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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. VT -30 -25 -20 -15 -10 -5 0 5 10 15 5 -11 -5 1 7 -16 <-10 -4 10 15 -13 -7 -46 -40 -34 -28 -22 -16 -53 -47 -41 -35 -28 -22 -58 -51 <-45 -39 -32 -26 <-19 -61 -55 -48 -42 <-35 -29 -22 <-15 -64 <-58 -51 -44 -37 -67 -60 -53 -46 -39 -69 -62 -55 -48 -41 -34 -71 -64 -57 -50 -43 -36 -29 -22 -15 -8 -1 -31 -24 -17 -33 -26 -19 -27 -21 -14 -7 0 20 25 30 35 40 20 13 3 9 0 6 -9 -2 -11 -4 -12 -5 4 3 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(zh) for small values of h. A partial derivative is a derivative of an appropriate trace.) 2h w (25, -10)- w (15, -10) = -37-(-32) 2 (5) 10 W(20,-5) _w (20, -15) 2 (5) W. (20,-10)- b. Estimate the partial derivative wr(20,-10). What are the units on this quantity and what does it mean? 1=-29-(-2 10 c. Use your results to estimate the wind chill w(18,-10). (Recall from single variable calculus that for a function f of x, f(x+h) f(x) + hf'(I).)

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. VT -30 -25 -20 -15 -10 -5 0 5 10 15 5 -11 -5 1 7 -16 <-10 -4 10 15 -13 -7 -46 -40 -34 -28 -22 -16 -53 -47 -41 -35 -28 -22 -58 -51 <-45 -39 -32 -26 <-19 -61 -55 -48 -42 <-35 -29 -22 <-15 -64 <-58 -51 -44 -37 -67 -60 -53 -46 -39 -69 -62 -55 -48 -41 -34 -71 -64 -57 -50 -43 -36 -29 -22 -15 -8 -1 -31 -24 -17 -33 -26 -19 -27 -21 -14 -7 0 20 25 30 35 40 20 13 3 9 0 6 -9 -2 -11 -4 -12 -5 4 3 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(zh) for small values of h. A partial derivative is a derivative of an appropriate trace.) 2h w (25, -10)- w (15, -10) = -37-(-32) 2 (5) 10 W(20,-5) _w (20, -15) 2 (5) W. (20,-10)- b. Estimate the partial derivative wr(20,-10). What are the units on this quantity and what does it mean? 1=-29-(-2 10 c. Use your results to estimate the wind chill w(18,-10). (Recall from single variable calculus that for a function f of x, f(x+h) f(x) + hf'(I).)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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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 15 20 5 1 7 13 10 3 9 15 0 6 v\T -30 -25 -20 -15 <-10 -5 0 5 -46 -40 -34 -28 -22 -16 -11 -5 -53 -47 -41 -35 -28 -22 -16 -10 -4 -58 -51 -45 -39 -32 -26 -19 -13 -7 -61 -55 -48 -42 -35 -29 -22 -15 -64 -58 -51 -44 -37 -31 -24 -17 -11 -4 3 -67 -60 -53 -46 -39 -33 -26 -19 -12 -5 1 -69 -62 -55 -48 -41 -34 -27 -21 -14 -7 0 -71 -57 -50 -43 -36 -29 -22 -15 -8 -1 20 -9 -2 4 25 -64 30 35 40 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.) W (25, -10) - W (15,-10) = -37-(-32) == un 2 (5) 10 W₂ (20₁-10)==-1221 b. Estimate the partial derivative wr(20,-10). What are the units on this quantity and what does it mean? ~(20₁-15) w (20₁5). 2 (5) ہا۔ ·-29-(-42) = 13 =13 10 10 c. Use your results to estimate the wind chill w(18,-10). (Recall from single variable calculus that for a function f of x, f(x+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.
Transcribed Image Text: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 15 20 5 1 7 13 10 3 9 15 0 6 v\T -30 -25 -20 -15 <-10 -5 0 5 -46 -40 -34 -28 -22 -16 -11 -5 -53 -47 -41 -35 -28 -22 -16 -10 -4 -58 -51 -45 -39 -32 -26 -19 -13 -7 -61 -55 -48 -42 -35 -29 -22 -15 -64 -58 -51 -44 -37 -31 -24 -17 -11 -4 3 -67 -60 -53 -46 -39 -33 -26 -19 -12 -5 1 -69 -62 -55 -48 -41 -34 -27 -21 -14 -7 0 -71 -57 -50 -43 -36 -29 -22 -15 -8 -1 20 -9 -2 4 25 -64 30 35 40 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.) W (25, -10) - W (15,-10) = -37-(-32) == un 2 (5) 10 W₂ (20₁-10)==-1221 b. Estimate the partial derivative wr(20,-10). What are the units on this quantity and what does it mean? ~(20₁-15) w (20₁5). 2 (5) ہا۔ ·-29-(-42) = 13 =13 10 10 c. Use your results to estimate the wind chill w(18,-10). (Recall from single variable calculus that for a function f of x, f(x+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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