Answer:
The value of average temperature during that period=[tex]58^{\circ}[/tex]
Step-by-step explanation:
We are given that
Temperature at time t is given by
[tex]T(t)=50+6t-\frac{1}{3}t^2[/tex]
We have to find the average temperature during a certain 24-hour period.
We know that
Average value of function
[tex]f_{av}=\frac{1}{b-a}\int_{a}^{b}f(x)dx[/tex]
Using the formula
Average temperature during the period
[tex]=\frac{1}{24-0}\int_{0}^{24}(50+6t-\frac{1}{3}t^2)dt[/tex]
[tex]=\frac{1}{24}[50t+3t^2-\frac{1}{9}t^3]^{24}_{0}[/tex]
[tex]=\frac{1}{24}(50\times 24+3(24)^2-\frac{1}{9}(24)^3)[/tex]
[tex]=58^{\circ}[/tex]
Hence, the value of average temperature during that period=[tex]58^{\circ}[/tex]
