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Sergeeva-Olga [200]
3 years ago
6

Choose the correct equation of the line

Mathematics
1 answer:
r-ruslan [8.4K]3 years ago
8 0

Answer:

b. y=2x-2

Step-by-step explanation:

y=mx+b

m= slope

b=y intercept

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Find an equation of a plane that satisfies the given conditions
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Find a potential function for F or determine that F is not conservative. (If F is not conservative, enter NOT CONSERVATIVE.) F =
xxMikexx [17]

For F to be conservative, we need to have

\dfrac{\partial f}{\partial x}=\cos z

\dfrac{\partial f}{\partial y}=10y

\dfrac{\partial f}{\partial z}=-x\sin z

Integrate the first PDE with respect to x:

\displaystyle\int\frac{\partial f}{\partial x}\,\mathrm dx+\int\cos z\,\mathrm dx\implies f(x,y,z)=x\cos z+g(y,z)

Differentiate with respect to y:

\dfrac{\partial f}{\partial y}=10y=\dfrac{\partial g}{\partial y}\implies g(y,z)=5y^2+h(z)

Now differentiate f with respect to z:

\dfrac{\partial f}{\partial z}=-x\sin z=-x\sin z+\dfrac{\mathrm dh}{\mathrm dz}\implies\dfrac{\mathrm dh}{\mathrm dz}=0\implies h(z)=C

So we have

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so F is indeed conservative.

8 0
3 years ago
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