### Applications and Extensions#### 91. Movement of a Minute HandThe minute hand of a clock is 6 inches long. How far does the tip of the minute hand move in 15 minutes? How far does it move in 25 minutes? Round answers to two decimal places.![Clock](data:image/png;base64,...) (An image of a clock with the minute hand pointing at 3 and the hour hand pointing at 12)Explanation:1. **Understanding Clock Movement:** - The minute hand completes a full circle (360 degrees) in 60 minutes. - In 15 minutes, the minute hand covers a quarter of the clock (360/4 = 90 degrees). - In 25 minutes, the minute hand covers 25/60 of the clock (360 * 25/60 = 150 degrees).2. **Calculations:** - **Arc Length Formula**: \( \text{Arc Length} = \theta \times r \times \left( \frac{\pi}{180} \right) \) - Where \( \theta \) is the angle in degrees, \( r \) is the radius (length of the minute hand), and \(\pi\) is approximately 3.14.### For 15 minutes:\[ \text{Arc Length} = 90 \times 6 \times \left( \frac{\pi}{180} \right) \]\[ = 90 \times 6 \times \left( \frac{3.14}{180} \right) \]\[ = 90 \times 6 \times 0.01745 \]\[ = 9.42 \text{ inches (rounded to two decimal places)} \]### For 25 minutes:\[ \text{Arc Length} = 150 \times 6 \times \left( \frac{\pi}{180} \right) \]\[ = 150 \times 6 \times \left( \frac{3.14}{180} \right) \]\[ = 150 \times 6 \times 0.01745 \]\[ = 15.71 \text{ inches (rounded to two decimal places)} \]Therefore:- The minute hand moves **9.42 inches** in 15 minutes.- The minute hand moves **15.71 inches** in 25 minutes.

Name: ### Applications and Extensions#### 91. Movement of a Minute HandThe
Uploaded: 2024-03-05T11:52:21.000Z
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Description: ### Applications and Extensions#### 91. Movement of a Minute HandThe minute hand of a clock is 6 inches long. How far does the tip of the minute hand move in 15 minutes? How far does it move in 25 minutes? Round answers to two decimal places.![Clock