Find the best solutions to your questions at Westonci.ca, the premier Q&A platform with a community of knowledgeable experts. Discover solutions to your questions from experienced professionals across multiple fields on our comprehensive Q&A platform. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.
Sagot :
Let's go through the solution step-by-step as if we're working this out carefully.
1. Understanding the Circumference:
- The circumference [tex]\( C \)[/tex] of a circle is given by [tex]\( C = \pi d \)[/tex], where [tex]\( d \)[/tex] is the diameter.
- Since the diameter [tex]\( d \)[/tex] is twice the radius [tex]\( r \)[/tex], we can write the circumference as [tex]\( C = 2 \pi r \)[/tex].
2. Dividing the Circle into Sectors:
- If we draw central angles each with a measure of [tex]\( n^\circ \)[/tex], the number of such sectors can be determined as [tex]\( \frac{360^\circ}{n^\circ} \)[/tex].
3. Arc Length of Each Sector:
- The arc length of a sector is the portion of the circumference that corresponds to a single central angle. For a circle divided into [tex]\( \frac{360^\circ}{n^\circ} \)[/tex] sectors, the arc length is the circumference divided by the number of such sectors.
- Therefore, the arc length [tex]\( L \)[/tex] for each sector is [tex]\( \frac{2 \pi r}{\frac{360^\circ}{n^\circ}} = 2 \pi r \cdot \frac{n^\circ}{360^\circ} \)[/tex].
4. Simplifying the Expression:
- The expression for the arc length can be simplified as:
[tex]\[ L = 2 \pi r \cdot \frac{n}{360} \][/tex]
So, we see that the arc length of a sector with a central angle of [tex]\( n^\circ \)[/tex] is [tex]\( 2 \pi r \cdot \frac{n}{360} \)[/tex]. This can also be presented as:
[tex]\[ L = r \pi \cdot \frac{n}{180} \][/tex]
By rechecking the provided options, the best fit to complete the argument is:
A. [tex]\( \frac{\pi n r}{180} \)[/tex].
Hence, each sector's arc length formula translates correctly to [tex]\( \frac{\pi n r}{180} \)[/tex] or equivalently [tex]\( 2 \pi r \cdot \frac{n}{360} \)[/tex].
1. Understanding the Circumference:
- The circumference [tex]\( C \)[/tex] of a circle is given by [tex]\( C = \pi d \)[/tex], where [tex]\( d \)[/tex] is the diameter.
- Since the diameter [tex]\( d \)[/tex] is twice the radius [tex]\( r \)[/tex], we can write the circumference as [tex]\( C = 2 \pi r \)[/tex].
2. Dividing the Circle into Sectors:
- If we draw central angles each with a measure of [tex]\( n^\circ \)[/tex], the number of such sectors can be determined as [tex]\( \frac{360^\circ}{n^\circ} \)[/tex].
3. Arc Length of Each Sector:
- The arc length of a sector is the portion of the circumference that corresponds to a single central angle. For a circle divided into [tex]\( \frac{360^\circ}{n^\circ} \)[/tex] sectors, the arc length is the circumference divided by the number of such sectors.
- Therefore, the arc length [tex]\( L \)[/tex] for each sector is [tex]\( \frac{2 \pi r}{\frac{360^\circ}{n^\circ}} = 2 \pi r \cdot \frac{n^\circ}{360^\circ} \)[/tex].
4. Simplifying the Expression:
- The expression for the arc length can be simplified as:
[tex]\[ L = 2 \pi r \cdot \frac{n}{360} \][/tex]
So, we see that the arc length of a sector with a central angle of [tex]\( n^\circ \)[/tex] is [tex]\( 2 \pi r \cdot \frac{n}{360} \)[/tex]. This can also be presented as:
[tex]\[ L = r \pi \cdot \frac{n}{180} \][/tex]
By rechecking the provided options, the best fit to complete the argument is:
A. [tex]\( \frac{\pi n r}{180} \)[/tex].
Hence, each sector's arc length formula translates correctly to [tex]\( \frac{\pi n r}{180} \)[/tex] or equivalently [tex]\( 2 \pi r \cdot \frac{n}{360} \)[/tex].
Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.