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zmey [24]
3 years ago
12

What is the angle in both radians and degrees determined by an arc of length 2pi meters on a circle of radius 8 meters?

Mathematics
1 answer:
aniked [119]3 years ago
6 0
\bf \textit{arc's length}\\\\
s=r\theta ~~
\begin{cases}
r=radius\\
\theta = angle~in\\
\qquad radians\\
------\\
r=18\\
s=2\pi 
\end{cases}\implies 2\pi =18\theta \implies \cfrac{2\pi }{18}=\theta\implies   \cfrac{\pi }{9}=\theta \\\\
-------------------------------

\bf \textit{arc's length}\\\\
s=\cfrac{\theta \pi r}{180} ~~
\begin{cases}
r=radius\\
\theta = angle~in\\
\qquad degrees\\
------\\
r=18\\
s=2\pi 
\end{cases}\implies 2\pi =\cfrac{\theta \pi 18}{180}
\\\\\\
2\pi =\cfrac{\theta \pi }{10}\implies \cfrac{2\pi (10)}{\pi }=\theta \implies 20=\theta
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100 is what percent of 250?
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Answer:

100 is 40% of 250

Step-by-step explanation:

1. We assume, that the number 250 is 100% - because it's the output value of the task.  

2. We assume, that x is the value we are looking for.  

3. If 100% equals 250, so we can write it down as 100%=250.  

4. We know, that x% equals 100 of the output value, so we can write it down as x%=100.  

5. Now we have two simple equations:

1) 100%=250

2) x%=100

where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:

100%/x%=250/100

6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 100 is what percent of 250

100%/x%=250/100

(100/x)*x=(250/100)*x       - we multiply both sides of the equation by x

100=2.5*x       - we divide both sides of the equation by (2.5) to get x

100/2.5=x  

40=x  

x=40

now we have:  

100 is 40% of 250

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Step-by-step explanation:

detailed explanation showed in the image above

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Y_Kistochka [10]

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slava [35]

Answer:

Option (1) is the correct option.

Step-by-step explanation:

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Therefore, Function 1 has the least minimum value and its coordinates are (-1, -3)

Option (1) is the correct option.

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