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Colt1911 [192]
3 years ago
5

Which phrase includes “being equal to 50”?

Mathematics
1 answer:
Afina-wow [57]3 years ago
3 0
What is being equal to 50
- 5*10 
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Evaluate c (y + 7 sin(x)) dx + (z2 + 9 cos(y)) dy + x3 dz where c is the curve r(t) = sin(t), cos(t), sin(2t) , 0 ≤ t ≤ 2π. (hin
saw5 [17]
Treat \mathcal C as the boundary of the region \mathcal S, where \mathcal S is the part of the surface z=2xy bounded by \mathcal C. We write

\displaystyle\int_{\mathcal C}(y+7\sin x)\,\mathrm dx+(z^2+9\cos y)\,\mathrm dy+x^3\,\mathrm dz=\int_{\mathcal C}\mathbf f\cdot\mathrm d\mathbf r

with \mathbf f=(y+7\sin x,z^2+9\cos y,x^3).

By Stoke's theorem, the line integral is equivalent to the surface integral over \mathcal S of the curl of \mathbf f. We have


\nabla\times\mathbf f=(-2z,-3x^2,-1)

so the line integral is equivalent to

\displaystyle\iint_{\mathcal S}\nabla\times\mathbf f\cdot\mathrm d\mathbf S
=\displaystyle\iint_{\mathcal S}\nabla\times\mathbf f\cdot\left(\dfrac{\partial\mathbf s}{\partial u}\times\dfrac{\partial\mathbf s}{\partial v}\right)\,\mathrm du\,\mathrm dv


where \mathbf s(u,v) is a vector-valued function that parameterizes \mathcal S. In this case, we can take

\mathbf s(u,v)=(u\cos v,u\sin v,2u^2\cos v\sin v)=(u\cos v,u\sin v,u^2\sin2v)

with 0\le u\le1 and 0\le v\le2\pi. Then

\mathrm d\mathbf S=\left(\dfrac{\partial\mathbf s}{\partial u}\times\dfrac{\partial\mathbf s}{\partial v}\right)\,\mathrm du\,\mathrm dv=(2u^2\cos v,2u^2\sin v,-u)\,\mathrm du\,\mathrm dv

and the integral becomes

\displaystyle\iint_{\mathcal S}(-2u^2\sin2v,-3u^2\cos^2v,-1)\cdot(2u^2\cos v,2u^2\sin v,-u)\,\mathrm du\,\mathrm dv
=\displaystyle\int_{v=0}^{v=2\pi}\int_{u=0}^{u=1}u-6u^4\sin^3v-4u^4\cos v\sin2v\,\mathrm du\,\mathrm dv=\pi<span />
4 0
3 years ago
I make $348 a week at my new job. what is my yearly salary?
rosijanka [135]

Answer:

$18,096 a year

Step-by-step explanation:

There are around 52 weeks in a year. You make $348 a week.

52 x 348 = $18,096

3 0
2 years ago
Read 2 more answers
Z^2+1+y when y=4, and z=3.
OlgaM077 [116]
3^2+1+4=14 the answers 14
7 0
2 years ago
<img src="https://tex.z-dn.net/?f=%5Csqrt%7B%5Cfrac%7B-140%7D%7B%5Csqrt%7B28%7D%20%7D" id="TexFormula1" title="\sqrt{\frac{-140}
Zanzabum

​

​
This is the answer

8 0
2 years ago
Whats the radius for the circle? x^2+2x+y^2+4y-6=0
MAXImum [283]

Answer:

r = \sqrt{11}

Step-by-step explanation:

So we need to complete the square for both parts of the equation

First though we can add the 6 to the other side so we have x² + 2x + y² + 4y = 6

So first we can complete the square for x² + 2x

To do so we need to use (\frac{b}{2} )^{2} to figure out the number we need to add to both sides

In this case our b is 2, so substituting this in we get (\frac{2}{2} )^{2} =(1)^{2} =1

Here we add 1 to both sides and now we have x² + 2x + 1 + y² + 4y = 6 + 1

Now we can follow the same steps to complete the square for y² + 4y

Here our b is 4, so substituting this in we get (\frac{4}{2} )^{2}=(2)^{2} =4

Now we add 4 to both sides and now we have x² + 2x + 1 + y² + 4y + 4 = 6 + 1 + 4

Now condensing everything we have (x + 1)² + (y + 2)² = 11

The formula for a circle is (x - h)² + (y - k)² = r²

In our equation we have r² = 11

To find the radius we need to take the square root of both sides \sqrt{r^{2}}  =\sqrt{11} to get r = \sqrt{11}

5 0
3 years ago
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