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Korvikt [17]
3 years ago
13

Write these in standard form :

Mathematics
1 answer:
kotegsom [21]3 years ago
7 0

8.23\cdot10^6=8.23\cdot1,000,000=8,230,000\\\\2.4\cdot10^5=2.4\cdot100,000=240,000

\text{The scientific notation:}\ a\cdot10^n\ (1\leq a < 10,\ n\in\mathbb{Z})\\\\4\underbrace{50000}_{\leftarrow5}=4.5\cdot10^5\\\\320=3.2\cdot100=3.2\cdot10^2\\\\0.\underbrace{0000006}_{7\rightarrow}73=6.73\cdot10^{-7}\\\\3\underbrace{2100000}_{\leftarrow7}=3.12\cdot10^7

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yuradex [85]
Parameterize the ellipsoid using the augmented spherical coordinates:

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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

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\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}
4 0
3 years ago
4 4/8 + 3/4 what is the answer
Tema [17]
<span>4 4/8 + 3/4
=4 1/2 + 3/4
=4 2/4 + 3/4
= 5 1/4</span>
6 0
3 years ago
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Answer:

Step-by-step explanation:

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Answer:

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hjlf

Answer:

107

Step-by-step explanation:

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2 years ago
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