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3 years ago

Whats 2(-1)2 +4(-1)-1=

Mathematics

1 answer:

Vinvika [58]3 years ago

8 0

Answer:

-5

Step-by-step explanation:

Distribute first: -2 + 2 - 4 -1 = -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

3 years ago

Did I do this right?

exis [7]

No. For instance, let’s look at 1)
It’s asking you to find what x is when x/10 = 6

So, consider the equation x/10=6
Multiply both sides by 10, and your answer is 60.
Now do this for each one.

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3 years ago

Which graph represents the function f(x) =1/3 |x|?

Arisa [49]

Step-by-step explanation:

f(x) = 1/3|x|

then

f(x) = 1/3x , if x ≥ 0

and

f(x) = -1/3x , if x ≤ 0

the slope of f(x) = 1/3x is 1/3

the slope of f(x) = -1/3x is -1/3

this two above conditions apply on to the fourth graph to the right.

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3 years ago

A circle has a diameter of 22mm. What is its circumference ?

Artist 52 [7]

Answer:

22 $\pi$

Step-by-step explanation:

Circumference = diameter * pi = 22 * pi

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3 years ago

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ivanzaharov [21]

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