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snow_tiger [21]

3 years ago

11

mr.Allen estimated that 50 people at a basketball game were cheering for the vsiting team.Select all of the statement that could

represent this estimate

1 answer:

nata0808 [166]3 years ago

8 0

What are the statements?

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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

What number can you divide 1/4 to get a number smaller than 1/4

stepan [7]

You can divide 1/2 by 1/4

that'll leave you with 1/8, which is smaller than 1/4

8 0

4 years ago

Read 2 more answers

What number needs to be added to both sides of the equation in order to complete the square?

Sever21 [200]

x^2+14x = (x+7)^2

7^2 = 49

so you would add 49 to both sides

5 0

3 years ago

Read 2 more answers

Write the slope-intercept form of the equation for the line. a. y=-8/7x+3/2 b.y= -3/2x+7/8 c.y=-7/8x-3/2 d.y=7/8x+3/2 Write the

fgiga [73]

Answer:

c)

Step-by-step explanation:

(-4,2) ; (4,-5)

$Slope=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\=\frac{-5-2}{4-[-4]}\\\\=\frac{-7}{4+4}\\\\=\frac{-7}{8}$

m = -7/8 ; (-4,2)

equation: y - y1 = m(x - x1)

$y-2=\frac{-7}{8}(x-[-4])\\\\y-2=\frac{-7}{8}(x+4)\\\\y-2=\frac{-7}{8}x +\frac{-7}{8}*4\\\\y=\frac{-7}{8}x-\frac{7}{2}+2\\\\y=\frac{-7}{8}x-\frac{7}{2}+\frac{4}{2}\\\\y=\frac{-7}{8}x-\frac{3}{2}\\$

5 0

3 years ago

Which segment is skew to bd

AVprozaik [17]

<span>Skew lines exist in a three-dimensional geometry. These are lines that are not parallel with each other but do not intersect. They are lines that do not lie on the same plane or non-coplanar. Hope this helps since there is no figure attached to the problem. </span>

6 0

3 years ago