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hammer [34]
1 year ago
12

Whats the solution set of the following equation -8×+×+15=-7×+12

Mathematics
1 answer:
Leno4ka [110]1 year ago
8 0

Given data:

The given equation is -8x+x+15=-7x+12.

The given equation can be written as,

\begin{gathered} -8x+x+15=-7x+12 \\ -7x+15=-7x+12 \\ 15=12 \end{gathered}

The above expression is false.

Thus, there is no value of x, so the answer is ϕ.

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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
GUYS PLEASE HELP ME
soldi70 [24.7K]

Answer:

x = 54°       y = 126°

Step-by-step explanation:

Interior angles of a triangle = 180°

Therefore x = 180 - 80 - 46 = 54°

y = 180 - x = 180 - 54 = 126°

6 0
2 years ago
Read 2 more answers
If you saved 2.00 on january 1, 4.00 on february 1, 6.00 on march 1 and so on how much money would you save in a year
Ronch [10]
The answer that I got:

$156


5 0
3 years ago
Find the missing number of each unit rate.<br><br> 20/4=?/1<br> 10/15=?/1
oksano4ka [1.4K]

Answer:

Step-by-step explanation:

divide 20 by four

20/4=5/1

now 10 and 15 can both be divided by 5 since 5 is the greatest common factor

10/15=2/3

7 0
2 years ago
Read 2 more answers
The population of pine bluff is 6791 and is decreasing at a rate of 7 per year.Write the linear equation that models this situat
Anna11 [10]

Answer:

y= 6971 -7 x  OR y = -7x + 6971

Step-by-step explanation:

the 6971 is the original number you started with, you are now decreasing by 7, so you use the value of -7. The x is the number of years that pass by, so the variable x affects the number 7 because it says decreases by 7 per year. The x does not go with 6971 as that number doesn't get directly affected.

3 0
4 years ago
Read 2 more answers
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