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hi guys i need to know a quick way to do this problem

How many ordered pairs of intergers (x,y) satisfy x^2+y^2<9.

note:that is x squared plus y squared.

grubers gives some ways but i dont understand them. Can someone give me quick way to do this. it can even be a TI-83 plus prog. Thnx

By incognito on Friday, January 31, 2003 - 10:21 pm: Edit

Bard, I have a question: Is this exactly what Gruber wrote?

How many ordered pairs of intergers (x,y) satisfy x^2+y^2<9.

or did he say how many ordered pairs of POSITVE integers satisfy the equation?...

By clo on Friday, January 31, 2003 - 10:44 pm: Edit

4 ordered pairs if it is positive and 6 if it is negative since you cant have positive and neg 0.

By incognito on Friday, January 31, 2003 - 11:09 pm: Edit

If they all have to be positive:
(1,1)
(2,1)
(1,2)
(2,2)
TOTAL:4

If none can be negative:
(0,0)
(1,1)
(2,1)
(1,2)
(2,2)
TOTAL:5

If it can be any integer:
(0,0)
(0,1) (0,-1)
(1,0) (-1,0)
(0,2) (0,-2)
(2,0) (-2,0)
(1,1) (-1,1) (1,-1) (-1,-1)
(2,1) (2,-1) (-2,1) (-2,-1)
(1,2) (-1,2) (1,-2) (-1,-2)
(2,2) (-2,2) (2,-2) (-2,-2)
TOTAL:25


Didn't spend TOO much time on this one, so I'm really not sure...


****Here's a short cut: There are 5 posibilities for each part of the set:{-2,-1,0,1,2}.
If there are 5 for the first part, then there are 5 posiblities for the second. So...

5 * 5 = 25.

Sooo...Bard, what's the answer here?

By Bard (Bard) on Friday, January 31, 2003 - 11:50 pm: Edit

incognito u are correct. Its 25

By incognito on Friday, January 31, 2003 - 11:57 pm: Edit

bard, do you undersand the reasoning behind it?

By olive oil on Friday, January 31, 2003 - 11:59 pm: Edit

excuse my ignorance, but what does "ordered pairs" mean?

By meryl on Saturday, February 01, 2003 - 12:29 am: Edit

OLIVE OIL HONEY!!!!!

what incognito meant by "ordered pairs" was like (x,y). So (1,0) would be one ordered pair. (1,2) would be another ordered pair, and so on. get it?
A guardian must always look over his/her people and make sure all is good!!!

By olive oil on Saturday, February 01, 2003 - 12:49 am: Edit

That's what I thought. Thanks to you all is good!!

By incognito on Saturday, February 01, 2003 - 08:52 am: Edit

OK, I know this posting is out of character for me, and that anyone who reads this will think that someone is impersonating me, but it occurred to me a couple hours ago, after deciding to abstain from these chatrooms for at least one hour out of my day, that I may be psychologically troubled. After reflecting upon the multitude of criticism I've recieved for my obsession with the SAT, particularly my fixation on attaining a perfect score, I suddenly recieved a little clarity. It happened when my mother burst into my room and caught me masturbating on a copy of a perfectly-scored SAT. Disgusted, she said, "You'll never get that f*cking 1600, you worthless sh*t! If you just got your filthy asss out of this filthy room and actually got some goddamn sunlight in your eyes maybe you'd have some real friends--people with faces and real names, people who might tell you the truth that you're f*cked-up!" After this, it became apparent to me that there is more to life than posting messages on collegeconfidential.com, pretending I got anything near a 1530 score. It feels good to admit that. Thus, I shall not return to these chatrooms any more. And so I bid farewell to the family I gained here, because I must move on. Next Monday I shall finally look into applying at the community college two miles from where I live, and with that my life shall begin anew! I know others will come after me, impersonating me in these chatrooms, but the real incognito will never return again. Adieu, incognito

By Jason817 (Jason817) on Saturday, February 01, 2003 - 10:54 am: Edit

Lol. Nice try.

By Simon on Saturday, February 01, 2003 - 11:36 am: Edit

What a loser this guy is.The real incognito is registered.

By Qofe (Qofe) on Tuesday, March 11, 2003 - 05:25 pm: Edit

You can get solution on www.helptosolve.com

By Incognito (Incognito) on Thursday, March 13, 2003 - 05:47 pm: Edit

not bad. But its sometimes better to figure it out yourself. "stretch your brain" lol