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3 years ago

Evaluate the function. f(x) = -x^2 Find f(-5)

Mathematics

1 answer:

mina [271]3 years ago

4 0

1) plug -5 in for the place of x.
2) solve -(-5)^2
3) f(-5)=25

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g Use Stokes' Theorem to evaluate C F · dr where C is oriented counterclockwise as viewed from above. F(x, y, z) = 7yi + xzj + (

Sati [7]

By Stokes' theorem,

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

where $S$ is any oriented surface with boundary $C$ . We have

$\vec F(x,y,z)=7y\,\vec\imath+xz\,\vec\jmath+(x+y)\,\vec k$

$\implies\nabla\times\vec F(x,y,z)=(1-x)\,\vec\imath-\vec\jmath+(z-7)\,\vec k$

Take $S$ to be the ellipse that lies in the plane $z=y+9$ with boundary on the cylinder $x^2+y^2=1$ . Parameterize $S$ by

$\vec s(u,v)=u\cos v\,\vec\imath+u\sin v\,\vec\jmath+(u\sin v+9)\,\vec k$

with $0\le u\le1$ and $0\le v\le2\pi$ . Take the normal vector to $S$ to be

$\vec s_u\times\vec s_v=-u\,\vec\jmath+u\,\vec k$

Then we have

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

$=\displaystyle\int_0^{2\pi}\int_0^1\big((1-u\cos v)\,\vec\imath-\vec\jmath+(u\sin v+2)\,\vec k\big)\cdot\big(-u\,\vec\jmath+u\,\vec k\big)\,\mathrm du\,\mathrm dv$

$=\displaystyle\int_0^{2\pi}\int_0^1(3u+u^2\sin v)\,\mathrm du\,\mathrm dv=\boxed{3\pi}$

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3 years ago

. <br> Find the measure of angle C if the area of triangle ABC (below) is 54 square inches.

Sonja [21]

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2 years ago

A movie theater has a seating capacity of 331. The theater charges $5.00 for children, $7.00 for students, and $12.00 for adults

nlexa [21]

Answer:

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Step-by-step explanation:

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1 year ago

What is this proper scientific notation for 0.000476?

Brilliant_brown [7]

To convert the number to one that is 1 or greater and less than 10 we must multiply by 10,000. Therefore the converted number is as follows:
$0.000476=4.76\times 10^{-4}$

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3 years ago

FOR 12 POINTS I NEED HELP ASAP! Consider the system of linear equations. 5 x + 10 y = 15. 10 x + 3 y = 13 To use the linear comb

Romashka [77]

Answer:

Do you mean which equation should the 5x+10=15 be multiplied to?

it would be -2

Step-by-step explanation:

This is because 5 times -2 is -10

and so when you add the (now) x value of the first equation to the x value of the second equation, it gets 0

which makes it eliminated!

-10x+10x=0

8 0

3 years ago