subject
Mathematics, 01.04.2021 22:30 donnafranks2003

When a foreign object lodged in the trachea (windpipe) forces a person to cough, the diaphragm thrusts upward causing an increase in pressure in the lungs. This is accompanied by a contraction of the trachea, making a narrower channel for the expelled air to flow through. For a given amount of air to escape in a fixed time, it must move faster through the narrower channel than the wider one. The greater the velocity of the airstream, the greater the force on the foreign object. X rays show that the radius of the circular tracheal tube contracts to about two-thirds of its normal radius during a cough. According to a mathematical model of coughing, the velocity v of the airstream is related to the radius r of the trachea by the equation v(r) = k(r0 βˆ’ r)r2 1 2 r0 ≀ r ≀ r0 where k is a constant and r0 is the normal radius of the trachea. The restriction on r is due to the fact that the trachea wall stiffens under pressure and a contraction greater than 1 2 r0 is prevented (otherwise the person would suffocate). a). Determine the value of r in the interval {1/2, r0, r0} at which v has an absolute maximum.

b). What is the absolute maximum value of v on the interval?

ansver
Answers: 2

Another question on Mathematics

question
Mathematics, 21.06.2019 16:20
Consider the function y = f(x)=3^x the values of f(1/2) and f(1/4). rounded to the nearest hundredth, are__and__ respectively
Answers: 3
question
Mathematics, 21.06.2019 16:30
The ratio of men to women working for a company is 4 to 5 . if there are 90 women working for the company, what is the total number of employees?
Answers: 1
question
Mathematics, 21.06.2019 19:10
Which equation results from adding the equations in this system? x+6y=9 and -x+2y=-15
Answers: 1
question
Mathematics, 22.06.2019 01:10
To find the inverse of a number a, one can use the equation f(c) = a-1/c=0 where c is the inverse of a use the secant method of finding roots of equations to find the inverse of a = 2.5 ,er = 0.001%
Answers: 3
You know the right answer?
When a foreign object lodged in the trachea (windpipe) forces a person to cough, the diaphragm thrus...
Questions
question
Mathematics, 09.07.2019 02:00