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2 years ago

An antique chair was purchased in the year 2013 for $500. At the time of purchase, an appraiser estimated that

Mathematics

1 answer:

kaheart [24]2 years ago

8 0

Answer:

Step-by-step explanation:

To find 10% of 500 you would multiply 500 by 0.1

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Which geometric figure are always paraelograms

kolbaska11 [484]

I don’t know I hope u get it

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2 years ago

How many square feet of outdoor carpet will we need for this hole?

adoni [48]

Answer:

36 sqaured feet

Step-by-step explanation:

24 plus 12 i believe?

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3 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

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

6 0

3 years ago

You and some friends go miniature golfing. Your score is 3 below par. One of your friends has a score that is 12 over par. What

Leona [35]

12-(-3)= 12+3=15, so the difference is 15 points

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3 years ago

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Simplify 9 − (−4). (1 point) a −13 b −5 c 5 d 13

Assoli18 [71]

Answer:

d 13

Step-by-step explanation:

Subtracting means adding the opposite.

To subtract -4, you add the opposite of -4 which is 4, so you add 4.

9 - (-4) = 9 + 4 = 13

Answer: d 13

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3 years ago

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