HSC 2014 MX2 Marathon ADVANCED (archive) (1 Viewer)

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Sy123

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Re: HSC 2014 4U Marathon - Advanced Level








EDIT: There is a small error with my solution when looking to the case that at least 2 of x,y,z are negative, it has been amended
 
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Sy123

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Re: HSC 2014 4U Marathon - Advanced Level

 

seanieg89

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Re: HSC 2014 4U Marathon - Advanced Level

Yep, good. It should be noted that this question is just a rearrangement of Schur's inequality, which is why the method is somewhat similar to how Schur's is proven.
 

TL1998

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Re: HSC 2014 4U Marathon - Advanced Level

Trig question.png

Someone try this :D
 

seanieg89

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Re: HSC 2014 4U Marathon - Advanced Level

Nice! However, is there another way around this problem?
I am sure there are lots of ways, its just an algebraic manipulation so you always have lots of choices with these things.
 

Sy123

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Re: HSC 2014 4U Marathon - Advanced Level

 

dunlop1234

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Re: HSC 2014 4U Marathon - Advanced Level

Hey guys!

Guess what, i forgot how to solve 4e^(-x)-6e^(-2x)=0. Can someone how to remind me how to find x when its in such form? (came up in some graph question - you need to find point of intersection with the axis blah blah)
 

Sy123

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Re: HSC 2014 4U Marathon - Advanced Level

 

RealiseNothing

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Re: HSC 2014 4U Marathon - Advanced Level

Let:



Using partial fractions we get:



Now for , we will let



Now this is just but for the next term. Hence what we have is a telescoping sum:



And we are left with just:

 

Sy123

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Re: HSC 2014 4U Marathon - Advanced Level

Thanks Dude.
If I may ask, did you state rank for any of the mathematics courses?
Yes I did for 4U

I don't get how you used the cosine rule to get the value of sin alpha. Did you a certain value for PC?
I meant triangle PAB, not sure why I wrote DPC!

Basically, the angle PAB = 90 - alpha, when you do cosine rule, it becomes a sin(alpha)


I'm just a little confused, by using the sine rule with alpha as angle ADP shouldn't we get sin(theta) = xsin(alpha)/2? unless that's meant to be angle DAP?
Yes my bad that is supposed to be angle DAP
 

Sy123

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Re: HSC 2014 4U Marathon - Advanced Level

Let:



Using partial fractions we get:



Now for , we will let



Now this is just but for the next term. Hence what we have is a telescoping sum:



And we are left with just:

Don't forget to divide by half!

But yes that was my method as well
 

Fade1233

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Re: HSC 2014 4U Marathon - Advanced Level








EDIT: There is a small error with my solution when looking to the case that at least 2 of x,y,z are negative, it has been amended
A hsc question? Remember doing this.
 
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