we know its diameter is 12, thus its radius must be half that, or 6.
![\bf \textit{area of a circle}\\\\ A=\pi r^2~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=6 \end{cases}\implies A=\pi 6^2\implies A=36\pi \implies A\approx 113.097](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Barea%20of%20a%20circle%7D%5C%5C%5C%5C%20A%3D%5Cpi%20r%5E2~~%20%5Cbegin%7Bcases%7D%20r%3Dradius%5C%5C%5B-0.5em%5D%20%5Chrulefill%5C%5C%20r%3D6%20%5Cend%7Bcases%7D%5Cimplies%20A%3D%5Cpi%206%5E2%5Cimplies%20A%3D36%5Cpi%20%5Cimplies%20A%5Capprox%20113.097)
Answer: The answer is ![2x^2+23x+66.](https://tex.z-dn.net/?f=2x%5E2%2B23x%2B66.)
Step-by-step explanation: The given functions are
![f(x)=2x^2+3x+1,\\\\g(x)=x+5.](https://tex.z-dn.net/?f=f%28x%29%3D2x%5E2%2B3x%2B1%2C%5C%5C%5C%5Cg%28x%29%3Dx%2B5.)
We are to find f(g(x)). To do this, first we need to evaluate g(x) and then we will apply the function f on the resulting function.
The evaluation is as follows:
![f(g(x))=f(x+5)=2(x+5)^2+3(x+5)+1=2(x^2+10x+25)+3x+15+1\\\\\Rightarrow f(g(x))=2x^2+23x+66.](https://tex.z-dn.net/?f=f%28g%28x%29%29%3Df%28x%2B5%29%3D2%28x%2B5%29%5E2%2B3%28x%2B5%29%2B1%3D2%28x%5E2%2B10x%2B25%29%2B3x%2B15%2B1%5C%5C%5C%5C%5CRightarrow%20f%28g%28x%29%29%3D2x%5E2%2B23x%2B66.)
Thus, the correct answer is ![2x^2+23x+66.](https://tex.z-dn.net/?f=2x%5E2%2B23x%2B66.)
As the sum of marks of others remain unchanged , let their sum be x . As the mean using 83 was 40 , we have ,
(x +83)/100 = 40
x + 83 = 4000
x = 3917
Now mean using 53 ,
(x +53)/100
(3917+53)/100
39.7.
Hope it helps , plz mark as brainiest :-)