which hill described in the table is the steepest and why?
A: bell hill; it rises 2/3 foot every 1 foot of horizontal travel
B: dixie hill; it rises one foot for every 3 feet of horizontal travel
C: bell hill; it rises 3 feet for every 2 feet of horizontal travel
D: liberty hill; it rises 2 feet for every 1 foot of horizontal travel
C: Bell hill is the steepest because it rises the most vertical distance for the least amount of horizontal distance, with a ratio of 3:2.
To determine which hill is the steepest, we need to compare the ratios of vertical rise to horizontal travel for each hill.
A: Bell Hill rises 2/3 foot for every 1 foot of horizontal travel.
B: Dixie Hill rises 1 foot for every 3 feet of horizontal travel.
C: Bell Hill rises 3 feet for every 2 feet of horizontal travel.
D: Liberty Hill rises 2 feet for every 1 foot of horizontal travel.
To compare these ratios, we need to find the slope or gradient of each hill. The slope is the ratio of the vertical rise to the horizontal distance. The steeper the slope, the greater the ratio.
Calculating the slopes:
A: Bell Hill slope = (2/3) / 1 = 2/3
B: Dixie Hill slope = 1 / 3 = 1/3
C: Bell Hill slope = 3 / 2 = 3/2
D: Liberty Hill slope = 2 / 1 = 2/1
Comparing the slopes:
The steepest hill is the one with the greatest slope. In this case, the hill with the greatest slope is **Bell Hill** as it has a slope of 3/2. This means Bell Hill rises 3 feet for every 2 feet of horizontal travel.