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21 March, 22:45

A rectangular field, bounded on one side by a building, is to be fenced in on the other three sides. if 3000 feet of fence is to be used, find the dimensions

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  1. 21 March, 22:58
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    The question is missing the detail, it is to find the dimensions of the largest field that can be fenced in.

    The formula for area is : A = xy

    The perimeter of the fencing is equal to the sum of two widths and the length: 2x + y = 3000

    Now, solve the second equation: y = 3000 - 2x

    When you plug this expression to the formula for the area, we will get:

    A = x (3000-2x) = 3000x - 2x^2

    Next take the derivative and equal it to 0: dA/dx = 3000 - 4x = 0

    Now solve for x, it will give us 750.

    Find the second derivative.

    d^2 A / dx^2 = - 4

    since we have a negative result, x = 75 - is a maximum. Then plug this in to x:

    3000 - 2 (750) = 1500. The largest field will measure 750 ft by 1500 ft.
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