In order for <em>F</em> to be conservative, there must be a scalar function <em>f</em> such that the gradient of <em>f</em> is equal to <em>F</em>. This means
![\dfrac{\partial f}{\partial x}=3x^2-2y^2](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cpartial%20f%7D%7B%5Cpartial%20x%7D%3D3x%5E2-2y%5E2)
![\dfrac{\partial f}{\partial y}=4xy+4](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cpartial%20f%7D%7B%5Cpartial%20y%7D%3D4xy%2B4)
Integrate both sides of the first equation with respect to <em>x</em> :
![f(x,y)=x^3-2xy^2+g(y)](https://tex.z-dn.net/?f=f%28x%2Cy%29%3Dx%5E3-2xy%5E2%2Bg%28y%29)
Differentiate both sides with respect to <em>y</em> :
![\dfrac{\partial f}{\partial y}=-4xy+\dfrac{\mathrm dg}{\mathrm dy}=4xy+4\implies\dfrac{\mathrm dg}{\mathrm dy}=8xy+4](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cpartial%20f%7D%7B%5Cpartial%20y%7D%3D-4xy%2B%5Cdfrac%7B%5Cmathrm%20dg%7D%7B%5Cmathrm%20dy%7D%3D4xy%2B4%5Cimplies%5Cdfrac%7B%5Cmathrm%20dg%7D%7B%5Cmathrm%20dy%7D%3D8xy%2B4)
But we assume <em>g</em> is a function of <em>y</em>, which means its derivative can't possibly contain <em>x</em>, so there is no scalar function <em>f</em> whose gradient is <em>F</em>. Therefore <em>F</em> is not conservative.
<span>14+2y+3-6y=
14+3+2y-6y=
17-4y</span>
Answer:
1 * 10^12
Step-by-step explanation:
Scientific notation is a representation of a large number in a short form. The answer, 1*10^12 (read as ten to the twelfth power) essentially says that the number when expanded is 1 with 12 zeros appended to it. If you did a number like 7 trillion you would have 7 * 10^12.
Same thing can be applied for 1,000,000 (one million).
1 * 10^6 because one million has 6 zeros appended to it.
I'm pretty sure its c
You just multiply 13 and 52