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Montano1993 [528]
3 years ago
10

A ( ) has at least on fraction in the numerator, denominator

Mathematics
1 answer:
vaieri [72.5K]3 years ago
6 0

Answer:

rational equation

Step-by-step explanation:

A rational equation is an equation containing at least one fraction whose numerator and denominator are polynomials, \frac{P(x)}{Q(x)}.

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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
−10x + 1 + 7x = 37 i need the answers for that
vaieri [72.5K]
-10x+7x=-3x
3x+1=37
(-1) (-1)
3x=36
(Divide by 3 each side)
3x divided by 3= x
36 divided by 3 = 6
Answer: x=6
4 0
3 years ago
An experiment consists of flipping a single coin followed by rolling a six-sided cube (a die).
Over [174]

Answer:\frac{1}{12}

Step-by-step explanation:

Okay, first, you want to find the probability of getting a head, which would be 1/2 because there are two options and we are only looking for one out of the two. Then, the probability of getting a 6 would be 1/6 because there is only one chance of getting a 6 and there are 6 options. Next, you would have to multiply both quantities to find out what the probability would be of getting both. So it would be \frac{1}{2} ×\frac{1}{6}=\frac{1}{12}

8 0
3 years ago
Read 2 more answers
A movie theatre sold 1,000 tickets and made $7160 in one night. If an adult tickets costs 9$ and a children's costs 5$, how many
victus00 [196]
540 adult tickets were sold and 460 kid tickets were sold
4 0
3 years ago
Given the function f(x) = 3x + 1 what is f(-2)?
Readme [11.4K]

Answer:

-5

Step-by-step explanation:

f(-2) means that -2 is going to be our input in this function.

To solve this, simply substitute -2 for x in the expression given.

If f(x) = 3x+1, then f(-2) = 3(-2) + 1

3(-2)+1 = -6+1 = -5

Hope this helped!

7 0
2 years ago
Read 2 more answers
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