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You might want to search up the HSC timetables for previous years and see what they were like.

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread Given any inscribed triangle T in the circle that has at least one vertex V not "diametrically" opposite its opposite side (which is a chord of the circle), the area of T can be increased by moving the vertex V to this point on...

$\noindent There's several ways to do this. You can do it using a multi-parameter reduction as HeroicPandas has done above. Alternatively, recall that for any $k\in \left\{0,1,\ldots,N\right\}$, we have $\int_0 ^1 \binom{N}{k}x^{k}\left(1-x\right)^{N-k}\, \mathrm{d}x=\frac{1}{N+1}$, as can be...

Here's my guess (Q seemed a little vague). $\noindent Since the number of people alive at each age is given to decrease in arithmetic progression, we will have to assume some maximum age. Let's just assume the maximum age is some positive integer $N$. So if a person gets to $N$ years old, then...

Part 2) is basically asking I think for E[X | X > 10], where X is the random variable ''age that person dies at''. This is known as a conditional expectation.

I think you would need to make an assumption about what the oldest possible age is, e.g. 100 years (or call it N years or something), because that'd clearly affect the answer. Also, Pr(X > 10 | X = 10) is 0, so I think you meant something else.

Find the discriminant in terms of m and solve for m so that the following two conditions hold: 1) m is negative, and 2) the discriminant is negative.

$\noindent We have$ $$\begin{align*} |1-\overline{z}w|^2 -|z-w|^2 &= \left(1-\overline{z}w\right)\left(1-z\overline{w}\right) -(z-w)(\overline{z}-\overline{w}) \\ &= 1 -z\overline{w} -\overline{z}w +|\overline{z}w|^2 -|z|^2 +z\overline{w} +w\overline{z} -|w|^2 \\ &= 1 + |z|^2 |w|^2 -|z|^2...

Re: MATH1231/1241/1251 SOS Thread When we have a smooth surface given by F(x,y,z) = const., a normal vector is grad F. So since here F(x,y,z) = x^2 + y^2 + z^2, grad F = (2x, 2y, 2z). So a normal at a point (x, y, z) on the surface is (2x, 2y, 2z). (Or just note in this case it's a sphere...

So there's different formulas because they tell us how to calculate different things or based on different given data (e.g. based on whether we're given displacement or time, one of formula 1 or 3 would be appropriate to find the velocity, etc.)

The first tells us the velocity at time t if you know the answer initial velocity (i.e. at t = 0) and the value of the constant acceleration. It lets us answer Q's like "A car is accelerating at a constant rate of 4 m/s^2. If it started at a speed of 1 m/s, how fast is it going after 10...

The formula is going to work for any units, it's just that your final answer will have units based on what units you used. Like if you did the distances in km and the time in s, the answer would be expressed in km/s.

Re: Discrete Maths Sem 2 2016 A way to show RHS is a subset of LHS. Note the RHS is a set of ordered pairs. Let (x,y) be an element of RHS. Then (x,y) is in A x B or in A x C. If it's in A x B, then x is in A and y is in B ==> x is in A and y is in B union C. (As B is a subset of B union...

Correct, since m is already SI. Edit: sorry misunderstood you. For this Q. there's no km involved. (Thought you were talking about that last Q.)

We don't need to, giving it in m/s is perfectly fine (and a common thing to do. In fact, m and s are SI units).

Yeah I did 80 – 20.

Average velocity is the change in displacement divided by the time interval. In the last two seconds (time interval being 2 s), the change in displacement is 60 m along the street. So the average velocity for this time interval is (60 m along the street)/(2 s) = 30 m/s along the street. (Main...

Re: Discrete Maths Sem 2 2016 To show A is a subset of B, you should start off by letting x be an element of A (you did A∩C), and then show it is an element of B. (You may want to consider cases along the way to help use the given info.) I think what you essentially did is show A∩C is a...

Re: MX2 2016 Integration Marathon $\noindent Find $\int \left(a^2 -x^2\right)^{\frac{3}{2}}\, \mathrm{d}x$.$

Re: MATH1231/1241/1251 SOS Thread $\noindent We can write $\alpha = \cos t + i\sin t$, for some $t\in \mathbb{R}$. So $|\alpha +1| +|\alpha -1|= \sqrt{\left(\cos t+1\right)^2 + \sin^2 t} + \sqrt{\left(\cos t -1\right)^2 + \sin^2 t} = \sqrt{2 +2\cos t} + \sqrt{2-2\cos t} = \sqrt{2}\left(\sqrt{1...