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cluponka [151]
3 years ago
15

Coughing forces the trachea (windpipe) to contract, which in turn affects the velocity of the air through the trachea. The veloc

ity of the air during coughing can be modeled by v = k(R – r)r2, 0 ≤ r < R, where k is a constant, R is the normal radius of the trachea, and r is the radius during coughing. What radius r will produce the maximum air velocity?
Mathematics
1 answer:
Rzqust [24]3 years ago
8 0
To find the maximum velocity you have to differentiate the function respect to r.

v = k(R - r)r^2 = kRr^2 - krr^2 = kRr^2 - kr^3

k and R are constants.

=> v' = 2kRr - 3kr^2 = kr(2R - 3r)

maximum velocity => v' = 0 => kr(2R - 3r) = 0

r = 0 or 2R - 3r = 0 => r = 2R / 3

Answer: r = 2R / 3




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