To evaluate Rhonda's claim, we need to calculate the slope of the zip line at each location (Zip line A, Zip line B, and Zip line C) and determine whether it meets the slope constraint criteria. The slope is defined as the vertical change divided by the horizontal distance. Here’s the detailed step-by-step approach:
### Given Data:
- Vertical change (change in height): 7 feet
- Final height above the ground: 9 feet
### Zip line A:
- Initial height: 15 feet
- Horizontal distance: 100 feet
### Zip line B:
- Initial height: 20 feet
- Horizontal distance: 120 feet
### Zip line C:
- Initial height: 25 feet
- Horizontal distance: 150 feet
We will calculate the slope for each zip line using the formula:
[tex]\[ \text{slope} = \frac{\text{vertical change}}{\text{horizontal distance}} \][/tex]
### Calculation:
#### Zip line A:
1. Vertical change = Initial height - Final height
[tex]\[ \text{Vertical change} = 15 - 9 = 6 \text{ feet} \][/tex]
2. Slope:
[tex]\[ \text{slope} = \frac{6}{100} = 0.06 \][/tex]
#### Zip line B:
1. Vertical change = Initial height - Final height
[tex]\[ \text{Vertical change} = 20 - 9 = 11 \text{ feet} \][/tex]
2. Slope:
[tex]\[ \text{slope} = \frac{11}{120} \approx 0.0917 \][/tex]
#### Zip line C:
1. Vertical change = Initial height - Final height
[tex]\[ \text{Vertical change} = 25 - 9 = 16 \text{ feet} \][/tex]
2. Slope:
[tex]\[ \text{slope} = \frac{16}{150} \approx 0.1067 \][/tex]
### Analysis:
1. For Zip line A:
- The vertical change here is 6 feet, and the slope we computed is 0.06.
2. For Zip line B:
- The vertical change here is 11 feet, and the slope we computed is approximately 0.0917.
3. For Zip line C:
- The vertical change here is 16 feet, and the slope we computed is approximately 0.1067.
### Conclusion:
To determine if Rhonda's claim about the 7 feet vertical change meeting the slope constraint is valid, we need the actual slope constraint criterion, which isn’t provided in the question. However, we can ascertain that each zip line must have a vertical change and corresponding slope to be analyzed individually to meet specific slope constraints. Rhonda's claim of a 7 feet vertical change being universally valid needs further specific slope requirements to be conclusively tested.
Without those specific constraints, we can only note that each zip line has a different vertical change and resulting slope based on the provided initial heights and horizontal distances. Therefore, each zip line should be tested against the actual slope constraint individually.
