Search results

$Should be $\frac{n^2 }{2}$ at the end.$

Yeah this is what I thought you meant when I searched up 'uncountable noun' (the use of 'uncountable' here is unrelated to uncountability of sets so it confused me initially since I was thinking of the mathematical 'uncountable').

Yeah lol I meant that I thought that he started talking about uncountability because of this, and once he started talking about uncountability, he mentioned countability too.

My guess is his countability statements came from when you said "most" functions.

I don't think he was reminding you of those facts (countability of the rationals etc.); rather, I think he was adding them in as more 'interesting statements' for this thread. Or maybe you were referring to his first paragraph haha. Not sure in that case why (if at all that was his purpose) he...

Re: HSC 2016 3U Marathon Must use limits from 0 to 1. The indefinite integral (primitive) can't be expressed in terms of elementary functions (turns out it requires polylogs; recall that in general it is likely that an arbitrary function will not have an anti-derivative in terms of elementary...

Re: HSC 2016 3U Marathon Requires non-elementary functions then.

Haha another cool function – the Popcorn Function :) : https://en.wikipedia.org/wiki/Thomae%27s_function (Well-known for being continuous at any irrational number and discontinuous at any rational number)

Re: HSC 2016 3U Marathon $\noindent Haha this should have limits from 0 to 1.$

In other words, you're saying that the distributions of marks for HSC Maths 2U/Japanese are generally positively skewed (longer tail toward the right) whilst for HSC Physics and Chemistry, they are generally negatively skewed (longer tail towards left).

Re: HSC 2016 3U Marathon $\noindent \textbf{NEW QUESTION}$ $\noindent Find $\int _0 ^1 x \sqrt{1-x^2} \text{ d}x$ using the substitution $u = 1-x^2$.$

Re: HSC 2016 3U Marathon $When we do the evaluation at the end, since we changed the limits already, we evaluate them in terms of $u$, i.e. $\Big{[} \sqrt{u}\Big{]}_{10} ^{2} = \sqrt{2} -\sqrt{10}$. We don't need to convert back to $x$ in the end (this is the purpose of changing the limits of...

Yeah if you do 4U maths eventually then your accelerated 2U is essentially irrelevant for you ATAR, even back-up wise. Some people also go on to do MX2 and a total of 10 units including the four units of MX1/MX2, which makes it impossible for 2U maths to count, because then they would only end...

Re: HSC 2016 3U Marathon $\noindent \textbf{NEW QUESTION}$ $\noindent Evaluate $\int _{-3} ^{1} \frac{x}{\sqrt{1+x^2}}\text{ d}x$ by using the substitution $u = 1+x^2$.$

You can probably apply for most things at WSU (other than Medicine).

Nah, if you do HSC 4U Maths, your 2U Maths won't count.* Only a maximum of four units of maths is allowed to count, so even if he does worse in HSC Geography than 2U Maths, 2U maths can't replace HSC Geography. * Unless he does really badly in 4U (badly enough so that even after scaling, it's...

$So TLDR version is that theory from linear algebra shows us that any line passing through $(x^*,y^*)$ can indeed be written in the form $a_1 x + b_1 y + c_1 + k(a_2 x + b_2 y + c_2) = 0$ (apart from the line $a_2 x + b_2 y + c_2=0$). What $k$ represents is what ratio of each line (or rather...

$Explaining this properly requires some linear algebra. Loosely speaking, $k$ represents the ratio of the ``combination'' of the two given lines' equations that add to give the equation of the desired line.$ $Let our two lines be $\ell_1: a_1 x+b_1 y + c_1 = 0$ and $\ell_2: a_2 x + b_2 y + c_2...

$It's probably easier just to convert everything to SI units at the start and then just do the question without needing to worry about units till the very end, when you know it'll be in newtons. This is because if everything is in SI units to start with, the end of a calculation is also in SI...

What about when English teachers calculate your yearly mark? :P