A person coughs when a foreign object is in the windpipe. The velocity of the cough depends on the size of the object. Suppose a person has a…

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A person coughs when a foreign object is in the windpipe.  The velocity of the cough depends on the size of the object.  Suppose a person has a windpipe with a 26-mm radius.  If a foreign object has radius, r in millimeters, then the velocity, V in millimeters/second needed to remove the object by a cough is given by the following equation, where k is some positive constant.  For what size object is the maximum velocity needed to remove the object.    V(r)= k(26r^2-r^3), 0less than or equal to r less than or equal to 26.

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