Wikipedia:Reference desk/Archives/Mathematics/2012 September 22

= September 22 =

a?
problem 20. I saw the answer key but still unable to understand what is going on. I understand the binary expansion part. I get lost in the statement "it follows that the coefficient of x^2012 is equal to 2^0 + 2^1 + 2^5 = 2^6. answer key part 1, answer key part 2. Thanks!Pendragon5 (talk) 00:02, 22 September 2012 (UTC)


 * A product of sums is the sum of all the possible products; say (a+b)*(c+d)*(e+f): the result will contain every product you can make by picking one of each sum,so for example a*d*e, b*c*e, b*c*f and five others.
 * In your polynomial, you know which factors supply the power of x part, so the rest must provide the coefficient: showing only the parts that make up the x2012 term : (x1024+..)*(x512+..)*(x256+..)*(x128+..)*(x64+..)*(..+ 32)*(x16+..)*(x8+..)*(x4+..)*(..+2)*(..+1). And 1*2*32=64=26 Ssscienccce (talk) 02:11, 22 September 2012 (UTC)
 * Oh okay I think I got it now. Thanks! I also have another question. How can I convert 2012 into binary number without the answer key?Pendragon5 (talk) 19:37, 22 September 2012 (UTC)
 * Binary_numeral_system, first paragraph. — Quondum 21:02, 22 September 2012 (UTC)
 * For a number like 2012, close to 2048, (=211), a shorter way is: you know that 211-1 = 2047 is 11111111111, and 2047-2012=35; So you have to subtract 35 which is expressed as a sum of powers of two: 32 + 2 + 1, so from (32;16;8;4;2;1) you know the positions that have to become zeros to get 2012: 11111011100  Ssscienccce (talk) 08:56, 25 September 2012 (UTC)

Commutability of integration
Is $$\int (\int f(r) dr) dv$$ the same as $$\int (\int f(r) dv) dr$$? 71.207.151.227 (talk) 21:04, 22 September 2012 (UTC)


 * See Fubini's theorem.  Sławomir Biały  (talk) 21:09, 22 September 2012 (UTC)