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Another method is using the Pythagorean identities Sin(LHS) = x \\ \\ Sin(RHS) = \sin(cos^{-1}(\sqrt{1-x^2}) = \sqrt{1-cos^2(cos^{-1}(\sqrt{1-x^2})} \\ \\ = \sqrt{1-(1-x^2)} = x \\ \\ \therefore LHS = RHS

2. $Co-efficient of $ \ x^7 \ $ is $ \\ \\ \binom{3}{3}\binom{5}{4}b + \binom{3}{2}\binom{5}{5}a = 9 $Co-efficient of $ \ x^6 \ $ is $ \\ \\ \binom{3}{3}\binom{5}{3}b^2 + \binom{3}{2}\binom{5}{4}ab + \binom{3}{1}\binom{5}{5}a^2 = 12

1. \ \ \frac{\binom{n}{3}(3)^3(2)^{n-3}}{\binom{n}{4}(3)^4(2)^{n-4}} = \frac{8}{15} From there you expand and simplify the algebra then solve for n.

Yeah as long as they understand, you've done your job :D. Ahhh I get what you mean, yeah some tutors don't seem to enjoy the subject they're teaching. Brah did that happen to you? Feels bad with your savings. Haven't known someone who's like that, how does that even work? But I agree that...

Re: UNSW chit chat thread 2017 Okay that too, the course itself is just crap.

So I stumbled an article about good and bad tutors, but I'd like so hear some personal experiences from my fellow peers here. So have you had a terrible tutor? if so then how? I'm a tutor myself, and let's just say that greed hasn't overcome my morals.

Re: UNSW chit chat thread 2017 No, it's a pretty useless course. The only good part of the course when I did it last year was the interview with Libo Li (apparently it's been shown in the tutes this year?) Rest of it was just explaining bullshit and hoping for the best.

Care to expand a little more on how some private tutors are bad ?

Re: UNSW chit chat thread 2017 I heard there's no mid sem breaks

Brah like 20 minutes into the exam, the supervisor would interrupt the time, noting a mistake in one of the questions. What is even proofreading?

Nope it's the bearing from David's perspective, not the mountain's.

Hsc questions are usually much harder than your typical textbook questions, it's natural that you struggle with those problems initially. If you consistently get into the habit of understanding those problems as you said, then you'll be fine since your mathematical abilities would improve a lot...

Question 9 and 12 basically uses the volume formula \pi \int_{a}^{b} y^2 \ \ dx Q11 b) can't be integrated with 2U knowledge unless there's a previous part given. Q13 Drawing the graph out you get a part of an area under the curve but an open rectangle at the bottom you must subtract...

Maccas easy game.

You could only consider the sum of roots and the product of roots of the polynomial, which fortunately is enough. $Let the roots be$ \ \ \alpha, \ 2 \ , 3. $ Product of roots gives $ \\ \\ \frac{72}{a} = (-3)(2)(\alpha) \Rightarrow \\ \\ a. \alpha = -12 \ \ (1) $ Sum of roots gives $ \\...

Re: HSC 2017 MX2 Integration Marathon Yes it involves that rule. This actually works for any integral, only that it'll be useless for a lot of them as it gives the exact same integral e.g \int_{0}^{1} x(1-x) \ dx

Sweet I know how b) works now, I'm not sure which transpose properties to consider for a), having a mind blank.

$a) Prove that a Square Matrix $ \ G \ $ is a positive definite if and only if $ \ G+G^T \ $ is a positive definite$ $b) Prove that an $ \ n \ times \ n \ $ symmetric matrix $ \ G \ $ is a positive definite if and only if $ \ G^{-1} \ $ is positive definite $

Yeah I personally knew someone in that situation, he legitimately failed during the first half including the half yearlies, then this is followed by 70% in the trials and then hitting a solid band 5 in the end. Although I'm saying that it's still possible, you'll have to work EXTRA HARD and...

I should tell you that it is NOT REQUIRED IN THE HSC to remember these formulas, should you have to use it, they either give it to you, or get you to prove it then use it in the next part.