If there is some scalar function
such that
as given, then this
satisfies the following partial differential equations:
![\dfrac{\partial f}{\partial x}=5y^2z^3](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cpartial%20f%7D%7B%5Cpartial%20x%7D%3D5y%5E2z%5E3)
![\dfrac{\partial f}{\partial y}=10xyz^3](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cpartial%20f%7D%7B%5Cpartial%20y%7D%3D10xyz%5E3)
![\dfrac{\partial f}{\partial z}=15xy^2z^2](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cpartial%20f%7D%7B%5Cpartial%20z%7D%3D15xy%5E2z%5E2)
Integrate the first PDE with respect to
:
![f(x,y,z)=5xy^2z^3+g(y,z)](https://tex.z-dn.net/?f=f%28x%2Cy%2Cz%29%3D5xy%5E2z%5E3%2Bg%28y%2Cz%29)
Differentiate with respect to
:
![\dfrac{\partial f}{\partial y}=10xyz^3+\dfrac{\partial g}{\partial y}=10xyz^3\implies\dfrac{\partial g}{\partial y}=0\implies g(y,z)=h(z)](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cpartial%20f%7D%7B%5Cpartial%20y%7D%3D10xyz%5E3%2B%5Cdfrac%7B%5Cpartial%20g%7D%7B%5Cpartial%20y%7D%3D10xyz%5E3%5Cimplies%5Cdfrac%7B%5Cpartial%20g%7D%7B%5Cpartial%20y%7D%3D0%5Cimplies%20g%28y%2Cz%29%3Dh%28z%29)
![f(x,y,z)=5xy^2z^3+h(z)](https://tex.z-dn.net/?f=f%28x%2Cy%2Cz%29%3D5xy%5E2z%5E3%2Bh%28z%29)
Differentiate with respect to
:
![\dfrac{\partial f}{\partial z}=15xy^2z^2+\dfrac{\mathrm dh}{\mathrm dz}=15xy^2z^2\implies\dfrac{\mathrm dh}{\mathrm dz}=0\implies h(z)=C](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cpartial%20f%7D%7B%5Cpartial%20z%7D%3D15xy%5E2z%5E2%2B%5Cdfrac%7B%5Cmathrm%20dh%7D%7B%5Cmathrm%20dz%7D%3D15xy%5E2z%5E2%5Cimplies%5Cdfrac%7B%5Cmathrm%20dh%7D%7B%5Cmathrm%20dz%7D%3D0%5Cimplies%20h%28z%29%3DC)
![f(x,y,z)=5xy^2z^3+C](https://tex.z-dn.net/?f=f%28x%2Cy%2Cz%29%3D5xy%5E2z%5E3%2BC)
So
is indeed conservative.
Answer:
There just reflected so its the same
Step-by-step explanation:
2(x+7)^2=0 would be your answer :)
Answer:
soln,
write the question
=9x^2+1-6x-2×9x^2+25+9x^2+25
=9x^2+1-6x-18x^2+25+9x^2+25
=9x^2-18x^2+9x^2+1+25+25-6x
=51-6x
if(3x+1)^2 mean that (3x+1)has power of 2 and u don't have to use the formula this is the answer
Step-by-step explanation:
it's just BODMAS method
We distribute 3 into X and that's gonna give us 3X then we distribute 3 into 2 and that's gonna give us 6... so 3x-6