Answer:
g(x) = 7√x
Step-by-step explanation:
Parent function: f(x) = √x
Parent function vertically stretched by a factor of 7: g(x) = 7√x
The pattern is: if you multiply the first two numbers in each set you will get the last number in that set
4/4 is a whole making it one.
1 is equal to 1 making 4/4 equal to 1
1. The mode is C. 18
2. The median is B. 16
3. The mean is D. 14.25
4. The median is 2.3
5. The mean is 18
However the
![x_i](https://tex.z-dn.net/?f=x_i)
are chosen, the sum is equivalent to the definite integral,
![\displaystyle\lim_{n\to\infty}\sum_{i=1}^n x_i\cos x_i\Delta x=\int_0^{2\pi}x\cos x\,\mathrm dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Clim_%7Bn%5Cto%5Cinfty%7D%5Csum_%7Bi%3D1%7D%5En%20x_i%5Ccos%20x_i%5CDelta%20x%3D%5Cint_0%5E%7B2%5Cpi%7Dx%5Ccos%20x%5C%2C%5Cmathrm%20dx)
which can be computed via integration by parts. If
![u=x](https://tex.z-dn.net/?f=u%3Dx)
and
![\mathrm dv=\cos x\,\mathrm dx](https://tex.z-dn.net/?f=%5Cmathrm%20dv%3D%5Ccos%20x%5C%2C%5Cmathrm%20dx)
, you have
![\displaystyle\int_0^{2\pi}x\cos x\,\mathrm dx=[uv]_0^{2\pi}-\int_0^{2\pi}v\,\mathrm du](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint_0%5E%7B2%5Cpi%7Dx%5Ccos%20x%5C%2C%5Cmathrm%20dx%3D%5Buv%5D_0%5E%7B2%5Cpi%7D-%5Cint_0%5E%7B2%5Cpi%7Dv%5C%2C%5Cmathrm%20du)
or equivalently,