During a sneeze, the radius of windpipe decreases. Suppose that the normal radius of the windpipe is R centimeters and the radius of the windpipe during a sneeze is r centimeters, where R is constant, and r is variable. The velocity of air through the windpipe can be shown to be a function of r, and if V (r) centimeters per second is this velocity then V (r) = kr²(R – r) where k is a positive constant and r is in R, R]. Determine the radius of the windpipe during a sneeze for which the velocity of air through the trachea is greatest.
During a sneeze, the radius of windpipe decreases. Suppose that the normal radius of the windpipe is R centimeters and the radius of the windpipe during a sneeze is r centimeters, where R is constant, and r is variable. The velocity of air through the windpipe can be shown to be a function of r, and if V (r) centimeters per second is this velocity then V (r) = kr²(R – r) where k is a positive constant and r is in R, R]. Determine the radius of the windpipe during a sneeze for which the velocity of air through the trachea is greatest.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![During a sneeze, the radius of windpipe decreases. Suppose that the normal radius of the windpipe is R
centimeters and the radius of the windpipe during a sneeze is r centimeters, where R is constant, and r
is variable. The velocity of air through the windpipe can be shown to be a function of r, and if V (r)
centimeters per second is this velocity then
V (r) = kr²(R – r)
where k is a positive constant and r is in R, R]. Determine the radius of the windpipe during a sneeze
for which the velocity of air through the trachea is greatest.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8fc92ab2-e697-4e14-b2cd-c58947e4fd4c%2Ff0b37a6c-2366-4669-99ea-83ae89cf5fe2%2Fryzw6c_processed.jpeg&w=3840&q=75)
Transcribed Image Text:During a sneeze, the radius of windpipe decreases. Suppose that the normal radius of the windpipe is R
centimeters and the radius of the windpipe during a sneeze is r centimeters, where R is constant, and r
is variable. The velocity of air through the windpipe can be shown to be a function of r, and if V (r)
centimeters per second is this velocity then
V (r) = kr²(R – r)
where k is a positive constant and r is in R, R]. Determine the radius of the windpipe during a sneeze
for which the velocity of air through the trachea is greatest.
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