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### AuthorTopic: Chavi's Mathematical adventure (+Karma for solutions)  (Read 11655 times) Tweet Share

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#### Chavi

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##### Chavi's Mathematical adventure (+Karma for solutions)
« on: November 28, 2010, 07:21:16 pm »
+1

1. $(x -a)(x -b) ... (x - z) = ?$
2. Complete the next three terms in the sequence: 1, 4, 9, 61,
3, Let x be an element of R. Find which term has a larger value, sin(cos x) or cos(sin x)?
4. Find a value of x such that: $\sqrt{4 + \sqrt{4 - \sqrt{4 + \sqrt{4 - x}}}} = x$

5. $a, b$ are integers and $(a, b) =2$. Solve the following two equations:
$\begin{cases}
(a + b)^2 = 25a, \\
18a^4 + b^4 = 41ab^2,
\end{cases}$

6. For the equation:
$\frac{1}{a} + \frac{1}{b} + \frac{1}{c} + \frac{1}{abc} = \frac{m}{a + b + c}$

Find the value of m for which the equation has infinite solutions. $a,b,c,m \subset R$
« Last Edit: November 29, 2010, 04:30:28 pm by Chavi »
2009: Math Methods CAS [48]
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#### taiga

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##### Re: Chavi's excellent mathematical adventure
« Reply #1 on: November 28, 2010, 07:23:57 pm »
0

1. $(x -a)(x -b) ... (x - z) = ?$
2. Complete the next three terms in the sequence: 1, 4, 9, 61,
3, Let x be an element of R. Find which term has a larger value, sin(cos x) or cos(sin x)?

1. 0

2. 52, 63, 94
It's not very mathsy

3. doing...
I subbed in values, and cos(sinx) is bigger becos
« Last Edit: November 28, 2010, 07:31:51 pm by taiga »
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#### Chavi

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##### Re: Mathematical adventure (+Karma for solutions)
« Reply #2 on: November 28, 2010, 07:25:06 pm »
0
1. look deeper
2. three terms. . .
2009: Math Methods CAS [48]
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#### funkyducky

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##### Re: Mathematical adventure (+Karma for solutions)
« Reply #3 on: November 28, 2010, 07:28:00 pm »
0
2. Typo? 61 meant to be 16? In which case the next three terms are 25,36,49
« Last Edit: November 28, 2010, 07:29:43 pm by funkyducky »
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#### Chavi

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##### Re: Mathematical adventure (+Karma for solutions)
« Reply #4 on: November 28, 2010, 07:28:58 pm »
0
2009: Math Methods CAS [48]
2010: English [47]|Specialist Maths[44]|Physics[42]|Hebrew[37]|Accounting[48]  atar: 99.80
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#### stonecold

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##### Re: Mathematical adventure (+Karma for solutions)
« Reply #5 on: November 28, 2010, 07:29:25 pm »
0
2. Typo? 61 meant to be 16?

That's what I initially thought haha
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#### taiga

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##### Re: Mathematical adventure (+Karma for solutions)
« Reply #6 on: November 28, 2010, 07:31:31 pm »
0
LOL! nice

1st one is zero (x-x) ends up in there xD
vce: english, methods, spesh, chemistry, physics, geography.

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#### Chavi

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##### Re: Mathematical adventure (+Karma for solutions)
« Reply #7 on: November 28, 2010, 07:38:14 pm »
0
LOL! nice

1st one is zero (x-x) ends up in there xD
you're on a roll mate.
2009: Math Methods CAS [48]
2010: English [47]|Specialist Maths[44]|Physics[42]|Hebrew[37]|Accounting[48]  atar: 99.80
My blog: http://diasporism.wordpress.com/

#### Chavi

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##### Re: Mathematical adventure (+Karma for solutions)
« Reply #8 on: November 28, 2010, 07:39:26 pm »
0
LOL! nice

1st one is zero (x-x) ends up in there xD
"Sorry, you can't repeat a karma action without waiting 12 hours. " - damn.
Well +1 here for you again
2009: Math Methods CAS [48]
2010: English [47]|Specialist Maths[44]|Physics[42]|Hebrew[37]|Accounting[48]  atar: 99.80
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#### iNerd

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##### Re: Mathematical adventure (+Karma for solutions)
« Reply #9 on: November 28, 2010, 07:39:35 pm »
0
LOL! nice

1st one is zero (x-x) ends up in there xD
OMG that is smart. What a sexy question, I'm going to use this on my MHS nerd-friends

#### funkyducky

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##### Re: Mathematical adventure (+Karma for solutions)
« Reply #10 on: November 28, 2010, 07:48:08 pm »
0
What's the rule for the sequence? It's neither arithmetic or geometric.
I won the GAT: 49/50/50.
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#### stonecold

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##### Re: Chavi's Mathematical adventure (+Karma for solutions)
« Reply #11 on: November 28, 2010, 07:49:44 pm »
0
What's the rule for the sequence? It's neither arithmetic or geometric.

i also am intrigued!
2011-13: BBiomed (Microbiology & Immunology Major) @ UniMelb

VCE 2009'10: English 46 | English Language 49 | Chemistry 50 | Biology 50 | Further Mathematics 48 | Mathematical Methods CAS 39
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"Failure is not when one falls down but rather when one fails to get up" - unknown

#### Chavi

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##### Re: Chavi's Mathematical adventure (+Karma for solutions)
« Reply #12 on: November 28, 2010, 07:52:39 pm »
+1
What's the rule for the sequence? It's neither arithmetic or geometric.
The more maths you know, the harder it is to complete
2009: Math Methods CAS [48]
2010: English [47]|Specialist Maths[44]|Physics[42]|Hebrew[37]|Accounting[48]  atar: 99.80
My blog: http://diasporism.wordpress.com/

#### funkyducky

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##### Re: Chavi's Mathematical adventure (+Karma for solutions)
« Reply #13 on: November 28, 2010, 07:57:57 pm »
0
x= (13^(1/2) +1)/2
I won the GAT: 49/50/50.
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#### Chavi

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##### Re: Chavi's Mathematical adventure (+Karma for solutions)
« Reply #14 on: November 28, 2010, 08:00:12 pm »
0
x= (13^(1/2) +1)/2
haha yep +1.

Hint: for those considering the question: This requires gof(x) (nested functions).
2009: Math Methods CAS [48]
2010: English [47]|Specialist Maths[44]|Physics[42]|Hebrew[37]|Accounting[48]  atar: 99.80
My blog: http://diasporism.wordpress.com/