• Best of luck to the class of 2025 for their HSC exams. You got this!
    Let us know your thoughts on the HSC exams here

Maths question! (1 Viewer)

jet

Banned
Joined
Jan 4, 2007
Messages
3,148
Gender
Male
HSC
2009
I did it. Got an equation in sin(x) and x. I cbb with approximating at that point in time, so I left it there :p

I will post my solution later, let me just work it out again :)

EDIT: Because this problem is extremely difficult, though not unrelated to the HSC, I'm moving it to the 4-unit Maths forums.
 
Last edited:

jet

Banned
Joined
Jan 4, 2007
Messages
3,148
Gender
Male
HSC
2009










Now, I can keep on going. Or someone can realise that this will involve differentiating very complicated expressions to apply Newton's method :p
Also, could someone please tell me if they find any mistakes? Thanks :)
 

Aquawhite

Retiring
Joined
Jul 14, 2008
Messages
4,942
Location
Gold Coast
Gender
Male
HSC
2010
Uni Grad
2013
Woah, that's an amazing solution o_O

The amazing thing is, I understood almost all of that :D... however I doubt I would have been able to solve so far if it were in an exam in the HSC.
 
Last edited:

shaon0

...
Joined
Mar 26, 2008
Messages
2,023
Location
Guess
Gender
Male
HSC
2009
If you have the Coordinates of C and where the larger circle meets the x-axis near B. Could you just use A=1/2 r^2(@-sin@) in both segments by constructing BD,BC,AD,AC?
 
Last edited by a moderator:

jet

Banned
Joined
Jan 4, 2007
Messages
3,148
Gender
Male
HSC
2009
Yes you could on second thought, though it would probably still be a bastard to solve. Will complete tomorrow.
 

Trebla

Administrator
Administrator
Joined
Feb 16, 2005
Messages
8,522
Gender
Male
HSC
2006
If you have the Coordinates of C and where the larger circle meets the x-axis near B. Could you just use A=1/2 r^2(@-sin@) in both segments by constructing BD,BC,AD,AC?
But how would you eliminate @? That method involves an angle and its sine hence might still give a transcendental equation.
 

shaon0

...
Joined
Mar 26, 2008
Messages
2,023
Location
Guess
Gender
Male
HSC
2009
But how would you eliminate @? That method involves an angle and its sine hence might still give a transcendental equation.
I don't know, as I haven't worked on the problem yet (and don't plan to). I was just suggesting another method to calculate the areas as a iterative process wouldn't have to be used in the method. @ would just be atan(y/x) where y,x are co-ords of C, i think.
 

untouchablecuz

Active Member
Joined
Mar 25, 2008
Messages
1,693
Gender
Male
HSC
2009
great work :) i did exactly the same thing, props on actually evaluating the integrals :p

for completion:

 
Last edited by a moderator:

untouchablecuz

Active Member
Joined
Mar 25, 2008
Messages
1,693
Gender
Male
HSC
2009
Actually, his final equation is incorrect.

The correct equation is

And when I put that one into wolframalpha, I get L=0.653742534637021....

Subsequent check of the sum of the areas of the 2 segments with this value of L indeed get's a value of exactly 0.5 for the area.

And this answer is NOT
o rly
 

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

Top