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# 161
05232011, 10:37 PM
Got the others for #1:
2 of bowl C, and 6 of bowl A
and 2 of bowl B and 4 of bowl A.
I'll let someone else get the tougher ones ^^ lol.
2 of bowl C, and 6 of bowl A
and 2 of bowl B and 4 of bowl A.
I'll let someone else get the tougher ones ^^ lol.
# 162
05232011, 10:43 PM
Krisnda is doomed ...
ColdAsLife, 90, Proud Sage ArcherArchRaziel, 5x, Cleric
XBushidoX, xbushidox.guildportal.com
Rectitude, Courage, Benelovence, Respect, Honesty, Honor, Loyalty.
# 163
05232011, 10:44 PM
# 164
05232011, 11:01 PM
Quote:
I gave up with the old problems since no one wanted to do them. I'll pull these straight from competitions from now on, entirely, I promise... :)
So here's this week's set: 1. Cafe de la Peche offers three fruit bowls: Bowl A has 2 apples and one banana; Bowl B has 4 apples, 2 bananas, and 3 pears; Bowl C has 2 apples, 1 banana, and 3 pears. Your doctor tells you to eat exactly:16 apples, 8 bananas, and 6 pears per day. How many of each type of bowl can you buy so there's no fruit left over? Find all possible answers, I dare you. Also, the number of bowls must be integers... 2. At a certain mathematical conference, every pair of mathematicians are either friends or strangers. At mealtime, every participant eats in one of two large dining rooms. Each mathematician insists upon eating in a room which contains an even number of his or her friends. Prove that the number of ways that the mathematicians may be split between the two rooms is a power of two (i.e., is of the form 2^k for some positive integer k). 3. A spider, in the topleftfront corner of a 10 x 10 x 10 foot room, sees a big fat fly in the bottomrightback corner. Describe the shortest path, and the length of the path, that the spider can crawl to get the fly. That's crawl, not jump, fly or spidermanlikewebshooting!  This time, no. 2 is the more challenging one. I pulled that from an old US Math Olympiad question booklet. 1 and 3 are from an old archive of weekly math contest questions that I have compiled for my students. Have at it! 
number one is just a system of equations which simplifies to A + B = 6 and B + C = 2.
so theres 3 ways to have B and C and u get uhm:
6 0 2
5 1 1
4 2 0
number 3 u just make it flat and draw straight line so it's 10 * sqrt(5).
going to try number 2 now. hm I actually did USAMO twice but that was a long time ago lol. haven't done much math since then.
# 165
05242011, 12:07 AM
poop too hard
# 166
05242011, 12:43 AM
I don't even wanna read through all of the pages I didn't read earlier.. Just.. gosh... Math T.T
# 167
05242011, 10:27 AM
*waves*
first time on this thread, still here since I poofed? o.o
Got exams coming up.. And I still dont get Histograms in general, or factoirizing (can expand though), never really got hold of them.
Any tips?
I got cookies for helping :3
<3 by Silvyfirst time on this thread, still here since I poofed? o.o
Got exams coming up.. And I still dont get Histograms in general, or factoirizing (can expand though), never really got hold of them.
Any tips?
I got cookies for helping :3
Reborn ditzy archer with a serious oreo addiction =3
'...cuz my IQ is just above what is required to function as a human'  tsumaru2
Last edited by Esnemyl  Dreamweaver; 05242011 at 10:34 AM.
# 168
05242011, 01:00 PM
Quote:
Got the others for #1:
2 of bowl C, and 6 of bowl A and 2 of bowl B and 4 of bowl A. I'll let someone else get the tougher ones ^^ lol. 
Quote:
O i just saw this.
number 3 u just make it flat and draw straight line so it's 10 * sqrt(5). going to try number 2 now. hm I actually did USAMO twice but that was a long time ago lol. haven't done much math since then. 
Cheze I didn't know you had a psy :o
Quote:
*waves*
first time on this thread, still here since I poofed? o.o Got exams coming up.. And I still dont get Histograms in general, or factoirizing (can expand though), never really got hold of them. Any tips? I got cookies for helping :3 
The thing that separates histograms from other types of bar graphs is that they graph continuous data. What I mean by that is, I graph frequencies of things that are discrete entities (like hair color or dress size) on a bar graph. Histograms instead graph nondiscrete data (like weight, height, or time) where the thing being controlled is continuous. It may help to think of a histogram as a collection of frequencies along a continuous axis whereas a bar graph is a collection of frequencies of separate things. (This is a bar graph and this is a histogram.)
Here's a guide for how to make one given some data. It's a little wordy, but the methods are good. Sorry if that seems like a wall of text, but I wasn't sure what bases to cover. Feel free to ask if I have muddled anything as I am still prone to mistakes.

