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Vera_Pavlovna [14]
3 years ago
13

Express the area of a circle, a, as a function of its circumference, c.

Mathematics
1 answer:
Naddika [18.5K]3 years ago
7 0
Area = PI * radius^2

Circumference = 2 * PI * radius
radius = Circumference / 2 * PI

So, Area = PI * (Circumference / 2 *PI) * (Circumference / 2 *PI)
So, Area = Circumference^2 / (4*PI)

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Find the area of the shaded region. Round your answer to the nearest tenth.
Alex
Check the picture below on the left-side.

we know the central angle of the "empty" area is 120°, however the legs coming from the center of the circle, namely the radius, are always 6, therefore the legs stemming from the 120° angle, are both 6, making that triangle an isosceles.

now, using the "inscribed angle" theorem, check the picture on the right-side, we know that the inscribed angle there, in red, is 30°, that means the intercepted arc is twice as much, thus 60°, and since arcs get their angle measurement from the central angle they're in, the central angle making up that arc is also 60°, as in the picture.

so, the shaded area is really just the area of that circle's "sector" with 60°, PLUS the area of the circle's "segment" with 120°.

\bf \textit{area of a sector of a circle}\\\\
A_x=\cfrac{\theta \pi r^2}{360}\quad 
\begin{cases}
r=radius\\
\theta =angle~in\\
\qquad degrees\\
------\\
r=6\\
\theta =60
\end{cases}\implies A_x=\cfrac{60\cdot \pi \cdot 6^2}{360}\implies \boxed{A_x=6\pi} \\\\
-------------------------------\\\\

\bf \textit{area of a segment of a circle}\\\\
A_y=\cfrac{r^2}{2}\left[\cfrac{\pi \theta }{180}~-~sin(\theta )  \right]
\begin{cases}
r=radius\\
\theta =angle~in\\
\qquad degrees\\
------\\
r=6\\
\theta =120
\end{cases}

\bf A_y=\cfrac{6^2}{2}\left[\cfrac{\pi\cdot 120 }{180}~-~sin(120^o )  \right]
\\\\\\
A_y=18\left[\cfrac{2\pi }{3}~-~\cfrac{\sqrt{3}}{2} \right]\implies \boxed{A_y=12\pi -9\sqrt{3}}\\\\
-------------------------------\\\\
\textit{shaded area}\qquad \stackrel{A_x}{6\pi }~~+~~\stackrel{A_y}{12\pi -9\sqrt{3}}\implies 18\pi -9\sqrt{3}

7 0
3 years ago
I don’t know how to answer this x.x
gulaghasi [49]

Answer:

2

Step-by-step explanation:

On the first side it shows 5 ones. If you add 5 by 2 it’s 7. Then on the other side it shows 3 X’s. 3x2 is 6. Plus you add that 1 which makes it 7.

Hope this Helps :)

8 0
3 years ago
Read 2 more answers
What is the mean of the following set of numbers? 121, 347, 45, 21, 300, 614, 312, 333, 421
Norma-Jean [14]
The mean is 279.3 repeating.
5 0
3 years ago
Read 2 more answers
Please help it’s asking the perimeter to the nearest tenth
valkas [14]

Pythagoras theoram? use it here!

That is,

  • H² = B² + P²

H² = 15² + 4²

H² = 225 + 16

H = √241

H = 15.5

You should opt for 15.5

P.S: Best of luck for your test! ;))

5 0
3 years ago
A rectangular prism is 4 inches long, 3 inches wide and 8 inches tall . Eli packs the prism with unit cubes to find the volume.
bulgar [2K]

Answer:

V=96\ inch^2

Step-by-step explanation:

Given that,

A rectangular prism is 4 inches long, 3 inches wide and 8 inches tall.

We need to find the volume of the rectangular prism. The formula for the volume of prism is given by :

V=lbh\\\\V=4\times 3\times 8\\\\V=96\ inch^2

So, the volume of the prism is equal to 96\ inch^2.

6 0
3 years ago
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