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That has only 44% efficiency, for each 9 blocks only 4 have sugar cane.

In order to grow 1 square unit of sugar cane, this 1 square unit of sugar cane must be next to 1 square unit of water. A farm is established with the goal of finding the most efficient layout of these water and sugar cane units. The efficiency of the farm is measured as a percentage of land...

re: HSC Chemistry Marathon Archive $An excess standard solution of 100mL 0.8M $ \ \ NaOH \ \ $is reacted with 20mL$ \ \ CH_3COOH \ \ $of unknown concentration$ $This mixture is then titrated with 1M$ \ \ HCl $The average titration volume turned out to be 15 mL$ $Find the concentration...

Re: HSC 2013 3U Marathon Thread :/ Can't believe I missed that, thanks for the heads up. I'll ask this question again once everyone has forgotten about it. ====================== New result: $Prove using the Binomial Theorem or Combinatorics$ \frac{1}{2} \binom{n}{0} + \frac{1}{3}...

Re: HSC 2013 3U Marathon Thread I considered the geometric series: (1+x)^n + (1+x)^{n+1} + \dots + (1+x)^{2n} = \frac{(1+x)^n ((1+x)^n -1)}{(1+x)-1} = \frac{(1+x)^{2n}-(1+x)^n}{x} Equate co-efficient of x^n on both sides of equation. Anything illegal in the proof?

Re: HSC 2013 3U Marathon Thread A nice result I've proven $Prove using Binomial Theorem or Combinatorics$ \binom{n}{n} + \binom{n+1}{n} + \binom{n+2}{n} + \dots + \binom{2n}{n} = \binom{2n}{n+1}

Re: HSC 2013 4U Marathon So would you say that most of the 1970/prior problems are good practise for problem solving skills for mx2 students? ============= $Find an expression for$ \cos 2\theta + \cos 4\theta + \cos 6\theta + \dots + \cos (2n\theta) $Hence prove that$ \int_0^{\pi/2}...

What do you mean what do I think about them? If you mean whether I would regard them as rote learners, I personally cannot draw a fine line between who we can classify a rote learner, and who isn't. (this doesn't mean I cannot draw a line).

You are completely wrong. There is no oxymoron present. Intelligent students will learn science how it should be learnt and that is with understanding, if it comes to a point whereby an intelligent student needs to rote learn, i.e. soft science, then no it does not put them in the same category...

Hmm, yes you are right I think. So simply going backwards is sufficient to fulfil the iff condition?

|z-\alpha|^2 \leq |1-\bar{\alpha}z|^2 (z-\alpha)\overline{(z-\alpha)} \leq (1-\bar{\alpha}z) \overline{(1-\bar{\alpha}z)} Distribute the conjugates, then expand, we are left with: |z|^2 + |\alpha|^2 \leq 1 + |\alpha z|^2 (1-|\alpha|^2)|z|^2 + |\alpha|^2 - 1 \leq 0 Common factor...

Re: HSC 2013 3U Marathon Thread

Re: HSC 2013 4U Marathon That is from the IMO.

- Astronaut - Neurosurgeon/Psychologist - Maths Teacher

So we need to find the amount of HCl need to neutralise, this means we need to find out how much H+ there is, and the amount of H+ should be the same as OH- HCl \rightarrow H^+ + Cl^- So the concentration of [H+] = 0.1 So we need the concentration of OH- in the mixture to be 0.1 Look at the...

It is not fair whatsoever It doesn't reward people who want to sit and think. It rewards people who put in the hard work and don't think, and that is NOT the point of an exam. The point of an exam is to assess how well you know the subject, it isn't about how much stuff you can rote learn and...

ok

:/ What if I convert the formula into my own version. i.e. \Delta y = u_y t + \frac{1}{2}a_y t^2 a_y = - g Where g is a positive constant, and direction of force is downwards hence negative Let V be the velocity of projection, by right angled trigonometry, u_y = V\sin \theta u_x =...

I'm much more comfortable with the 3U way, and what I do is, I make everything a pronumeral until I find an expression for the final answer i.e. $Range$ \ = \frac{V^2 \sin 2\theta}{g} And then I plug in the values from there because I only need to use a calculator once, hence saving time. I...

In the Physics course, for projectile motion, and possibly other topics, I prefer to use the formulas for the 3U course. i.e y=-\frac{1}{2}gt^2 +Vt\sin \theta + y_0 x=Vt\cos \theta + x_0 I can easily derive these, and gives me the power of calculus, they are similar to the ones given on...