Wikipedia:Reference desk/Archives/Mathematics/2009 January 9

= January 9 =

a question regarding liters and milliliters
can anyone answer me how many milliliters are in a 1/16 liter? i dont think it could be answered; my friend thinks it is approx 62.5(?) would appreciate a quick response. thank you04:28, 9 January 2009 (UTC)Anilas (talk)
 * 1 litre is 1000 millilitres, by definition. Thus 1/16 of a litre is 1/16 of 1000 millilitres. For more, see long division. Algebraist 04:38, 9 January 2009 (UTC)
 * Or calculator. ;) --Tango (talk) 12:49, 9 January 2009 (UTC)
 * It is exactly 62.5 mL; your friend is a genius (I am dumbfounded as to why he is still solving these trivial problems).


 * P.S What I am trying to say is that you can just evaluate 1000/16 on google (search 1000/16 on google). Please don't ask trivial problems at the reference desk.


 * PST —Preceding unsigned comment added by Point-set topologist (talk • contribs) 12:59, 9 January 2009 (UTC)
 * Google can do more than that. . Taemyr (talk) 13:38, 9 January 2009 (UTC)

Is this equation solveable without a computer/brute force?
let a,b & c exist in set of natural numbers { 0,1,2 ... }

a < b < c

a^2 + b^2 = c^2

a + b + c = 1000

Find a,b and c.212.23.11.198 (talk) 11:49, 9 January 2009 (UTC)


 * Find a right triangle composed of three line segments; the sum of the lengths of which equals 1000 and such that lengths of the line segments form a set of three distinct natural numbers. --Point-set topologist (talk) 11:51, 9 January 2009 (UTC)
 * Yes, it is. There is a unique solution which can be found in under ten minutes of thought. Algebraist 12:19, 9 January 2009 (UTC)


 * (After edit conflict - maybe it took me 11 minutes !) Yes, there is a straightforward algebraic approach. The numbers a, b and c form a Pythagorean triple, so their sum has a particular factorisation, which allows you to find candidate triples quite easily if you are given their sum. For a sum of 1000 there is, I think, only one solution. Gandalf61 (talk) 12:26, 9 January 2009 (UTC)


 * Hint: use Euclid's formula for generating pythagorean triples (see the first section of Pythagorean triple) and figure out what k, m, and n have to be for the sum a+b+c to equal 1000. You should get two answers for triples k, m, and n, but these two will turn out to give the same triple a, b, c. kfgauss (talk) 17:58, 9 January 2009 (UTC)

Algebra II word problem
I've hit a brick wall on this word problem:

"In his job at the post office, Eddie Thibodeaux works a 6.5-hr day. He sorts mail, sells stamps, and does supervisory work. One day he sold stamps twice as long as he sorted mail, and he supervised 0.5 hr longer than he sorted mail. How many hours did he spend at each task?"

Word problems are my Kyptonite. --24.33.75.35 (talk) 23:23, 9 January 2009 (UTC)
 * Algebraist 23:25, 9 January 2009 (UTC)
 * I only need help with writing the exact equation. After that, I can solve it myself. I know there are 3 jobs or 3 "x's". All of which = 6.5. Should it be x + x(2) + x(0.05) = 6.5? --24.33.75.35 (talk) 23:33, 9 January 2009 (UTC)
 * There are three quantities involved, as you correctly observe, so calling them all by the same letter is a bit silly. Why not call them x, y and z, or perhaps m, s, and w (for Mail, Stamps, and supervisory Work)? Algebraist 23:34, 9 January 2009 (UTC)
 * Ok. m + s(2) + w(0.05) = 6.5. Even with the newly labeled quantities, that equation does not look right to me. --24.33.75.35 (talk) 23:47, 9 January 2009 (UTC)
 * It's dangerous to write down symbols without knowing what they are supposed to mean. What, for example, does w(0.05) mean in your formula? Algebraist 23:51, 9 January 2009 (UTC)
 * It's where he worked 0.5 hr longer supervising than he did sorting. Just multiply the two and add the difference to one of the quantities. However, I'm starting to think this word problem has more than one equation. --24.33.75.35 (talk) 23:56, 9 January 2009 (UTC)
 * Very good. Why don't you forget about equations for a second and think about what relations between your quantites are given by the question? Algebraist 23:59, 9 January 2009 (UTC)
 * I've got to go to work. I'll toy with it on my breaks and tell you what I come up with. Thanks for the help so far. --24.33.75.35 (talk) 00:07, 10 January 2009 (UTC)
 * I'll give you a hint - in order to solve a problem with 3 variables you need 3 equations. Read through the information given and try and find 3 relationships. --Tango (talk) 00:49, 10 January 2009 (UTC)

Using x to represent "sort", 24.33...'s original approach seems fine but his/her 3rd term is wrong. It shouldn't be (x(0.05)) but should be (x+0.5), thus using one variable and one equasion:


 * (x)+(2*x)+(x+0.5)=6.5
 * 4*x+0.5=6.5
 * 4*x=6
 * x=1.5

hydnjo talk 03:06, 10 January 2009 (UTC)


 * True, although I think it is best to do it step by step when learning rather than substituting the 2nd two equations into the first without writing them down. It makes it less likely to make mistakes like the OP did with the final term. --Tango (talk) 03:13, 10 January 2009 (UTC)


 * Also true except that the OP grasped the concept but made a bit of a beginner's mis-step with that third term which could happen regardless of method. I'd encourage the original method as he/she did understand the simplest notation (forgiving that 3rd term). hydnjo talk 03:21, 10 January 2009 (UTC)
 * As I said, doing it step by step and writing down all the steps makes it less likely that you will make such a mistake. --Tango (talk) 23:34, 10 January 2009 (UTC)

Now this thread is a bit silly. The OP was just driven away and is not going to learn anything (despite your efforts to make him learn something). I am not saying that you didn't follow the right path in teaching the OP, but I think that you could have done it a lot quicker and more easily. PST —Preceding unsigned comment added by Point-set topologist (talk • contribs) 12:56, 11 January 2009 (UTC)