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3 years ago

PLEAASE HELP DUE TODAY

Mathematics

1 answer:

Kryger [21]3 years ago

8 0

Answer:

I'm not sure but try 13.5.

Step-by-step explanation:

It might not be correct sorry

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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

Rosey knows that she needs a minimum of $1776 each month to pay all of her expenses. If she works 37 hours a week, with 4 weeks

solong [7]

Answer: $12 an hour

Step-by-step explanation:

Rosey works 37 hours a week and 4 weeks in a month.

Total hours are:

= 37 * 4

= 148 hours

In order to at least cover the $1,776 in expenses she incurs every month, Rosey's hourly pay must be:

= expenses / working hours in month

= 1,776 / 148

= $12 an hour

8 0

3 years ago

The area of a circle is 529 inches. Find the radius.

ruslelena [56]

$\sqrt{529}$
square root it and divide by pi. square root of 529 is 23. then divided by pi (3.14) is 7.32.

6 0

3 years ago

Read 2 more answers

How is this problem factored? 35x^2-57x-44

faust18 [17]

You can use the quadratic formula with it which will be easier
or simple factoring
it will be (5x-11)(7x+4)

7 0

3 years ago

Two friends share 7 cookies equally .How many cookies does each friend get

algol13

Answer:

they would get 3 1/2

Step-by-step explanation:

because if there's two friends and seven cookies one friend we get three and the other one will get three and they could split the other cookie in half so that each Friend can have three cookies and a half if they split

7 0

3 years ago