2 Points

Help me with this please

Gala2k [10]

Answer: the answer is -5

Step-by-step explanation:

k

6 0

2 years ago

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

Marta has 1 cubic yard of sand to build a wall in the shape of a rectangular prism that is 20 inches tall and 5 inches wide. To

DanielleElmas [232]

Answer:

466,56 inches

Step-by-step explanation:

1 yard = 36 inches

1 cubic yard = 36*36*36 = 46656 cubic inches

46656 = 20*5*l => l = 46656/100 = 466, 56 inches

7 0

3 years ago

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Help please look below

Gwar [14]

A is located, as you look A is past -2 almost hitting -3 making the mark 2.8 so the answer is A

3 0

2 years ago

7.5.5. I usually walk from home to work. This morning, I walked for 10 minutes until I was halfway to work. I then realized that

olya-2409 [2.1K]

Answer:

Given:

I usually walk from home to work. This morning, I walked for 10 minutes until I was halfway to work.

I then realized that I would be late if I kept walking.

I ran the rest of the way. I run twice as fast as I walk.

Find:

The number of minutes in total did it take me to get from home to work

Step-by-step explanation:

Had I kept walking, the second half of my trip would have taken 10 more minutes.

By doubling my speed for the second half of my trip,

I halved the amount of time it took me to finish.

So, the second half of my trip took 5 minutes, for a total trip time of 10+5 = 15 minutes.

The number of minutes in total did it take me to get from home to work is 15 minutes.

3 0

2 years ago

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