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Find the exact length of the arc intercepted by a central angle on a circle of radius . Then round to the nearest tenth of a unit.
Part:
Part 1 of 2
The exact length of the arc is
Fhes.

Ask by Bush Valdez. in the United States
Mar 23,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The exact length of the arc is cm, and when rounded to the nearest tenth, it is 84.8 cm.

Solution

Step 1: Write down the formula for arc length
The arc length of a circle intercepted by a central angle (in radians) is given by
Step 2: Substitute the given values
Given cm and , substitute these into the formula:
Step 3: Simplify the expression
Multiply the values:
This is the exact length of the arc.
Step 4: Round to the nearest tenth
To round to the nearest tenth, first approximate using :
Rounded to the nearest tenth:
Final Answer
Exact length: cm
Rounded length: cm

Answered by UpStudy AI and reviewed by a Professional Tutor

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Extra Insights

The exact length of the arc intercepted by a central angle on a circle can be calculated using the formula . Given and , we can substitute these values into the formula:
Now, to round to the nearest tenth, we approximate as :
Rounding to the nearest tenth gives us:
So, the exact length of the arc is , and when rounded, it is .

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