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Inga [223]
3 years ago
12

Verify that the divergence theorem is true for the vector field f on the region

Mathematics
1 answer:
schepotkina [342]3 years ago
4 0
\mathbf f(x,y,z)=5x\,\mathbf i+xy\,\mathbf j+2xz\,\mathbf k

\mathrm{div}(\mathbf f)=\dfrac{\partial(5x)}{\partial x}+\dfrac{\partial(xy)}{\partial y}+\dfrac{\partial(2xz)}{\partial z}=5+x+2x=5+3x


By the divergence theorem, the flux of \mathbf f across the boundary of E is given by


\displaystyle\iint_{\mathcal S}\mathbf f\cdot\mathrm d\mathbf S=\iiint_E\mathrm{div}(\mathbf f)\,\mathrm dV

=\displaystyle\int_{z=0}^{z=2}\int_{y=0}^{y=2}\int_{x=0}^{x=2}(5+3x)\,\mathrm dx\,\mathrm dy\,\mathrm dz=64
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Two cities are 3450 miles apart. A plane leaves one of​ them, traveling towards the other at an average speed of 310 miles per h
Amiraneli [1.4K]

Answer:

5 hours.

Step-by-step explanation:

let they meet after t hours.

310t+380t=3450

690t=3450

69t=345

t=345/69=5

8 0
2 years ago
jody wants to figure out how he spends his time. currently, he spends 12 days out of a 30-day month practicing the piano. How mu
shtirl [24]

Answer:

percent- 40%

decimal- 0.4

percent- 2/5

Step-by-step explanation:

you divide 30 by 12 because he practices piano 12/30 days of the month

3 0
3 years ago
PLEASE ANSWER FAST AS YOU CAN and answer like
OLga [1]

Answer:

number 1. answer is  5

number 2. answer is  2 1/2

number 3. answer is 9/16

number 4. answer is 45.7

number 5. answer is 18.7

8 0
2 years ago
Read 2 more answers
5.) $28,000 invested at a rate of 4% compounded annually
liq [111]

Answer:

ok so we know the amount we know the interest amount but we do know know the period of time so the equation would look like this

28000(0.4)T=I

T=Time

I=interest

3 0
3 years ago
Plz hurry, brainliest and lots of points plz explain answer and only answer if you are actually gonna do it.
Citrus2011 [14]

Answer and Step-by-step explanation:

1st box:

0, -3

2nd box

-2, -9/4

3rd box:

2, -3/2

4th box:

4, 0

Btw 0, -2, 2, 4 are in the x-coordinate column if you didn’t know, and 1, -9/4, -3/2 are in the y-coordinate column

Basically to solve if you plug in 0 into x, so basically it’s 3(0)-4y=12, which you simplify gives you 0-4y=12, subtract 0 from 12 which is 12 and then do 12 divided by -4 and then you get y = -3 and that’s how you get the box answer

Idk how to the rest srry lol!

3 0
3 years ago
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