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Calculus / Calculus with Applications 10 / Chapter 4.1 / Problem 66A

Calculus with Applications | 10th Edition | ISBN: 9780321749000 | Authors: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

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Human Cough To increase the velocity of the air flowing

Chapter 4, Problem 66A

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QUESTION:

Human Cough To increase the velocity of the air flowing through the trachea when a human coughs, the body contracts the windpipe, producing a more effective cough. Tuchinsky formulated that the velocity of air that is flowing through the trachea during a cough isV ? C(R0 ? R)R2,where C is a constant based on individual body characteristics, R0 is the radius of the windpipe before the cough, and R is the radius of the windpipe during the cough. It can be shown that the maximum velocity of the cough occurs when dV/dR = 0. Find the value of R that maximizes the velocity. Source: COMAP, Inc.

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QUESTION:

Human Cough To increase the velocity of the air flowing through the trachea when a human coughs, the body contracts the windpipe, producing a more effective cough. Tuchinsky formulated that the velocity of air that is flowing through the trachea during a cough isV ? C(R0 ? R)R2,where C is a constant based on individual body characteristics, R0 is the radius of the windpipe before the cough, and R is the radius of the windpipe during the cough. It can be shown that the maximum velocity of the cough occurs when dV/dR = 0. Find the value of R that maximizes the velocity. Source: COMAP, Inc.

ANSWER:

SolutionStep 1 of 2In this problem, we have to determine the radius of the windpipe that maximises the velocity of the air flowing through a trachea during a cough.Given equation

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