Andy C. answered • 06/02/18

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(A)-(C)

X is the width and Y is the length. As these are dimensions , they must be positive and non-zero.

The Perimeter is 2X+Y = 760 ----> Y = 760-2X

The area is XY = X(760-2X) = A(x)

(D)

20000 < XY < 40000

20000 < x(760-2x) < 40000

20000 < 760x - 2x^2 < 40000

-20000 > 2x^2 - 760x > -40000

0 > 2x^2 - 760x + 20000 > -20000

Per quadratic formula and examining the graph at www.desmos.com,

the values are x=28.4451 and x=351.555, which will produce an area in this range

(E) The max occurs at the average of the zeros of this quadratic function

The zeros of A(x) are x=0 and x= 380

The max area is then 190*(760-2*190) = 190* (760-380) = 190*380 = 72200