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YES! My class has finally moved on to Integration. It's a shame though that I already did Integration on my own at the beginning of term because I was bored with the Ext-1 e/log/trig/inverse trig functions we were doing at that time. Maybe I should just stop for a while and take the time to do...

Finally. Now I can complete my list of results for "Assessment Task 1". Ext-1 English: 10/10 Rank 1/30-some Ext-2 English: 8/10 Rank 5/16 It's a good thing I made my EE2 teacher sign my subject withdrawl form before she handed back our marks and ranks. Heh.

I don't see what the problem is here. x is an arbitrary representation of the angle that you're dealing with. Don't let the x's in the question confuse you. Regardless of what this angle is, you would let t = tan(half the angle) - so in the cases such 3c/d where the angle happens to 2x, t will...

You're right. It's technetium-99m. The industrial one is americium-241.

Are you still eligible to sit the 2U trial/HSC exams if you are enrolled in Ext-2? I am quite confident with getting 99+ in 2U and this apparently has a more positive effect on my UAI than a 95 in Ext-2, according to SAM. I would like 2U to count for the sake of my UAI but for the love and...

I wonder if it is sufficient to simply say "ethylene is produced industrially by the cracking of some of the fractions from the refining of petroleum" or would it be necessary to identify (as was asked) the particular fractions used such as LPG and naphtha which come from fractional distillation...

When the BOS liaison officer came to my school for the routine Yr 12 talk, she mentioned that the highest and lowest internal assessment marks will be equated to the highest and lowest HSC exam marks from the school and everything in between will be scaled up/down accordingly.

For industry, try strontium-90 which is used in thickness gauges for industrial sheeting of materials such as plastics, paper and steel.

As shown, the given result is true for n=k+1 if it is assumed true for n=k. Since it is proven true for n=1, it must be true for n=1+1=2. Therefore by mathematical induction, the result is true for all positive intergers n. Induction is the absolute critical word in the final statement and it...

Stationary pts occur at f'(x) = 0. However if also f"(x) = 0 at this pt, in most cases it is no longer a turning pt but instead a horizontal pt of inflexion. You do need to take care to determine the concavity on either side of a pt for which f"(x) = 0 because for example y = x^4 will have...

I started off Yr 12 with 14 units but was forced to make a choice between Legal Studies and Ext-2 Maths as my school proposed to run the two classes on the same line. It was a really tough decision for me at the time because I was ranked 1st in Legal after the Prelim course and I wasn't sure...

A friend of mine very recently reminded me of a function of SAM which, surprisingly, I had never realised. She made me put the percentages of all my assessment results from last term into it, and with the assumption that I shall perform to the same (or preferrably, better) level for the rest of...

Rearrange: int cos(x)/[2-cos(x)] dx = int {2/[2 - cos(x)]} - 1 dx Let t = tan (x/2) --> cos(x) = (1 - t^2)/(1 + t^2) Now, dt/dx = (1/2)*sec^2(x/2) = (1/2)*(1 + t^2) [using Pythagorean identity tan^2(a) + 1 = sec^2(a)] So, dx = (2 dt)/(1 + t^2) Now you can rewrite the integral...

Oops. Y=0. Thanks for picking out the typo.

Do you mean the x-coordinates of the boundaries of the strips? For the length of each individual strip, you need to divide the length of your total restriction into the number of strips. In your case, your total length is 1 unit and you need 5 strips so that's 0.2 units each. This means that...

Take limits? as x -> infinity, f(x) -> infinity as x -> - infinity, f(x) -> 0 from below So x=0 is the horiz. asymptote.

I thought nothing of the sort, and to be honest I'm a bit puzzled as to which phrase I was supposed to have mistaken for being critical. Hehe. :P Lol. You're right. I might end up wasting too much time here. I should probably erm.. turn my computer off right now. Yeah.. But I do agree...

That is a lot. And it means we're 2 topics behind. Nice.

I've just recently started participating in the student community (.. perhaps not so good a thing for my HSC) so you're the first I've noticed. I do have my eye on that course and hopefully I will do well enough to score an interview for it. Again, thank you for the suggestions. I will surely...

Thanks a lot for that. Just one thing though: cos(x) cos(2x) cos(3x) ...... cos((2^(n-1))x) By the expression for the nth term, shouldn't the third term be cos(4x)? Or was that a typo so the nth term is cos((2*(n-1))x)? I'll give both cases a try. [Edit] Oh wait, but if the nth term...