SOLUTION: For altitudes h up to 10,000 meters, the density D of the earth's atmosphere (in kg/m3) can be approximated by the following formula: D=1.225-(1.12x10^-4)h+(3.24x10^-9)h^2 Appr

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: For altitudes h up to 10,000 meters, the density D of the earth's atmosphere (in kg/m3) can be approximated by the following formula: D=1.225-(1.12x10^-4)h+(3.24x10^-9)h^2 Appr      Log On

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Question 647719: For altitudes h up to 10,000 meters, the density D of the earth's atmosphere (in kg/m3) can be approximated by the following formula:
D=1.225-(1.12x10^-4)h+(3.24x10^-9)h^2
Approximate the altitude if the density of the atmosphere is 0.63 kg/m3. (Round to the nearest meter.)
Answer by DrBeeee(684) About Me  (Show Source):
You can put this solution on YOUR website!
Set D = 0.63 and get
(1) ah^2 + bh + c = 0
When h is in km, we have
a = 3.24 E-3
b = -1.12 E-1
c = 0.595
Or
a = 0.00324
b = -0.112
c = 0.595
Using these simpler decimals we can easily apply the quadratic equation to determine the two roots of (1) as
(2) h = abt 28, 6.5558 km
The first root of ~28 is not a choice because it is out of the solution domain of the equation for the density D.
Answer: The density of earth's atmosphere is 0.63 kg/m^3 at an altitude of 6,556 meters.