Access Ramp A wooden access ramp is being built to reach a platform that sits 30 inches above the floor. The ramp drops 2 inches for every 25 -inch run. Write a linear equation that relates the height y of the ramp above the floor to the horizontal distance x from the platform. Find and interpret the x -intercept of the graph of your equation. Design requirements stipulate that the maximum run be 30 feet and that the maximum slope be a drop of 1 inch for each 12 inches of run. Will this ramp meet the requirements? Explain. What slopes could be used to obtain the 30 -inch rise and still meet design requirements?
Access Ramp A wooden access ramp is being built to reach a platform that sits 30 inches above the floor. The ramp drops 2 inches for every 25 -inch run. Write a linear equation that relates the height y of the ramp above the floor to the horizontal distance x from the platform. Find and interpret the x -intercept of the graph of your equation. Design requirements stipulate that the maximum run be 30 feet and that the maximum slope be a drop of 1 inch for each 12 inches of run. Will this ramp meet the requirements? Explain. What slopes could be used to obtain the 30 -inch rise and still meet design requirements?
Access Ramp A wooden access ramp is being built to reach a platform that sits
30
inches above the floor. The ramp drops
2
inches for every
25
-inch run.
Write a linear equation that relates the height y of the ramp above the floor to the horizontal distance
x
from the platform.
Find and interpret the
x
-intercept of the graph of your equation.
Design requirements stipulate that the maximum run be
30
feet and that the maximum slope be a drop of
1
inch for each
12
inches of run. Will this ramp meet the requirements? Explain.
What slopes could be used to obtain the
30
-inch rise and still meet design requirements?
(a)
Expert Solution
To determine
A linear equation that relates the height y of the ramp above the floor to the horizontal distance x from the platform, where a wooden access ramp is being built to reach a platform that sits 30 inches above the floor. The ramp drops 2 inches for every 25- inch run.
Answer to Problem 123AYU
Solution:
A linear equation that relates the height y of the ramp above the floor to the horizontal distance x from the platform is y=−225x+30.
Explanation of Solution
Given Information:
A wooden access ramp is being built to reach a platform 30 inches above the floor.
The ramp drops 2 inches for every 25- inch run.
Explanation:
The general form linear equation is y=mx+b where m is a slope and b is y− intercept.
By looking the graph, the highest vertical distance is 30 inches. That is for x=0, y=30.
Substitute x=0, y=30 in y=mx+b, get
30=m⋅0+b
⇒b=30
The slope is the change in x divided by change in y.
Since, if the ramp drops 2 inches, then change in y is −2 and if the run is 25 inches, then change in x is 25.
Therefore, slope is −225.
The linear equation becomes y=−225x+30.
Therefore, a linear equation that relates the height y of the ramp above the floor to the horizontal distance x from the platform is y=−225x+30.
(b)
Expert Solution
To determine
The x− intercept of the graph of equationthat relates the height y of the ramp above the floor to the horizontal distance x from the platform, where a wooden access ramp is being built to reach a platform that sits 30 inches above the floor. The ramp drops 2 inches for every 25- inch run.
Answer to Problem 123AYU
Solution:
The x− intercept of the graph of equation y=−225x+30 is x=375.
Explanation of Solution
Given Information:
A wooden access ramp is being built to reach a platform 30 inches above the floor.
The ramp drops 2 inches for every 25- inch run.
Explanation:
From the part (a), the linear equation is y=−225x+30.
To find x− intercept set y=0.
⇒−225x+30=0
⇒−225x=−30
Multiply both sides by −252,
⇒x=−30⋅(−252)
⇒x=15⋅25
⇒x=375
Therefore, the x− intercept of the graph of equation y=−225x+30 is x=375.
(c)
Expert Solution
To determine
The ramp will meet the requirements or not, where design requirements stipulate that the maximum run be 30 feet and the maximum slope be a drop of 1 inch for each 12 inches of run.
Answer to Problem 123AYU
Solution:
It will meet the design requirements for the slope.
Explanation of Solution
Given Information:
A wooden access ramp is being built to reach a platform 30 inches above the floor.
The ramp drops 2 inches for every 25- inch run.
Explanation:
Let the maximum run if of the ramp is equal to 30 feet.
From the part (b), run of the ramp is 375 inches.
Here, need to convert 375 inches into feet.
By using 12 inches = 1 feet.
Implies that, 1 inches = 112 feet.
Implies that, 375 inches = 37512 feet.
=31.25 feet
Since, the ramp exceed the maximum run, the ramp will not meet the design requirements.
The slope is division of the change in y by the change in x.
Since, if the ramp drops 1 inches, then change in y is −1 and if the run is 12 inches, then change in x is 12.
Therefore, slope is −112.
Compare the slopes −225 and −112.
It is observed that, ramp slope is less than that of the design requirements.
Since maximum slope can be −112.
It will meet the design requirements for the slope.
(d)
Expert Solution
To determine
The slope that could be used to obtain the 30 inch rise and still meet design requirements.
Answer to Problem 123AYU
Solution:
The slope that could be used to obtain the 30 inch rise and still meet design requirements is m=−112.
Explanation of Solution
Given Information:
A wooden access ramp is being built to reach a platform 30 inches above the floor.
The ramp drops 2 inches for every 25- inch run.
Explanation:
The maximum run of the ramp cannot larger 30 feet.
The x intercept of the graph in part (b) is also the run of the ramp in inches.
Convert 30 feet into inches by using 1 feet =12 inches.
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