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stellarik [79]
3 years ago
12

Pleeeeeas helpp mehh pleeeeeas pleeeeease......​

Mathematics
1 answer:
Law Incorporation [45]3 years ago
8 0

Answer:

10

Step-by-step explanation:

Each time she sells the burger she earns $10

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Use stoke's theorem to evaluate∬m(∇×f)⋅ds where m is the hemisphere x^2+y^2+z^2=9, x≥0, with the normal in the direction of the
ludmilkaskok [199]
By Stokes' theorem,

\displaystyle\int_{\partial\mathcal M}\mathbf f\cdot\mathrm d\mathbf r=\iint_{\mathcal M}\nabla\times\mathbf f\cdot\mathrm d\mathbf S

where \mathcal C is the circular boundary of the hemisphere \mathcal M in the y-z plane. We can parameterize the boundary via the "standard" choice of polar coordinates, setting

\mathbf r(t)=\langle 0,3\cos t,3\sin t\rangle

where 0\le t\le2\pi. Then the line integral is

\displaystyle\int_{\mathcal C}\mathbf f\cdot\mathrm d\mathbf r=\int_{t=0}^{t=2\pi}\mathbf f(x(t),y(t),z(t))\cdot\dfrac{\mathrm d}{\mathrm dt}\langle x(t),y(t),z(t)\rangle\,\mathrm dt
=\displaystyle\int_0^{2\pi}\langle0,0,3\cos t\rangle\cdot\langle0,-3\sin t,3\cos t\rangle\,\mathrm dt=9\int_0^{2\pi}\cos^2t\,\mathrm dt=9\pi

We can check this result by evaluating the equivalent surface integral. We have

\nabla\times\mathbf f=\langle1,0,0\rangle

and we can parameterize \mathcal M by

\mathbf s(u,v)=\langle3\cos v,3\cos u\sin v,3\sin u\sin v\rangle

so that

\mathrm d\mathbf S=(\mathbf s_v\times\mathbf s_u)\,\mathrm du\,\mathrm dv=\langle9\cos v\sin v,9\cos u\sin^2v,9\sin u\sin^2v\rangle\,\mathrm du\,\mathrm dv

where 0\le v\le\dfrac\pi2 and 0\le u\le2\pi. Then,

\displaystyle\iint_{\mathcal M}\nabla\times\mathbf f\cdot\mathrm d\mathbf S=\int_{v=0}^{v=\pi/2}\int_{u=0}^{u=2\pi}9\cos v\sin v\,\mathrm du\,\mathrm dv=9\pi

as expected.
7 0
3 years ago
If the temperature degrees above zero are denoted by positive numbers, what does - 10 degrees denoted?
kogti [31]

Answer:

-10 degrees denotes 10 degrees below zero.

Step-by-step explanation:


3 0
3 years ago
|3x−2|=19 please help quick thanks
12345 [234]

Answer:

x=7,-17/3

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Cant solve this please help me <br><br> 9x-2y=8 <br> Y=2x+1
ki77a [65]
Substitute 2x+1 where y is in the equation:

9x-2(2x+1)=8

Then distribute the -2(2x+1)

9x-4x+2=8

Then combine like terms (the x)

5x+2=8

Then do -2 on both side of the equation sign

5x+2=8
- 2 -2

Then you'd get

5x=6

Then divide 5 on both sides

X= 1.2
5 0
3 years ago
Read 2 more answers
Can someone please show me how to divide 22 and 121 please and take your time explaining so that way I can understand it. Thank
Aleonysh [2.5K]

When dividing 22 into 121 , you are cosidering how many times 22 goes into 121. This is called division.

Now how do we use division to find this?

well we do 22 over 121 or 22/121

The next step is the conversion to decimal.

How do we figure this out? well we use multiplication through the remainder theorem. The way this works is we figure out how many times 121 goes into a quantity of another number so,

121 goes into 22 how many times. Well 0, thus by the reaminder theorem we will add a zero assuming that we put a decimal place so now we know the number is atleast .XX

Now we have 220, so how many times does 121 go into 220? Well 1. We can add that to our number .1XX and we subtract that from 220 and then add a zero.

220-121 is 99 plus add a zero so we now have 990. 121 goes into 990 how many times? 8 times so we know the number is .18

This process could be continued forever, but there is no need. I hope I explained this well. Explaining core concepts like this generally should be done in person with someone.

7 0
3 years ago
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