The minute hand of a clock is 5 inches long and moves from 12 to 8 o'clock. How far does the tip of the minute hand move? Use 3.14 as an approximation for and then round your answer to the nearest tenth. 20.9 inches 4.2 inches 10.3 inches 7.5 inches
The minute hand of a clock is 5 inches long and moves from 12 to 8 o'clock. How far does the tip of the minute hand move? Use 3.14 as an approximation for and then round your answer to the nearest tenth. 20.9 inches 4.2 inches 10.3 inches 7.5 inches
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![### Problem Statement:
**The minute hand of a clock is 5 inches long and moves from 12 to 8 o'clock. How far does the tip of the minute hand move? Use 3.14 as an approximation for π and then round your answer to the nearest tenth.**
### Answer Choices:
- 20.9 inches
- 4.2 inches
- 10.3 inches
- 7.5 inches
**Explanation:**
To solve this problem, you need to calculate the arc length that the minute hand sweeps out as it moves from 12 to 8. This represents a move of 8 hours on the clock, which is equivalent to \(\frac{8}{12} = \frac{2}{3}\) of a full circle.
1. **Calculate the Fraction of the Circle:** Each hour on the clock represents \(\frac{1}{12}\) of a full circle, so moving from 12 to 8 covers \(\frac{8}{12} = \frac{2}{3}\) of the circle.
2. **Determine the Circumference of the Circle:** The full circumference \(C\) of the circle with radius \(r\) (minute hand length) is given by \(C = 2πr\). Substituting \(r = 5\) inches and \(\pi = 3.14\):
\[
C = 2 \times 3.14 \times 5 = 31.4 \text{ inches}
\]
3. **Compute the Arc Length:** The arc length \(L\) for \(\frac{2}{3}\) of the circle is:
\[
L = \left(\frac{2}{3}\right) \times 31.4 = 20.9333 \text{ inches}
\]
4. **Round to the Nearest Tenth:** The final step is to round 20.9333 to the nearest tenth, resulting in 20.9 inches.
Thus, the tip of the minute hand moves **20.9 inches**.
### Solution:
The correct choice is:
- **20.9 inches**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe9fc99ab-b3a9-4577-a5d7-bccfea12d417%2F2972cae8-78ea-4c4c-a4f5-828e2716cdb8%2Fa6msa0q_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem Statement:
**The minute hand of a clock is 5 inches long and moves from 12 to 8 o'clock. How far does the tip of the minute hand move? Use 3.14 as an approximation for π and then round your answer to the nearest tenth.**
### Answer Choices:
- 20.9 inches
- 4.2 inches
- 10.3 inches
- 7.5 inches
**Explanation:**
To solve this problem, you need to calculate the arc length that the minute hand sweeps out as it moves from 12 to 8. This represents a move of 8 hours on the clock, which is equivalent to \(\frac{8}{12} = \frac{2}{3}\) of a full circle.
1. **Calculate the Fraction of the Circle:** Each hour on the clock represents \(\frac{1}{12}\) of a full circle, so moving from 12 to 8 covers \(\frac{8}{12} = \frac{2}{3}\) of the circle.
2. **Determine the Circumference of the Circle:** The full circumference \(C\) of the circle with radius \(r\) (minute hand length) is given by \(C = 2πr\). Substituting \(r = 5\) inches and \(\pi = 3.14\):
\[
C = 2 \times 3.14 \times 5 = 31.4 \text{ inches}
\]
3. **Compute the Arc Length:** The arc length \(L\) for \(\frac{2}{3}\) of the circle is:
\[
L = \left(\frac{2}{3}\right) \times 31.4 = 20.9333 \text{ inches}
\]
4. **Round to the Nearest Tenth:** The final step is to round 20.9333 to the nearest tenth, resulting in 20.9 inches.
Thus, the tip of the minute hand moves **20.9 inches**.
### Solution:
The correct choice is:
- **20.9 inches**
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