Question: Coughing forces the trachea (windpipe) to contract, which affects the velocity of the air passing through the trachea. The velocity of the air during coughing

Coughing forces the trachea (windpipe) to contract, which affects the velocity of the air passing through the trachea. The velocity of the air during coughing is

where is a constant, is the normal radius of the trachea, and r is the radius during coughing. What radius will produce the maximum air velocity?

v = k(Rr)r, 0r < R

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