_1^bx^2\,dx\]and\[V_x=\pi\int_1^b(3x)^2\,dx=9\pi\int_1^b x^2\,dx\]Assuming \(b\) is fixed, what do you think? Hint: Try writing \(V_x\) in terms of \(V_y\), or the other way around.

blackstreet23
 one year ago
Best ResponseYou've already chosen the best response.0Thanks a lot pal for your help!!!
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