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Problem 17 Medium Difficulty
In a certain city the temperature (in $ ^\circ F $) $ t $ hours after 9 am was modeled by the function
$$ T(t) = 50 + 14 \sin \frac{\pi t}{12} $$
Find the average temperature during the period from 9 am to 9 pm.
Answer
$T_{a v e} \approx 59^{\circ} F$
Topics
Applications of Integration
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Top Calculus 2 / BC Educators
Anna Marie V.
Campbell University
Heather Z.
Oregon State University
Samuel H.
University of Nottingham
Joseph L.
Boston College
Watch More Solved Questions in Chapter 6
Video Transcript
we know we can use the average value Formula one over B with just 12 months. A, which is zero from 0 12 of 50 was 14. Sign party over 12 g. We know that if you is pi ti over 12 done 12 over pie Do you equals deity? Therefore, we know that we can apply u substitution m plug end. This gives us 50 28 over pi which is 59 degrees Fahrenheit approximately.
Topics
Applications of Integration
Top Calculus 2 / BC Educators
Anna Marie V.
Campbell University
Heather Z.
Oregon State University
Samuel H.
University of Nottingham
Joseph L.
Boston College