Concept explainers
(a)
The heating degree hours that were experienced on a particular day from
(a)
Answer to Problem 5P
On a particular day when temperature was modeled by the function
Explanation of Solution
Given:
The formula for heating degree-hours is,
The temperature was modeled by the function is,
Where, t was measured hours since midnight.
Calculation:
The area under the function
Calculate the area under the function
Formula to calculate the value of
Substitute 0 for a and 24 for b in equation (2) to find the value of
Substitute 0 for a and
Find the value of
Substitute
The value of,
Substitute n for
Substitute
Thus, on a particular day when temperature was modeled by the function
(b)
To find: The maximum temperature that was on the day when temperature was modeled by the function
(b)
Answer to Problem 5P
The maximum temperature on that day is
Explanation of Solution
Given:
The function of temperature is,
Calculation:
The maximum temperature occurs when the graph of the function is at its vertex which is,
Substitute
Substitute 15 fro x in function
The maximum temperature on that day is
(c)
The heating degree hours that were experienced on a particular day from
(c)
Answer to Problem 5P
On a particular day when temperature was modeled by the function
Explanation of Solution
Given:
The formula for heating degree-hours is,
The temperature was modeled by the function is,
Where, t was measured hours since midnight.
Calculation:
The area under the function
Calculate the area under the function
Formula to calculate the value of
Substitute 0 for a and 24 for b in equation (5) to find the value of
Substitute 0 for a and
Find the value of
Substitute
The value of,
Substitute n for
Substitute
Thus, on a particular day when temperature was modeled by the function
(d)
To find: The maximum temperature that was on the day when temperature was modeled by the function
(d)
Answer to Problem 5P
The maximum temperature on that day is
Explanation of Solution
Given:
The function of temperature is,
Calculation:
The maximum temperature occurs when the graph of the function is at its vertex which is,
Substitute 5 for b and
Substitute 10 fro x in function
Thus, the maximum temperature on that day is
(e)
The hotter day between the day with temperature
(e)
Answer to Problem 5P
The day with temperature
Explanation of Solution
From part (a), when temperature was modeled by the function
From part (c), when temperature was modeled by the function
So, the heating degree hours of the day of part(a) is more than the heating degree hours of the day of part (b).
Thus, the day with temperature
Chapter 13 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning