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3 years ago

8

An office supply store scans document pages. The store charges the same amount for each scanned page and a one-time charge for t

he scan of any number of pages. The equation below gives the total cost of scanning x document pages. What does the 0.25 represent in this situation?

1 answer:

Monica [59]3 years ago

4 0

Answer:

$0.25

Step-by-step explanation:

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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

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

6 0

3 years ago

Some one please help me with these questions I’m struggling :(

Juliette [100K]

Answer: 6) 15 1/10

Step-by-step explanation:

Add the whole numbers and then find a common number for the bottom fraction. So that'd be ten. To get to ten from 2 you'd multiply by five then multiply the top number by five too. That gets you 5/10 and do the same for the other fraction. Get the bottom number to ten then whatever you multiply by do the same to the top. After doing that putting the fractions together which gets you 11/10. That'd make 1 1/10 so that makes it 15 instead of 14 whole

8 0

3 years ago

Read 2 more answers

Два фермена пробовали яблоки на ярмарке. Первый продовал в ящиках по15 кг по цене 90леев за ящик а второй в покетах по2 кг по це

Marina86 [1]

Answer:

could you translate it

Step-by-step explanation:

8 0

3 years ago

¿Look at the picture

kkurt [141]

Answer:

16.2 Kilometers

Step-by-step explanation:

81 divided by 5

You get 16.2 kilometers

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3 years ago

Today, the price of a new cell phone is $129.

Gnom [1K]

Answer:

54%

Step-by-step explanation:

129/240 = 0.5375 (divided to find the % change)

0.5375 * 100 (to convert decimal to percent form)

53.7 which is rounded to 54 percent (I needed to round it to the nearest whole percent number)

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2 years ago

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