5. A rancher plans to fence a rectangular pasture adjacent to a river. The rancher has 100 meters of fencing, and no fencing is needed along the river (see figure). (a) Write the area A of the pasture as a function of x, the length of the side parallel to the river. What is the domain of A? (b) Graph the area function A(x) and estimate the dimensions that yield the maximum amount of area for the pasture. (c) Find the dimensions that yield the maximum amount of area for the pasture by completing the square. X Figure for 5 Figure for 6

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter4: Polynomial And Rational Functions
Section4.1: Quadratic Functions
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I have issue with question c.

5. A rancher plans to fence a rectangular pasture adjacent to a river.
The rancher has 100 meters of fencing, and no fencing is needed
along the river (see figure).
(a) Write the area A of the pasture as a function of x, the length
of the side parallel to the river. What is the domain of A?
(b) Graph the area function A(x) and estimate the dimensions
that yield the maximum amount of area for the pasture.
(c) Find the dimensions that yield the maximum amount of area
for the pasture by completing the square.
y
y
Figure for 5
Figure for 6
Transcribed Image Text:5. A rancher plans to fence a rectangular pasture adjacent to a river. The rancher has 100 meters of fencing, and no fencing is needed along the river (see figure). (a) Write the area A of the pasture as a function of x, the length of the side parallel to the river. What is the domain of A? (b) Graph the area function A(x) and estimate the dimensions that yield the maximum amount of area for the pasture. (c) Find the dimensions that yield the maximum amount of area for the pasture by completing the square. y y Figure for 5 Figure for 6
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