15. A farmer wishes to enclose a rectangular region. He has 500 feet of fencing and plans to use his barn as one side of the enclosure. Let x represent the length of one of parallel sides of the fencing. a) Express the length of the remaining side in terms of x. b) Determine a function A that represents the area of the region in terms of x. 500x c) What is the value of x that will give a maximum area and what will this area be?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 67E
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71 Inenes tall.
2414 BMI
A farmer wishes to enclose a rectangular region. He has 500 feet
of fencing and plans to use his barn as one side of the enclosure. Let x
represent the length of one of parallel sides of the fencing.
15.
Barn wall
a) Express the length of the remaining side in terms of x.
b) Determine a function A that represents the area of the region in terms of x.
500
c) What is the value of x that will give a maximum area and what will this area be?
Transcribed Image Text:71 Inenes tall. 2414 BMI A farmer wishes to enclose a rectangular region. He has 500 feet of fencing and plans to use his barn as one side of the enclosure. Let x represent the length of one of parallel sides of the fencing. 15. Barn wall a) Express the length of the remaining side in terms of x. b) Determine a function A that represents the area of the region in terms of x. 500 c) What is the value of x that will give a maximum area and what will this area be?
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