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4 years ago

The point(5/13,Y) IS IN THE 4TH quadrant corresponds to angle on the unit circle

1 answer:

6 0

4th quadrant is positive x (cos) and negative y (sin)

Use the Pythagorean Theorem to calculate the value of y (sin).
x² + y² = c²
5² + y² = 13²
25 + y² = 169
y² = 144
y = 12

Since the y-value is negative in the 4th quadrant, then y = -12

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asambeis [7]

Hello,

Answer A

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Bess [88]

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Step-by-step explanation:

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3 years ago

What is the area of a sector with a central angle of 108 degrees and a diameter of 21.2 cm?

Rasek [7]

Answer:

$105.84\ cm^2$

Step-by-step explanation:

step 1

Find the area of the circle

The area of the circle is

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we have

$r=21.2/2=10.6\ cm$ ----> the radius is half the diameter

substitute

$A=\pi (10.6)^{2}$

$A=112.36\pi\ cm^2$

step 2

Find the area of a sector

Remember that

The area of the circle subtends a central angle of 360 degrees

using proportion

Find out the area of a sector with a central angle of 108 degrees

$\frac{112.36\pi}{360^o}=\frac{x}{108^o}\\\\x=112.36\pi(108)/360\\\\x=33.708\pi\ cm^2$

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3 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

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$\displaystyle2\pi\int_R^{R+2r}2xy\,\mathrm dx$

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

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

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

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3 years ago