Concept explainers
(a)
To find: At which rate the water is draining from the tank after 5 min.
(a)
Answer to Problem 18E
The rate at which the water is draining from the tank after 5 min is,
Explanation of Solution
The volume of the remaining water after t minutes is,
The rate of change of the volume with respect to time is,
Substitute t = 5 in
Thus, the rate at which the water is draining from the tank after 5 min is,
(b)
To find: The rate at which the water is draining from the tank after 10 min.
(b)
Answer to Problem 18E
The rate at which the water is draining from the tank after 10 min is,
Explanation of Solution
From part (a), the rate of change of the volume with respect to time is,
Substitute t = 10 in
Thus, the rate at which the water is draining from the tank after 10 min is,
(c)
To find: The rate at which the water is draining from the tank after 20 min.
(c)
Answer to Problem 18E
The rate at which the water is draining from the tank after 20 minutes is,
Explanation of Solution
From part (a), the rate of change of the volume with respect to time is,
Substitute t = 20 in
Thus, the rate at which the water is draining from the tank after 20 min is,
(d)
To find: The rate at which the water is draining from the tank after 40 min; at what time is the water is draining out fastest and the slowest; summarize the results obtained from the parts (a), (b), (c) and (d).
(d)
Answer to Problem 18E
The rate at which the water is draining from the tank after 40 min is,
The water is flowing out the fastest at t = 5 min. and the slowest at t = 40 min.
Explanation of Solution
From part (a), the rate of change of the volume with respect to time is,
Substitute t = 40 in
Thus, the rate at which the water is draining from the tank after 40 min is,
From the above sub parts, it is identified that the water flow is very fast at t = 5 min. and is too slow at t = 40 min.
Also, notice that at t = 40 min. the velocity is 0 and hence the water flow is very slow.
Chapter 3 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced 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