Use this information to answer questions 9-10: Arancher wishes to enclose a rect

Question

Use this information to answer questions 9-10: Arancher wishes to enclose a rectangular corral. To save fencing costs, a river is used along one side of the corral and the other three sides are formed by 3000 feet of fence. Assume that x represents the width (in feet) of the two parallel fenced sides, y will be the length of the third fenced side adjacent to the parallel sides, and A will be the area of the corral. 91 Express the area.A as a function of x. (That is, A(x) = ???m 10] Find the dimensions of the corral which would produce an enclosure with the largest area. 11] Name all of the transformations performed onf(x) to obtain h (x) =-30x-8) +5 12] Sketch an accurate graph offx)- and g(x) (2x 6 4 on the same set of axis using transformations. On the sketch, clearly show to where the points (0, 0) and (2, 8) on the graph off () have been tranformed on the graph of g(r) You might find it interestingly important to notice that (2x+6) +4 can be written at(23)+4 -3x + 10 x 4 13] Sketch the graph of f(x)- x if 4

Explanation / Answer

9) width = x

length = y

fencing is to be done on 3 sides

so we can write

3000 = 2x + y

y = 3000 - 2x

area as a function of x can be written as

A(x) = xy

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

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

10) dimensions that will produce maximum area

x = -3000/2(-2)

x = 750 feet

y = 1500 feet

dimensions that will produce maximum area is

length = 1500 feet , width = 750 feet

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