HSC 2014 MX2 Marathon (archive) (2 Viewers)

Tugga · Sep 21, 2014

Re: HSC 2014 4U Marathon

Sy123 said:
$\\ $Let$ \ a,b,c \ $be positive real numbers such that$ \ ab + ac + bc = 1 \\ \\ $ Prove that$ \ \frac{1}{a+b} + \frac{1}{b+c} + \frac{1}{a+c} \geq \sqrt{3} + \frac{ab}{a+b} + \frac{ac}{a+c} + \frac{bc}{b+c} \\ \\ $and show where equality holds$$

Equality holds when a+b=b+c=a+c=sqrt(3)

dunjaaa · Sep 21, 2014

Re: HSC 2014 4U Marathon

exactly the same as mine

dunjaaa · Sep 21, 2014

Re: HSC 2014 4U Marathon

Screen shot 2014-09-21 at 9.21.47 PM.png

Tugga · Sep 21, 2014

Re: HSC 2014 4U Marathon

dunjaaa said:
View attachment 30936

Did it a different way by letting w=x+iy and simplifying z, to get z=i(y/(1-x))=+-i(sqrt((1-x)/(1+x)), which for -1(lessthan)x(lessthan)1 ,draws out the imaginary axis with a hole at origin.

Like your solution better though

edit: how do you use less than signs without stuffing up...

Kurosaki · Sep 21, 2014

Re: HSC 2014 4U Marathon

Tugga said:
Did it a different way by letting w=x+iy and simplifying z, to get z=i(y/(1-x))=+-i(sqrt((1-x)/(1+x)), which for -1(lessthan)x(lessthan)1 ,draws out the imaginary axis with a hole at origin.

Like your solution better though

edit: how do you use less than signs without stuffing up...

Do you mean in Latex

You just do <

Fizzy_Cyst · Sep 22, 2014

Re: HSC 2014 4U Marathon

Four digits numbers are formed from the digits 1,2,3,4. Each digit is only used once. What is the sum of all the numbers that can be formed?

Kurosaki · Sep 22, 2014

Re: HSC 2014 4U Marathon

Fizzy_Cyst said:
Four digits numbers are formed from the digits 1,2,3,4. Each digit is only used once. What is the sum of all the numbers that can be formed?

It's over 9000!!!

Is it about 66660?

Carrotsticks · Sep 22, 2014

Re: HSC 2014 4U Marathon

Kurosaki said:
It's over 9000!!!

Is it about 66660?

No

Carrotsticks · Sep 22, 2014

Re: HSC 2014 4U Marathon

Carrotsticks said:
No

Never mind, read the question as finding the sun of the digits.

mreditor16 · Sep 22, 2014

Re: HSC 2014 4U Marathon

Carrotsticks said:
Never mind, read the question as finding the sun of the digits.

*sum

And lol I made that mistake originally as well haha

Kurosaki · Sep 22, 2014

Re: HSC 2014 4U Marathon

Carrotsticks said:
Never mind, read the question as finding the sun of the digits.

Does this have some special mathematical meaning?

mreditor16 · Sep 22, 2014

Re: HSC 2014 4U Marathon

Kurosaki said:
Does this have some special mathematical meaning?

its a typo. he means sum.

faisalabdul16 · Sep 22, 2014

Re: HSC 2014 4U Marathon

Fizzy_Cyst said:
Four digits numbers are formed from the digits 1,2,3,4. Each digit is only used once. What is the sum of all the numbers that can be formed?

Ruse's multiple choice for trials

Fizzy_Cyst · Sep 22, 2014

Re: HSC 2014 4U Marathon

Kurosaki said:
It's over 9000!!!

Is it about 66660?

YEP!

Fizzy_Cyst · Sep 22, 2014

Re: HSC 2014 4U Marathon

faisalabdul16 said:
Ruse's multiple choice for trials

Was it? I got it from Normanhursts trial from this year. It was Q10. Perhaps they used the same paper?

EDIT:

just checked -- a couple of MCQ's the same, but that is it

dan964 · Sep 22, 2014

Re: HSC 2014 4U Marathon

yeah it is 66660.

Fizzy_Cyst · Sep 22, 2014

Re: HSC 2014 4U Marathon

$\\ I_n = \int_0^{2\pi} \(1 + $cos \theta$)^{n} \ d \theta \ \ $for$ \ n \geq 0 \\ \\ $i) Show$ \ \ I_{n+1} = \frac{2n+1}{n+1}I_{n} \ \ \ \fbox{3} \\ \\ $ii) Hence, or otherwise, find I_{3}\ \ \ \fbox{2}$

mreditor16 · Sep 22, 2014

Re: HSC 2014 4U Marathon

Fizzy_Cyst said:
$\\ I_n = \int_0^{2\pi} \(1 + $cos \theta$)^{n} \ d \theta \ \ $for$ \ n \geq 0 \\ \\ $i) Show$ \ \ I_{n+1} = \frac{2n+1}{n+1}I_{n} \ \ \ \fbox{3} \\ \\ $ii) Hence, or otherwise, find I_{3}\ \ \ \fbox{2}$

haven't tried it, but I think double angle has to be used here....

Fizzy_Cyst · Sep 27, 2014

Re: HSC 2014 4U Marathon

Fizzy_Cyst said:
$\\ I_n = \int_0^{2\pi} \(1 + $cos \theta$)^{n} \ d \theta \ \ $for$ \ n \geq 0 \\ \\ $i) Show$ \ \ I_{n+1} = \frac{2n+1}{n+1}I_{n} \ \ \ \fbox{3} \\ \\ $ii) Hence, or otherwise, find I_{3}\ \ \ \fbox{2}$

Any takers?

dunjaaa · Sep 27, 2014

Re: HSC 2014 4U Marathon

Screen shot 2014-09-27 at 6.25.45 PM.png

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