   Chapter 9.5, Problem 51E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Wind chill Each winter the so-called “polar vortex” of deep frigid air plunges into the United States and sometimes brings record cold and dangerous wind chills. If s is the wind speed in miles per hour and s   ≥ 5 , then the wind chill (in degrees Fahrenheit) for an air temperature of 0°F can be approximated by the function f ( s ) =  289 .173  −  58 .5731 s s + 1 (a) At what rate is the wind chill changing when the wind speed is 20 mph?(b) Explain the meaning of your answer to part (a).

(a)

To determine

To calculate: The rate of change of the wind chill when the wind speed is, if the model function of wind chill(in degrees Fahrenheit) for an air temperature at 0°F is f(s)=289.17358.5731ss+1, where s is the wind speed in miles per hour and the s5.

Explanation

Given Information:

The model function of wind chill (in degrees Fahrenheit) for an air temperature at 0°F is f(s)=289.17358.5731ss+1 and the speed of the wind speed is greater than or equal to 5 mph.

Formula Used:

The quotient rule for the derivative of the two function, ddx(fg)=gdfdxfdgdxg2.

The sum or difference rule of derivate of functions, ddx[u(x)±v(x)]=ddxu(x)±ddxv(x).

The simple power rule of derivative ddx(xn)=nxn1.

Calculation:

Consider the model function for wind chill f(s)=289.17358.5731ss+1.

Differentiate the provided wind chill function,

df(s)ds=dds(289.17358.5731ss+1)

Use the quotient rule for the derivative of the two function f(x) and g(x) is, df(s)ds=(s+1)dds(289.17358.5731s)(289.17358.5731s)dds(s+1)(s+1)2.

Use the sum and difference rule of derivative, ddx[u(x)±v(x)]=ddxu(x)±ddxv(x)

(b)

To determine

The meaning of the rate of change of the wind chill when the speed is 20 mph, if the model function of wind chill (in degrees Fahrenheit) for an air temperature at 0°F is f(s)=289.17358.5731ss+1, where s is the wind speed in miles per hour and the s5.

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### What is the value of (X + 1) for the following scores: 0, 1, 4, 2? a. 8 b. 9 c. 11 d. 16

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

#### In Exercises 724, compute the indicated products. 

Finite Mathematics for the Managerial, Life, and Social Sciences

#### Find the limit. limx0sin5x3x

Single Variable Calculus: Early Transcendentals

#### True or False: Du f(a, b) = ∇(a, b) · u.

Study Guide for Stewart's Multivariable Calculus, 8th

#### True or False: converges conditionally.

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 