A dog owner has 20 meters of chain-link fencing. She wishes to construct a rectangular dog run against the side of her house. Dimension "x" represents the distance between the house wall and the exterior side of the fence. Here is a sketch of the situation: X House Wall L, length X The goal is to construct the dog run to maximize the enclosed area. a. Find a quadratic model for the enclosed area in square meters as a function of dimension x only. Follow these steps: Write an equation for the perimeter of fencing (20) relating x and L: Solve for L in terms of x (isolate L on the left side of the equation): Write the formula for the enclosed rectangular area, A, in terms of x and L: Now write the formula for the area, A, in terms of x only (this will be quadratic!): b. Graph the relation for Area in terms of x by constructing an appropriate table of values. Show your table of values below and then sketch the graph at the top of the next page.
A dog owner has 20 meters of chain-link fencing. She wishes to construct a rectangular dog run against the side of her house. Dimension "x" represents the distance between the house wall and the exterior side of the fence. Here is a sketch of the situation: X House Wall L, length X The goal is to construct the dog run to maximize the enclosed area. a. Find a quadratic model for the enclosed area in square meters as a function of dimension x only. Follow these steps: Write an equation for the perimeter of fencing (20) relating x and L: Solve for L in terms of x (isolate L on the left side of the equation): Write the formula for the enclosed rectangular area, A, in terms of x and L: Now write the formula for the area, A, in terms of x only (this will be quadratic!): b. Graph the relation for Area in terms of x by constructing an appropriate table of values. Show your table of values below and then sketch the graph at the top of the next page.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
Related questions
Question
The equation for question 1 is A = x (20 - 2x)
Transcribed Image Text:A dog owner has 20 meters of chain-link fencing. She wishes to construct a rectangular dog run against
the side of her house. Dimension "x" represents the distance between the house wall and the exterior side
of the fence. Here is a sketch of the situation:
X
House Wall
L, length
X
The goal is to construct the dog run to maximize the enclosed area.
a. Find a quadratic model for the enclosed area in square meters as a function of dimension x only.
Follow these steps:
Write an equation for the perimeter of fencing (20) relating x and L:
Solve for L in terms of x (isolate L on the left side of the equation):
Write the formula for the enclosed rectangular area, A, in terms of x and L:
Now write the formula for the area, A, in terms of x only (this will be quadratic!):
b. Graph the relation for Area in terms of x by constructing an appropriate table of values. Show
your table of values below and then sketch the graph at the top of the next page.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps with 5 images
Follow-up Questions
Read through expert solutions to related follow-up questions below.
Follow-up Question
Transcribed Image Text:Show your graph (labeled and titled) here. Is your scaling indicated? Are units included?
Inspect your graph and then determine the optimum dimensions for x and L to maximize the area from
the graph. Show where the area is maximum on your graph.
X =
L=
c. Identify the part of the graph that is relevant in this problem context (Practical Domain).
d. Express the area relation, in terms of x only, in both the expanded and fully factored forms:
Expanded form A=
Factored form A=
Explain the relationship between the algebraically factored form of the relation and the graph.
(Specifically, note the geometric relationship between the x-intercepts and the vertex.)
Solution
by Bartleby ExpertRecommended textbooks for you
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning