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

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter1: Variables, Expressions, And Integers

Section1.5: Adding Integers

Problem 45E

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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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