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
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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.
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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