Concept explainers
Coughing When a foreign object that is lodged in the trachea (windpipe) forces a person to cough, the diaphragm thrusts upward, causing an increase in pressure in the lungs. At the same time, the trachea contracts, causing the expelled air to move faster and increasing the pressure on the foreign object. According to a mathematical model of coughing, the velocity v (in cm/s) of the airstream through an average-sized person’s trachea is related to the radius r of the trachea (in cm) by the function
Determine the value of r for which v is a maximum.
The value of r for which v is maximum.
Answer to Problem 55E
The value of r is 0.6667 for which the value of v is maximum.
Explanation of Solution
A function of velocity v of the airstream through trachea of radius r is given by
Use graph calculator to draw thee graph of the function
Figure (1)
Locate the point of local maximum in the above graph to find the value of r for which v is maximum.
The value
From Figure (1), it is noticed that there is a local maximum between
Point
The value 0.474 is the local maximum value at
Therefore, the value of r is 0.6667 for which the value of v is maximum.
Chapter 2 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
Additional Math Textbook Solutions
Calculus and Its Applications (11th Edition)
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
Precalculus (10th Edition)
Precalculus: A Unit Circle Approach (3rd 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