In cold weather, we feel colder when the wind blows. This is quantified by the wind chill index W, which is supposed to predict how cold we will feel for a given air temperature T, in degrees Fahrenheit, and wind speed V, in miles/hour. The National Weather Service uses the following formula: W=35.74+0.6215T−35.75V^0.16+0.4275TV^0.16, for T≤50 and V≥3. What is the wind chill index when the air temperature is 25 degrees and the wind speed is 18 miles/hour?
In cold weather, we feel colder when the wind blows. This is quantified by the wind chill index W, which is supposed to predict how cold we will feel for a given air temperature T, in degrees Fahrenheit, and wind speed V, in miles/hour. The National Weather Service uses the following formula:
for T≤50 and V≥3.
What is the wind chill index when the air temperature is 25 degrees and the wind speed is 18 miles/hour?
Answer:
Calculate the partial derivatives WT and WV when T=25 and V=18.
WT=
WV=
Use your answer above to do the following question: When the air temperature is 25 degrees, estimate the change in the wind chill index if the wind speed increases by 2 miles/hour from 18 miles/hour.
Answer:
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