Question

An airplane ascends to a crushing altitude at the rate of 1,000 ft/min for m minutes. What constraints, if any, are there on the domain? Explain.

Answer 1

The domain for the variable 'm' has no constraints and can take any positive value as long as it represents a valid amount of time.

Step-by-step explanation:

The domain of the problem refers to the restrictions or constraints on the values that the variable 'm' can take. In this case, the variable 'm' represents the number of minutes that the airplane ascends.

However, there are no constraints on the domain for this problem. The variable 'm' can take any positive value, as long as it represents a valid amount of time. For example, 'm' could be 5 minutes, 10 minutes, or any other positive value.

Answer 2

Since time is the x value due to that the altitude is based off of the time, there are a few things that we can establish here.
First, you can't be a certain speed for negative time, as there is no such as negative time. Although there is a way to have negative time which defines the time before, the way the question is asked ("for m minutes") prevents this as you cannot have the rate of 1,000 ft/min for negative minutes. If the question was different (e.g. if it asked for the speed starting when it was 1,000 ft/min, there was a time where the plane got to 1,000 ft/min, so before that is fine), it could have negative time, but it cannot here.

Next, how long can the plane be flying at the rate of 1,000 ft/min for? There's no limit on jet fuel stated in the question (or anything similar), so we can assume that the plane goes on forever, making the domain of m, or the time, equal to [0, inf)

Feel free to ask further questions!