You want to form a rectangular pen of area a = 120 square feet. (See the figure below.) One side of the pen is to be formed by an existing building and the other three sides by a fence. If w is the length, in feet, of the sides of the rectangle perpendicular to the building, then the length of the side parallel to the building is 120/w, so the total amount F= F(w), in feet, of fence required is the rational function 120 F = 2w - (a) Make a graph of Fversus w. 100 14 (b) Explain in practical terms the behavior of the graph near the pole at w = 0. The amount of fence required gets larger and larger v as the width gets smaller and smaller. (c) Determine the dimensions of the rectangle that requires a minimum amount of fence. (Round your answers to two decimal places.) width 30 length x ft x ft 1800

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ISBN:9781337282291
Author:Ron Larson
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Chapter3: Polynomial Functions
Section3.5: Mathematical Modeling And Variation
Problem 6ECP: The resistance of a copper wire carrying an electrical current is directly proportional to its...
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You want to form a rectangular pen of area a = 120 square feet. (See the figure below.) One side of the pen is to be formed by an existing building and the other three sides by a fence. If w is the
length, in feet, of the sides of the rectangle perpendicular to the building, then the length of the side parallel to the building is 120/w, so the total amount F = F(w), in feet, of fence required is the
rational function
120
F = 2w +
(a) Make a graph of Fversus w.
100
100
60
40
20
20
10
12
14
10
12
14
100
100
20
20
10
12
14
10
12
14
(b) Explain in practical terms the behavior of the graph near the pole at w = 0.
The amount of fence required gets larger and larger
as the width gets smaller and smaller.
(c) Determine the dimensions of the rectangle that requires a minimum amount of fence. (Round your answers to two decimal places.)
width
30
length
|x ft
x ft
1800
Transcribed Image Text:You want to form a rectangular pen of area a = 120 square feet. (See the figure below.) One side of the pen is to be formed by an existing building and the other three sides by a fence. If w is the length, in feet, of the sides of the rectangle perpendicular to the building, then the length of the side parallel to the building is 120/w, so the total amount F = F(w), in feet, of fence required is the rational function 120 F = 2w + (a) Make a graph of Fversus w. 100 100 60 40 20 20 10 12 14 10 12 14 100 100 20 20 10 12 14 10 12 14 (b) Explain in practical terms the behavior of the graph near the pole at w = 0. The amount of fence required gets larger and larger as the width gets smaller and smaller. (c) Determine the dimensions of the rectangle that requires a minimum amount of fence. (Round your answers to two decimal places.) width 30 length |x ft x ft 1800
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