Concept explainers
(a)
To express: The horizontal distance (in miles) covered by a plane as a function of time t.
(a)
Answer to Problem 56E
The function that represents the horizontal distance in terms of time t is
Explanation of Solution
Given:
The plane is flying at a speed of 350 mi/h and at an altitude of one mile.
The plane passes the radar station at time
Result used:
Calculation:
Let the horizontal distance be d.
Substitute t for time and 350 for speed in the distance formula,
Thus, the function is
Therefore, the horizontal distance covered by the plane after t hours is
(b)
To express: The distance (s) between the plane and radar station in terms of d.
(b)
Answer to Problem 56E
The function that represents the distance between the plane and radar station in terms of the distance d is
Explanation of Solution
Let the horizontal distance be d in mi/hr.
It is given that the altitude is 1 mile.
Use the Pythagoras formula and obtain the value of s as follows.
Thus, the function is
Therefore, the distance between the plane and radar station as a function of d is
(c)
To find: The expression for
(c)
Answer to Problem 56E
The value of
Explanation of Solution
The composite function
From part (a), the value of
Thus,
Substitute
Thus, the required composition function,
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