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AVIATION An air traffic controller manages the flow of aircraft in and out of airport airspace by guiding pilots during
takeoff and landing. An air traffic controller is monitoring two planes that are in flight near a local airport. The first
plane is at an altitude of 1000 meters and is ascending at a rate of 400 meters per minute. The second plane is at an
altitude of 5900 meters and is descending at a rate of 300 meters per minute.

Respuesta :

Using linear functions, it is found that the two planes will be at the same altitude in 7 minutes.

What is a linear function?

A linear function is modeled by:

[tex]y = mx + b[/tex]

In which:

  • m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
  • b is the y-intercept, which is the value of y when x = 0.

For the first plane:

  • Initial altitude of 1000 meters, hence [tex]b = 1000[/tex].
  • Ascending t a rate of 400 meters per minute, hence [tex]m = 400[/tex].

Hence, the equation is:

[tex]y_1(x) = 400x + 1000[/tex]

For the second plane:

  • Initial altitude of 5900 meters, hence [tex]b = 5900[/tex].
  • Descending t a rate of 300 meters per minute, hence [tex]m = -300[/tex].

Hence, the equation is:

[tex]y_2(x) = -300x + 5900[/tex]

They will be at the same altitude at the value of x for which:

[tex]y_1(x) = y_2(x)[/tex]

Hence:

[tex]400x + 1000 = -300x + 5900[/tex]

[tex]700x = 4900[/tex]

[tex]x = \frac{4900}{700}[/tex]

[tex]x = 7[/tex]

The two planes will be at the same altitude in 7 minutes.

To learn more about linear functions, you can take a look at brainly.com/question/25823744