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3 years ago

What is the slope and y-intercept?

Mathematics

1 answer:

allsm [11]3 years ago

4 0

Answer:

7 is the y-intercept

slope is 2/1

Step-by-step explanation:

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g Use Stokes' Theorem to evaluate C F · dr where C is oriented counterclockwise as viewed from above. F(x, y, z) = 7yi + xzj + (

Sati [7]

By Stokes' theorem,

$\displaystyle\int_C\vec F\cdot\mathrm d\vec r=\iint_S(\nabla\times\vec F)\cdot\mathrm d\vec S$

where $S$ is any oriented surface with boundary $C$ . We have

$\vec F(x,y,z)=7y\,\vec\imath+xz\,\vec\jmath+(x+y)\,\vec k$

$\implies\nabla\times\vec F(x,y,z)=(1-x)\,\vec\imath-\vec\jmath+(z-7)\,\vec k$

Take $S$ to be the ellipse that lies in the plane $z=y+9$ with boundary on the cylinder $x^2+y^2=1$ . Parameterize $S$ by

$\vec s(u,v)=u\cos v\,\vec\imath+u\sin v\,\vec\jmath+(u\sin v+9)\,\vec k$

with $0\le u\le1$ and $0\le v\le2\pi$ . Take the normal vector to $S$ to be

$\vec s_u\times\vec s_v=-u\,\vec\jmath+u\,\vec k$

Then we have

$\displaystyle\int_C\vec F\cdot\mathrm d\vec r=\iint_S(\nabla\times\vec F)\cdot\mathrm d\vec S$

$=\displaystyle\int_0^{2\pi}\int_0^1\big((1-u\cos v)\,\vec\imath-\vec\jmath+(u\sin v+2)\,\vec k\big)\cdot\big(-u\,\vec\jmath+u\,\vec k\big)\,\mathrm du\,\mathrm dv$

$=\displaystyle\int_0^{2\pi}\int_0^1(3u+u^2\sin v)\,\mathrm du\,\mathrm dv=\boxed{3\pi}$

5 0

3 years ago

What is the slope-intercept form of the equation y-7 = 3(x-11) ?

german

Y=3x-26

explanation: -33+7=-26 so that would be the y-intercept

4 0

3 years ago

Is this a fair or biased sample.

hichkok12 [17]

Answer:

biased

Step-by-step explanation:

even with the computer randomly picking people, they are still all on the mailing list.

5 0

2 years ago

Maria boards boards a car at the bottom of a ferris wheel. she rides to the top and then it stops. maria tells her friends they

DaniilM [7]

Maria is wrong because they have completed 1/2.

Step-by-step explanation:

At the top of the Ferris wheel,the ride is 1/2 done. All that is left is to go down,which is the other half. Maria is wrong in saying they are 1/4 done,that is a quarter,not half.

6 0

3 years ago

N + 9 >_ 13 (with the “_” under the “>”

Step2247 [10]

Answer:

n >_ 4

Step-by-step explanation:

move 9 to the other side

n >_ 13 - 9

n >_ 4

8 0

3 years ago

Read 2 more answers