anonymous
  • anonymous
TuringTest, what now?
Mathematics
chestercat
  • chestercat
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saifoo.khan
  • saifoo.khan
Party time! :D
TuringTest
  • TuringTest
lol I dunno...
anonymous
  • anonymous
What can you teach me?

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TuringTest
  • TuringTest
a lot, there's a fair amount to algebra, but what's the next logical step?
anonymous
  • anonymous
Teach about polynomial.
TuringTest
  • TuringTest
I have already to an extent, but where to go next...
anonymous
  • anonymous
Ratios?
anonymous
  • anonymous
In maths the fundamentals concepts are limited but the problems are not, so how about practicing what you have already learned?
TuringTest
  • TuringTest
That's a good point FFM so lets do simplification that you know, but a little more intense: I think I need to make sure you can simplify bigger things:\[\frac{x^2y^5z}{xy^9z^3}\]
saifoo.khan
  • saifoo.khan
1 Attachment
TuringTest
  • TuringTest
awww, you're making me think of my cat in the hospital :(
anonymous
  • anonymous
http://a4.sphotos.ak.fbcdn.net/hphotos-ak-snc6/271016_253886774622476_100000034671401_1128907_4380462_n.jpg
anonymous
  • anonymous
How did it go with her?
TuringTest
  • TuringTest
broken leg... waiting for an operation
anonymous
  • anonymous
You beat you cat Turing?!!!
anonymous
  • anonymous
aww :(
saifoo.khan
  • saifoo.khan
turing sat on her leg. :(
TuringTest
  • TuringTest
she fell off the roof. how pessimistic
saifoo.khan
  • saifoo.khan
awww, sorry i was jking..
TuringTest
  • TuringTest
It's all good :P
anonymous
  • anonymous
Due to Turing's intense physics stress his cat decided to commit suicide :P
anonymous
  • anonymous
(x^2)*(y^5)*(z) ------------ = (x)*(y^5/9)*(z^1/3)? (x)*(y^9)*(z^3)
saifoo.khan
  • saifoo.khan
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anonymous
  • anonymous
Cats are cool.
anonymous
  • anonymous
why \( y^{5/9} \) ?
saifoo.khan
  • saifoo.khan
no doubt. ;)
TuringTest
  • TuringTest
you have inconsistent rules above inopeki\[\frac{x^a}{x^b}=x^{a-b}\]always...
anonymous
  • anonymous
http://i.imgur.com/48wOw.jpg
anonymous
  • anonymous
Oh right
anonymous
  • anonymous
(x^2)*(y^5)*(z) ------------ = (x)*(y^5-9)*(z^1-3)? (x)*(y^9)*(z^3)
TuringTest
  • TuringTest
yes, simplify...
saifoo.khan
  • saifoo.khan
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anonymous
  • anonymous
(x)*(y^5-9)*(z^1-3)=(x)*(y^-4)*(z^-2)?
anonymous
  • anonymous
http://i.imgur.com/6uzXf.jpg
saifoo.khan
  • saifoo.khan
cute^
TuringTest
  • TuringTest
yes, do you know another way to write\[x^{-a}\]???
anonymous
  • anonymous
No
anonymous
  • anonymous
http://i.imgur.com/eqTIb.jpg
TuringTest
  • TuringTest
\[x^{-a}=\frac{1}{x^a}\]so it's probably nicer to rewrite your expression with all positive exponents in this way.
anonymous
  • anonymous
Oh right, all negative exponents make the "total number" divided by one.
anonymous
  • anonymous
Btw who can explain why x^0 = 1?
anonymous
  • anonymous
(x)*(1/y^4)*(1/z^2)
TuringTest
  • TuringTest
Oh dear... I have my answers about x^0=1 (not true for x=0), but I'm sure FFM would not approve of them :/ @inopeki, yes now rewrite it as 1 fraction...
anonymous
  • anonymous
Turing that's a very important yet fundamental question.
anonymous
  • anonymous
another one is why \( (a^b)^c = a^{bc} \) ?
TuringTest
  • TuringTest
well I have a very simple proof of it and I can show why it is not true for x=0 what more do I need in your opinion?
