Algebra/Trig Competition Ahmed VS Lev

I will give you the honor of starting =]

Okey Dokes Young one
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Let's start out easy:

Rewrite the expression as an algebraic expression in x:

cos(sin^-1 (x) + cos^-1 (x))

Zero

Show your work man.

solution:
cos(x+y)= cosxcosy-sinxsiny
cos(sin^-1x + cos^-1 x)

Let sin^-1x = u
Let cos^-1 x= v

cos( u + v) = cos u cos v - sin u sin v = cos(sin ^-1x) cos (cos-1x) - sin( sin^-1x) sin (cos -1x)

ok so... we know sin(sin-x) and cos(-x) are both equal to x and cos(sin ^-1x)= sin (cos -1x)
so we can assume x-x=0

Ok Im waiting and it seems you got it. Very good.

Ahmed: 0
Lev: 1

Your turn.

Here is something easy
Simplify
(2x^2+(3a+4b)x+a^2+3ab+2b^2)/(x^2+(a+b-2)x-2a-2b)

Hint: it can be done

Thanks for the hint

(a+2(b+x))/(x-2)

I don't think there is a point in showing work for a simplifying question.

Good?

I not very smart. I think you maybe need to explain it to me?

Comon man. It's annoying writing it on the computer. Ill show you tomorrow in class you noob

Could it be my turn?

ok fine but i better be right!!

Right about what?

Your solution of course. Go on with your question please....

Of course Im right. You should have known the answer BTW.

Find the partial fraction decomposition of the rational function:

(2x-4)/(x(x-1)^2)

ahmed dear, ur over confident..

What did I do? All I am doing is answering and asking Qs.

+ da "i'm betta than all of u" attitude

I have no attitude. And I never said that. I just said I know more than you.

lolz.. big difference

kay dear.. i'll watch the ownage

Ahmed:1
Lev:1

I think Lev doesn't know this one

You could always give up Lev

Your are kidding right?? Do you know how long this took me?!?

(-4+2 x)/((-1+x)^2 x) = q_1/(x-1)+q_2/(x-1)^2+q_3/x
2 x-4 = (x-1)^2 q_3+x (x-1) q_1+x q_2
2 x-4 = x^2 (q_1+q_3)+x (-q_1+q_2-2 q_3)+q_3
-4 = q_3
2 = -q_1+q_2-2 q_3
0 = q_1+q_3

Solve the system which took awhile:
q1=4
q2=-2
q3=-4

-4/x+4/(x-1)-2/(x-1)^2

Very nice Lev! Good Job

Ahmed: 1
Lev: 2

Now I actually have sympathy for you not getting into AB Cal...I now know you truly are a good candidate for it...but anyways, let's continue our competition.

I think it was just the stupid system that the school uses cause Daniel got in and he is in my class and has like a 85 average.

Anyways...

If the probability of an event occurring is x and the probability of it not occurring is 6x^2, what is the value of x. this is simple

He told me he has a 90...but yeah he is a dumb***. Anyways, I do know the reason why you didn't get in...my English teacher told me. She was obviously talking for AP English, but ti seems like they did it for all. She told us that they maximized the class, but the number of applicants doubled from prior years so instead of traditionally looking at just the subject grade (math or English) they looked at your accumulative grade since freshman year.
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x+6x^2=1
6x^2+x-1=0
(2x+1)(3x-1)=0
x=-1/2, 1/3
Reject -1/2

Good?

It should really matter what your overall is. Math is the only subject that has something to do with Math. You cant compare oranges with apples. Plus we have about the same overall average.

yes good
Another one??