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3 years ago

What is the greatest common factor of 16 and 30

Mathematics

1 answer:

fomenos3 years ago

6 0

I think the answers are 1,2,4

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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

Solving a Real-World Problem

lisov135 [29]

Answer:

C would be your answer as the formula for the volume of a cone is pi*r²*h/3

Step-by-step explanation:

5 0

2 years ago

Read 2 more answers

Make x the subject of the following: b = x - 5

nevsk [136]

B=x-5
To get x on its own you have to add 5 to both sides. This gives you:
b+5=x
or
x=b+5

8 0

3 years ago

Justin is training for a hamburger eating competition. He is eventually able to eat 15 hamburgers in 10 minutes. What is justin’

user100 [1]

Answer:

1.5 hamburgers per minute

Step-by-step explanation:

In 10 minutes, Justin can eat 15 burgers.

In 1 minute, Justin can eat 15/10 burgers.

15/10 = 1.5

7 0

2 years ago

Ten times the sum of half a number and 6 is 8

Gelneren [198K]

10(1/2x + 6) = 8
5x + 60 = 8
5x = 8 - 60
5x = - 52
x = -52/5

5 0

3 years ago

Read 2 more answers