(a)
To express: The radius of the circular ripple as a function of time t.
(a)
Answer to Problem 53E
The function of the radius in terms of time t is
Explanation of Solution
It is given that the stone travel at a speed of 60 cm/s.
Let the radius of the circular ripple as r.
Note that the radius is same as the distance travelled by a stone.
Recall the formula, Distance = Time × Speed.
Substitute t for time and 60 for speed in a distance formula.
Thus, the function is
Therefore, the radius of the circular ripple after t seconds is
(b)
To find: The expression for
(b)
Answer to Problem 53E
The value of
Explanation of Solution
Area of the circle is,
The composite function
From part (a), the value of
Thus,
Substitute
Thus,
Chapter 1 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