Which is steeper & why? SHOW ALL YOUR WORK TO GET FULL CREDIT. A ramp with a rise of 2ft and a run of 6ft OR A ramp with a rise of 1ft and a run of 4ft
Which is steeper & why? SHOW ALL YOUR WORK TO GET FULL CREDIT. A ramp with a rise of 2ft and a run of 6ft OR A ramp with a rise of 1ft and a run of 4ft
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Problem:** Determine which ramp is steeper and explain your reasoning. Show all your work to get full credit.
**Scenario 1:** A ramp with a rise of 2 feet and a run of 6 feet.
**Scenario 2:** A ramp with a rise of 1 foot and a run of 4 feet.
For both scenarios, calculate the slope of each ramp. The slope is given by the formula:
\[ \text{Slope} = \frac{\text{Rise}}{\text{Run}} \]
**Ramp Calculations:**
- **Scenario 1:**
- Rise: 2 ft
- Run: 6 ft
- Slope: \( \frac{2}{6} = \frac{1}{3} \)
- **Scenario 2:**
- Rise: 1 ft
- Run: 4 ft
- Slope: \( \frac{1}{4} \)
**Conclusion:**
- Compare the slopes: \(\frac{1}{3}\) (first ramp) vs. \(\frac{1}{4}\) (second ramp).
- The first ramp (\(\frac{1}{3}\)) is steeper than the second ramp (\(\frac{1}{4}\)) because a larger slope value indicates a steeper incline.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F30349753-ac03-4e61-ba38-81f239656501%2F3304dc58-3fac-4b4f-8191-1abee41b6e55%2Fbj4twr8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem:** Determine which ramp is steeper and explain your reasoning. Show all your work to get full credit.
**Scenario 1:** A ramp with a rise of 2 feet and a run of 6 feet.
**Scenario 2:** A ramp with a rise of 1 foot and a run of 4 feet.
For both scenarios, calculate the slope of each ramp. The slope is given by the formula:
\[ \text{Slope} = \frac{\text{Rise}}{\text{Run}} \]
**Ramp Calculations:**
- **Scenario 1:**
- Rise: 2 ft
- Run: 6 ft
- Slope: \( \frac{2}{6} = \frac{1}{3} \)
- **Scenario 2:**
- Rise: 1 ft
- Run: 4 ft
- Slope: \( \frac{1}{4} \)
**Conclusion:**
- Compare the slopes: \(\frac{1}{3}\) (first ramp) vs. \(\frac{1}{4}\) (second ramp).
- The first ramp (\(\frac{1}{3}\)) is steeper than the second ramp (\(\frac{1}{4}\)) because a larger slope value indicates a steeper incline.
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