TuringTest
  • TuringTest
the last rule is easier to explain, perhaps I should...
anonymous
  • anonymous
(x)*(1/y^4)*(1/z^2) (x)*(1/y^4*z^2)?
TuringTest
  • TuringTest
yes, now write it as a fraction what goes on the bottom? what goes on the top?
TuringTest
  • TuringTest
@FFMactually that's not so easy to explain now that I think about it.
anonymous
  • anonymous
Can you explain the second rule intuitively?
anonymous
  • anonymous
1 x* -------- y^4*z^2
TuringTest
  • TuringTest
no, I was thinking more of how easy it is to show x^ax^b=x^(a+b) intuitively, the other is tricky to me.
TuringTest
  • TuringTest
@ inopeki you can put the x on top, it means the same thing and looks nicer
anonymous
  • anonymous
x*1 -------- y^4*z^2
anonymous
  • anonymous
Can we say that all power function obeys the functional equation \( f(x)f(y)= f(x+y) \)?
anonymous
  • anonymous
Whats that f?
TuringTest
  • TuringTest
@Inopeki yes, no need to write the 1 though @FFM, I'd have to think about that :/
TuringTest
  • TuringTest
unspecified functions he's asking how far the rule about exponents can be extended..
anonymous
  • anonymous
x -------- Oh right y^4*z^2
anonymous
  • anonymous
Actually we can't but I believe that is true for exponential functions though.
anonymous
  • anonymous
Umm, ok?
TuringTest
  • TuringTest
it must be for simple ones\[2^x2^y=2^{x+y}\]of course
anonymous
  • anonymous
Tha's whats Inopeki is using right ?
TuringTest
  • TuringTest
basically Inopeki do you see the connection between what you are doing and the rule for multiplying exponents like\[x^ax^b\]?
anonymous
  • anonymous
Yeah, but does that mean that it becomes x -------- ? yz^6
TuringTest
  • TuringTest
no because y and z are different bases notice the rule above had both base x.
anonymous
  • anonymous
YEah but then i dont see the connection..
TuringTest
  • TuringTest
just that dividing and multiplying are inverse operations x^a=x*x*x*...*x (a times) x^b=x*x*x*...*x (b times) so if we have a=3 b=2 we get x^a --- x^b x*x*x =-----= x x*x which is x^(a-b) if we have (x^a)(x^b) we get (x*x*x)(x*x)=x*x*x*x*x=x^(a+b) so the rules for exponents here come directly from their definitions. You can count the x and see that this relationship holds.
anonymous
  • anonymous
I know about that, like x^2*x^8=x^10
anonymous
  • anonymous
x^10/x^5=x^5
anonymous
  • anonymous
Basic
TuringTest
  • TuringTest
right, I want you to see how that and the rule for division are inverses of each other for a reason...
anonymous
  • anonymous
Turing you have a heck of patience :D
TuringTest
  • TuringTest
eh it's easy FFM, doesn't require too much concentration. good practice too I learn by teaching ;) ok factor \[3x^3y^3+6xy+9x^2y\]
anonymous
  • anonymous
:-)
anonymous
  • anonymous
The GCF of 3,6,9 is 3 The GCF of x,x^2,x^3 is x The GCF of y,y^2,y^3 is y 3xy(3x^3*y^3/3xy)+3xy(6xy/3xy)+3xy(9x^2*y/3xy) ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Middle step, right?
TuringTest
  • TuringTest
yes exactly
anonymous
  • anonymous
3xy(3x^3*y^3/3xy)+3xy(6xy/3xy)+3xy(9x^2*y/3xy)=3xy(x^2*y^2+2+3x)?
TuringTest
  • TuringTest
yep :) great!
anonymous
  • anonymous
Really? :D
anonymous
  • anonymous
Note to Inopeki: Turing is a great resource, learn new things from him and practice as much as you can on your own :-)
TuringTest
  • TuringTest
Yes I've stressed the importance of studying on your own as well and yes Inopeki really, FFM would have noticed a mistake I'm sure ok quick, foil (a-b)(a+b)
anonymous
  • anonymous
When hes not here i try to go on purplemath and khan :)
anonymous
  • anonymous
a^2+ab-ba-b^2
TuringTest
  • TuringTest
simplify
anonymous
  • anonymous
Books books books!! online learning has it's own limitation :-)
anonymous
  • anonymous
a^2-b^2?
