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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
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...
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The equation for question 1 is A = x (20 - 2x)

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.
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.
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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.)
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.)
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