2/7 because there is a total of 7 people and they are 2 out of that 7
Answer:
y=2x-3
Step-by-step explanation:
2x=y+3
2x-3=y
35 = 4x+3
If they're vertical then they're worth the same or equal. So 4x+3 is equal to 35 and then you solve for x from there.
Integration by parts will help here. Letting
![u=\arctan x](https://tex.z-dn.net/?f=u%3D%5Carctan%20x)
and
![\mathrm dv=\mathrm dx](https://tex.z-dn.net/?f=%5Cmathrm%20dv%3D%5Cmathrm%20dx)
, you end up with
![\mathrm du=\dfrac{\mathrm dx}{1+x^2}](https://tex.z-dn.net/?f=%5Cmathrm%20du%3D%5Cdfrac%7B%5Cmathrm%20dx%7D%7B1%2Bx%5E2%7D)
and
![v=x](https://tex.z-dn.net/?f=v%3Dx)
. Now
![\displaystyle\int\arctan x\,\mathrm dx=uv-\int v\,\mathrm du](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint%5Carctan%20x%5C%2C%5Cmathrm%20dx%3Duv-%5Cint%20v%5C%2C%5Cmathrm%20du)
![\displaystyle\int\arctan x\,\mathrm dx=x\arctan x-\int\frac x{1+x^2}\,\mathrm dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint%5Carctan%20x%5C%2C%5Cmathrm%20dx%3Dx%5Carctan%20x-%5Cint%5Cfrac%20x%7B1%2Bx%5E2%7D%5C%2C%5Cmathrm%20dx)
For the remaining integral, setting
![y=1+x^2](https://tex.z-dn.net/?f=y%3D1%2Bx%5E2)
gives
![\dfrac{\mathrm dy}2=x\,\mathrm dx](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20dy%7D2%3Dx%5C%2C%5Cmathrm%20dx)
, so
![\displaystyle\int\frac x{1+x^2}\,\mathrm dx=\frac12\int\frac{\mathrm dy}y=\frac12\ln|y|+C=\frac12\ln(1+x^2)+C](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint%5Cfrac%20x%7B1%2Bx%5E2%7D%5C%2C%5Cmathrm%20dx%3D%5Cfrac12%5Cint%5Cfrac%7B%5Cmathrm%20dy%7Dy%3D%5Cfrac12%5Cln%7Cy%7C%2BC%3D%5Cfrac12%5Cln%281%2Bx%5E2%29%2BC)
Putting everything together, you end up with