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Ronch [10]
3 years ago
9

Match the vocabulary word to the definition. Use the word bank. You will NOT use all the words in the word bank.

Mathematics
1 answer:
kotykmax [81]3 years ago
5 0

Answer:

Diameter

Complementary Angles

Obtuse Triangle

Adjacent Angles

Supplementary Angles

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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
What is 1.9961 x 10^-7
kakasveta [241]

Answer:0.00000019961

Step-by-step explanation:

I moved the decimal place by the number of the exponent

4 0
3 years ago
Please help!!<br>solve for x
timurjin [86]

Answer:

4

Step-by-step explanation:

These both angles are vertically opposite angles. And, vertically opposite angles are equal. So,

→ 5x ― 6 = 3x + 2

→ 5x ― 3x = 2 + 6

→ 2x = 8

→ x = 8/2

→ x = 4

<u>Therefore</u><u>,</u><u> </u><u>the</u><u> </u><u>value</u><u> </u><u>of</u><u> </u><u>x</u><u> </u><u>is</u><u> </u><u>4</u><u>.</u>

4 0
2 years ago
HELP IM IN CLASS AND I NEED IT DONE TODAY!
Nesterboy [21]

Answer:

<h2><u><em>at x = 3      D = .1086</em></u></h2><h2><u><em /></u></h2><h2><u><em>at x = 4      D =  .0869</em></u></h2><h2><u><em /></u></h2><h2><u><em>at x = 5      D = .0724</em></u></h2>

<u><em /></u>

6 0
2 years ago
I don’t know the answer
anastassius [24]
I THINK IT IS B

B) D(X)= X-8x4 
7 0
3 years ago
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