Question
Question content area top
Part 1
Most new buildings are required to have a ramp for the handicapped that has a maximum vertical rise of 11 feet for every 132 feet of horizontal distance.
Question content area bottom
Part 1
(a) What is the value of the slope of a ramp for the handicapped? Select the correct choice below and fill in any answer boxes within your choice.
A.
m equals one twelfth
(Simplify your answer.)
Your answer is correct.B.
The slope is undefined.
Part 2
(b) If the builder constructs a new building in which the ramp has a horizontal distance of 108 feet, what is the maximum height of the doorway above the level of the parking lot where the ramp begins?
9 feet
(Type an integer or decimal rounded to one decimal place.)
Part 3
(c) What is the shortest possible distance between the building and the end of the ramp if the architect redesigns the building so that the doorway is 1.2 feet above the parking lot?
19.2 feet
Part 1
Most new buildings are required to have a ramp for the handicapped that has a maximum vertical rise of 11 feet for every 132 feet of horizontal distance.
Question content area bottom
Part 1
(a) What is the value of the slope of a ramp for the handicapped? Select the correct choice below and fill in any answer boxes within your choice.
A.
m equals one twelfth
(Simplify your answer.)
Your answer is correct.B.
The slope is undefined.
Part 2
(b) If the builder constructs a new building in which the ramp has a horizontal distance of 108 feet, what is the maximum height of the doorway above the level of the parking lot where the ramp begins?
9 feet
(Type an integer or decimal rounded to one decimal place.)
Part 3
(c) What is the shortest possible distance between the building and the end of the ramp if the architect redesigns the building so that the doorway is 1.2 feet above the parking lot?
19.2 feet
Answers
Answered by
GPT-4o mini
Let's break down the problem step by step.
### Part 1
**(a)** You are given that the ramp has a maximum vertical rise of 11 feet for every 132 feet of horizontal distance. The slope (m) can be calculated using the formula:
\[
m = \frac{\text{vertical rise}}{\text{horizontal distance}}
\]
Substituting the values:
\[
m = \frac{11}{132}
\]
When you simplify \( \frac{11}{132} \):
\[
m = \frac{1}{12}
\]
So the answer is:
**A. \( m = \frac{1}{12} \)**.
### Part 2
**(b)** You want to find the maximum height of the doorway (the vertical rise) when the horizontal distance is 108 feet. The slope remains the same at \( \frac{1}{12} \).
Using the slope formula:
\[
\text{vertical rise} = \text{slope} \times \text{horizontal distance}
\]
Substituting the known values:
\[
\text{vertical rise} = \frac{1}{12} \times 108
\]
Calculating this gives:
\[
\text{vertical rise} = 9 \text{ feet}
\]
So, the maximum height of the doorway is **9 feet**.
### Part 3
**(c)** Now, if the doorway is redesigned to be 1.2 feet above the parking lot, we need to find the horizontal distance based on the same slope.
Using the rearranged slope formula:
\[
\text{horizontal distance} = \frac{\text{vertical rise}}{\text{slope}}
\]
Substituting the vertical rise of 1.2 feet and the same slope of \( \frac{1}{12} \):
\[
\text{horizontal distance} = \frac{1.2}{\frac{1}{12}} = 1.2 \times 12 = 14.4 \text{ feet}
\]
Now, taking into account the original ramp distance (108 feet), the shortest possible distance between the building and the end of the ramp can be calculated as:
\[
\text{new horizontal distance} = 108 - 14.4 = 93.6 \text{ feet}
\]
However, if you're looking for the distance the ramp actually runs in total, you would just calculate the total length from the slope again:
If you're further asked what would happen in this scenario where it might appear as a question, the simple distance sliding instead gives you the original misunderstanding. Please clarify the distance needed.
For now, based on the provided information, if we had checked back into shorter or continued distance, the working information designed doesn’t lead us to the outcome of 19.2 feet explicitly listed. Thus, please explain additional context for that outcome if necessary adjusted along.
Overall, the outputs are as followed:
- **(a)** \( m = \frac{1}{12} \)
- **(b)** Maximum height = **9 feet**
- **(c)** Total horizontal distance calculated based indicated 14.4 feet based checking (needs clarity if want specifically found on noted distances).
### Part 1
**(a)** You are given that the ramp has a maximum vertical rise of 11 feet for every 132 feet of horizontal distance. The slope (m) can be calculated using the formula:
\[
m = \frac{\text{vertical rise}}{\text{horizontal distance}}
\]
Substituting the values:
\[
m = \frac{11}{132}
\]
When you simplify \( \frac{11}{132} \):
\[
m = \frac{1}{12}
\]
So the answer is:
**A. \( m = \frac{1}{12} \)**.
### Part 2
**(b)** You want to find the maximum height of the doorway (the vertical rise) when the horizontal distance is 108 feet. The slope remains the same at \( \frac{1}{12} \).
Using the slope formula:
\[
\text{vertical rise} = \text{slope} \times \text{horizontal distance}
\]
Substituting the known values:
\[
\text{vertical rise} = \frac{1}{12} \times 108
\]
Calculating this gives:
\[
\text{vertical rise} = 9 \text{ feet}
\]
So, the maximum height of the doorway is **9 feet**.
### Part 3
**(c)** Now, if the doorway is redesigned to be 1.2 feet above the parking lot, we need to find the horizontal distance based on the same slope.
Using the rearranged slope formula:
\[
\text{horizontal distance} = \frac{\text{vertical rise}}{\text{slope}}
\]
Substituting the vertical rise of 1.2 feet and the same slope of \( \frac{1}{12} \):
\[
\text{horizontal distance} = \frac{1.2}{\frac{1}{12}} = 1.2 \times 12 = 14.4 \text{ feet}
\]
Now, taking into account the original ramp distance (108 feet), the shortest possible distance between the building and the end of the ramp can be calculated as:
\[
\text{new horizontal distance} = 108 - 14.4 = 93.6 \text{ feet}
\]
However, if you're looking for the distance the ramp actually runs in total, you would just calculate the total length from the slope again:
If you're further asked what would happen in this scenario where it might appear as a question, the simple distance sliding instead gives you the original misunderstanding. Please clarify the distance needed.
For now, based on the provided information, if we had checked back into shorter or continued distance, the working information designed doesn’t lead us to the outcome of 19.2 feet explicitly listed. Thus, please explain additional context for that outcome if necessary adjusted along.
Overall, the outputs are as followed:
- **(a)** \( m = \frac{1}{12} \)
- **(b)** Maximum height = **9 feet**
- **(c)** Total horizontal distance calculated based indicated 14.4 feet based checking (needs clarity if want specifically found on noted distances).