# Algebra/Trig Competition Ahmed VS Lev

**Justice****NH Member**- Number of posts : 741

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I will give you the honor of starting =]

**Ahmed****NH Admin**- Number of posts : 51452

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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))

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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))

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**Justice****NH Member**- Number of posts : 741

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Zero

**Ahmed****NH Admin**- Number of posts : 51452

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Show your work man.

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**Justice****NH Member**- Number of posts : 741

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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

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

Last edited by lev_93 on Thu May 13, 2010 7:53 pm; edited 1 time in total

**Ahmed****NH Admin**- Number of posts : 51452

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

Ahmed: 0

Lev: 1

Your turn.

Ahmed: 0

Lev: 1

Your turn.

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**Justice****NH Member**- Number of posts : 741

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Here is something easy

(2x^2+(3a+4b)x+a^2+3ab+2b^2)/(x^2+(a+b-2)x-2a-2b)

Hint: it can be done

*Simplify*(2x^2+(3a+4b)x+a^2+3ab+2b^2)/(x^2+(a+b-2)x-2a-2b)

Hint: it can be done

**Ahmed****NH Admin**- Number of posts : 51452

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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?

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

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

Good?

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**Justice****NH Member**- Number of posts : 741

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

**Ahmed****NH Admin**- Number of posts : 51452

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

Could it be my turn?

Could it be my turn?

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**Justice****NH Member**- Number of posts : 741

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ok fine but i better be right!!

**Ahmed****NH Admin**- Number of posts : 51452

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Right about what?

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**Justice****NH Member**- Number of posts : 741

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

**Ahmed****NH Admin**- Number of posts : 51452

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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)

Find the partial fraction decomposition of the rational function:

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

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**The Banker****NH Member**- Number of posts : 15240

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ahmed dear, ur over confident..

**Ahmed****NH Admin**- Number of posts : 51452

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

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**The Banker****NH Member**- Number of posts : 15240

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

**Ahmed****NH Admin**- Number of posts : 51452

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

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**The Banker****NH Member**- Number of posts : 15240

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lolz.. big difference

kay dear.. i'll watch the ownage

kay dear.. i'll watch the ownage

**Ahmed****NH Admin**- Number of posts : 51452

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Ahmed:1

Lev:1

I think Lev doesn't know this one

You could always give up Lev

Lev:1

I think Lev doesn't know this one

You could always give up Lev

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**Justice****NH Member**- Number of posts : 741

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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

(-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

**Ahmed****NH Admin**- Number of posts : 51452

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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.

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.

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**Justice****NH Member**- Number of posts : 741

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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

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

**Ahmed****NH Admin**- Number of posts : 51452

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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?

===================================================================

x+6x^2=1

6x^2+x-1=0

(2x+1)(3x-1)=0

x=-1/2, 1/3

Reject -1/2

Good?

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**Justice****NH Member**- Number of posts : 741

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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??

yes good

Another one??