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To find: The average temperature during the period from 9 AM to 9 PM. Answer≈59 ℉ Explanation1) Concept: Use the mean value theorem for integral to find the average temperature during the period from 9 AM to 9 PM. 2) Mean Value Theorem for Integrals If f is continuous on a,b then there exists a number c in a,b such that fc=fave=1b-a∫abfx dx that is, ∫abfx dx=fcb-a 3) Given: Tt=50+14sinπt12 4) Calculation: During the period from 9 AM to 9 PM, it completes t=12 hours The average temperature during the period from 9 AM to 9 PM means t=0 to t=12 is, Ttave=112-0∫012Ttdt =112∫01250+14sinπt12dt =112∫01250 dt+∫01214sinπt12dt Integrating, =11250t012-14cosπt12π12012 =1125012-500-14cosπ1212π12-14cos0π12 =1125012-14cosππ12-14cos0π12 =1125012--14-14π12 =1125012--28π12 =112600+336π =112600+106.95 =706.9512 ≈59 ℉ Conclusion: The average temperature during the period from 9 AM to 9 PM≈59 ℉. James Z. In a certain city the temperature (in °F) t hours after 9 AM was modeled by the function . Find the average temperature Tave during the period from 9 AM to 9 PM. (Round your answer to the nearest whole number.) 1 Expert Answer |