An airplane is flying at an altitude of 4000 feet and descends at rate of 200 feet per minute. Determine whether the altitude is proportional to the number of minutes.
To determine whether the altitude is proportional to the number of minutes, we need to compare the change in altitude with the change in time.
In this case, we are given that the airplane descends at a rate of 200 feet per minute. This means that for every minute that passes, the altitude decreases by 200 feet.
To find out if this is proportional, we can use the concept of proportionality. In a proportional relationship, the ratio between the two quantities remains constant.
Let's set up a proportion to compare the change in altitude with the change in time:
Change in Altitude / Change in Time = Rate of Descent
Let's calculate the change in altitude. The airplane starts at an altitude of 4000 feet and descends at a rate of 200 feet per minute. After 1 minute, the altitude decreases by 200 feet, so the new altitude is 4000 - 200 = 3800 feet.
Using this information, we can set up the proportion:
(4000 - 3800) / 1 = 200
Let's simplify this:
200 / 1 = 200
We can see that the proportion is equal on both sides, which indicates that the altitude is indeed proportional to the number of minutes. In this case, the proportionality constant is 200, which means that for every minute that passes, the altitude decreases by 200 feet.
To determine whether the altitude is proportional to the number of minutes, we need to check if the rate at which the altitude changes remains constant.
Given that the airplane is descending at a rate of 200 feet per minute, we can calculate the altitude after a certain number of minutes by subtracting 200 times the number of minutes from the initial altitude of 4000 feet.
Let's calculate the altitude after 1 minute:
Altitude after 1 minute = 4000 - (200 * 1) = 3800 feet
Now, let's calculate the altitude after 2 minutes:
Altitude after 2 minutes = 4000 - (200 * 2) = 3600 feet
And finally, let's calculate the altitude after 3 minutes:
Altitude after 3 minutes = 4000 - (200 * 3) = 3400 feet
By comparing these altitudes, we can observe that the altitude decreases linearly as the number of minutes increases. Therefore, the altitude is proportional to the number of minutes, with a constant rate of change of 200 feet per minute.
no
if it were ascending from the ground at 200 ft/min the height would be proportional.
as it is, the change in altitude is proportional to the time.