When a foreign object lodged in the trachea (windpipe) forces a person to cough, the diaphragm thrusts upward causing an increase in pressure in the lungs. This is accompanied by a contraction of the trachea, making a narrower channel for the expelled air to flow through. For a given amount of air to escape in a fixed time, it must move faster through the narrower channel than the wider one. The greater the velocity of the air- stream, the greater the force on the foreign object. X rays show that the radius of the circular tracheal tube contracts to about two-thirds of its normal radius during a cough. According to a mathematical model of coughing, the velocity v of the air- stream is related to the radius r of the trachea by the equation
where k is a constant and r0 is the normal radius of the trachea. The restriction on r is due to the fact that the tracheal wall stiffens under pressure and a contraction greater than
(a) Determine the value of r in the interval
(b) What is the absolute maximum value of v on the interval?
(c) Sketch the graph of v on the interval
Calculus: Early Transcendental Functions
Applied Calculus
Single Variable Calculus: Early Transcendentals, Volume I
Calculus: An Applied Approach (MindTap Course List)
Finite Mathematics and Applied Calculus (MindTap Course List)
Multivariable Calculus
Precalculus: Mathematics for Calculus (Standalone Book)
Calculus: Early Transcendentals
Essentials Of Statistics
Statistics for The Behavioral Sciences (MindTap Course List)
Essentials of Statistics for The Behavioral Sciences (MindTap Course List)
Single Variable Calculus
Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach
Finite Mathematics
Understanding Basic Statistics
Mathematical Applications for the Management, Life, and Social Sciences
Intermediate Algebra
Probability and Statistics for Engineering and the Sciences
Elementary Geometry For College Students, 7e
Mathematical Excursions (MindTap Course List)
Elementary Technical Mathematics
Calculus of a Single Variable
Single Variable Calculus: Early Transcendentals
Elements Of Modern Algebra
Trigonometry (MindTap Course List)
Contemporary Mathematics for Business & Consumers
Calculus: Early Transcendental Functions (MindTap Course List)
Study Guide for Stewart's Multivariable Calculus, 8th
Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th
Finite Mathematics for the Managerial, Life, and Social Sciences
Elementary Geometry for College Students
Multivariable Calculus
Calculus (MindTap Course List)
College Algebra (MindTap Course List)
Introduction To Statistics And Data Analysis
Research Methods for the Behavioral Sciences (MindTap Course List)
STATISTICS F/BUSINESS+ECONOMICS-TEXT
Statistics for Business & Economics, Revised (MindTap Course List)
Research Methods for the Behavioral Sciences (MindTap Course List)
Mathematics For Machine Technology
Essentials Of Statistics For Business & Economics
Discrete Mathematics With Applications
Mathematics: A Practical Odyssey
Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List)
A First Course in Differential Equations with Modeling Applications (MindTap Course List)
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
Calculus Volume 1
Introductory Statistics