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No, the negative powers of h in the speeds mean 'per hour'. So 60 km h-1 means 60 kilometres per hour (or 60 km/h); the reason for this is that h-1 just means 1/h, so km h-1 means km/h.

Re: HSC 2016 4U Marathon $Another problem is that in general, $\arg \left(\omega \right) \neq \tan^{-1} \left( \frac{y}{x}\right)$ (that equality is true if and only if $x>0$), where $x$ and $y$ are the real and imaginary parts of $\omega$, respectively. It is always true though that if $x\neq...

$Let the frame have dimensions $x$ (horizontal dimension) and $y$ (vertical dimension). (All lengths in fm and all areas in $\text{cm}^2$.) Then the area of the frame is $A = xy$. Now, drawing a diagram, we see that the area of the border is: $2\times \2x + 2\times 3\left(y-4 \right)$ (just...

Re: HSC 2016 4U Marathon $\textbf{NEW QUESTION}$ $Sketch and describe the locus $\arg (z) -\arg \left(z +i\right) = \frac{5\pi}{4}$.$

Re: HSC 2016 4U Marathon $This is simply due to the choice of axis (there is only one axis since it is 1-dimensional motion). For upwards motion, it is generally more convenient to have the positive direction be upwards, so the weight force would point in the negative direction (as it points...

The Conics topic is being removed if I recall correctly.

Re: HSC 2016 MX2 Combinatorics Marathon My Q was also directed at current HSC students.

Re: MX2 2016 Integration Marathon For those who want to treat it as though that integral is still given, it is this: .

I'm guessing the marks shown in the column graphs of that Liverpool Boys High School annual report are final HSC mark (average of moderated internal mark and external mark).

Re: HSC 2016 3U Marathon This is the definition of tan (or the most common one anyway).

Re: HSC 2016 4U Marathon $Conventionally $g$ refers to the positive quantity, like 9.8 m/s$^2$.$

Maybe malcolm21 means "in the centre" as in rank-wise.

Re: HSC 2016 4U Marathon $How can this be 0? Since $g,k>0$ and $\frac{g}{k}> \frac{g}{k^3 +k}$, the L.H.S. is positive. The L.H.S. is dimensionally dodgy too.$

$If we instead assume that the force provided by the water is a constant $F_W$, water is ejected out at a constant rate of $k>0$ (dimensions are mass per unit time), then the mass of the water-rocket at time $t$ is $m(t) = M_0 - kt$ for $0\leq t < \frac{M_W}{k}$, where $M_W$ is the mass of the...

$Note that this is technically not the case if the mass is not constant. The general equation is $\bold{F} = m\frac{\mathrm{d} \bold{v}}{\mathrm{d}t}+ \bold{v}\frac{\mathrm{d}m}{\mathrm{d}t}$.

Re: HSC 2016 2U Marathon Yes, this is a circle geometry theorem from HSC 3U ("tangents from a common external point are equal").

Re: HSC 2016 3U Marathon Reverse chain rule is substitution done in the head.

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread $Note that the slope of $OP$ is $m_{OP}=\frac{ap^2}{2ap}=\frac{p}{2}$. Similarly, the slope of $OQ$ is $m_{OQ}=\frac{q}{2}$. Since $\angle POQ$ is a right angle, we have $OP \perp OQ$, so the two lines' slopes must multiply to...

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread $Depends on the example. For example, if the parameterisation of the point $P$ was $x(t)=t^2$ and $y(t)=2$, $t\in \mathbb{R}$, then since the range of the function $x(t) = t^2$ is the set of non-negative real numbers, the locus...

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread Because as the parameter varies through its domain, one of the coordinates stays fixed. You still need to check to see whether the other coordinate has any restrictions on it.