Explanation Given: T ( t ) = 20 + 5 cos ( π t 12 ) For part a) [ t 1 , t 2 ]=[0,24] For part b)[ t 1 , t 2 ]=[2,6] Formula used: Average temperature= 1 t 2 − t 1 ∫ t 1 t 2 T ( t ) d t over the time period [ t 1 , t 2 ] Calculation: Average temperature= 1 t 2 − t 1 ∫ t 1 t 2 T ( t ) d t For part a : Put t 2 = 24 and t 1 = 0 = 1 24 − 0 ∫ 0 24 ( 20 + 5 cos ( π t 12 ) ) d t = 1 24 ∫ 0 24 20 d t + 1 24 ∫ 0 24 5 cos ( π t 12 ) d t = 1 24 × 20 ∫ 0 24 1 d t + 1 24 × 5 ∫ 0 24 cos ( π t 12 ) d t = 5 6 [ x ] 0 24 + 5 24 [ sin ( π t 12 ) ( π 12 ) ] 0 24 ...

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Question

Chapter 6.2, Problem 49E

To determine

To find: The average temperature of museum over the time period [0, 24] and [2,6] if the temperature varies according to $T (t) = 20 + 5 \cos (\frac{π t}{12})$ .

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Chapter 6.2, Problem 48E

Chapter 6.2, Problem 50E

Chapter 6 Solutions

Calculus - Standalone book

Ch. 6.1 - Prob. 1PQ Ch. 6.1 - Prob. 2PQ Ch. 6.1 - Prob. 3PQ Ch. 6.1 - Prob. 4PQ Ch. 6.1 - Prob. 5PQ Ch. 6.1 - Prob. 6PQ Ch. 6.1 - Prob. 1E Ch. 6.1 - Prob. 2E Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E

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The average temperature of museum over the time period [0, 24] and [2,6] if the temperature varies according to T ( t ) = 20 + 5 cos ( π t 12 ) .

Solution Summary: The author calculates the average temperature of the museum over the time period [0,24] and [2,6] if the temperature varies according to T ( t ) = 20 + 5 cos

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To find: The average temperature of museum over the time period [0, 24] and [2,6] if the temperature varies according to $T (t) = 20 + 5 \cos (\frac{π t}{12})$ .

Want to see the full answer?

Chapter 6 Solutions

The average temperature of museum over the time period [0, 24] and [2,6] if the temperature varies according to T ( t ) = 20 + 5 cos ( π t 12 ) .

Solution Summary: The author calculates the average temperature of the museum over the time period [0,24] and [2,6] if the temperature varies according to T ( t ) = 20 + 5 cos

Videos

To find: The average temperature of museum over the time period [0, 24] and [2,6] if the temperature varies according to T(t)=20+5cos(πt12).

Want to see the full answer?

Chapter 6 Solutions

To find: The average temperature of museum over the time period [0, 24] and [2,6] if the temperature varies according to $T (t) = 20 + 5 \cos (\frac{π t}{12})$ .