anonymous
  • anonymous
Is there an ISBN that has the form : x - 315266-78-2?
Physics
  • Stacey Warren - Expert brainly.com
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chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
This question I have right now in my math course, we've had null information about how to do it? could anyone explain to me how to?
anonymous
  • anonymous
@IrishBoy123 you know anything bout this?
IrishBoy123
  • IrishBoy123
ISBN is something to do with books and unique ID numbers and that is everything i know, assuming it is actually correct :-)

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Astrophysics
  • Astrophysics
I don't see how this is a question, ISBN's are on the back of your book, is it asking you to get a book with the certain ISBN maybe?
anonymous
  • anonymous
@Astrophysics no, you are suppose to show with math calculation if it is a true ISBN or not!
anonymous
  • anonymous
@perl
Astrophysics
  • Astrophysics
Oh, I have no idea then, sorry :\
anonymous
  • anonymous
It has to do with somekind of sequence, and congruity
anonymous
  • anonymous
we are studying residue class arithmetic or what it is called in english
perl
  • perl
Here is an example ISBN numbers for published books. The ISBN number for our textbook is 0-13-184-868-2. The information is decoded in the first 9 digits. The last digit is for parity check 1 * a1 + 2 * a2 + ... + 9 * a9 = a10 Applying this to our textbook 1 * 0 + 2 * 1 + 3 * 3 + 4 * 1 + 5 * 8 + 6 * 4 + 7 * 8 + 8 * 6 + 9 * 8 = 255 = 2 mod 11 The sum of 9 digits is 255 and it equals to the last digit mod 11.
anonymous
  • anonymous
⇒ a10 = 4 eftersom 11 | 103 + 40 = 143 \[a _{1}, a _{2}, a _{3}, ..., a _{10}\] the numbers in ISBN \[a _{10}\] is choosen like: \[a _{1}+ 2a _{2}+ 3a _{3}+ ..., 9a _{9}+10a_{10}≡ 0 (mod 11)\] if \[a_{10}=10\] you write X Example ISBN=093603103a10 \[a_{10}\] is choosen like \[1 · 0 + 2 · 9 + 3 · 3 + · · · + 9 · 3 + 10 · a_{10} = 103 + 10a_{10} ≡ 0 (mod 11)\] ⇒ \[a_{10} = 4 \] because \[11 | 103 + 40 = 143\]
anonymous
  • anonymous
ah wait I gotta write this down and see
anonymous
  • anonymous
so here I got x+226=2 (mod10)?
perl
  • perl
so we need to check that x - 315266-78-2 can be an isbn number, only if 1*x + 2*3 + 3*1 + 4*5 + 5*2 + 6 * 6 + 7*6 + 8*7 + 9*8 = 2 mod 11
anonymous
  • anonymous
x+226=2 mod 11
perl
  • perl
check again, I got x + 245 = 2 mod 11
perl
  • perl
1*x + 2*3 + 3*1 + 4*5 + 5*2 + 6 * 6 + 7*6 + 8*7 + 9*8 = x + 245
anonymous
  • anonymous
yea.. i got the same
anonymous
  • anonymous
so then should x+245/11 give something with the rest 2..
perl
  • perl
x + 245 = 2 mod 11 x = 2 - 245 mod 11 x = -243 mod 11 x = 10 mod 11
anonymous
  • anonymous
can you explain the last step?
perl
  • perl
but notice that 10 is not a choice for an isbn digit, since it has to be a digit from 0 to 9 so the answer is, there is no x
anonymous
  • anonymous
i mean from -243 to 10 mod 11
anonymous
  • anonymous
yeah but how did you make -243 mod 11 to 10 mod 11?
perl
  • perl
it is easier to use multiple of 11's
perl
  • perl
I am actually using my calculator for negative mod
perl
  • perl
x + 245 = 2 mod 11 with respect to 245 where is the closest multiple of 11 ?
perl
  • perl
22*11 = 242 23*11 = 253
perl
  • perl
245 = 3 mod 11 , so we can substitute (x + 245) mod 11 = (x + 3) mod 11 now solve (x+3) mod 11 = 2 mod 11 x = 2-3 mod 11 x = -1 mod 11
perl
  • perl
when you do negative integers, it is like going backwards with a clock
perl
  • perl
0 mod 11 = 11 mod 11 -1 mod 11 = 10 mod 11 -2 mod 11 = 9 mod 11 -3 mod 11 = 8 mod 11
perl
  • perl
|dw:1442861614220:dw|
perl
  • perl
imagine we have an 11 hour clock
perl
  • perl
|dw:1442861679974:dw|
perl
  • perl
-1 aclock = 10 aclock mod 11 -2 aclock = 9 aclock mod 11 , etc
perl
  • perl
also because -1 mod 11 = (-1 + 11 ) mod 11 = 10 mod 11
perl
  • perl
thats the easiest way to see it. or you can use definition of mod a = b mod n iff b -a is divisible by n -1 = 10 mod because 10 -(-1) is divisible by 11
anonymous
  • anonymous
I got it perl:D thanks alot, but the answear is it isnt a ISBN just because it have to be a integer between 1 and 9?
anonymous
  • anonymous
@perl
anonymous
  • anonymous
between 0 and 9 i mean
perl
  • perl
the answer is, there is no such ISBN, since the only way it would work is if x = 10 but the possible choices for x is 0 - 9 .
perl
  • perl
the only way the total x + 245 can equal 2 mod 11 is if x is 10. but that is not possible for the isbn, x must be integer 0 through 9
anonymous
  • anonymous
@perl thanks alot! :D

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