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A hot-air balloon is 1200 feet off the ground and its altitude is slowly changing at a constant rate of −7 1/2 feet per second. How many seconds, s, will it take for the balloon to drop to below 310 feet? Drag and drop a symbol and value to correctly complete the solution to this inequality.

Sagot :

Using a linear function, it is found that it will take 118.7 seconds for the balloon to drop to below 310 feet.

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.

In this problem:

  • A hot-air balloon is 1200 feet off the ground, hence [tex]b = 1200[/tex].
  • Its altitude is slowly changing at a constant rate of −7 1/2 feet per second, hence [tex]m = -7\frac{1}{2} = -7.5[/tex]

Then, the equation is:

[tex]y(t) = -7.5t + 1200[/tex]

It will drop below 310 feet when:

[tex]y(t) < 310[/tex]

Hence:

[tex]-7.5t + 1200 < 310[/tex]

[tex]-7.5t < -890[/tex]

[tex]7.5t > 890[/tex]

[tex]t > \frac{890}{7.5}[/tex]

[tex]t > 118.7[/tex]

It will take 118.7 seconds for the balloon to drop to below 310 feet.

You can learn more about linear functions at https://brainly.com/question/25823744

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