Given parameters:
Recommend wheelchari ramp slope = [tex]\frac{1}{12}[/tex]
Rise of the new wheel chair ramp = 22 inches
Horizontal length = 24feet
Unknown:
Is the ramp steeper than the recommended = ?
Slope is the ratio of rise to the horizontal distance covered
Mathematically;
Slope = [tex]\frac{Rise}{horizontal distance}[/tex]
Slope of the wheel chair ramp;
covert 24 feet to inches;
1 foot = 12 inches
24 feet = 24 x `12 = 288inches
Slope = [tex]\frac{22}{288 }[/tex] = [tex]\frac{11}{144}[/tex]
The two slopes being compared are;
[tex]\frac{1}{12}[/tex] and [tex]\frac{11}{144}[/tex]
The steeper of the first one 1/12. It has a higher slope compared to the second one.
Using the concept of slope, it is found that since the ramp has a lower slope than [tex]\frac{1}{12} = 0.0833[/tex], it is not steeper than the recommended.
The slope is given by the vertical change divided by the horizontal change, that is:
[tex]m = \frac{\Delta_y}{\Delta_x}[/tex]
In this problem, it rises 22 inches over a horizontal length of 24 feet, hence:
[tex]\Delta_y = 22[/tex]
[tex]\Delta_x = 24(12) = 288[/tex]
Hence, the slope is:
[tex]m = \frac{\Delta_y}{\Delta_x} = \frac{22}{288} = 0.0764[/tex]
Which is less than the threshold of [tex]\frac{1}{12} = 0.0833[/tex], hence it is not steeper than the recommended.
A similar problem is given at https://brainly.com/question/16900875
