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Re: MATH1231/1241/1251 SOS Thread The gradient vector isn't tangent to the graph (a level curve of F), it's normal to it.

Re: MATH1231/1241/1251 SOS Thread $\noindent If $F(x,y) := y - f(x)$, where $f$ is a function of a \emph{single} real variable, then the graph is $y = f(x)$ is one of the level curves of $F$, namely $F(x,y) = 0$. (Remember, the level curves of $F$ are the family of curves $F(x,y) = C$, where...

A thread for it would probably get created soon.

Re: MATH1231/1241/1251 SOS Thread $\noindent We want a basis for $\mathbb{R}^{3}$ (not just for $\mathrm{im}\left(C\right)$) that contains a basis for the image of $C$. We could ensure we obtain this by instead row-reducing the augmented matrix $\left[C \mid I_{3}\right]$ (where $I_{3}$ is the...

Well do you have any reasons for wanting to do English Advanced over Standard other than better aligning and the courses not having much difference in difficulty? If so, what are they? You could write about those.

Re: MATH1231/1241/1251 SOS Thread $\noindent I assume you got out the one about showing it's a linear map. Now, the kernel of $T$ is just the set of all vectors in $\mathbb{R}^{n}$ that get sent to $\bold{0}$. Note that $T(\bold{x}) = \bold{0}$ iff $\bold{x}\cdot \bold{b} = 0$ (of course we're...

Re: HSC 2016 MX2 Combinatorics Marathon You would need to account for making sure the cubelets are rotated the correct way too (so that their painted faces are outside).

Well theoretically they would've seen the material before probably (in university), and it's not like the material would be too advanced, should be able to be learnt relatively easily (guessing)? Like from what I can see there isn't too much deep stuff regarding matrices for example (iirc)...

Drongoski advised against being confrontational though.

Re: Discrete Maths Sem 2 2016 $\noindent b) Yeah it's stars and bars. Recall that stars and bars is basically placing identical (indistinguishable) dots into distinct boxes. Here, the `boxes' are the possible results of a die role: $1,2,3,4,5,6$. (So there's $6$ boxes, i.e. $5$ `bars' in the...

Re: Discrete Maths Sem 2 2016 $\noindent (For the meeting people one) Let $|S| = N$, where $N$ is a positive integer at least $2$. Note that all we need to do is show that the function $f$ described earlier can't be one-to-one (injective). Observe that the range of $f$ is actually a subset of...

You had been doing Advanced since beginning of the year, but that would have been Prelim. English Advanced. So they probably didn't consider themselves as suddenly kicking you out after months of doing the course, because they did so at the start of HSC English Advanced, which they may have...

Re: Discrete Maths Sem 2 2016 You can try investigating what happens for small values of |S| (e.g. |S| = 2 or 3 etc.) before generalising to |S| = N for arbtitrary N.

For how many months had you been doing the HSC English Advanced course when they kicked you out? Didn't you say it was effective from the start of Term 4 (which is usually when people would start the HSC English Advanced course?)?

Re: Discrete Maths Sem 2 2016 $\noindent Let $S$ be the set of all people in Australia yesterday (roughly, $|S| = 20 \text{ million}$). We can define a function $f \colon S \to \mathbb{N}$ by $f(p) = n$, where $n$ is the no. of members in $S-\left\{p\right\}$ that person $p$ met yesterday...

$\noindent No need for `mod-arg' form, just use Cartesian form. Noting that $\cos \frac{\pi}{6}+ i\sin \frac{\pi}{6} = \frac{\sqrt{3}}{2} + \frac{1}{2}i$, the answer to the question is$ $$\begin{align*}(1+2i)\left(\cos \frac{\pi}{6} + i \sin \frac{\pi}{6}\right) &=...

Re: MATH1231/1241/1251 SOS Thread Using LaTeX. A Short Guide to using LaTeX on this forum may be found here: http://community.boredofstudies.org/14/mathematics-extension-2/234259/short-guide-latex.html . There's a thread for practising it here...

You always keep your own external mark. So you'd basically keep your great external mark and get a bad or average internal mark (depends on how the cohort went externally).

$\noindent Poisson approximation will only work well if $n$ is large and \textbf{$p$ is small}. This is because we recall that the result is that if $X_{n}$ is $\text{Bin}\left(n,\frac{\lambda}{n}\right)$, where $\lambda >0$ is a constant (in other words, $np$ is a constant $\lambda$), then...

$\noindent For the last one (assuming counter-clockwise rotation), the answer is just $\left(1+2i\right)\left(\cos \frac{\pi}{6} + i\sin \frac{\pi}{6}\right)$ (simplify this of course). Remember in general, we multiply $z$ by $\cos \theta + i \sin \theta$ to rotate $z$ counter-clockwise by angle...