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Re: HSC 2016 3U Marathon ohh ye my bad thanks. Is this better? \int_{0}^{64}\sqrt{1+\frac{4}{x^{2/3}}}$ d$x \\ \int_{0}^{64}\frac{\sqrt{x^{2/3}+4}}{x^{1/3}} $ d$x\\ $ let $ u=x^{2/3}, $ d$u=\frac{2}{3x^{1/3}}$ d$x \\\therefore $ d$x= \frac{3}{2}x^{1/3}$ d$u \\...

Re: HSC 2016 3U Marathon I have a feeling I did it the long way

Soz but I'm not exactly sure about the stimulus, I think it had something to do with high school students and jobs, but yeah not entirely sure. About the forms, I went to the school directly to hand it in.

Re: MX2 2016 Integration Marathon \int_{0}^{\frac{\pi}{2}}\frac{\mathrm{d} x }{1+\tan ^{\sqrt{2}}x} not sure if this question was already posted, but a fun integral to try. It's from the Putnam 1980 competition

Re: MX2 2016 Integration Marathon latex code crashed half way through :( I might have did the long way

Yup! There's also an extra 2 solution

Unfortunately nope, have another try haha

Not really a help post, but I found a couple of interesting trig questions if any of you prelim people wanna try it out $\noindent$ 1)$ $ $solve $ 5\sin ^{2}x-2\sin 2x +3\cos^{2}x=2 $ for $ 0\leq x\leq 360^{\circ}\\ \\ 2) $ show that $ \frac{1+\sin 2x}{1+\cos 2x}\equiv \frac{1}{2}(1+\tan x)^{2}

tru

https://www.change.org/p/english-should-not-count-towards-your-atar-although-necessary-to-pass-for-the-hsc?recruiter=402071752&utm_source=share_petition&utm_medium=facebook&utm_campaign=autopublish&utm_term=mob-md-petitions_show_components_action_panel_wrapper-no_msg

True

Oxygen: glowing splint test Carbon dioxide: Limewater turns cloudy white; Ca(OH)2 + CO2 --> CaCO3 + H2O Ca(OH)2 solution is the limewater, and CaCO3 is the white precipitate that turns the solution cloudy white Hydrogen: pop test

haha thankyou!

haven't done motions yet soz

1/sinθ = -2 -2sinθ = 1 sinθ = -1/2 acute angle is 30 so θ = (180+30), (360-30) θ = 210, 330

apparently my friend got that q from functions chapter 3 from Cambridge 3u yr11. Which is before series and sequence. But looking at it now, it has walkthrough questions before that, sorry about that haha. Thanks both

any formal way of proving this? Prove f(x) = 1 + x + x^2 ... + x^(2n -1) + x^(2n) is always positive did one, but not sure if right

cos(θ+10) = -1/2 [10<=θ+10<=370] acute angle is 60, therefore θ+ 10 = (180-60), (180+60) [All Stations To Central] θ + 10 = 120, 240 θ = 110, 230

Question: A driver of mass 75kg travelling in a 1200 kg sedan collides with a stationary police car with total mass of 1500 kg. The tangled wreck moves off after the collision at 8 ms^-1. Assuming negligible frictional force on both vehicles: Calculate the impulse on the police car due to the...