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2 years ago

The equation y=−15x+12 is the slope-intercept form of which equation?

Mathematics

1 answer:

Sliva [168]2 years ago

6 0

I honestly don't know but I think it would come out to be 4/5

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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,

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

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

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

6 0

2 years ago

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Serhud [2]

Answer:

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Step-by-step explanation:

5 0

2 years ago

Simplify: 3r+n²-r+5-2n+2

lutik1710 [3]

3r+n2−r+5−2n+2=3r+n2+−r+5+−2n+2=3r+n2+−r+5+−2n+2=(n2)+(−2n)+(3r+−r)+(5+2)=n2+−2n+2r+7
=n2−2n+2r+7

7 0

2 years ago

Read 2 more answers

A closed container has 7.05 ⋅ 1023 atoms of a gas. Each atom of the gas weighs 1.67 ⋅ 10-24 grams. Which of the following shows

Gnesinka [82]

Answer:

Step-by-step explanation:

7 0

2 years ago

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Solve 4d = 1/3a. 4/3b. 1/7c. 1/12d. 1/4

ELEN [110]

4d = 1/3
d = 1/3/4
d = 1/12
Thus, c is the correct choice.

4 0

2 years ago