Welcome to Westonci.ca, your one-stop destination for finding answers to all your questions. Join our expert community now! Discover reliable solutions to your questions from a wide network of experts on our comprehensive Q&A platform. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.
Sagot :
To find the exact length of an arc in a circle, we can use the formula:
[tex]\[ s = r \theta \][/tex]
where [tex]\( s \)[/tex] is the length of the arc, [tex]\( r \)[/tex] is the radius, and [tex]\( \theta \)[/tex] is the central angle in radians.
Given the values:
- [tex]\(\theta = \frac{\pi}{12}\)[/tex] (central angle in radians)
- [tex]\(r = 8\)[/tex] yards (radius of the circle)
We substitute these values into the formula:
[tex]\[ s = 8 \cdot \frac{\pi}{12} \][/tex]
Now, simplify this fraction:
[tex]\[ s = 8 \cdot \frac{\pi}{12} = \frac{8\pi}{12} = \frac{2\pi}{3} \][/tex]
Therefore, the exact length of the arc is:
[tex]\[ s = \frac{2\pi}{3} \text{ yards} \][/tex]
So, the exact, fully simplified answer is:
[tex]\[ s = \frac{2\pi}{3} \text{ yards} \][/tex]
[tex]\[ s = r \theta \][/tex]
where [tex]\( s \)[/tex] is the length of the arc, [tex]\( r \)[/tex] is the radius, and [tex]\( \theta \)[/tex] is the central angle in radians.
Given the values:
- [tex]\(\theta = \frac{\pi}{12}\)[/tex] (central angle in radians)
- [tex]\(r = 8\)[/tex] yards (radius of the circle)
We substitute these values into the formula:
[tex]\[ s = 8 \cdot \frac{\pi}{12} \][/tex]
Now, simplify this fraction:
[tex]\[ s = 8 \cdot \frac{\pi}{12} = \frac{8\pi}{12} = \frac{2\pi}{3} \][/tex]
Therefore, the exact length of the arc is:
[tex]\[ s = \frac{2\pi}{3} \text{ yards} \][/tex]
So, the exact, fully simplified answer is:
[tex]\[ s = \frac{2\pi}{3} \text{ yards} \][/tex]
We hope this was helpful. Please come back whenever you need more information or answers to your queries. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.