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2 years ago

What is 1/3 of 26 2/3. Please help me

Mathematics

1 answer:

Sergio [31]2 years ago

4 0

Answer:

8.888(8)

Step-by-step explanation:

(26 +2/3)/ 1/3 =8.8888888889

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2 years ago

Two friends leave there houses and go towards each others, one friend runs 8 miles a hour, the other runs 7 miles an hour, there

natka813 [3]

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3 years ago

What 2 numbers multiply to -100 and add to -21

mylen [45]

Answer:

-25 and 4

Step-by-step explanation:

-25×4=-100 and -25+4=-21

6 0

2 years ago

Read 2 more answers

Mind helping a random person out with some math

victus00 [196]

Answer:

may be 7 and 8

but not sure.

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2 years ago

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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

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

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

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2 years ago