In a certain city the temperature (in degrees Fahrenheit) t hours after 9am was approximated by the function. How to determine the temperature at 9 am ? and How to find the average temperature during the period from 9 am to 9 pm ?

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Answer 1 · 2016-03-05T20:48:37

#68.276^@F#

The temperature at #9am# is equivalent to #T(0)#, ie #0# hours after 9am, and given by

#T(0)=60+13sin((pi(0))/12)=60^@F#.

The temperature at #9 p m # is #T(12)#, ie #12# hours after 9am, and given by

#T(12)=60+13sin((pi(12))/12)=60^@F#.

We may now apply the formula

#barT(t)=1/(12-0)int_0^12(60+13sin((pit)/12))dt#

#=1/12[60t-(12(13))/picos((pit)/12)]_0^12#

#=1/12[720+156/pi+156/pi]#

#=68.276^@F#