   Chapter 9.4, Problem 57E Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340

Solutions

Chapter
Section Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340
Textbook Problem

Wind chill One form of the formula that meteorologists use to calculate wind chill temperature WC is W C = 35.74   +   0.6215 t −   35.75 s 016 +   0.4275 t s 0.16 where s is the wind speed in mph and t is the actual air temperature in degrees Fahrenheit. Suppose temperature is constant at 15 ° .(a) Express wind chill WC as a function of wind speed s.(b) Find the rate of change of wind chill with respect to wind speed when the wind speed is 25 mph.(c) Interpret your answer to part (b).

(a)

To determine

To calculate: The wind chill as a function of wind speed s at temperature t=15°, the wind chill is expressed as WC=35.74+0.6215t35.75s0.16+0.4275ts0.16.

Explanation

Given Information:

The wind chill is expressed as WC=35.74+0.6215t35.75s0.16+0.4275ts0.16 and t=15°.

Formula Used:

According to property of functions,

If f(x)=xn, then f(a)=an.

Calculation:

It is provided that the wind chill is expressed as WC=35.74+0.6215t35.75s0.16+0.4275ts0.16.

To calculate the wind chill as a function of s,

Put t=15, using property of functions

WC=35.74+0.6215(15)35.75s0.16+0.4275(15)s0

(b)

To determine

To calculate: The rate of change of wind chill with respect to wind speed when the wind speed is s=25mph at temperature t=15°, the wind chill is expressed as WC=35.74+0.6215t35.75s0.16+0.4275ts0.16.

(c)

To determine

The interpretation of result obtained in part (b).

And interpret the result.

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