SOLUTION: A hostile army fires a missile at you. The path of the missile has a function {{{y=-2x^2+24x-40}}} where x is the number of seconds after the missile is fired and y is the height o

Question 972336: A hostile army fires a missile at you. The path of the missile has a function where x is the number of seconds after the missile is fired and y is the height of the missile in 1000s of feet. You fire an intercepting missile whose path has the function . How long after the enemy missile is fired do they collide? How high are the missiles when the collide?
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
A hostile army fires a missile at you. The path of the missile has a function where x is the number of seconds after the missile is fired and y is the height of the missile in 1000s of feet. You fire an intercepting missile whose path has the function . How long after the enemy missile is fired do they collide? How high are the missiles when the collide?
.
in order for the missiles to collide, they must both be at the same height. Therefore, the y's are equal. So we can set the two equations equal to each other and solve for x:

seconds
How long after the enemy missile is fired do they collide? 2.5 seconds
How high are the missiles when the collide?
solve for y with either of the two equations with x=2.5

thousands of feet
answer: 7500 feet
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