SOLUTION: Help would be REALLY REALLY REALLY appreciated! 1. 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 de

Question 768523: Help would be REALLY REALLY REALLY appreciated!
1. 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.)

2. Suppose the altitude of a rising hot-air balloon is given by h = 0.04 t2 + 2t, where "t" is the time in seconds after the balloon leaves the ground. How long will it take for the balloon to reach an altitude of 200 feet?
3. Devon tosses a horseshoe at a stake 30 feet away. The horseshoe lands no more than 3 feet from the stake. Write an absolute value inequality that represents the range of distances that the horseshoe travels.

How in gods name do you do these problems?
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
1. 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?

d = 143117.3 feet
----------------------
(b) How tall is the mountain, if the surveyor can see 15 miles? (Note: 1 mile equals 5280 feet.)

h =~ 612.5 feet
------------------------
2. Suppose the altitude of a rising hot-air balloon is given by h = 0.04 t2 + 2t, where "t" is the time in seconds after the balloon leaves the ground. How long will it take for the balloon to reach an altitude of 200 feet?
h = 0.04t^2 + 2t = 200

(t + 100)*(t - 50) = 0
t = 50 seconds
===============
3. Devon tosses a horseshoe at a stake 30 feet away. The horseshoe lands no more than 3 feet from the stake. Write an absolute value inequality that represents the range of distances that the horseshoe travels.
------------
Minimum is 30 - 3 feet
Max is 30 + 3 feet
---
27 <= d <= 33
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