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3 years ago

I need a formula for this problem. Three workers each take home two packs Post-It Notes, at a cost of $.67 per pack

Mathematics

2 answers:

enot [183]3 years ago

8 0

3(0.67x), x being number of post it notes

ludmilkaskok [199]3 years ago

4 0

3[2(.67x)] I think and I hope I'm right

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Serggg [28]

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

By Stokes' theorem,

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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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3 years ago

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Fiesta28 [93]

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3 years ago

Read 2 more answers

Please answer fast please

juin [17]

#1:

A,B,C,E

#2:

12 edges, 12 vertices

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PLEASE SOMEONE HELP ME. I WILL BRAINLIEST YOU AND GIVE YOU POINTS.

almond37 [142]

Answer:

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Step-by-step explanation:

-3x+2 and[(-)(x^2+5x)

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ANTONII [103]

Answer:

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