Question

T.

Answer 1

Answer:

  a) 5000 m²

  b) A(x) = x(200 -2x)

  c) 0 < x < 100

Step-by-step explanation:

b) The remaining fence, after the two sides of length x are fenced, is 200-2x. That is the length of the side parallel to the building. The product of the lengths parallel and perpendicular to the building is the area of the playground:

  A(x) = x(200 -2x)

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a) A(50) = 50(200 -2·50) = 50·100 = 5000 . . . . m²

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c) The equation makes no sense if either length (x or 200-2x) is negative, so a reasonable domain is (0, 100). For x=0 or x=100, the playground area is zero, so we're not concerned with those cases, either. Those endpoints could be included in the domain if you like.