Question 768523
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 = 3200.2*sqrt(2000)}}}
d = 143117.3 feet
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(b) How tall is the mountain, if the surveyor can see 15 miles? (Note: 1 mile equals 5280 feet.)
{{{d = 3200.2*sqrt(2000)}}}
{{{15*5280 = 3200.2*sqrt(h)}}}
{{{79200/3200.2 = sqrt(h)}}}
{{{h = (79200/3200.2)^2}}}
h =~ 612.5 feet
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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
{{{0.04t^2 + 2t - 200 = 0}}}
{{{t^2 + 50t - 5000 = 0}}}
(t + 100)*(t - 50) = 0
t = 50 seconds
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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.
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Minimum is 30 - 3 feet
Max is 30 + 3 feet
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27 <= d <= 33