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3 years ago

In the expression -12+m-9m+13, name the coefficients

Mathematics

2 answers:

velikii [3]3 years ago

7 0

13 ion know how I got the answer but I think is 13

torisob [31]3 years ago

4 0

Answer:

-12

Step-by-step explanation:

its just the numbers in front of the variables

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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

3 years ago

PLEASE HELP!!! <br> find the length of arc LN. Round to the nearest hundredth.<br> SHOW WORK....

patriot [66]

9514 1404 393

Answer:

15.71 units

Step-by-step explanation:

The arc length is given by the formula ...

s = rθ

where r represents the radius, and θ represents the central angle in radians.

The angle of 60° is π/3 radians, so the arc length is ...

s = 15(π/3) = 5π ≈ 15.71 . . . units

LN ≈ 15.71 units

<em>Note</em>: if you use 3.14 for π, you will get 15.70.

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3 years ago

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WITCHER [35]

Answer:

Step-by-step explanation:

It increased 3 meters every second if you look closely at chart

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gavmur [86]

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Step-by-step explanation:

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3 years ago

Read 2 more answers

In the expression -12+m-9m+13, name the coefficients​

In the expression -12+m-9m+13, name the coefficients