Mathematics: 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?

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During a certain24 -hour period, the temperature

abhibhambhani

16.03.2022

The value of average temperature during that period= $58^{\circ}$

Step-by-step explanation:

We are given that

Temperature at time t is given by

$T(t)=50+6t-\frac{1}{3}t^2$

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

We know that

Average value of function

$f_{av}=\frac{1}{b-a}\int_{a}^{b}f(x)dx$

Using the formula

Average temperature during the period

$=\frac{1}{24-0}\int_{0}^{24}(50+6t-\frac{1}{3}t^2)dt$

$=\frac{1}{24}[50t+3t^2-\frac{1}{9}t^3]^{24}_{0}$

$=\frac{1}{24}(50\times 24+3(24)^2-\frac{1}{9}(24)^3)$

$=58^{\circ}$

Hence, the value of average temperature during that period= $58^{\circ}$

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