Coughing When a foreign object that is lodged in the tra- chea (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 v(r) = 3.2(1 – r)r Įsrsl Determine the value of r for which v is a maximum.
Coughing When a foreign object that is lodged in the tra- chea (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 v(r) = 3.2(1 – r)r Įsrsl Determine the value of r for which v is a maximum.
Chapter3: Polynomial Functions
Section3.5: Mathematical Modeling And Variation
Problem 7ECP: The kinetic energy E of an object varies jointly with the object’s mass m and the square of the...
Related questions
Question
Transcribed Image Text:Coughing When a foreign object that is lodged in the tra-
chea (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
v(r) = 3.2(1 – r)r Įsrsl
Determine the value of r for which v is a maximum.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps
Recommended textbooks for you
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell