Question

During a certain24 ​-hour ​period, the temperature at time t​ (measured in hours from the start of the​ period) was T(t)=50+6t-1/3t^2

degrees. What was the average temperature during that​ period?

Answer 1

The value of average temperature during that period=
`58^(\circ)`

Explanation:

We are given that

Temperature at time t is given by

`T(t)=50+6t-(1)/(3)t^2`

We have to find the average temperature during a certain 24-hour period.

We know that

Average value of function

`f_(av)=(1)/(b-a)\int_(a)^(b)f(x)dx`

Using the formula

Average temperature during the period

`=(1)/(24-0)\int_(0)^(24)(50+6t-(1)/(3)t^2)dt`

`=(1)/(24)[50t+3t^2-(1)/(9)t^3]^(24)_(0)`

`=(1)/(24)(50* 24+3(24)^2-(1)/(9)(24)^3)`

`=58^(\circ)`

Hence, the value of average temperature during that period=
`58^(\circ)`