• Best of luck to the class of 2020 for their HSC exams. You got this!
    Let us know your thoughts on the HSC exams here
  • Looking for HSC notes and resources?
    Check out our Notes & Resources page

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

Status
Not open for further replies.

Sy123

This too shall pass
Joined
Nov 6, 2011
Messages
3,735
Gender
Male
HSC
2013
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
 
Last edited:

Sy123

This too shall pass
Joined
Nov 6, 2011
Messages
3,735
Gender
Male
HSC
2013
Re: HSC 2014 4U Marathon - Advanced Level

 

seanieg89

Well-Known Member
Joined
Aug 8, 2006
Messages
2,671
Gender
Male
HSC
2007
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

Member
Joined
Apr 19, 2014
Messages
39
Gender
Male
HSC
2016
Re: HSC 2014 4U Marathon - Advanced Level

Trig question.png

Someone try this :D
 

seanieg89

Well-Known Member
Joined
Aug 8, 2006
Messages
2,671
Gender
Male
HSC
2007
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

This too shall pass
Joined
Nov 6, 2011
Messages
3,735
Gender
Male
HSC
2013
Re: HSC 2014 4U Marathon - Advanced Level

 

dunlop1234

New Member
Joined
Jan 10, 2013
Messages
29
Gender
Male
HSC
2014
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

This too shall pass
Joined
Nov 6, 2011
Messages
3,735
Gender
Male
HSC
2013
Re: HSC 2014 4U Marathon - Advanced Level

 

RealiseNothing

what is that?It is Cowpea
Joined
Jul 10, 2011
Messages
4,608
Location
Sydney
Gender
Male
HSC
2013
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

This too shall pass
Joined
Nov 6, 2011
Messages
3,735
Gender
Male
HSC
2013
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

This too shall pass
Joined
Nov 6, 2011
Messages
3,735
Gender
Male
HSC
2013
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

Active Member
Joined
Jun 1, 2014
Messages
344
Gender
Undisclosed
HSC
N/A
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.
 
Status
Not open for further replies.

Users Who Are Viewing This Thread (Users: 0, Guests: 1)

Top