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A trough is 12 feet long and 3 feet across the top (see figure). Its ends are isosceles triangles with altitudes of 3 feet.
(a) If water is being pumped into the trough at 2 cubic feet per minute, how fast is the water level rising when h is 1.3 foot deep?
(b) If the water is rising at a rate of inch per minute when h = 2.1, determine the rate at which water is being pumped into the trough.