To increase the velocity of the air flowing through the trachea when a human coughs, the body contracts the windpipe, producing a more effective cough. Tuchinsky formulated that the velocity of air that is flowing through the trachea during a cough isV = C(R0 - R)R2,where C is a constant based on individual body characteristics, R0 is the radius of the windpipe before the cough, and R is the radius of the windpipe during the cough. It can be shown that the maximum velocity of the cough occurs when dV/dR = 0. Find the value of R that maximizes the velocity.* Source: COMAP, Inc.
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To increase the velocity of the air flowing through the trachea when a human coughs, the body contracts the windpipe, producing a more effective cough. Tuchinsky formulated that the velocity of air that is flowing through the trachea during a cough is
V = C(R0 - R)R2,
where C is a constant based on individual body characteristics, R0 is the radius of the windpipe before the cough, and R is the radius of the windpipe during the cough. It can be shown that the maximum velocity of the cough occurs when dV/dR = 0. Find the value of R that maximizes the velocity.* Source: COMAP, Inc.
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