Answer: xsquared + 9x - 11
Step-by-step explanation:
We're looking for a scalar function
such that
. That is,
![\dfrac{\partial f}{\partial x}=2x-6y](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cpartial%20f%7D%7B%5Cpartial%20x%7D%3D2x-6y)
![\dfrac{\partial f}{\partial y}=-6x+6y-7](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cpartial%20f%7D%7B%5Cpartial%20y%7D%3D-6x%2B6y-7)
Integrate the first equation with respect to
:
![f(x,y)=x^2-6xy+g(y)](https://tex.z-dn.net/?f=f%28x%2Cy%29%3Dx%5E2-6xy%2Bg%28y%29)
Differentiate with respect to
:
![-6x+6y-7=-6x+\dfrac{\mathrm dg}{\mathrm dy}\implies\dfrac{\mathrm dg}{\mathrm dy}=6y-7](https://tex.z-dn.net/?f=-6x%2B6y-7%3D-6x%2B%5Cdfrac%7B%5Cmathrm%20dg%7D%7B%5Cmathrm%20dy%7D%5Cimplies%5Cdfrac%7B%5Cmathrm%20dg%7D%7B%5Cmathrm%20dy%7D%3D6y-7)
Integrate with respect to
:
![g(y)=3y^2-7y+C](https://tex.z-dn.net/?f=g%28y%29%3D3y%5E2-7y%2BC)
So
is indeed conservative with the scalar potential function
![f(x,y)=x^2-6xy+3y^2-7y+C](https://tex.z-dn.net/?f=f%28x%2Cy%29%3Dx%5E2-6xy%2B3y%5E2-7y%2BC)
where
is an arbitrary constant.
-47 = x + 15
Rearrange it to isolate x:
-47 - 15 = x
-62 = x
Answer:
7 in both boxes
Step-by-step explanation:
In the picture, it shows
4 (x - 3) = 20
and then it shows
4 (x) - 4 (3) = 20
so practically you separate the x and 3 and put them in parentheses and then put a 4 next to both of them.
It should be the same as your question.
7 x (8 - 3)
and then separate 8 and 3 and put a 7 next to both of them.
( 7 x 8) - ( 7 x 3)
Hope it helps and have a great day! =D
~sunshine~