A trough is 14 ft long and its ends have the shape of isosceles triangles that a

Question

A trough is 14 ft long and its ends have the shape of isosceles triangles that are 3 ft across at the top and have a height of 1 ft. If the trough is being filled with water at a rate of 12 ft^3/min, how fast is the water level rising when the water is 4 inches deep? Step 1 Let b be the water s height and b be the distance across the top of the water. Using the diagram below, find the relation between b and h. 3/1 = Step 2 The volume of the water is as follows. V = 1/2bhl Step 3 We must find dh/dt. We have 21 = dV/dt = Step 4 In feet, we know that h = Step 5 Consequently, we can conclude the following. dh/dt =

Explanation / Answer

v = 21h^2

dv/dt = 42h*dh/dt

dh/dt = 42h/12 = 42*0.3332/12 = 1.1662 ft/sec

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