Factoring is a big topic... is there anything with which you specifically have an issue? A good way to check is if I give you a few things, which of them you can do, if any? (Btw: There's no shame in not knowing so long as you know on what you should direct your attention.)
3x + 9xy > ?
x^2 + 4x  60 > ?
x^2  25 > ?
x^3 + 3x^2  2x  6 > ?
There's a tad bit more advanced stuff than this, but I started with that since I am not sure how much you have covered.
Also, hi! Nice to see you back. No need for cookies, I do this purely for fun =)
EDIT: I just realized I assumed you meant "factoring polynomials!" If you instead were talking about prime factorization for numbers and radicals, that's something else. Stupid me for jumping to conclusions before asking. Normally I'd erase what I wrote earlier but I invested enough effort in it to warrant it staying there till I better understand what you want me to explain :3
Current math challenge: pwiforum.perfectworld.com/showthread.php?t=1029711&page=45
"Any skills that can be used to kill you will interrupt BB when successful." truekossy  "...Sage archers are kind of like Mac owners. They are proud of the weirdest and most unnecessary things." Aesthor  "We ALL know Jesus doesn't play PWI. He may have suffered a lot for humanity, but he'd NEVER punish himself this way." Abstractive  "I approve of bananas." SashaGray
Last edited by Decus  Dreamweaver; 05242011 at 01:30 PM.
# 169
05262011, 10:42 AM
Quote:
EDIT: I just realized I assumed you meant "factoring polynomials!" If you instead were talking about prime factorization for numbers and radicals, that's something else. Stupid me for jumping to conclusions before asking. Normally I'd erase what I wrote earlier but I invested enough effort in it to warrant it staying there till I better understand what you want me to explain :3

i can expand like this, using FOIL
x(2+5)
First xXX= X2(squared)
Outside x X 5 = 5X]
Inside x X 2 = 2X] add these two togewther, makes 7x
Last 2X5= 10
Result: x2+7x+10
The thing with factorising(oppositge of what i jsut displayed there) is, I can sometimes find it hard to find the Highest Common Factor between the numbers..
does this clear things up any mroe o master of math?
Reborn ditzy archer with a serious oreo addiction =3
'...cuz my IQ is just above what is required to function as a human'  tsumaru2
# 170
05262011, 12:13 PM
Quote:
The thing with factorising(oppositge of what i jsut displayed there) is, I can sometimes find it hard to find the Highest Common Factor between the numbers..
does this clear things up any mroe o master of math? 
Take the first example I posted:
3x + 9xy
First, look to the coefficients.
3 and 9 share what factors?
3 > 1 and 3
9 > 1, 3, and 9
So 3 is the highest factor shared by both.
Now we look at the variables:
x > only one x, so just x as a factor
xy > x and y as factors
Both share an x, so that's the highest factor.
Now we pull 3 and x out from both:
3x / 3x = 1 and 9xy / 3x = 3y
Place the GCF outside of the set of parentheses > 3x(1 + 3y)
Thus we've found the GCF and factored it out of the expression.

Now, when we have a trinomial (three terms) of degree 2 (highest power is 2), the process is a little different. Let's look at the second example I gave:
x^2 + 4x  60
You almost always factor quadratic expressions like this in this style:
(x + __)(x + __)
The way we fill in the blanks is as such...
We want to find two numbers that add up to the middle coefficient and that multiply to give the rightmost term
x^2 + 4x  60
I like to start with the latter: What numbers multiply to be 60? (i.e. what are the factors of 60?)
1*60, 2*30, 3*20, 4*15, 5*12, and 6*10 (with one of the numbers being negative in each pair to get 60 instead of pos. 60)
Now which of those pairs can I add/subtract to get 4?
60 +/ 1 isn't = 4 and neither is the second, third, fourth, or fifth pair...
But... (6, 10) works if I do it like this: 10 + 6 = 4 and 10 * 6 = 60
So now we take those two numbers and place them into the sets of parenthesis:
(x + 10)(x + 6) or (x  6)
If you expand that out, it should give you the original polynomial.
(x + 10)(x  6) > x^2 + 10x  6x  60 > x^2 + 4x  60
It takes practice, but you get better at it by doing. Eventually you just look at expressions and you know the factors you'll need almost intuitively.

If none of that was helpful let me know and I'll provide better examples.
Current math challenge: pwiforum.perfectworld.com/showthread.php?t=1029711&page=45
"Any skills that can be used to kill you will interrupt BB when successful." truekossy  "...Sage archers are kind of like Mac owners. They are proud of the weirdest and most unnecessary things." Aesthor  "We ALL know Jesus doesn't play PWI. He may have suffered a lot for humanity, but he'd NEVER punish himself this way." Abstractive  "I approve of bananas." SashaGray
Last edited by Decus  Dreamweaver; 05262011 at 12:15 PM.
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