To find the length of the arc [tex]\( AC \)[/tex] given [tex]\( x = \frac{32}{3} \pi \)[/tex]:
1. Understand the meaning of [tex]\( x \)[/tex]:
- [tex]\( x \)[/tex] represents a fraction of the full circumference of a circle.
- The full circumference of a circle is [tex]\( 2 \pi r \)[/tex] where [tex]\( r \)[/tex] is the radius.
2. Determine the length of the arc [tex]\( AC \)[/tex]:
- The problem essentially provides the length of the arc [tex]\( AC \)[/tex] directly via [tex]\( x \)[/tex].
- Here, [tex]\( x \)[/tex] is given as [tex]\( \frac{32}{3} \pi \)[/tex].
3. Conclude the arc length:
- The length of the arc [tex]\( AC \)[/tex] is simply [tex]\( x \)[/tex] which was computed earlier.
Thus, the length of arc [tex]\( AC \)[/tex] is [tex]\( 33.510321638291124 \)[/tex].
