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Novosadov [1.4K]
3 years ago
9

1821.5/0.7 ... can someone please explain and answer this? Thank you SO much!!

Mathematics
1 answer:
S_A_V [24]3 years ago
8 0
So you cant have a decimal in your divisor which means the problem sill become 18215/7 if that helps
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For F to be conservative, we need to have

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

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\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

f(x,y,z)=x\cos z+5y^2+C

so F is indeed conservative.

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3 years ago
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3 years ago
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