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Concept explainers
8. A rectangle is inscribed in a semicircle of radius 2. See the figure. Let be the point in quadrant I that is a vertex of the rectangle and is on the circle.
(a) Express the area A of the rectangle as a function of x.
(b) Express the perimeter p of the rectangle as a function of x.
(c) Graph . For what value of x is A largest?
(d) Graph . For what value of x is p largest?
![Check Mark](/static/check-mark.png)
To find:
a. To express the area of the rectangle as a function of .
Answer to Problem 8AYU
Solution:
a.
Explanation of Solution
Given:
Calculation:
a. To express the area of the rectangle as a function of :
Area of the given rectangle .
Since the rectangle is inscribed in the semi circle of radius 2. (i.e) . Also, be the point in quadrant I that is the vertex of the rectangle and it is on the circle.
Substitute for . Then
![Check Mark](/static/check-mark.png)
To find:
b. To express the perimeter of the rectangle as a function of .
Answer to Problem 8AYU
Solution:
b.
Explanation of Solution
Given:
Calculation:
b. To express the perimeter of the rectangle as a function of :
Perimeter of the given rectangle .
Since the rectangle is inscribed in the semi circle of radius 2. (i.e) . Also, be the point in quadrant I that is the vertex of the rectangle and it is on the circle.
Substitute for . Then
![Check Mark](/static/check-mark.png)
To find:
c. To graph and to find the value of is largest.
Answer to Problem 8AYU
Solution:
c. is largest when .
Explanation of Solution
Given:
Calculation:
c. To graph and to find the value of is largest:
From the graph it can be seen that is largest when .
![Check Mark](/static/check-mark.png)
To find:
d. To graph ) and to find the value of is largest.
Answer to Problem 8AYU
Solution:
d. is largest when
Explanation of Solution
Given:
Calculation:
d. To graph and to find the value of is largest:
From the graph it can be seen that is largest when .
Chapter 2 Solutions
Precalculus Enhanced with Graphing Utilities
Additional Math Textbook Solutions
Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book
Glencoe Math Accelerated, Student Edition
Calculus, Single Variable: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (2nd Edition)
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
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