Wikipedia:Reference desk/Archives/Mathematics/2013 January 22

= January 22 =

calculus
what do the two problems of recovering two numbers from their sum and product or from their difference and product have to do with quadratic equations as we understand them today?

mesopotamians mathematics — Preceding unsigned comment added by Merlyn123 (talk • contribs) 13:19, 22 January 2013 (UTC)
 * If S=x+y and P=xy, then P=x(S-x) which is quadratic in x . Bo Jacoby (talk) 13:41, 22 January 2013 (UTC).

MDAS method
2+2+2x0=4 because you need to do multiplication first before addition. This is know to me as the MDAS (multiply, divide, add, subtract) method. My question is, why do you need to do it like that? Whats the logic behind this method? 203.112.82.128 (talk) 17:12, 22 January 2013 (UTC)


 * See order of operations. Short answer is there is no reason why the order of operations has to be MDAS. That just happens to be an order that seems natural to many people. For an alternative, see reverse Polish notation. In RPN your sum would be written as 2 2 + 2 0 x +. Gandalf61 (talk) 17:23, 22 January 2013 (UTC)


 * Totting up money is what people mostly use maths for. If you consider that you'll see why the rule is pretty sensible for addition and multiplication. Try writing three apples at 50p and 2 oranges at 60p as a calculation to get the total cost. Dmcq (talk) 18:16, 22 January 2013 (UTC)

The J (programming language) set implicite parentheses to the right like this 3+4*5 23   3*4+5 27 Bo Jacoby (talk) 21:54, 22 January 2013 (UTC)

Essentially, it's arbitrary. In theory, these operators are functions, and we could write everything in function notation if we wanted to. 3 + 5 is really +(3, 5), and 2 * 4 + 5 is +(*(2, 4), 5). We chose our order of operations so we wouldn't have to put parentheses all over the place. It turns out that giving multiplication higher priority over addition makes many common formulae much easier to write. BlueBattery (talk) 05:12, 23 January 2013 (UTC)


 * There isn't really an order of operations. In the expression 1 + 2 + 3 x 4 you can reduce 1+2 first, getting 3 + 3 x 4, and the final result will be the same. The so-called "order of operations" is really a set of rules for introducing missing grouping parentheses. Once you've added the correct parentheses (in this case, "1 + 2 + (3 × 4)") you can reduce things in any order as long as you don't cross an unbalanced parenthesis (it makes no sense to reduce "2 + (3", for example).


 * The rule that multiplication binds tighter than addition exists because it's convenient for writing polynomials like x² + 2·x·y + y². The rule that mixed × and ÷ are left-parenthesized (((1 ÷ 2) ÷ 3) × 4) exists only in grade school. Even the symbol ÷ only exists in grade school. In real mathematics / is used for division, but inconsistently: a·b / c·d probably means (a·b) / (c·d), while 1/√2·x probably means (1/√2)·x. Of course, in most programming languages, / and * behave like the grade-school ÷ and ×. -- BenRG (talk) 20:00, 23 January 2013 (UTC)

Examples of (1+1/n)^n in nature.
Can you give me real world examples this function? — Preceding unsigned comment added by Ap-uk (talk • contribs) 18:27, 22 January 2013 (UTC)
 * I don't know if this counts as "nature", but it shows up pretty straightforwardly when you work with compound interest. Looie496 (talk) 19:26, 22 January 2013 (UTC)


 * Not sure about "in nature", but $$(1+r/n)^n$$ is the effective annual rate of return of an annuity that is compounded n times at an annual rate of r: see compound interest. Also $$(1-1/n)^n$$ is the probability of placing n labelled letters into n mailboxes so that no person gets the right letter.  :-)  Sławomir Biały  (talk) 19:28, 22 January 2013 (UTC)
 * Is that right? If n=2, there are two mailboxes and two envelopes, so either the first envelope goes into the right mailbox or the wrong one, with equal probabilities of 1/2, so the probability of no box getting the right letter is 1/2; but the formula gives 1/4. Am I confused? Duoduoduo (talk) 13:34, 24 January 2013 (UTC)
 * The first letter has probability $$1/2$$ of going into the wrong mailbox, and the second letter also has probability $$1/2$$ of going into the wrong mailbox. (That is, the mail is placed into the boxes "with replacement".)  Sławomir Biały  (talk) 13:58, 24 January 2013 (UTC)

Why only one real cube root?
Under "Cube roots" in the "Nth-root" article it says "Every real number x has exactly one real cube root". Why isn't for example -2 considered a real root of 8, but 2 is? — Preceding unsigned comment added by 84.215.10.99 (talk) 23:24, 22 January 2013 (UTC)
 * The cube of &minus;2 is not 8. It's &minus;8. --Trovatore (talk) 23:27, 22 January 2013 (UTC)

Ofcourse, thanks. Starting to get a bit late I guess... — Preceding unsigned comment added by 84.215.10.99 (talk) 23:30, 22 January 2013 (UTC)