Melbourne High Sac Revision driving me crazy!

[chickenpop]

As if putting the sac on the day of the gat, right after midyears, wasn't bad enough, now I'm completely stuck on a whole bunch of questions even with answers! Can anybody please help out? 

Question: What point on the parabola y^2 = 2 px is nearest to the point (a, 0), where 0 < p < a.

Ans: Where did the second equation come from? Is it a formula we have to learn for these questions?

Question: No idea what to do 

Question: Diff with respect to x: ln(ln(3-cos x))

Ans: How did they get from step one to two?

Question: Prove logx y = 1/logy x

Ans: No idea what's going on

[kyzoo]

Diff with respect to x: ln(ln(3-cos x))

Let a = 3 - cos x
b = ln(a) = ln(3-cosx)
c = ln(b) = ln(ln(a))=ln(ln(3-cosx))

dc/dx = (dc/db)(db/da)(da/dx)

= (1/b)(1/a)(sin x)
= (1/ln(3-cos x)) (1/(3-cos x)) (sin x)
= (sin x)/[(3-cos x)(ln(3-cos x))]

---

Prove logx y = 1/logy x

logx y = (log y)/(log x) = 1/[(log x)/(log y)] = 1/(logy x)

[TrueTears]

For the first question, it is the 'distance formula' however don't remember this formula just use Pythagoras, that way you can work out the magnitude of the distance between any 2 points in 2-D plane, for a 3-D version you can apply Pythagoras in 3-D.

For second question, substitute in x = 4 into gradient function to work out the gradient at x = 4. Then the normal's gradient is just the negative reciprocal of this number. Also find the y ordinate at x = 4, then just make a line with these information.

[chopz]

wow.. im so lucky i dont go melbourne high lol..

[/0]

For Question one it's usually easier to find instead.

[TyErd]

do you have any revison SACs that you got that you can upload?

[vidang]

^ im with him, got any revision

[chickenpop]

thanks heaps guys, you guys are absolute legends 

btw, my teacher was already raging about TSFX stealing his questions, so I think he'll kill me if I put it up on the internet

But those are definitely the most challenging questions, the rest were quite standard questions that I think he just plucked from the Essential book

[TyErd]

c'mon sharing is caring, its not like he knows about this site...

[taiga]

PM me and ill drop you a link to them I'ld rather not openly post it

[pi]

lol, thx chickenpop. at least i'll know what i'm up against next year at melb high. Although we did some of these questions in class during general advanced maths this year, nothing to stress too much about (day of the GAT means nothing at melb high).