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24 November, 19:14

A rectangular area adjacent to a river is fenced in; no fence is needed on the river side. The enclosed area is 1000 square feet. Fencing for the side parallel to the river is $ 8 per foot, and fencing for the other two sides is $ 4 per foot. The four corner posts are $ 20 each. Let x be the length of one of the sides perpendicular to the river.

(a) Write a function C (x) that describes the cost of the project.

(b) What is the domain of C?

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  1. 24 November, 19:42
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    C (x) = 8*x + 8 * (1000) / x + 80

    C (x) Domain x > 0

    Step-by-step explanation:

    enclosed area 1000 ft²

    let x be side perpendicular to the river

    and y parallel to the river

    Then:

    A = x*y y = A / x y = 1000/x

    Cost of one side (x) 4*x $ then two sides cost = 4*2*x cost = 8*x

    Cost of one side (y) 8*y $ 8 * (1000/x)

    Cost of four cornes posts 4*20 = 80 $

    Total cost C (x)

    C (x) = 8*x + 8 * (1000) / x + 80

    R { x > 0}

    Taking derivatives both sides of the equation

    C' (x) = 8 - 8000/x² C' (x) = 0 8 - 8000/x² = 0

    8x² - 8000 = 0 x² = 1000

    x = 100
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