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Gelneren [198K]
3 years ago
8

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Mathematics
3 answers:
Serjik [45]3 years ago
6 0

Answer:

Helloooo wasup!

Step-by-step explanation:

:)

Arturiano [62]3 years ago
3 0
Hi, have a good day :)!!!!!
Brisa Margarita2 years ago
0 0

Hello, how you doing. I hope you are having a great day so far.
:)

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elena55 [62]

Answer: 160

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How many square metres is equivalent to 12 370 cm2?<br> please answser ASAP
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Twice the difference between a number and 10 is equal to 6 times the number plus 16. What is the number?
oksano4ka [1.4K]
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3 years ago
Rewrite the polynomial in the form ax^2+bx+c and then identify the values of a, b, and c. 6+9x^2
Ulleksa [173]

Answer:

see below

Step-by-step explanation:

6+9x^2

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9x^2 +0x + 6

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5 0
3 years ago
A torus is formed by rotating a circle of radius r about a line in the plane of the circle that is a distance R (&gt; r) from th
jeyben [28]

Consider a circle with radius r centered at some point (R+r,0) on the x-axis. This circle has equation

(x-(R+r))^2+y^2=r^2

Revolve the region bounded by this circle across the y-axis to get a torus. Using the shell method, the volume of the resulting torus is

\displaystyle2\pi\int_R^{R+2r}2xy\,\mathrm dx

where 2y=\sqrt{r^2-(x-(R+r))^2}-(-\sqrt{r^2-(x-(R+r))^2})=2\sqrt{r^2-(x-(R+r))^2}.

So the volume is

\displaystyle4\pi\int_R^{R+2r}x\sqrt{r^2-(x-(R+r))^2}\,\mathrm dx

Substitute

x-(R+r)=r\sin t\implies\mathrm dx=r\cos t\,\mathrm dt

and the integral becomes

\displaystyle4\pi r^2\int_{-\pi/2}^{\pi/2}(R+r+r\sin t)\cos^2t\,\mathrm dt

Notice that \sin t\cos^2t is an odd function, so the integral over \left[-\frac\pi2,\frac\pi2\right] is 0. This leaves us with

\displaystyle4\pi r^2(R+r)\int_{-\pi/2}^{\pi/2}\cos^2t\,\mathrm dt

Write

\cos^2t=\dfrac{1+\cos(2t)}2

so the volume is

\displaystyle2\pi r^2(R+r)\int_{-\pi/2}^{\pi/2}(1+\cos(2t))\,\mathrm dt=\boxed{2\pi^2r^2(R+r)}

6 0
3 years ago
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