Quick math problem

There's no justification for rounding here. For instance, clocks that are accurate to within 1 tenth of a second (or whatever) would always be half a second off if they "rounded to the nearest whole second" or something strange like that. There is absolutely no reason why you'd round to the nearest minute, either. If it's 3:12 and 55 seconds, you still say it's still 3:12, and "rounding" would just make half a minute off compared to the way the rest of the world tells time.

This is a case where, if unspecified, rounding is completely unjustified.

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Original post by cowsarenotevil There's no justification for rounding here. For instance, clocks that are accurate to within 1 tenth of a second (or whatever) would always be half a second off if they "rounded to the nearest whole second" or something strange like that. There is absolutely no reason why you'd round to the nearest minute, either. This is a case where, if unspecified, rounding is completely unjustified.

Oh, excellent example. I'll present that to him, perhaps he'll change his mind. I doubt it, though. I'm going to find the director of math and talk to her.

I revised my post slightly while you're replying, if you didn't see it; I think it's slightly more convincing.

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Original post by cowsarenotevil I revised my post slightly while you're replying, if you didn't see it; I think it's slightly more convincing.

I just saw it. Once again, thanks. I don't like teachers like this :( Now I have to find time to talk to the director of the math department.

Some teachers are just awful, and get something into their head and regardless of technical correctness will mark you wrong. Some professors will say to you, "I write y' instead of dy/dx and GOD HELP YOU IF YOU DON'T DO THE SAME" even if you're perfectly in the right to write y'.

In other words: don't waste the energy worrying. You're in the right, he's a douchebag, and there's nothing you can do about it.

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Original post by nullsquared x is a positive number of hours f(x) = 25 Using a quick graph, we find f(6.2108) = 25 (that's given, f itself doesn't matter)

The MEANING of f matters!

For example, if you earn 3 dollars per hour, and you need 10 dollars total to buy something, how many hours should you work, 3 or 4? In this case, 3 isn't enough, so 4 is the correct answer.

On the other hand, if you are an employer who pays his employee said 3 dollars per minute and all you have is 10 dollars, then you can only pay him for 3 hours, not 4. So the answer depends on what f actually means. Makes sense?

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Original post by DevFred The MEANING of f matters! For example, if you earn 3 dollars per hour, and you need 10 dollars total to buy something, how many hours should you work, 3 or 4? In this case, 3 isn't enough, so 4 is the correct answer.

You're right, but the question would be "how many hours do you need to work to earn at least 10 dollars?" because you get paid every hour, not continuously.

My function is not step-based, so this doesn't apply. The question wasn't "at the beginning of what minute will f(x) be at least 25?" in which case the answer would indeed be 3:13.

As others suggested, I would not worry about talking to the director. Some teachers are just like this. Just be happy it was one problem, and not an entire test (I have had that before). If you stir the pot on this one, you may find your teacher has a knee-jerk reaction which really puts you on the outs. There are only a couple more weeks left in the semester, so I would just let it go.

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Original post by jackolantern1 As others suggested, I would not worry about talking to the director. Some teachers are just like this. Just be happy it was one problem, and not an entire test (I have had that before). If you stir the pot on this one, you may find your teacher has a knee-jerk reaction which really puts you on the outs. There are only a couple more weeks left in the semester, so I would just let it go.

Alright, I guess I'll let it be. Teachers like this really annoy me, though. Especially since he's also my APCS teacher (and in there it's practically as if he's in a relationship with Java). I think he has it out for me since I always get the top score of the class, yet I don't pay attention in class at all. USA high school education FTL

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Original post by nullsquared My function is not step-based, so this doesn't apply.

So what exactly is the function/the question?

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Original post by DevFred Quote: Original post by nullsquared My function is not step-based, so this doesn't apply. So what exactly is the function/the question?

The question is in my OP:
Since x is the number of hours, if the starting hour is 9 AM, at what time (hour and minute) will f(x) = 25?

f(x) itself happens to be the amount of a drug left in a body where x = 0 is the initial consumption.

