Answer: 12
Step-by-step explanation:
i will tell you the answer later if i find the same question in my homework ok?
We're looking for
such that
, which requires
![\dfrac{\partial f}{\partial x}=xyz^2](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cpartial%20f%7D%7B%5Cpartial%20x%7D%3Dxyz%5E2)
![\dfrac{\partial f}{\partial y}=x^9yz^2](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cpartial%20f%7D%7B%5Cpartial%20y%7D%3Dx%5E9yz%5E2)
![\dfrac{\partial f}{\partial z}=x^9y^2z](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cpartial%20f%7D%7B%5Cpartial%20z%7D%3Dx%5E9y%5E2z)
Integrating both sides of the first PDE wrt
gives
![f(x,y,z)=\dfrac12x^2yz^2+g(y,z)](https://tex.z-dn.net/?f=f%28x%2Cy%2Cz%29%3D%5Cdfrac12x%5E2yz%5E2%2Bg%28y%2Cz%29)
Differenting this wrt
gives
![\dfrac{\partial f}{\partial y}=x^9yz^2=\dfrac12x^2z^2+\dfrac{\partial g}{\partial y}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cpartial%20f%7D%7B%5Cpartial%20y%7D%3Dx%5E9yz%5E2%3D%5Cdfrac12x%5E2z%5E2%2B%5Cdfrac%7B%5Cpartial%20g%7D%7B%5Cpartial%20y%7D)
![\implies\dfrac{\partial g}{\partial y}=\dfrac12x^2z^2(2x^7y-1)](https://tex.z-dn.net/?f=%5Cimplies%5Cdfrac%7B%5Cpartial%20g%7D%7B%5Cpartial%20y%7D%3D%5Cdfrac12x%5E2z%5E2%282x%5E7y-1%29)
but we're assuming
is a function that doesn't depend on
, which is contradicted by this result, and so there is no such
and
is not conservative.
Apnswer:
p = 1
q = -2
Step-by-step explanation:
5p - 2q = 9 eqn 1
3p + 2q = 7 eqn 2
subtract equation 2 from 1
2p = 2
p = 1
Substitute for p in equation 1
5(1) - 2q = 9
5 - 2q = 9
-2q = 4
q = -2