An airplane is flying at an altitude of 4000 feet and descends at a rate of 200 ft./m determine whether the altitude is proportional to the number of minutes. Explain your reasoning?
I'm sure Alaniz is not your School Subject.
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To determine whether the altitude of the airplane is proportional to the number of minutes, we need to check if there is a constant ratio between the altitude and the corresponding number of minutes.
First, let's define the variables:
- A: altitude of the airplane (in feet)
- t: time in minutes
We are given that the airplane starts at an altitude of 4000 feet and descends at a rate of 200 ft./m, which means it descends 200 feet for every minute passed. Mathematically, we can express this as:
A = 4000 - 200t
Now, let's calculate the altitude for different values of time:
- For t = 0 minutes:
A = 4000 - 200(0) = 4000
So, when t = 0, the altitude is 4000 feet.
- For t = 1 minute:
A = 4000 - 200(1) = 4000 - 200 = 3800
So, when t = 1, the altitude is 3800 feet.
- For t = 2 minutes:
A = 4000 - 200(2) = 4000 - 400 = 3600
So, when t = 2, the altitude is 3600 feet.
By calculating the altitude for multiple values of time, we can see that the altitude decreases by 200 feet for each minute passed. This means there is a constant ratio of 200 feet per minute, indicating a proportional relationship between altitude and the number of minutes.
Therefore, we can conclude that in this scenario, the altitude of the airplane is proportional to the number of minutes.