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3 years ago

A. A numberis greater than an - 8 and less than or equal to 4.

Mathematics

1 answer:

densk [106]3 years ago

7 0

Answer:

-8<n≤4

Step-by-step explanation:

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Use the divergence theorem to calculate the surface integral s f · ds; that is, calculate the flux of f across s. f(x, y, z) = x

valkas [14]

$\mathbf f(x,y,z)=x^4\,\mathbf i-x^3z^2\,\mathbf j+4xy^2z\,\mathbf k$
$\mathrm{div}(\mathbf f)=\dfrac{\partial(x^4)}{\partial x}+\dfrac{\partial(-x^3z^2)}{\partial y}+\dfrac{\partial(4xy^2z)}{\partial z}=4x^3+0+4xy^2=4x(x^2+y^2)$

Let $\mathcal D$ be the region whose boundary is $\mathcal S$ . Then by the divergence theorem,

$\displaystyle\iint_{\mathcal S}\mathbf f\cdot\mathrm d\mathbf S=\iiint_{\mathcal D}4x(x^2+y^2)\,\mathrm dV$

Convert to cylindrical coordinates, setting

$x=r\cos\theta$
$y=r\sin\theta$

and keeping $z$ as is. Then the volume element becomes

$\mathrm dV=r\,\mathrm dr\,\mathrm d\theta\,\mathrm dz$

and the integral is

$\displaystyle\iiint_{\mathcal D}4x(x^2+y^2)\,\mathrm dV=\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=1}\int_{z=0}^{z=r\cos\theta+7}4r\cos\theta\cdot r^2\cdot r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta$
$=\displaystyle4\iiint_{\mathcal D}r^4\cos\theta\,\mathrm dz\,\mathrm dr\,\mathrm d\theta$
$=\dfrac{2\pi}3$

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3 years ago

Identify the postulate that proves the triangles are congruent.

Ratling [72]

Answer:

ASA

Step-by-step explanation:

Triangle ABD is congruent to triangle BDC by ASA because angle B in ABD is 30 degrees. Then they give you BD which equals BD by the reflexive property. And finally angle D in ABD is also 30 degrees. In triangle BCD, angle B is 30 degrees, BD = BD, and angle D in BCD is 30 degress. So we have an angle (B), side (BD), and another angle (D)

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3 years ago

Can someone answer this for me? Thanks!

MrRa [10]

Hiii :))

Answer is in the attachment.

Identity used :-

1) cosec² α = 1 + cot² α

Trigonometric Ratio :-

1) cot 30° = √3

_____

Reddam is an expensive school, right?

RainbowSalt2222 ☔

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2 years ago

Read 2 more answers

Audrey is buying a new car for $32,998 she plans to make a down payment of $4200 if she makes monthly payment of $225 for the ne

marta [7]

32,998 -4,200 = 28,798 Total Loan Amount

Monthly Loan Payments = 225 for months = 13,500.00 for five years

This amount doesn't equal the principal so the problem could be worded incorrectly.

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3 years ago

Find the product of (3.7 * 104) and 2. 74 x 103 0.74 x 10 4 74x10 74 x 104 *

padilas [110]

Answer:

your answer is 7.4 X 104 and if you further multiply then you will get 769.6

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3 years ago