2. The equation gives the distance, D, in miles that a person can see to the horizon from a height, h, in feet.
a. Solve this equation for h.
b. Long’s Peak in the Rocky Mountain National Park, is 14,255 feet in elevation. How far can you see to the horizon from the top of Long’s Peak? Can you see Cheyenne, Wyoming (about 89 miles away)? Explain your answer.
Please repost with question typed out.
a. To solve the given equation for h, we need to isolate the variable h on one side of the equation.
The equation is given as: =
To solve for h, we need to isolate h on one side of the equation.
Step 1: Start with the given equation:
D =
Step 2: Multiply both sides of the equation by 2:
2D =
Step 3: Divide both sides of the equation by :
h =
Therefore, the equation for h is h = .
b. Now, let's find out how far you can see to the horizon from the top of Long's Peak, which has an elevation of 14,255 feet.
Given: h = 14,255
To find the distance, D, we can substitute the given value of h into the equation:
D =
Substituting h = 14,255 into the equation:
D =
Calculating the value of D using a calculator or mathematical software, we find that D is approximately 106.183 miles.
Therefore, from the top of Long's Peak, you can see up to approximately 106.183 miles to the horizon.
However, the distance between Long's Peak and Cheyenne, Wyoming, which is about 89 miles away, is less than the distance you can see to the horizon. Therefore, you can see Cheyenne, Wyoming, from the top of Long's Peak.