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.

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!

Hello! i hope this
since the cosine is the ratio of the adjacent side to the hypotenuse, you can see that cos 60° = ½. answer. according to the property of cofunctions (topic 3), sin 30° is equal to cos 60°. sin 30° = ½.