In a certain city the temperature (in °f) t hours after 9 am was modeled by the function t(t) = 54 + 11 sin πt 12 . find the average temperature tave during the period from 9 am to 9 pm. (round your answer to the nearest whole number.)

Step-by-step explanation:

Given :

To Find :  Find the average temperature Tave during the period from 9 AM to 9 PM.

Solution:

Where t is hours after 9 AM

Now we are supposed to find the average temperature Tave during the period from 9 AM to 9 PM

Period : 9 a.m. to 9 p.m.

Hours between 9 am to 9 pm  = 12

Interval of function: [0,12]

So, we will use mean value theorem

let

u(0)=0

u(12)=π

Now apply this substitution on right integral

So,

Hence the average temperature Tave during the period from 9 AM to 9 PM is

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step-by-step explanation:

1+2+3+4+5+6+7+8+9+10 = 55

2*10 = 20

55-20 = 35