A trough 5 feet long and 1 foot high is filled with water. The vertical cross-sections of the trough parallel to the ends are shaped like the graph of y=x¹ for x = -1 to z = 1. The amount of work required to empty the trough by pumping the water over the top edge is: foot-pounds

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A: Please see the below picture for detailed solution.

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A: We can solve it as below.

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Q: Maximizing Profits A manufacturer of tennis rackets finds that the total cost C(x) (in dollars) of…

A: We first find the profit function.  P(x)=R(x)-C(x)P(x)=px-C(x)P(x)=(10 − 0.0003x)x-700 + 8x +…