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2 years ago

What are the coordinates of point S on the graph? Put your answer in parenthesis (x,y).

Mathematics

1 answer:

gregori [183]2 years ago

4 0

(2,-2) is the answer

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Cooper earned $214.50 at his job when he worked for 13 hours. How much money did he earn each hour?

Lerok [7]

Answer:

$16.50

Step-by-step explanation:

8 0

2 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 (> 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

2 years ago

URGENT! IM TIMED! 2.35•2/3 in fraction form?

liberstina [14]

Answer:

Simplified: 1.56

fraction form 47/30

7 0

3 years ago

Pls help ASAP find the slope !!

Sedaia [141]

Answer:

4,-4 I think

Step-by-step explanation:

My brain is off right now so might be wrong

3 0

3 years ago

Use the slope intercept form to,graph the equation 4x+y=-4

zvonat [6]

slope intercept form is y=4/3x-2 slope is 4/3 and y=-2

5 0

2 years ago