Precalculus: Mathematics for Calculus - 6th Edition
6th Edition
ISBN: 9780840068071
Author: Stewart, James, Redlin, Lothar, Watson, Saleem
Publisher: Cengage Learning
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Textbook Question
Chapter 5.4, Problem 58E
Length of a Shadow On a day when the sun passes directly overhead at noon, a 6-ft-tall man casts a shadow of length
where S is measured in feet and t is the number of hours since 6 a.m.
- (a) Find the length of the shadow al 8:00 a.m., noon, 2:00 p.m., and 5:45 p.m.
- (b) Sketch a graph of the function S for 0 < t < 12.
- (c) From the graph, determine the values of t at which the length of the shadow equals the man’s height. To what lime of day does each of these values correspond?
- (d) Explain what happens to the shadow as the time approaches 6 p.m. (that is, as t → 12−).
(a)
Expert Solution
To determine
To compute: The length of the shadow at
Answer to Problem 58E
The length of the shadow at
The length of the shadow at
The length of the shadow at
The length of the shadow at
Explanation of Solution
Given:
Shadow of length
Calculation:
Compute the length of the shadow at
Here, number of hours from
Therefore, the value of
Compute the value of
Therefore, the length of the shadow at
Compute the length of the shadow at
Here, number of hours from
Therefore, the value of
Compute the value of
Therefore, the length of the shadow at
Compute the length of the shadow at
Here, number of hours from
Therefore, the value of
Compute the value of
Therefore, the length of the shadow at
Compute the length of the shadow at
Here, number of hours from
Therefore, the value of
Compute the value of
Therefore, the length of the shadow at 11.45 P.M is
(b)
Expert Solution
To determine
To sketch: The graph of the function
Explanation of Solution
Use online graphing calculator and obtain the graph of
From the Figure 1, observed that the time function
(c)
Expert Solution
To determine
The values of
Answer to Problem 58E
The length of the shadow equals man’s height for
The length of the shadow equals man’s height at 9 A.M and 3 P.M.
Explanation of Solution
Given:
The man’s height is 6 feet.
Observation:
From the above Figure 1, observed that the function
That is, the length of the shadow equal to 6 feet for
That is, the length of the shadow equal to 6 feet at 9 A.M and 3 P.M.
Calculation:
Compute the length of the shadow at
Here, number of hours from
Therefore, the value of
Compute the value of
Therefore, the length of the shadow at 9 P.M is
Compute the length of the shadow at
Here, number of hours from
Therefore, the value of
Compute the value of
Therefore, the length of the shadow at 3 P.M is
(d)
Expert Solution
To determine
To analyze: The shadow as the time approaches to 6 P.M.
Explanation of Solution
From the above Figure 1, observed that the function
That is, As the time reaches to 6 P.M the length of the shadow become infinity.
Observation:
Compute the length of the shadow as the time approaches to 6 P.M.
That is, compute the value of
Therefore, as the time reaches to 6 P.M the length of the shadow become infinity.
Chapter 5 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
Ch. 5.1 - Prob. 1ECh. 5.1 - Prob. 2ECh. 5.1 - Prob. 3ECh. 5.1 - Prob. 4ECh. 5.1 - Prob. 5ECh. 5.1 - Prob. 6ECh. 5.1 - Prob. 7ECh. 5.1 - Prob. 8ECh. 5.1 - Prob. 9ECh. 5.1 - Prob. 10E
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