Can someone please help me with this??

9514 1404 393

Answer

  a) correct

  b) (30, 100) would mean an area of 100 square feet is enclosed when the width is 30 feet. (Kristina's vertex coordinates are incorrect.)

Step-by-step explanation:

a) The derivation and expression for A(w) are correct

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b) Kristina made a mistake in using her graphing calculator to find the vertex. The actual vertex is (27.5, 756.25). The coordinates of the vertex are (w, A(w)). The vertex (w, A(w)) means that the area of the enclosed space is A(w) when the width of the enclosure is w.

If Kristina's vertex coordinates were correct (which they are not), they would tell you the enclosed area is 100 square feet when the width of the enclosure is 30 feet.

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

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