EBK PRECALCULUS W/LIMITS
EBK PRECALCULUS W/LIMITS
4th Edition
ISBN: 9781337516853
Author: Larson
Publisher: CENGAGE CO
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Concept explainers

Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
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Question
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Chapter 2, Problem 9RE

(a)

To determine

To write: the width y as a function of the length x , to write the area A as a function of x .

(a)

Expert Solution
Check Mark

Answer to Problem 9RE

The product of length and width

  A=500x−x2 .

Explanation of Solution

Given information:

The perimeter of a rectangle is 1000 meters.

Calculation:

Since perimeter is the length of the outer boundary,

  x+x+y+y=P2x+2y=1000x+y=500y=500−x

So, width in terms of length is y=500−x

Also, area is the product of length and width, So,

  A=x×y=x(500−x)=500x−x2

(b)

To determine

To find: the dimensions of the one with the maximum area.

(b)

Expert Solution
Check Mark

Answer to Problem 9RE

The dimensions of the rectangle with maximum area are

  x=250 meters and y=250 meters

Explanation of Solution

Given information:

Of all possible rectangles with perimeter of 1000 meters.

Calculation:

Since area should be maximum, first write this equation in the standard form.

  A=500x−x2=−(x2−500x+62500)+62500 Completing the square=-(x−250)2+62500

Maximum area occurs at the vertex, when

  x=250y=500−250=250

So, the dimensions of the rectangle with maximum area are

  x=250 meters and y=250 meters

Previous
Chapter 2, Problem 8RE
Next
Chapter 2, Problem 10RE

Chapter 2 Solutions

EBK PRECALCULUS W/LIMITS

Ch. 2.1 - Prob. 1ECh. 2.1 - Prob. 2ECh. 2.1 - Prob. 3ECh. 2.1 - Prob. 4ECh. 2.1 - Prob. 5ECh. 2.1 - Prob. 6ECh. 2.1 - Prob. 7ECh. 2.1 - Prob. 8ECh. 2.1 - Prob. 9ECh. 2.1 - Prob. 10E
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Prob. 3PSCh. 2 - Prob. 4PSCh. 2 - Prob. 5PSCh. 2 - Prob. 6PSCh. 2 - Prob. 7PSCh. 2 - Prob. 8PSCh. 2 - Prob. 9PSCh. 2 - Prob. 10PSCh. 2 - Prob. 11PSCh. 2 - Prob. 12PSCh. 2 - Prob. 13PS
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