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2 years ago

Which point is the intersection of RS and VT?

Mathematics

1 answer:

Ilya [14]2 years ago

3 0

Answer:

point U

Step-by-step explanation:

I learned this before

Hope this helps

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Let f(x,y,z) = ztan-1(y2) i + z3ln(x2 + 1) j + z k. find the flux of f across the part of the paraboloid x2 + y2 + z = 3 that li

Sophie [7]

Consider the closed region $V$ bounded simultaneously by the paraboloid and plane, jointly denoted $S$ . By the divergence theorem,

$\displaystyle\iint_S\mathbf f(x,y,z)\cdot\mathrm dS=\iiint_V\nabla\cdot\mathbf f(x,y,z)\,\mathrm dV$

And since we have

$\nabla\cdot\mathbf f(x,y,z)=1$

the volume integral will be much easier to compute. Converting to cylindrical coordinates, we have

$\displaystyle\iiint_V\nabla\cdot\mathbf f(x,y,z)\,\mathrm dV=\iiint_V\mathrm dV$
$=\displaystyle\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=1}\int_{z=2}^{z=3-r^2}r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta$
$=\displaystyle2\pi\int_{r=0}^{r=1}r(3-r^2-2)\,\mathrm dr$
$=\dfrac\pi2$

Then the integral over the paraboloid would be the difference of the integral over the total surface and the integral over the disk. Denoting the disk by $D$ , we have

$\displaystyle\iint_{S-D}\mathbf f\cdot\mathrm dS=\frac\pi2-\iint_D\mathbf f\cdot\mathrm dS$

Parameterize $D$ by

$\mathbf s(u,v)=u\cos v\,\mathbf i+u\sin v\,\mathbf j+2\,\mathbf k$
$\implies\mathbf s_u\times\mathbf s_v=u\,\mathbf k$

which would give a unit normal vector of $\mathbf k$ . However, the divergence theorem requires that the closed surface $S$ be oriented with outward-pointing normal vectors, which means we should instead use $\mathbf s_v\times\mathbf s_u=-u\,\mathbf k$ .

Now,

$\displaystyle\iint_D\mathbf f\cdot\mathrm dS=\int_{u=0}^{u=1}\int_{v=0}^{v=2\pi}\mathbf f(x(u,v),y(u,v),z(u,v))\cdot(-u\,\mathbf k)\,\mathrm dv\,\mathrm du$
$=\displaystyle-4\pi\int_{u=0}^{u=1}u\,\mathrm du$
$=-2\pi$

So, the flux over the paraboloid alone is

$\displaystyle\iint_{S-D}\mathbf f\cdot\mathrm dS=\frac\pi2-(-2\pi)=\dfrac{5\pi}2$

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3 years ago

Mr. Thomas deposited 2500 in a new bank account. The bank pays 6.5% interest compounded annually on this account. He makes no de

kotykmax [81]

Answer:

ghjghf

Step-by-step explanation:

8 0

3 years ago

PLEASE PLEASE HELP 50 POINTS

Crank

Answer:

The claim is " oreos are the most popular cookie at my house". The evidence is because you said that " oreos run out twice as fast as snickerdoodles." The reasoning is because my family eats twice as many oreos than snickerdoodles.

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3 years ago

The formula that describes an objects motion is given by s=ut+1/2at^2, where s is the distance traveled, u is the initial veloci

attashe74 [19]

We have the following equation:
s = ut + 1 / 2at ^ 2
Clear a for the equation:
1 / 2at ^ 2 = s-ut
at ^ 2 = 2s-2ut
a = 2s / t ^ 2-2ut / t ^ 2
Rewriting:
a = (2s-2ut) / (t ^ 2)
Answer:
An equation that represents a in terms of other variables is:
C. 2s-2ut / t ^ 2

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3 years ago

What is the parallel slope intercept form pls answerr

lys-0071 [83]

Answer:

the paralell slope is -4. The slope intercept equation is -4x-4

Step-by-step explanation:

hope this helps!

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3 years ago