Question

Question 20 In a certain city, the temperature (in °F)t hours after 9:00 AM was modeled by the function art T(t) = 50 + 14 sin Which expression represents the average temperature during the 12 period from 10:00 AM to 5:00 PM? art dt 12 0 1 S (50 +14 sin (T) S (50 50+ 14 sin dt 50 + 14 sin dt 12 сле 50 + 14 sin dt 12 1° (50 50 + 14 sin (F)) dt 12

Answer 1

$T(t)=50+14sin\left ( \frac{\pi t}{12} \right )$

periods from 10 am to 5 pm , t = hours after 9 am

therefore interval of function [ 1 , 8 ]

$T_{ave}=\frac{1}{b-a}\int_{a}^{b}T(t)dt$

  $T_{ave}=\frac{1}{7}\int_{1}^{8}50+14sin\left ( \frac{\pi t}{12} \right )dt$