Question

et the temperature in Gotham (the fictional city where Batman lives) in degrees Fahrenheit (°F) t hours after 9 AM be modeled by the function F(t) = 50 + 15 sin πt 12 (a) Find the average value of F, Fave, from t = 0 to t = 12.

Answer 1

Step-by-step explanation:

It is given that, the temperature in Gotham in degrees Fahrenheit (°F) t hours after 9 AM be modeled by the function as :

`F(t)=50+15\ sin((\pi t)/(12))`

We need to find the average value of F from t = 0 to t = 12 s

The average value of an integral over and interval a to b is given by :

`f(c)=\frac{\int\limits^a_b {f(x).dx}}{b-a}`

`F(t)=(1)/(12){\int\limits^(12)_(0) {50+15\ sin((\pi t)/(12)).dt}}`

Using online calculator, the integral is given by :

`F_(avg)=(60\pi +360)/(12\pi)`

`F_(avg)=14.54^(\circ)F`

So, the average value of From t = 0 to t = 12 s is 14.54 degrees Fahrenheit. Hence, this is the required solution.