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my word problem is :  a pilot of a downed airplane fire the emeregency flare into the sky. the path of the flare is modeled by the equation h = -.096)d-25)^2 +60. where h is the height of the flare in metres when its horisontal distance from where it was propelled is d metres.  an emeregency helicopter equipped with special binoculars has a line of sight to the spot where the flare was launched.  the lon of sight from the binoculars is modeled by the equation 9x-10y=-14.  solve the system.

Answer
Your formula is a little garbled but I think it is

h = -(0.96)・(d-25)^2+60.

This is a parabola with apex of 60 m at d=25  (dh/dd = -2(0.96)(d-25) = 0 when d=25 which is where the slope = 0).

The eqn for the line-of-sight (LOS) is 9x-10=-14, which can be written in the more familiar form

y = 14/10 + (9/10)x.

I assume what you mean by "solve the system" is to find where these curves intersect. Just set them equal to each other with d=x and h=y and solve for x.

Let me know if this is the right form of the question.

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randy patton

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college mathematics, applied math, advanced calculus, complex analysis, linear and abstract algebra, probability theory, signal processing, undergraduate physics, physical oceanography

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