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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.

College Algebra
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter2: Functions
Section2.3: Getting Information From The Graph Of A Function
Problem 66E
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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.
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.
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