Question

Question 11 or 12 whichever u can answer see photo

Answer 1

`-(216)/(5115)`

Step-by-step explanation

(11)

`f(t)=(t^2)/(t^3+4)`

the average value of a function is given by:

`average=(F(b)-f(a))/(b-a)`

Step 1

evaluate the function in the given limits

a)t=3

`\begin{gathered} f(t)=(t^2)/(t^3+4) \\ f(3)=(3^2)/(3^3+4) \\ f(3)=(9)/(27+4)=(9)/(31) \\ f(3)=(9)/(31) \\ so \\ a=3,\text{ f\lparen a\rparen=}(9)/(31) \end{gathered}`

b) t= 6

`\begin{gathered} f(t)=(t^2)/(t^3+4) \\ f(6)=(6^2)/(6^3+4) \\ f(6)=(36)/(216+4)=(36)/(220)=(18)/(110)=(9)/(55) \\ f(6)=(9)/(55) \\ b=6\text{ and F\lparen b\rparen=}(9)/(55) \end{gathered}`

Step 2

now, replace in the formula

`\begin{gathered} average=(F(b)-f(a))/(b-a) \\ average=((9)/(55)-(9)/(31))/(6-3) \\ average=((9)/(55)-(9)/(31))/(3)=(-(216)/(1705))/((3)/(1))=-(216)/(5115) \end{gathered}`

.so the answer is

`-(216)/(5115)`

I hope this helps you