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3 years ago

What is 1/4 ➗ 9 in simplest form? and how do i simplify it?

Mathematics

1 answer:

iren [92.7K]3 years ago

6 0

Answer:

1/36

Step-by-step explanation:

1/4 ÷ 9

= 1/4 x 1/9

= 1/36

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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 (> r) from th

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So the volume is

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

Substitute

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

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

Write

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

so the volume is

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

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2 years ago

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Subsitution is subsituting
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