I need help solving the b portion of the equation.
15. Assume that a surveyor stands at the top of a mountain that is “h” feet tall. If the distance (in feet) that he can see is defined by d = 3200.2 SQRT(h), then answer the following. (a) How far can the surveyor see from the top of a 2000-foot mountain? (b) How tall is the mountain, if the surveyor can see 15 miles? (Note: 1 mile equals 5280 feet.)
I would really appreciate help...tahnkys
for b)
d = 15 miles, so
15(5280) = 3200.2√h
24.74845 = √h
612.5 = h
so the mountain is 612.5 feet high.
Thank you
To solve part (b) of the equation, where the surveyor can see 15 miles, we can use the given formula d = 3200.2 SQRT(h).
First, we need to convert the distance from miles to feet. Since 1 mile is equal to 5280 feet, we multiply 15 miles by 5280 to find the equivalent distance in feet:
Distance in feet = 15 miles × 5280 feet/mile = 79,200 feet.
Now that we have the distance in feet, we can substitute it into the formula and solve for h:
79,200 = 3200.2 SQRT(h).
To isolate the SQRT(h), divide both sides of the equation by 3200.2:
79,200 / 3200.2 = SQRT(h).
Simplifying the left side, we have:
24.7496093425 ≈ SQRT(h).
Now, square both sides of the equation to remove the square root:
(24.7496093425)^2 = h.
Simplifying further, we have:
611.516869 ≈ h.
Therefore, the height of the mountain is approximately 611.516869 feet if the surveyor can see 15 miles.