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Natasha_Volkova [10]
3 years ago
6

Can someone please help me with this?​

Mathematics
2 answers:
aleksandr82 [10.1K]3 years ago
7 0

Answer:

False

Step-by-step explanation:

Premise: 8n-1 = 2n+8

6n-1 = 8

6n = 9

n = 1.5 Since n must be an integer, this is an extraneous solution. The premise is false.

Scorpion4ik [409]3 years ago
5 0

Answer:

true 8 is the common

please follow me so I will follow you

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3 years ago
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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

Converting to spherical coordinates, we have

\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.
3 0
4 years ago
A line, y = mx + b, passes through the point (10, 3) and is parallel to the line 2x+5y=12.
slava [35]

We have been given that a line y=mx+b passes through the point (10, 3) and is parallel to the line 2x+5y=12. We are asked to find the y-intercept of the line.

First of all we will rewrite our given equation in slope-intercept form as:

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y=-\frac{2}{5}x+\frac{12}{5}

We know that slope of parallel lines is equal, so slope of parallel line to our given line would be -\frac{2}{5}.

Now we will use slope-intercept form of equation to find y-intercept.

y=mx+b, where,

m = Slope,

b = The y-intercept.

Let us substitute m=-\frac{2}{5} and coordinates of point (10,3) in above equation as:

3=-\frac{2}{5}(10)+b

3=-2(2)+b

3=-4+b

3+4=-4+4+b

7=b

Therefore, the y-intercept is 7 and our required equation would be y=-\frac{2}{5}x+7.

5 0
3 years ago
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