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2 years ago

May someone do this for me I don’t under the top part only but you can do the bottom if you feel like it the first gets branlist

Mathematics

1 answer:

UNO [17]2 years ago

4 0

For the first answer it would be y=mc+b

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Use Stokes' Theorem to evaluate C F · dr F(x, y, z) = xyi + yzj + zxk, C is the boundary of the part of the paraboloid z = 1 − x

Serggg [28]

I assume $C$ has counterclockwise orientation when viewed from above.

By Stokes' theorem,

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

so we first compute the curl:

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

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

Then parameterize $S$ by

$\vec r(u,v)=\cos u\sin v\,\vec\imath+\sin u\sin v\,\vec\jmath+\cos^2v\,\vec k$

where the $z$ -component is obtained from

$1-(\cos u\sin v)^2-(\sin u\sin v)^2=1-\sin^2v=\cos^2v$

with $0\le u\le\dfrac\pi2$ and $0\le v\le\dfrac\pi2$ .

Take the normal vector to $S$ to be

$\vec r_v\times\vec r_u=2\cos u\cos v\sin^2v\,\vec\imath+\sin u\sin v\sin(2v)\,\vec\jmath+\cos v\sin v\,\vec k$

Then the line integral is equal in value to the surface integral,

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

$=\displaystyle\int_0^{\pi/2}\int_0^{\pi/2}(-\sin u\sin v\,\vec\imath-\cos^2v\,\vec\jmath-\cos u\sin v\,\vec k)\cdot(\vec r_v\times\vec r_u)\,\mathrm du\,\mathrm dv$

$=\displaystyle-\int_0^{\pi/2}\int_0^{\pi/2}\cos v\sin^2v(\cos u+2\cos^2v\sin u+\sin(2u)\sin v)\,\mathrm du\,\mathrm dv=\boxed{-\frac{17}{20}}$

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2 years ago

Convert the cartesian equations to a polar equation<br> y=4x^2

alexdok [17]

Answer:

Step-by-step explanation:

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2 years ago

If the sum of all interior angles of a regular polygon is 1080 degrees then number of sides of the polygon is?

MakcuM [25]

Answer: 8

<u>Step-by-step explanation:</u>

The formula for the sum of the angles of a polynomial is:

$S_n=180(n-2)$

1080 = 180(n - 2)

1080 = 180n - 360

1440 = 180n

8 = n

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2 years ago

Find the measure of X<br> Find the measure of PS and QR

AveGali [126]

Answer: x=4. PS=QR=15

Step-by-step explanation:

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2 years ago

Twelve pounds of oranges are shared equally among 5 people. How many

lana66690 [7]

Answer:

12/5 = 2.4 pounds of oranges per person

Step-by-step explanation:

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2 years ago

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