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2 years ago

Divide (3x^3 + x2 – 4) by (x + 2).

Mathematics

1 answer:

OLga [1]2 years ago

6 0

Answer:

$(x+2)(3x^3-5x-10)$

Step-by-step explanation:

If you don't know how to divide polynomials then I can help with that too or you can just search it up

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Connor said, "To the nearest hundred, I've attended school for 800 days of my life!" State 3 numbers that could be the actual nu

joja [24]

How many school are in a year at your school? You need to figure that out before you answer the question.

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3 years ago

G verify that the divergence theorem is true for the vector field f on the region

Alenkasestr [34]

$\mathbf f(x,y,z)=\langle z,y,x\rangle\implies\nabla\cdot\mathbf f=\dfrac{\partial z}{\partial x}+\dfrac{\partial y}{\partial y}+\dfrac{\partial x}{\partial z}=0+1+0=1$

Converting to spherical coordinates, we have

$\displaystyle\iiint_E\nabla\cdot\mathbf f(x,y,z)\,\mathrm dV=\int_{\varphi=0}^{\varphi=\pi}\int_{\theta=0}^{\theta=2\pi}\int_{\rho=0}^{\rho=6}\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi=288\pi$

On the other hand, we can parameterize the boundary of $E$ by

$\mathbf s(u,v)=\langle6\cos u\sin v,6\sin u\sin v,6\cos v\rangle$

with $0\le u\le2\pi$ and $0\le v\le\pi$ . Now, consider the surface element

$\mathrm d\mathbf S=\mathbf n\,\mathrm dS=\dfrac{\mathbf s_v\times\mathbf s_u}{\|\mathbf s_v\times\mathbf s_u\|}\|\mathbf s_v\times\mathbf s_u\|\,\mathrm du\,\mathrm dv$
$\mathrm d\mathbf S=\mathbf s_v\times\mathbf s_u\,\mathrm du\,\mathrm dv$
$\mathrm d\mathbf S=36\langle\cos u\sin^2v,\sin u\sin^2v,\sin v\cos v\rangle\,\mathrm du\,\mathrm dv$

So we have the surface integral - which the divergence theorem says the above triple integral is equal to -

$\displaystyle\iint_{\partial E}\mathbf f\cdot\mathrm d\mathbf S=36\int_{v=0}^{v=\pi}\int_{u=0}^{u=2\pi}\mathbf f(x(u,v),y(u,v),z(u,v))\cdot(\mathbf s_v\times\mathbf s_u)\,\mathrm du\,\mathrm dv$
$=\displaystyle36\int_{v=0}^{v=\pi}\int_{u=0}^{u=2\pi}(12\cos u\cos v\sin^2v+6\sin^2u\sin^3v)\,\mathrm du\,\mathrm dv=288\pi$

as required.

3 0

4 years ago

How do you work this out

Digiron [165]

Check the picture below.

notice, is just a circle inscribed in a square.

now for the first one, we know the diameter is 14, so the square is a 14x14, and the radius of that is half the diameter or 7.

now, if we get the area of the square, which includes the area of the circle, and THEN get the area of the circle and subtract it from the square's, what's leftover is the shaded section.

$\bf \textit{area of a circle}\\\\ A=\pi r^2\\\\
-------------------------------\\\\
\stackrel{\textit{square's area}}{14\cdot 14}~-~\stackrel{\textit{circle's area}}{\pi 7^2}\implies 196-49\pi$

now, for the one on the right-hand-side, the radius is 8, and square's area is 16x16,

$\bf \stackrel{\textit{square's area}}{16\cdot 16}~-~\stackrel{\textit{circle's area}}{\pi 8^2}\implies 256-64\pi$

5 0

4 years ago

A professional basketball court is in the shape of a rectangle. It is 50 ft wide and 94 ft long. A player runs one time around t

mote1985 [20]

Answer:

288 feet PLEASE GIVE BRAINLIEST

Step-by-step explanation:

94 x 2 = 188 ft

50 x 2 = 100 ft

188 + 100 = 288 ft

The player ran 288 feet.

7 0

3 years ago

What is the height of a cone when the radius is 4 and the volume is 32

Lerok [7]

Answer:

1.9099

Step-by-step explanation:

V = (PI) * r^2 * (h/3)

32 = (PI) * (16) * (h/3)

6/PI = h

1.9099 = h

7 0

3 years ago

Read 2 more answers