A water trough is 10m long and a cross-section has the shape of an isosceles triangle that is 1m across at the top and 0.5m high. The trough is being filled with water at a rate of 0.4m^3/min. How fast will the water level rise when the water is 0.4 cm deep?
I'm stuck on this one. Not sure how to approach it.
you have to set up a funtion that models the volume of the trough..
V = 1/2(b*h)L
the hardest part of these problems is relating the variables to one another. you have to solve for b in terms of h to differentiate, then you can find a derivative that will model the rate at which the volume changes then solve for the rate at which the hieght changes(dh/dt). The easiest way to solve for b in terms of h is to set up a proportion within the triangle. I uploaded a pic at the bottom i hope it helps.
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