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3 years ago

The triangles below are similar. Find the value of x. 9 8 10.5 11

Mathematics

1 answer:

RoseWind [281]3 years ago

8 0

X=9
This is the answer because the relationship is dividing by 2.
14÷2=7 so 18÷2=9

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The amount of money, in dollars, Sarah has in her savings account is modeled as a function of time in months. This function is r

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330.60.330.60.330.60.

Step-by-step explanation:

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3 years ago

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Jesse added two more numbers to his expression, but the sum did not change. What could the two new numbers be? Explain why the n

kenny6666 [7]

Answer:

0 and 0

Step-by-step explanation:

The only number that can be applied to the expression without changing the sum is 0, for example 5 + 10 = 15, adding 2 0's will be 0 + 5 + 10 + 0 = 15 :D

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Evaluate the surface integral:S

rjkz [21]

Assuming $S$ does not include the plane $z=0$ , we can parameterize the region in spherical coordinates using

$\mathbf r(u,v)=\left\langle3\cos u\sin v,3\sin u\sin v,3\cos v\right\rangle$

where $0\le u\le2\pi$ and $0\le v\le\dfrac\pi/2$ . We then have

$x^2+y^2=9\cos^2u\sin^2v+9\sin^2u\sin^2v=9\sin^2v$
$(x^2+y^2)=9\sin^2v(3\cos v)=27\sin^2v\cos v$

Then the surface integral is equivalent to

$\displaystyle\iint_S(x^2+y^2)z\,\mathrm dS=27\int_{u=0}^{u=2\pi}\int_{v=0}^{v=\pi/2}\sin^2v\cos v\left\|\frac{\partial\mathbf r(u,v)}{\partial u}\times \frac{\partial\mathbf r(u,v)}{\partial u}\right\|\,\mathrm dv\,\mathrm du$

We have

$\dfrac{\partial\mathbf r(u,v)}{\partial u}=\langle-3\sin u\sin v,3\cos u\sin v,0\rangle$
$\dfrac{\partial\mathbf r(u,v)}{\partial v}=\langle3\cos u\cos v,3\sin u\cos v,-3\sin v\rangle$
$\implies\dfrac{\partial\mathbf r(u,v)}{\partial u}\times\dfrac{\partial\mathbf r(u,v)}{\partial v}=\langle-9\cos u\sin^2v,-9\sin u\sin^2v,-9\cos v\sin v\rangle$
$\implies\left\|\dfrac{\partial\mathbf r(u,v)}{\partial u}\times\dfrac{\partial\mathbf r(u,v)}{\partial v}\|=9\sin v$

So the surface integral is equivalent to

$\displaystyle243\int_{u=0}^{u=2\pi}\int_{v=0}^{v=\pi/2}\sin^3v\cos v\,\mathrm dv\,\mathrm du$
$=\displaystyle486\pi\int_{v=0}^{v=\pi/2}\sin^3v\cos v\,\mathrm dv$
$=\displaystyle486\pi\int_{w=0}^{w=1}w^3\,\mathrm dw$

where $w=\sin v\implies\mathrm dw=\cos v\,\mathrm dv$ .

$=\dfrac{243}2\pi w^4\bigg|_{w=0}^{w=1}$
$=\dfrac{243}2\pi$

4 0

3 years ago

Stock A ‘s returns have a standard deviation of 0.5, and stock B’s returns have standard deviation of 0.6.The correlation coeffi

galben [10]

Answer:

The variance of the profile is 0.2179.

Step-by-step explanation:

We are given the following in the question:

$\sigma_A = 0.5\\\sigma_B = 0.6\\\rho_{A,B} = 0.5\\w_A = 70\% = 0.7\\w_B = 30\% = 0.3$