Question 1189873
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Richard has available 400 yards of fencing and wishes to enclose a rectangular area.
a.) Express the area A of the rectangle as a function of the width x of the rectangle?
b.) What is the domain of A?
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(a)  the Length + the Width = 400/2 = 200,

     so if the length is x yards, then the width is (200-x) yards.


     Then the area is A = xy square yards, which is A(x) = x*(200-x) = -x^2 + 200x.



(b)  The function is A(x) = x*(200-x) = -x^2 + 200x,

     and it makes sense where A(x) is non-negative and x is non-negative, 

     so the domain of the function A(x), defined in this way for the area, is  0 <= x <= 200.
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Solved.