Driving down a mountain, Tom finds that he has descended 1800 ft. in elevation by the time he is 3.25 mi horizontally away from the top of the mountain. Find the slope of his descent to the nearest hundredth.
slope is descent divided by distance from base. Change one of the units to the other and divide.
To find the slope of Tom's descent, we need to determine the descent (change in elevation) and the distance from the base (horizontal distance).
From the given information, we know that Tom has descended 1800 ft and traveled 3.25 mi horizontally. However, we need to convert these quantities to a consistent unit before calculating the slope.
Let's start by converting the horizontal distance to feet. Since 1 mile is equal to 5280 feet, we can multiply the distance in miles by 5280 to get the equivalent distance in feet:
3.25 mi * 5280 ft/mi = 17,160 ft
Now that we have the horizontal distance in feet, we can proceed to calculate the slope. The formula for slope is:
slope = descent / distance from base
Plugging in the values we know:
slope = 1800 ft / 17,160 ft
Dividing these two values:
slope ≈ 0.105
Therefore, the slope of Tom's descent, rounded to the nearest hundredth, is approximately 0.105.