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Mathematics

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Yuri [45]3 years ago

4 0

Answer:

STOP REPORTING ME YOU WASTE OF BREATH

Step-by-step explanation:

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Find the volume of the ellipsoid x^2+y^2+9z^2=64

yuradex [85]

Parameterize the ellipsoid using the augmented spherical coordinates:

$\begin{cases}x=\frac18\rho\cos\theta\sin\varphi\\\\y=\frac18\rho\sin\theta\sin\varphi\\\\z=\frac38\rho\cos\varphi\end{cases}$

Then the Jacobian for the change of coordinates is

$\mathbf J=\dfrac{\partial(x,y,z)}{\partial(\rho,\theta,\varphi)}=\begin{bmatrix}\frac18\cos\theta\sin\varphi&-\frac18\rho\sin\theta\sin\varphi&\frac18\rho\cos\theta\cos\varphi\\\\\frac18\sin\theta\sin\varphi&\frac18\rho\cos\theta\sin\varphi&\frac18\rho\sin\theta\cos\varphi\\\frac38\cos\varphi&0&-\frac38\rho\sin\varphi\end{bmatrix}$

which has determinant

$\det\mathbf J=-\dfrac3{512}\rho^2\sin\varphi$

Then the volume of the ellipsoid is given by

$\displaystyle\iiint_E\mathrm dx\,\mathrm dy\,\mathrm dz=\iiint_E|\det\mathbf J|\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi$

where $E$ denotes the spaced contained by the ellipsoid. In particular, we have the definite integral and volume

$\displaystyle\frac3{512}\int_{\varphi=0}^{\varphi=\pi}\int_{\theta=0}^{\theta=2\pi}\int_{\rho=0}^{\rho=1}\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi=\dfrac\pi{128}$

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4 years ago

Which number is the additive inverse of -5

Y_Kistochka [10]

The simple answer would be 5 because te additive inverse means the opposite of what the number is and the opposite of -5 is 5, also you can think of it as what can you add to -5 to get 0 and your answer would be 5

3 0

3 years ago

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Peter sells cards in packs of 12 and envelopes in packs of 27. If Martha wants the same number of each, what is the minimum numb

n200080 [17]

The lowest common multiple of 12 and 27 is 108.

12 x 9 = 108 and
27 x 4 = 108 .

So she has to buy 9 packs of cards ... 108 of them ... and 4 packs of envelopes.

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4 years ago

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The partially filled contingency table gives the frequencies of the data on age (in years) and sex from the residents of a

Nataly_w [17]

Answer:

D. 2/5

Step-by-step explanation:

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3 years ago

Hi can someone please help me.

Dafna11 [192]