Wikipedia:Reference desk/Archives/Mathematics/2015 October 9

= October 9 =

Copper price
BENCHMARK copper on the London Metal Exchange closed at $US5,135 a tonne. Please help me, I want to find out how much a kilogram of copper costs 175.45.116.59 (talk) 04:54, 9 October 2015 (UTC)


 * The London Metal Exchange uses the metric tonne, which makes this nice and simple. A tonne is 1,000 kilograms, so to work out the price per kilogram, just divide the price per tonne by 1,000 - in other words, replace the comma with a decimal point. 1 kg of copper costs $5.135. Smurrayinchester 08:10, 9 October 2015 (UTC)


 * Just to clarify, "metric tonne" is a redundancy. There is only one unit spelled tonne, which as Smurray says is a metric one equal to 1,000 kilograms.  There are several units called ton and, since "tonne" and "ton" are commonly pronounced the same, "metric ton" is sometimes used as another name for "tonne" in a context where people may speak also of other kinds of tons. --174.88.134.156 (talk) 02:50, 10 October 2015 (UTC)

Laplace transform
What is the most complete laplace transform table on web?--95.250.182.104 (talk) 14:43, 9 October 2015 (UTC)


 * I'm not sure about "on the web", but Erdelyi's "Tables of integral transforms" contains about 100 pages of tables of Laplace transforms.  S ławomir  Biały  14:59, 9 October 2015 (UTC)


 * Together, these    are fairly comprehensive. While not a table per se, Wolfram alpha can give many Laplace transforms. SemanticMantis (talk) 15:47, 9 October 2015 (UTC)


 * Those are missing Bessel functions, Gamma functions, elliptic functions, parabolic cylinder functions, hyperbolic functions, hypergeometric functions, and Legendre functions. Erdelyi also includes Laplace transforms of orthogonal polynomials.   S ławomir  Biały  14:41, 10 October 2015 (UTC)

Where should I have gotten gas?
I figured out eight years ago when I bought my current car that it got 22 miles to the gallon. I haven't determined whether this is still the case, but let's assume it is. Let us also assume consistent gas mileage regardless of whether I am in the city or the country, or whether I am running my air condtioning or not.

I am approximately 176 miles from the beach. After 70 miles, with my usual route, I cross the border from North Carolina into South Carolina. Regular unleaded gas which may contain ethanol (referred to as "gas" from now on) in the last town before the border was around $2.09.9 (".9" is assumed from now on). At the border, gas was $1.94. South Carolina gas taxes are lower. In the first town, about 15 miles from the border, one place is $1.89, though it is cash only (I try to avoid using cash but it wouldn't have been impossible) and there is a higher price if I use my credit card. One place is $1.87 but there's no place to wash my hands after I finish. Another place is $1.89 but I wasn't close enough to see if that was a credit price. 20 miles farther down the road is the place where I ate lunch, and gas was $1.89. But I figured I could do better. About 20 miles from the beach, one place was $1.79 but I recalled that it was cash only. Another place was $1.79 but it was on the wrong side of the road and the clerk gave me attitude about filling up, explaining how easy it was to "pay at the pump". Well, maybe for her. The one place that had the lowest price some years ago was $1.83, about 15 miles from the beach. I decided it was probably going to go up from there and I filled up.

I was so wrong. In fact, the price kept going down and several places at the beach were $1.79. This has never happened. Still, I was gambling because I had never seen prices continue to go down. One place was $1.78 as I was going home, but I couldn't benefit. The two places that were $1.79 were the same, even though some places were a penny higher and some were a penny lower. I still couldn't benefit. But I returned to that last town and had a decision to make. Now I could have gone to that one other place that was $1.89. By this time I was going to benefit at least a little. Instead, I stopped at the place where I would pay cash and just got milk to eat with my lunch bought 20 miles away. I just decided to wait because gas would be that low soon.

Gas went back up, then down. This week with the "low fuel" light on, I passed a place that was $1.98, though most places were much higher. I got $20 worth.

So are there any mathematical formulas that might tell me what the best move would have been?— Vchimpanzee  •  talk  •  contributions  •  18:28, 9 October 2015 (UTC)


 * This sounds like an optimal stopping problem. It's not the secretary problem, since the prices aren't randomly ordered, but that article may be worth a read anyway. -- BenRG (talk) 21:49, 9 October 2015 (UTC)


 * I've given this problem lots of thought previously. The main issue is that you always have incomplete information.  Even if you knew what every gasoline price was in driving range yesterday, they are subject to change on a daily basis, and they don't always change proportionately either.  Another consideration is that if gas prices are likely to go down over the next few days, you don't want to fill up until it does, whereas if prices are going up, you want to fill up right now.


 * Also note that the fuel you burn to get to a further gas station with lower prices isn't the only cost. There's also wear and tear on the car/depreciation, the value of your time, the chance you'll get a ticket, etc.  I've pretty much concluded that I should try to gas up when on the way to somewhere else, and I've learned there's a small set of gas stations which typically have the lowest prices, so I try to gas up at one of those when I am near.


 * I've also thought it would be great to have an app that could tell you the best gas station to use, but there the problem is getting every gas station, even those with high prices, to send it an update of their prices every day. About the only way I can see to get past that would be a camera aimed at every gas station sign, that does character recognition to determine the current prices. StuRat (talk) 01:11, 10 October 2015 (UTC)


 * By the way, you're allowed to write "$2.099". It's a decimal fraction like any other. —Tamfang (talk) 05:55, 10 October 2015 (UTC)
 * Thanks, optimal stopping was what I was looking for. Anyway, since there's all that extra information and only a finite number of stations, plus the fact that they COULD have changed stations, there's probably not much point.— Vchimpanzee  •  talk  •  contributions  •  15:46, 10 October 2015 (UTC)