Question

A rain gutter is made from sheets of aluminum that are 10 inches wide by turning up the edges to form right angles. Determine the depth of the gutter that will maximize its cross- sectional area and allow the greatest amount of water to flow. What is the maximum cross-section al area?

Answer 1

Explanation:

Let the height be "x"

Then base is 12-2x

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Area = x(12-2x) = -2x^2 + 12x

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Maximum of this parabola occurs when x = -b/(2a) = -12/(-4) = 3

That is the depth of gutter.

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That cross-section area is x(12-x) = 3*9 = 27 sq in.