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Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643

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Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643
Textbook Problem

The wind-chill index is modeled by the function

W = 13.12 + 0.6215T − 11.37v0.16 + 0.3965Tv0.16

where T is the temperature (°C) and v is the wind speed (km/h). When T = − 15°C and v = 30 km/h, by how much would you expect the apparent temperature W to drop if the actual temperature decreases by 1°C? What if the wind speed increases by 1 km/h?

To determine

To find: The rate of temperature when the actual temperature decreases by 1°C and if the wind speed increases by 1km/h when T=15°C and v=30km/h .

Explanation

Given:

The wind-chill index function is, W=13.12+0.6215T11.37v0.16+0.3965Tv0.16 , where T is temperature (°C) and v is the wind speed (km/h) .

The value of T=15°C and v=30km/h .

Calculation:

The wind-chill index function is, W=13.12+0.6215T11.37v0.16+0.3965Tv0.16 .

Take the partial derivative with respect to T and obtain WT .

WT=T(13.12+0.6215T11.37v0.16+0.3965Tv0.16)=T(13.12)+T(0.6215T)T(11.37v0.16)+T(0.3965Tv0.16)=0+0.6215T(T)0+0.3965v0.16T(T)=0.6215+0.3965v0.16

Substitute T=15°C and v=30km/h in the above equation,

WT=0.6215+0.3965(30)0.16=0.6215+0.3965(1.7232)=0.6215+0.6833=1.3047

Thus, it is clear that the rate of temperature decreases approximately by 1.3°C when the actual temperature decreases by 1°C

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Chapter 14 Solutions

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P-14RECh-14 P-15RECh-14 P-16RECh-14 P-17RECh-14 P-18RECh-14 P-19RECh-14 P-20RECh-14 P-21RECh-14 P-22RECh-14 P-23RECh-14 P-24RECh-14 P-25RECh-14 P-26RECh-14 P-27RECh-14 P-28RECh-14 P-29RECh-14 P-30RECh-14 P-31RECh-14 P-32RECh-14 P-33RECh-14 P-34RECh-14 P-35RECh-14 P-36RECh-14 P-37RECh-14 P-38RECh-14 P-39RECh-14 P-40RECh-14 P-41RECh-14 P-42RECh-14 P-43RECh-14 P-44RECh-14 P-45RECh-14 P-46RECh-14 P-47RECh-14 P-48RECh-14 P-49RECh-14 P-50RECh-14 P-51RECh-14 P-52RECh-14 P-53RECh-14 P-54RECh-14 P-55RECh-14 P-56RECh-14 P-57RECh-14 P-58RECh-14 P-59RECh-14 P-60RECh-14 P-61RECh-14 P-62RECh-14 P-63RECh-14 P-64RECh-14 P-65RECh-14 P-1PCh-14 P-2PCh-14 P-3PCh-14 P-4PCh-14 P-5PCh-14 P-6PCh-14 P-7PCh-14 P-8P

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