SOLUTION: 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= -0.09

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
RELATED QUESTIONS
Can someone please help me work through this word problem? A flare is fired directly... (answered by solver91311)

A flare is shot upwards from the deck of a ship. The initial upward velocity of the flare (answered by solver91311)

Can someone please walk me through this. A flare is fired directly upward into the... (answered by ankor@dixie-net.com)

please help me answer this question: a flare is launched from a life raft with an... (answered by stanbon)

Hi, I was hoping you can help me on this: Two students standing 3000M apart see the... (answered by ankor@dixie-net.com)

help me please!!!!!This is for a test!!!!! How do you get the answer!!!!! A small... (answered by Earlsdon)

how would you solve this problem and show work i'm trying to understand the concept, i... (answered by Alan3354)

how would you solve this problem and show work i'm trying to understand the concept, I... (answered by Theo)

How would you solve this problem and show work i'm trying to understand the concept, i... (answered by solver91311)