52. According to one model of coughing, the flow F (volume per unit time) of air through the windpipe during a cough is a function of the radius r of the windpipe, given by 1 F = k(ro - r)rA for ro
52. According to one model of coughing, the flow F (volume per unit time) of air through the windpipe during a cough is a function of the radius r of the windpipe, given by 1 F = k(ro - r)rA for ro
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![52. According to one model of coughing, the flow F (volume
per unit time) of air through the windpipe during a cough
is a function of the radius r of the windpipe, given by
1
F = k(ro – r)r4 for ro <r< ro
%3D
where k is a positive constant and ro is the normal
(noncoughing) radius.
a. Find the value of r that maximizes the flow F.
b. According to the same model, the velocity v of air
through the windpipe during a cough is given by
1
k
(ro - r)r2 for ro <r<ro
V =
TT
2
Find the value of r that maximizes the velocity v.
c. During a cough the windpipe is constricted. According
to parts (a) and (b), is that likely to assist or hinder the
cough?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3a5868e7-7e56-4802-a6f9-4239b407ceeb%2F9d61245c-60a1-41f3-b3e7-c6b5129f82a2%2Fdb57xq9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:52. According to one model of coughing, the flow F (volume
per unit time) of air through the windpipe during a cough
is a function of the radius r of the windpipe, given by
1
F = k(ro – r)r4 for ro <r< ro
%3D
where k is a positive constant and ro is the normal
(noncoughing) radius.
a. Find the value of r that maximizes the flow F.
b. According to the same model, the velocity v of air
through the windpipe during a cough is given by
1
k
(ro - r)r2 for ro <r<ro
V =
TT
2
Find the value of r that maximizes the velocity v.
c. During a cough the windpipe is constricted. According
to parts (a) and (b), is that likely to assist or hinder the
cough?
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