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Answer :
Final answer:
The independent quantity is time and the dependent quantity is the plane's altitude. For a constant ascent rate of 900 feet per minute, it takes 20 minutes for the plane to reach 18,000 feet.
Explanation:
The student's question involves calculating the rate of change in altitude for a commuter plane flight, which is a mathematics problem in algebra involving rates of change and linear functions.
The independent quantity in this scenario is time since the altitude change depends on the passage of time.
The dependent quantity is the altitude of the plane because it varies depending on the time elapsed.
Since the plane ascends at a constant rate of 900 feet per minute, and the total ascent distance is 18,000 feet, we can use a linear function to model this situation.
To climb to 18,000 feet, it would take 18,000 feet / 900 feet per minute = 20 minutes. Since the ascent is the first half of the flight, and the flight takes 40 minutes in total, this makes intuitive sense.
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