Akshay_Budhkar
  • Akshay_Budhkar
it doesnt @ffm i disagree
anonymous
  • anonymous
Foolformath, im having trouble finding books here in sweden
TuringTest
  • TuringTest
and what is the name of that form? remember?
anonymous
  • anonymous
The fundamental theorem of algebra? Or want that the one with the multiplex?
TuringTest
  • TuringTest
Multiplex? no I think you're thinking of 'multiplicity' but this is the 'difference of squares' \[a^2-b^2=(a-b)(a+b)\]
Akshay_Budhkar
  • Akshay_Budhkar
with ocw.mit , khan, purple math and openstudy and people like turing there is no limit to online education ^
TuringTest
  • TuringTest
Thanks but you get what you put in, I think is true with all this stuff.
anonymous
  • anonymous
Oh right
TuringTest
  • TuringTest
The fundamental theorem of algebra: "the sum of the multiplicity of the roots of a polynomial is equal to its order" difference of squares\[a^2-b^2=(a-b)(a+b)\]both important, but very different
TuringTest
  • TuringTest
so remember that we can run this backwards, and I can say 'factor'\[x^2-4\]using difference of squares wanna try?
TuringTest
  • TuringTest
run the FOIL backwards I meant*
anonymous
  • anonymous
x(x-4)?
anonymous
  • anonymous
Oh
TuringTest
  • TuringTest
no look at the form\[a^2-b^2=(a-b)(a+b)\]so what is a and b in\[x^2-4\]???
anonymous
  • anonymous
(x-2)(x+2)?
TuringTest
  • TuringTest
there ya go :)
TuringTest
  • TuringTest
how about\[x^4-y^4\](this is a favorite question on OS)
anonymous
  • anonymous
(x^2-y^2)(x^2+y^2)
anonymous
  • anonymous
Why?
TuringTest
  • TuringTest
good, now is that all we can do with it though? (I've seen a lot of tutors stop here too ;-)
TuringTest
  • TuringTest
hint:look at the first set of parentheses
anonymous
  • anonymous
Ummm
TuringTest
  • TuringTest
what is the first sett of parentheses?
anonymous
  • anonymous
(x^2-y^2)?
TuringTest
  • TuringTest
yes, and can you factor that?
anonymous
  • anonymous
GCF of x^2 is x GCF of y^2 is y xy(x^2/xy)-xy(y^2/xy)?
TuringTest
  • TuringTest
no you're over-thinking x^2-y^2 is difference of squares again!
TuringTest
  • TuringTest
\[a^2-b^2=(a-b)(a+b)\]
anonymous
  • anonymous
So (x-y)(x+y)?
TuringTest
  • TuringTest
yes! so now factor\[p^4-q^4\]completely!!
TuringTest
  • TuringTest
you will apply difference of squares twice
anonymous
  • anonymous
(p^2-q^2)(p^2+q^2) (p-q)(p+q)(p+q)+(p+q)?
anonymous
  • anonymous
Without the +
anonymous
  • anonymous
between the parenthesis
TuringTest
  • TuringTest
(p^2-q^2)(p^2+q^2) stop here we cannot factor the second set of parentheses, it is not a /difference/ of squares, it is a /sum/ of squares, and we have no formula for that. check that (a+b)(a+b) is not a^2+b^2 so only factor the one that is a /difference/ of squares
anonymous
  • anonymous
(p-q)(p+q)(p^2+q^2) You said i had to do difference in squares 2 times? Btw, lets move to a new thread, this one is starting to lag a little bit
TuringTest
  • TuringTest
That is above correct, you did difference of squares twice: p^4-q^4 (p^2-q^2)(p^2+q^2) <-once (p-q)(p+q)(p^2+q^2) <-twice ok new thread...
anonymous
  • anonymous
Ohhh

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