Calculating Water Level Rise in Trapezoid Trough

rocomath
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Homework Statement


A water trough is 10m long and a cross-section has a shape of an isosceles trapezoid that is 30cm wide at the bottom, 80cm wide at the top, and has a height of 50cm. If the bottom of the trough is being filled with water at the rate of .2m^3/min, how fast is the water level rising when the water is 30cm deep?


Homework Equations


A (trapezoid) = .5(b1+b2)


The Attempt at a Solution


http://img218.imageshack.us/img218/5321/22806877ce9.jpg
 
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nvm i got it, my geometry isn't that great but i pulled through!
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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