Thread: Maths.....

Well i`m glad i`m not the only one confused by the wording on this.
As i said not the best maths teacher.

And thank you all so very very much.

I really do appriciate it

Ian

Yes, the question is not particularly well-worded, but I would argue that since the function is approximating the temperature during maintenance a second-order polynomial is not too far-fetched.

I'd say the use of that particular functional form directly relates to the material being taught at the moment. Linear decrease and subsequent increase would make the question too trivial (as the point of the "V" would need to be specified), and I'd imagine a stochastic differential equation describing the temperature change through time would be beyond the scope of the course.

James.

What he said...

Originally Posted by Hydaral

Part A is easy, t=0, so:

Tmax = 0^2 - 9*0 + 61/4
Tmax = 0 - 0 + 15.25
Tmax = 15.25

I have no idea what completing the square means, but if I sub in a random time for t, let's say 1000 hours, I get:

Tmax = 1000^2 - 9*1000 + 61/4
Tmax = 1000000 - 9000 + 61/4
Tmax = 991015.25

Which doesn't make sense in the given scenario, the temperature should keep going down. It bottoms out at 4.5 hours at -5 degrees and then starts rising again, what happened, the sun come out?

Originally Posted by Jimbo

Yes, the question is not particularly well-worded, but I would argue that since the function is approximating the temperature during maintenance a second-order polynomial is not too far-fetched.

Yeah, that's the only thing you fakemathicst can do, argue...
It is very far fetched, indeed, by Newton's law the temperature change is exponential.

I think students need to learn to deal with singularities, instead of taking the parabolic deus machina. After all in the complex world non-analytic rules!

Originally Posted by Jimbo

Yes, the question is not particularly well-worded, but I would argue that since the function is approximating the temperature during maintenance a second-order polynomial is not too far-fetched.

James.

For the cooling down period, over a short time, this might be true.
However, as soon as the heating starts up again, the temperature graph would be come asymmetrical and then it would look nothing like the 2nd order function anymore.

Originally Posted by Bruno

it would look nothing like the 2nd order function anymore.

but nowhere does the problem state what the reheating period looks like

Originally Posted by BigIan

Well i`m glad i`m not the only one confused by the wording on this.
As i said not the best maths teacher.

I'm reminded of a recent "Frazz" comic strip (sorry, can't get a workable link) where Caulfield plunks a great stack of paper onto Mrs. Olson's desk and later says, "If she can assign story problems, then I can turn in story answers."

But my head hurts just from skimming this thread. And I have a kid in high school whom I'd like to be able to help with math sometimes. (We try to minimize the terror by using the singular form here in the U.S. It doesn't help.) I'm an old-fashioned guy and I need a book--to walk me through from first principles to (let's say) midlevel calculus, and maybe to serve as a reference when I need to refresh what I laughingly call my memory. Any recommendations, to add to the help you've already given Ian?

Thanks in advance!

~Rich

Look at it this way. It's a math exercise. The equation describing the temperature change is stated in the problem description, so it is not in question. It is a taken as fact. What ever odd physical circumstances that might produce this result are not the issue. The math solutions are the issue.

I remember learning this solution method in high school. I'm sure I never used it in my 34-year career as a civil engineer. In my work practical considerations and external factors always seemed to overwhelm the theoretical. I suppose this is not true if you are a research scientist or a mathematician.

Originally Posted by hoglahoo

but nowhere does the problem state what the reheating period looks like

According to this:

whe the heating system is switched off for maintenance the temperature falls untill the work is completed and the system is switched on again.
The temperature then increases untill it once again reaches Tmax. the temperature at ant time (t hours) during the maintenance period is given by:

I concluded that the re-heating is part of the maintenance cycle because it explicitly mentions the rise to Tmax as part of the cycle.

You are quite right Bruno, it does mention the reheating phase. But the reheating phase does not play a role in the solution required, which is simply to find the minimum and the abscissa at the minimum. If a local quadratic approximation to the decline phase is accurate enough in the immediate neighbourhood of the minimum, it does not matter, in the context of the question, what the approximation is like during the reheating phase.

However, I do agree that if you were trying to do this as a real problem, and not a school math exercise, you'd perhaps want to utilise something more realistic. Having said that, I think you guys would be amazed at the number of things that are locally approximated by low-order polynomials in quantitative research and methodological development. A lot of operations research is based on polynomial interpolation and approximation.

James.