Activity 10.2.5 The wind chill, as frequently reported, is a measure of how cold it feels outside when the wind is blowing. In Table 10.2.3, the wind chill w, measured in degrees Fahrenheit, is a function of the wind speed v, measured in miles per hour, and the ambient air temperature T, also measured in degrees Fahrenheit. We thus view w as being of the form w= w(v, T). Table 10.2.3 Wind chill as a function of wind speed and temperature. 10 5 -5 1 -4 3 -19 -13 0 v\T -30 -25 -20 -15 -10 -5 0 5 -46 -40 -34 -28 -22 -16 -11 -53-47 -41 -35 -28 -22 -16 -10 15 -58 -51 -45 -39 -32 -26 -42-35 -29 -64-58 -51 -44 -37 -31 -24 -17 -67 -60 -53 -46 -39 -33 -26 -69-62 -55 -48 -41 -34 -27 -21 -71 -64 -57 -50 -43 -7 -22 -15 -9 -2 -61 -55 -48 4 -11 -4 3 -19 -12 -5 1 -14 -7 0 -15 -8 -1 -36-29 -22 10 18 20 25 30 35 40 15 20 7 13 9 6 a. Estimate the partial derivative w, (20,-10). What are the units on this quantity and what does it mean? (Recall that we can estimate a partial derivative of a single variable function f using the symmetric difference quotient f(a+h)-f(z-h) for small values of h. A partial derivative is a derivative of an appropriate trace.) 2h b. Estimate the partial derivative wr(20,-10). What are the units on this quantity and what does it mean? d. Use your results to estimate the wind chill w(20, -12). c. Use your results to estimate the wind chill w(18,-10). (Recall from single variable calculus that for a function f of z, f(a+h) f(x) + hf'(z).)
Activity 10.2.5 The wind chill, as frequently reported, is a measure of how cold it feels outside when the wind is blowing. In Table 10.2.3, the wind chill w, measured in degrees Fahrenheit, is a function of the wind speed v, measured in miles per hour, and the ambient air temperature T, also measured in degrees Fahrenheit. We thus view w as being of the form w= w(v, T). Table 10.2.3 Wind chill as a function of wind speed and temperature. 10 5 -5 1 -4 3 -19 -13 0 v\T -30 -25 -20 -15 -10 -5 0 5 -46 -40 -34 -28 -22 -16 -11 -53-47 -41 -35 -28 -22 -16 -10 15 -58 -51 -45 -39 -32 -26 -42-35 -29 -64-58 -51 -44 -37 -31 -24 -17 -67 -60 -53 -46 -39 -33 -26 -69-62 -55 -48 -41 -34 -27 -21 -71 -64 -57 -50 -43 -7 -22 -15 -9 -2 -61 -55 -48 4 -11 -4 3 -19 -12 -5 1 -14 -7 0 -15 -8 -1 -36-29 -22 10 18 20 25 30 35 40 15 20 7 13 9 6 a. Estimate the partial derivative w, (20,-10). What are the units on this quantity and what does it mean? (Recall that we can estimate a partial derivative of a single variable function f using the symmetric difference quotient f(a+h)-f(z-h) for small values of h. A partial derivative is a derivative of an appropriate trace.) 2h b. Estimate the partial derivative wr(20,-10). What are the units on this quantity and what does it mean? d. Use your results to estimate the wind chill w(20, -12). c. Use your results to estimate the wind chill w(18,-10). (Recall from single variable calculus that for a function f of z, f(a+h) f(x) + hf'(z).)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please help with d
Transcribed Image Text:CHAPTER 10. DERIVATIVES OF MULTIVARIABLE FUNCTIONS 58
Activity 10.2.5 The wind chill, as frequently reported, is a measure of how
cold it feels outside when the wind is blowing. In Table 10.2.3, the wind chill
w, measured in degrees Fahrenheit, is a function of the wind speed v, measured
in miles per hour, and the ambient air temperature T, also measured in degrees
Fahrenheit. We thus view w as being of the form w=w(v, T).
Table 10.2.3 Wind chill as a function of wind speed and temperature.
v\T -30 -25
10 15
20
5
-46 -40
1 7 13
10
-53 -47
-4
3
9
15
-13 -7
0
-20 -15 -10 -5 0 5
-34 -28 -22 -16 -11 -5
-41 -35 -28 -22 -16 -10
-58 -51 -45 -39 -32 -26 -19
20 -61 -55 -48 -42 -35
-35 -29 -22 -15
25 -64-58
-58 -51 -44 -37 -31 -24 -17
-11 -4 3
30 -67 -60 -53 -46 -39 -33 -26 -19 -12 -5 1
35 -69 -62 -55 -48 -41 -34
-21 -14 -7 0
-71 -64 -57 -50 -43 -36 -29 -22 -15 -8 -1
-9 -24
-27
40
6
a. Estimate the partial derivative w, (20,-10). What are the units on this
quantity and what does it mean? (Recall that we can estimate a partial
derivative of a single variable function f using the symmetric difference
quotient f(a+h)-f(-h) for small values of h. A partial derivative is a
derivative of an appropriate trace.)
2h
b. Estimate the partial derivative wr(20,-10). What are the units on this
quantity and what does it mean?
c. Use your results to estimate the wind chill w(18,-10). (Recall from single
variable calculus that for a function f of z, f(a+h) f(x) + hf'(x).)
d. Use your results to estimate the wind chill w(20, -12).
e. Consider how you might combine your previous results to estimate the
wind chill w(18, -12). Explain your process.
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