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.
Chapter3: Polynomial Functions
Section3.5: Mathematical Modeling And Variation
Problem 7ECP: The kinetic energy E of an object varies jointly with the object’s mass m and the square of the...
Related questions
Question
![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.
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![College Algebra](https://www.bartleby.com/isbn_cover_images/9781337282291/9781337282291_smallCoverImage.gif)
![Functions and Change: A Modeling Approach to Coll…](https://www.bartleby.com/isbn_cover_images/9781337111348/9781337111348_smallCoverImage.gif)
Functions and Change: A Modeling Approach to Coll…
Algebra
ISBN:
9781337111348
Author:
Bruce Crauder, Benny Evans, Alan Noell
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
![College Algebra](https://www.bartleby.com/isbn_cover_images/9781337282291/9781337282291_smallCoverImage.gif)
![Functions and Change: A Modeling Approach to Coll…](https://www.bartleby.com/isbn_cover_images/9781337111348/9781337111348_smallCoverImage.gif)
Functions and Change: A Modeling Approach to Coll…
Algebra
ISBN:
9781337111348
Author:
Bruce Crauder, Benny Evans, Alan Noell
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
![Algebra: Structure And Method, Book 1](https://www.bartleby.com/isbn_cover_images/9780395977224/9780395977224_smallCoverImage.gif)
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell
![Trigonometry (MindTap Course List)](https://www.bartleby.com/isbn_cover_images/9781305652224/9781305652224_smallCoverImage.gif)
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781305652224
Author:
Charles P. McKeague, Mark D. Turner
Publisher:
Cengage Learning
![Big Ideas Math A Bridge To Success Algebra 1: Stu…](https://www.bartleby.com/isbn_cover_images/9781680331141/9781680331141_smallCoverImage.jpg)
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Algebra
ISBN:
9781680331141
Author:
HOUGHTON MIFFLIN HARCOURT
Publisher:
Houghton Mifflin Harcourt