First one = 9x3=27
Second one 12x9=108
3rd one = 3x4=12
Idk what that last one is
Answer: ![\dfrac{x^2+1}{2}](https://tex.z-dn.net/?f=%5Cdfrac%7Bx%5E2%2B1%7D%7B2%7D)
Step-by-step explanation:
Given
![f(x)=\sqrt{2x-1}](https://tex.z-dn.net/?f=f%28x%29%3D%5Csqrt%7B2x-1%7D)
We can write it as
![\Rightarrow y=\sqrt{2x-1}](https://tex.z-dn.net/?f=%5CRightarrow%20y%3D%5Csqrt%7B2x-1%7D)
Express x in terms of y
![\Rightarrow y^2=2x-1\\\\\Rightarrow x=\dfrac{y^2+1}{2}](https://tex.z-dn.net/?f=%5CRightarrow%20y%5E2%3D2x-1%5C%5C%5C%5C%5CRightarrow%20x%3D%5Cdfrac%7By%5E2%2B1%7D%7B2%7D)
Replace y be x to get the inverse
![\Rightarrow f^{-1}(x)=\dfrac{x^2+1}{2}](https://tex.z-dn.net/?f=%5CRightarrow%20f%5E%7B-1%7D%28x%29%3D%5Cdfrac%7Bx%5E2%2B1%7D%7B2%7D)
To prove, it is inverse of f(x). ![f(f^{-1}(x))=x](https://tex.z-dn.net/?f=f%28f%5E%7B-1%7D%28x%29%29%3Dx)
![\Rightarrow f(f^{-1}(x))=\sqrt{2\times \dfrac{x^2+1}{2}-1}\\\\\Rightarrow f(f^{-1}(x))=\sqrt{x^2+1-1}\\\\\Rightarrow f(f^{-1}(x))=x](https://tex.z-dn.net/?f=%5CRightarrow%20f%28f%5E%7B-1%7D%28x%29%29%3D%5Csqrt%7B2%5Ctimes%20%5Cdfrac%7Bx%5E2%2B1%7D%7B2%7D-1%7D%5C%5C%5C%5C%5CRightarrow%20f%28f%5E%7B-1%7D%28x%29%29%3D%5Csqrt%7Bx%5E2%2B1-1%7D%5C%5C%5C%5C%5CRightarrow%20f%28f%5E%7B-1%7D%28x%29%29%3Dx)
So, they are inverse of each other.
Perpendicular = opposite sign and reciprocal slope
Slope would be 3
Y = 3x + b, plug in point
9 = 3(5) + b, b = -6
Solution: y = 3x - 6
L = rc
= 26.9 * 9*3.14 / 5
= 152.04 to nearest 1/100