(Taken from Hughes-Hallett, et. al.) When you cough, your windpipe contracts. The speed, v, at which the air comes out depends on the radius, r, of your windpipe. If R is the normal (rest) radius of your windpipe, then for 0

Mathematics For Machine Technology
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Author:Peterson, John.
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Chapter39: Symbolism And Algebraic Expressions
Section: Chapter Questions
Problem 32A: For Exercises 23 through 34, round the answers to 1 decimal place. 32. All dimensions are in...
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Could you help me just answer 8b. and 8c.?

(Taken from Hughes-Hallett, et. al.) When you cough, your windpipe contracts. The speed, v, at which the
air comes out depends on the radius, r, of your windpipe. If R is the normal (rest) radius of your windpipe,
then for 0 <r< R, the speed is given by v = a(R – r)r², where a is a positive constant. What value of r
maximizes the speed?
Transcribed Image Text:(Taken from Hughes-Hallett, et. al.) When you cough, your windpipe contracts. The speed, v, at which the air comes out depends on the radius, r, of your windpipe. If R is the normal (rest) radius of your windpipe, then for 0 <r< R, the speed is given by v = a(R – r)r², where a is a positive constant. What value of r maximizes the speed?
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