Is there any other information?
Step-by-step explanation:
1 is the starting point since it is on the the axis.
then you would use the rise over run method to get the fraction. it rises by two and runs by 1 which would get you 2/1. so the answer should be y=1+2/1
(it is an addition sign since it is a positive slope)
Answer:
-13.95
Step-by-step explanation:
0.3(-32.48-14.02)
0.3(-46.5)
=-13.95
hope this helps!
![\ln(3x)^2=2\ln(3x)](https://tex.z-dn.net/?f=%5Cln%283x%29%5E2%3D2%5Cln%283x%29)
Take
![y=3x](https://tex.z-dn.net/?f=y%3D3x)
, so that
![\dfrac{\mathrm dy}3=\mathrm dx](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20dy%7D3%3D%5Cmathrm%20dx)
, and you have
![\displaystyle\int\ln(3x)^2\,\mathrm dx=\frac23\int\ln y\,\mathrm dy](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint%5Cln%283x%29%5E2%5C%2C%5Cmathrm%20dx%3D%5Cfrac23%5Cint%5Cln%20y%5C%2C%5Cmathrm%20dy)
Integrate by parts, setting
![u=\ln y](https://tex.z-dn.net/?f=u%3D%5Cln%20y)
and
![\mathrm dv=\mathrm dy](https://tex.z-dn.net/?f=%5Cmathrm%20dv%3D%5Cmathrm%20dy)
, which give
![\mathrm du=\dfrac{\mathrm dy}y](https://tex.z-dn.net/?f=%5Cmathrm%20du%3D%5Cdfrac%7B%5Cmathrm%20dy%7Dy)
and
![v=y](https://tex.z-dn.net/?f=v%3Dy)
. Then
![\displaystyle\frac23\int\ln y\,\mathrm dy=\frac23\left(y\ln y-\int\frac yy\,\mathrm dy\right)=\frac23y\ln y-\frac23y+C](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cfrac23%5Cint%5Cln%20y%5C%2C%5Cmathrm%20dy%3D%5Cfrac23%5Cleft%28y%5Cln%20y-%5Cint%5Cfrac%20yy%5C%2C%5Cmathrm%20dy%5Cright%29%3D%5Cfrac23y%5Cln%20y-%5Cfrac23y%2BC)
which in terms of
![x](https://tex.z-dn.net/?f=x)
is
![\displaystyle\frac23y\ln (3x)-\frac23(3x)+C](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cfrac23y%5Cln%20%283x%29-%5Cfrac23%283x%29%2BC)
![\displaystyle\frac23y\ln x-2x+C](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cfrac23y%5Cln%20x-2x%2BC)
where the last term uses the property that
![\ln(ab)=\ln a+\ln b](https://tex.z-dn.net/?f=%5Cln%28ab%29%3D%5Cln%20a%2B%5Cln%20b)
, and the
![\dfrac23\ln3](https://tex.z-dn.net/?f=%5Cdfrac23%5Cln3)
term is absorbed into
![C](https://tex.z-dn.net/?f=C)
.