A sloped skate rail starts at 3.25 feet from the ground and slopes down to 12 inches from the ground. The rail travels 8 feet horizontally. Which of the following calculations will give the correct value for slope?
To calculate the slope, we need to find the change in height divided by the change in horizontal distance.
Given:
Initial height = 3.25 feet = 39 inches
Final height = 12 inches
Horizontal distance = 8 feet = 96 inches
The change in height is 39 inches - 12 inches = <<39-12=27>>27 inches.
The change in horizontal distance is 96 inches.
Therefore, the correct calculation for the slope is:
Slope = change in height / change in horizontal distance
Slope = 27 inches / 96 inches
To find the slope of the skate rail, we need to determine the change in height (vertical distance) relative to the change in horizontal distance.
Given:
Starting height = 3.25 feet
Ending height = 12 inches (which is 1 foot)
Horizontal distance = 8 feet
The correct calculation to find the slope is to divide the change in height by the change in distance:
Slope = (Ending height - Starting height) / Horizontal distance
Let's substitute the given values into the equation:
Slope = (1 foot - 3.25 feet) / 8 feet
To calculate the slope, we need to convert both measurements to the same unit. Let's convert 12 inches to feet:
Slope = (1 foot - 3.25 feet) / 8 feet
Slope = (-2.25 feet) / 8 feet
Slope ≈ -0.28125 feet
Therefore, the correct calculation to find the slope of the skate rail is (-2.25 feet) / 8 feet, which yields a slope of approximately -0.28125 feet.
To find the slope of a sloped skate rail, you need to determine the change in vertical distance (rise) divided by the change in horizontal distance (run). In this case:
The starting height is 3.25 feet from the ground, which is 39 inches.
The ending height is 12 inches from the ground.
The change in vertical distance (rise) is 39 inches - 12 inches = 27 inches.
The horizontal distance (run) is given as 8 feet.
To find the slope, divide the change in vertical distance (rise) by the horizontal distance (run):
Slope = Rise / Run
Substituting the values:
Slope = 27 inches / (8 feet × 12 inches/foot)
Now, you need to convert the units to ensure they are consistent:
Slope = 27 inches / (8 × 12 × 12 inches)
Simplify by canceling out the inches:
Slope = 27 / (8 × 12 × 12)
Now calculate:
Slope = 27 / 1152
Slope ≈ 0.0234
So, the correct value for the slope of the sloped skate rail is approximately 0.0234.
The calculation that gives the correct value for the slope is 27 / (8 × 12 × 12).