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Use the proportional relationship between an arc length and the circumference of a circle to calculate the length of arc [tex]\( AC \)[/tex].

A. [tex]\( x = \frac{32}{3} \pi \)[/tex]

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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].
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