Question 845256: Hi
Would you please help me to answer this problem:
A pilot of a downed airplane fires the emergency flare into the sky. The path of the flare is modeled by the equation h= -0.096(d-25)^2 + 60, where h is the height of the flare in metres when its horizontal distance from where it was propelled is d metres. An emergency helicopter equipped with special binoculars has a line of sight to the spot where the flare was launched. The line of sight from the binocular is modeled by the equation 9x-10y=-14
a) solve the system and give answers rounded to two decimal places.
b) the line of sight from the binoculars spots the flare twice. How high was the flare closest to the ground when it was spotted the first time?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A pilot of a downed airplane fires the emergency flare into the sky.
The path of the flare is modeled by the equation h= -0.096(d-25)^2 + 60, where h is the height of the flare in metres when its horizontal distance from where it was propelled is d metres.
An emergency helicopter equipped with special binoculars has a line of sight to the spot where the flare was launched.
The line of sight from the binocular is modeled by the equation 9x-10y=-14
:
Rewrite the first equation using x and y
y = -.096(x-25)^2 + 60
Write the 2nd equation in the slope intercept form
y = .9x + 1.4
:
a) solve the system and give answers rounded to two decimal places.
-.096(x-25)^2 + 60 = .9x + 1.4
-.096(x^2 - 50x + 625) + 60
-.096x^2 + 4.8x - 60 + 60 = .9x + 1.4
-.096x^2 + 4.8x - .9x - 1.4 = 0
-.096x^2 + 3.9x - 1.4 = 0
using the quadratic formula, obtained two solutions
x = 40.26 m, horizontal distance
x = .36 m " "
:
b) the line of sight from the binoculars spots the flare twice.
How high was the flare closest to the ground when it was spotted the first time?
Replace x with .36 in the easiest equation y = .9x + 1.4
y = .9(.36) + 1.4
y = 1.72 m above the ground, when spotted the 1st time
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