I think I agree with your teacher -- the nearest minute is sort of implied. But I can see it's a grey area too, so if I was your teacher, and you argued your point to me, I'd probably give it to you. I do that kind of thing almost every semester, actually. This semester it's statistics, but seriously, you'd be shocked at how much tripe I get from students... the occasional well-reasoned, polite argument is refreshing, so if you keep it civil, you might have a shot 8)

I'm going to side with the teacher on this one; the question specifically asks for 'hours and minutes'. When talking about hours and minutes you don't talk in fractions of minutes, at best you'll talk in seconds however the question already precludes the use of seconds in the answer.

Thus following on from that, using standard rounding rules, the answer would be 3:13.

The question could have been worded better I admit, but thats life.

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Original post by phantom Thus following on from that, using standard rounding rules, the answer would be 3:13.

I don't understand these "standard rounding rules."

If event A happens at 6:50 and you're asked at which hour this event happens, it would be at the 6th hour, not the 7th hour.

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Original post by nullsquared at what time (hour and minute) will f(x) = 25? f(x) itself happens to be the amount of a drug left in a body where x = 0 is the initial consumption.

As I said, it depends on the question. If a police officer wants to know up to which point the drug can be detected in the body (I presume 25 is some sort of threshold?), 3:12 is the correct answer. If he wants to know when the drug cannot be detected anymore, 3:13 is the correct answer.

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Original post by DevFred Quote: Original post by nullsquared at what time (hour and minute) will f(x) = 25? f(x) itself happens to be the amount of a drug left in a body where x = 0 is the initial consumption. As I said, it depends on the question. If a police officer wants to know up to which point the drug can be detected in the body (I presume 25 is some sort of threshold?), 3:12 is the correct answer. If he wants to know when the drug cannot be detected anymore, 3:13 is the correct answer.

.. and as I said, the question was "Since x is the number of hours, if the starting hour is 9 AM, at what time (hour and minute) will f(x) = 25?" Not a threshold, but a value.

I understand your point, but that is not the case here.

So it really is a pure math question without any background story? How lame :)

I'm going to take your word that you've presented the situation fairly. If you haven't, then disregard what I'm about to say. Otherwise, read on.

If you're willing to risk developing a bad relationship with this teacher, contrary to what others have suggested I would urge you to take this further. Obviously you should be nice about it, but--if you are willing to face the potential consequences--you should make sure your teacher understands that he's being unreasonable, unnecessarily hard to get along with, and above all disrespectful. On the surface, absolutely nothing will happen because universities virtually never do anything with student feedback, but there's a possibility your teacher may remember you and do a better job in the future. You could potentially spare future students from similar frustration.

While there are legitimate reasons for seeing the problem from your teacher's perspective, there are also legitimate reasons for seeing the problem from your perspective. If he won't admit this or make any compromise at all, it's obvious he doesn't have any respect for you as a student. He either derives perverse enjoyment from exercising arbitrary authority over you or he is too blinded by some irrational emotion (such as arrogance) in order to interact with students in a respectful manner.

Teachers like this are the one of the most fundamental problems with modern education, not just in mathematics but in all subjects.

In my completely anecdotal experience, I've noticed that there's a correlation between incompetence in a teacher and the teacher's unwillingness to compromise with students and listen to their ideas. For instance, I haven't had any problems like this with tenured professors, but I've had more problems like this than I can count on one hand with graduate student teachers. Am I the only one who has noticed this correlation? (Note: I exclude from these considerations large lecture hall courses, which are pedagogical nightmares and constitute another fundamental problem with modern university education.)

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Original post by nullsquared Quote: Original post by phantom Thus following on from that, using standard rounding rules, the answer would be 3:13. I don't understand these "standard rounding rules." If event A happens at 6:50 and you're asked at which hour this event happens, it would be at the 6th hour, not the 7th hour.

Nope, it would be the 7th hour;
0 -> 1 = 1st hour
1 -> 2 = 2nd hour
2 -> 3 = 3rd hour
3 -> 4 = 4th hour
4 -> 5 = 5th hour
5 -> 6 = 6th hour
6 -> 7 = 7th hour