Answered: PART C & D PLEASE! Wind chill factor…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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PART C & D PLEASE!

Wind chill factor Wind chill, a measure of the apparent tem-
perature felt on exposed skin, is a function of air temperature and

wind speed. The precise formula, updated by the National Weather

Service in 2001 and based on modern heat transfer theory, a hu-
man face model, and skin tissue resistance, is

W = W(y, T) = 35.74 + 0.6215 T - 35.75 y0.16

+ 0.4275 T # y0.16,

where T is air temperature in °F and y is wind speed in mph. A
partial wind chill chart is given.

c. Find the linearization L(y, T) of the function W(y, T) at the
point (25, 5).
d. Use L(y, T) in part (c) to estimate the following wind chill
values. i) W(24, 6) ii) W(27, 2) iii) W(5, -10) (Explain why this value is much different from the value found in the table.)

wind speed. The precise formula, updated by the National Weather
Service in 2001 and based on modern heat transfer theory, a hu-
man face model, and skin tissue resistance, is
W = W(v, T) = 35.74 + 0.6215 T – 35.75 vº.16
+ 0.4275 T· v0.16
where T is air temperature in °F and v is wind speed in mph. A
partial wind chill chart is given.
T(°F)
30
25
20
15
10
-5 - 10
25
19
13
7
1
-5
-11 -16 -22
10
21
15
9.
3
-4
- 10 -16 –22 -28
15
19
13
-7 -13 –19 -26 -32
(mph)
20
17
11
4
-2
-9 -15 -22 -29 -35
25
16
9
3
-4
-11 -17 -24 -31 -37
30
15
8
1
-5
-12 -19 –26 -33 -39
35
14
7
-7
-14 -21 -27 –34 -41
a. Use the table to find W(20, 25), W(30, – 10), and W(15, 15).
b. Use the formula to find W(10, –40), W(50, –40), and
W(60, 30).
c. Find the linearization L(v, T) of the function W(v, T) at the
point (25, 5).
d. Use L(v, T) in part (c) to estimate the following wind chill
values.
i) W(24, 6)
ii) W(27, 2)
iii) W(5, – 10) (Explain why this value is much different
from the value found in the table.)

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