Answered: A person coughs when a foreign object…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.3: Zeros Of Polynomials

Problem 67E

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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

13-mm

radius. If a foreign object has a 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 13r2−r3,

0≤r≤13

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 13-mm radius. If a foreign object has a 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() = k (13 -r), 0srs 13
An object that has a radius of
will need maximum velocity to remove it.
(Type an integer or a simplified fraction. )

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