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MakcuM [25]
3 years ago
12

2-3x=8 what does x equal?

Mathematics
2 answers:
juin [17]3 years ago
7 0
If you would like to solve the equation 2 - 3 * x = 8 for x, you can calculate this using the following steps:

2 - 3 * x = 8
-3 * x = 8 - 2
-3 * x = 6    /(-3)
x = 6 / (-3)
x = -2

Result: x equals to -2.
spin [16.1K]3 years ago
7 0
-3x=8-2
-3x=6
 3x=-6
 x=-6/3
 x=-2
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G verify that the divergence theorem is true for the vector field f on the region
Alenkasestr [34]
\mathbf f(x,y,z)=\langle z,y,x\rangle\implies\nabla\cdot\mathbf f=\dfrac{\partial z}{\partial x}+\dfrac{\partial y}{\partial y}+\dfrac{\partial x}{\partial z}=0+1+0=1

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\displaystyle\iiint_E\nabla\cdot\mathbf f(x,y,z)\,\mathrm dV=\int_{\varphi=0}^{\varphi=\pi}\int_{\theta=0}^{\theta=2\pi}\int_{\rho=0}^{\rho=6}\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi=288\pi

On the other hand, we can parameterize the boundary of E by

\mathbf s(u,v)=\langle6\cos u\sin v,6\sin u\sin v,6\cos v\rangle

with 0\le u\le2\pi and 0\le v\le\pi. Now, consider the surface element

\mathrm d\mathbf S=\mathbf n\,\mathrm dS=\dfrac{\mathbf s_v\times\mathbf s_u}{\|\mathbf s_v\times\mathbf s_u\|}\|\mathbf s_v\times\mathbf s_u\|\,\mathrm du\,\mathrm dv
\mathrm d\mathbf S=\mathbf s_v\times\mathbf s_u\,\mathrm du\,\mathrm dv
\mathrm d\mathbf S=36\langle\cos u\sin^2v,\sin u\sin^2v,\sin v\cos v\rangle\,\mathrm du\,\mathrm dv

So we have the surface integral - which the divergence theorem says the above triple integral is equal to -

\displaystyle\iint_{\partial E}\mathbf f\cdot\mathrm d\mathbf S=36\int_{v=0}^{v=\pi}\int_{u=0}^{u=2\pi}\mathbf f(x(u,v),y(u,v),z(u,v))\cdot(\mathbf s_v\times\mathbf s_u)\,\mathrm du\,\mathrm dv
=\displaystyle36\int_{v=0}^{v=\pi}\int_{u=0}^{u=2\pi}(12\cos u\cos v\sin^2v+6\sin^2u\sin^3v)\,\mathrm du\,\mathrm dv=288\pi

as required.
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