Explanation Given: Width of aluminum sheet = 20 inches. Calculation: The cross-sectional area of the gutter is rectangular. If the depth of the gutter is x then, the other dimension is 20 − 2 x . Thus, the cross-sectional area = x ( 20 − 2 x ) Consider A ( x ) = x ( 20 − 2 x ) = 20 x − 2 x 2 A ( x ) = − 2 x 2 + 20 x Since Area function A ( x ) is in the form f ( x ) = a x 2 + b x + c which is a parabola

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Chapter 8.3, Problem 67E

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To calculate: 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-sectional area?

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Chapter 8.3, Problem 66E

Chapter 8.3, Problem 68E

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Chapter 8 Solutions

EBK INTERMEDIATE ALGEBRA FOR COLLEGE ST

Ch. 8.1 - Check Point 1 Solve: . Ch. 8.1 - Prob. 2CP Ch. 8.1 - Prob. 3CP Ch. 8.1 - Prob. 4CP Ch. 8.1 - Prob. 5CP Ch. 8.1 - Prob. 6CP Ch. 8.1 - Prob. 7CP Ch. 8.1 - Prob. 8CP Ch. 8.1 - Prob. 9CP Ch. 8.1 - Prob. 10CP

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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-sectional area?

Solution Summary: The author explains how to calculate the maximum cross-sectional area of a gutter. If the depth of the gutter is x, the other dimension is 20-2x.

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To calculate: 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-sectional area?

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