Search results

First start with T = N + Ae^{-kt} Given that the room temperature is 25, \lim_{t\to\infty} T = 25 . \lim_{t\to\infty} T = 25 = \lim_{t\to\infty} N + Ae^{-kt} Looking at the RHS: as t \to \infty , e^{-t} shrinks to zero and so the second term Ae^{-kt} approaches zero...

P = 200 + 1600e^{-kt} If t=0,\, P = 1800. Substituting in t=56,\, P = 900, \begin{aligned} 900 &= 200 + 1600e^{-56k} \\ e^{-56k} &= {7 \over 16} \\ k &= -{1\over56}\log{7\over16} \end{aligned} Refreshing the equation, P = 200 + 1600e^{\left({1\over56}\log{7\over16}\right)t}...

Well... that sort of behaviour is hardly exclusive to Ruse. That sounds typical for any selective school. Like every other selective school, Year 7 entry at SBHS is dependent on the selective test. If you get a crappy score you're just not going to get in even if you pitch a tent next to the...

Your parents could probably provide a lot of help to you if you do Economics but ultimately they aren't the ones sitting the HSC - you are. Pick the subject you're most interested in. Don't worry about how much work you might need to do because your enjoyment of a subject can massively shift...

I think you should keep in mind that studying is not about hitting a target of "x" hours a week - it's about learning the content. Everyone is different in this regard - for example it might take somebody a week to understand a chemistry topic but they might get the hang of a maths topic in a...

If the direction of the projectile's velocity makes an angle \theta with the horizontal, then it is true that: \begin{aligned} \tan \theta = \frac{\dot y}{\dot x} &= \frac{-gt + V \sin \alpha}{V \cos \alpha} \\ &= -\frac{gt}{V}\sec \alpha + \tan \alpha\end{aligned} At the point where the...

SBHS has a very heavy focus on sport. In particular many of the offered sports have weekday training and Saturday sessions. But if your son doesn't care much for sport he can pick a more casual sport that won't require any training. But it is still highly academic so you don't need to worry...

The report goes on to say that a set of simultaneous equations are created and solved. That sounds reasonable enough to me. For example if there were two subjects then there would be two equations for their scaled means each with two unknowns, so a unique solution would exist.

The key is to analyse the sentences and turn them into math. 4) Let D denote the number of DVD's and C the number of CD's. This means that C + D = 17 . She paid $25 for each DVD and $18 for each CD, and spent $390 total. That implies that 25D + 18C = 390. Start with two...

For your second question: Let z = {\rm cis\,} \theta. {\rm cis \,} 4\theta + 1 = ({\rm cis\,} 2\theta - \sqrt2{\rm cis\,}\theta + 1)({\rm cis\,} 2\theta + \sqrt2{\rm cis\,}\theta + 1) Note: \begin{aligned} ({\rm cis\,} 2\theta + \sqrt2{\rm cis\,}\theta + 1) &=[(\cos 2\theta + 1 +...

1 + \cos \theta = \left(\sin^2{\theta\over2} + \cos^2{\theta\over2}\right)+\left( \cos^2{\theta\over2} - \sin^2{\theta\over2}\right) = 2 \cos^2{\theta\over2} 1 - \cos \theta = \left(\sin^2{\theta\over2} + \cos^2{\theta\over2}\right)-\left( \cos^2{\theta\over2} - \sin^2{\theta\over2}\right) =...

Might be nice reading: https://www.uac.edu.au/assets/documents/scaling-reports/Scaling-Report-2017-NSW-HSC.pdf i.e. the scaling of a subject is determined by how well its participants perform in other subjects (after scaling).

You are asked to find the initial velocity. Because the drain is horizontal, the initial vertical velocity must be zero (which means the initial velocity is purely horizontal). Given that \ddot y = -g , integrate to get \dot y = -gt + C (where C is the initial vertical velocity - zero)...

Because it's a huuuuge pain to write out the entire thing in TeX and using the sigma notation is just faster.

Your second answer is correct. First, suppose we are adding 5 X's to GUMTREE. (These X's will represent the letters of KOALA which we will deal with later) There are \frac{12!}{5! \cdot 2!} unique arrangements this way. For each of these arrangements there is exactly one way the X's...

Note that \begin{aligned} \alpha + \beta + \gamma &= -3 \\ \alpha \beta +\alpha \gamma + \beta \gamma &=-2\\ \alpha \beta \gamma &=-1 \end{aligned} 14a) Let the expression in a) be denoted as \sum (\alpha_i)^2 (\alpha_j). Now, \begin{aligned}(\alpha + \beta + \gamma) (\alpha \beta...

You could consider researching polymer chemistry. This would double up with the Production of Materials topic and you'd still save quite a bit of time.

The answer is 1728 (it's from the Cambridge book, I looked it up myself). 1728 = \binom{3}{2}\times 4! \times 4! There are three "free" women who can row anywhere on the boat. Consider the bow and stroke sides separately. For the bow side, three specific women MUST be there, so one spot...

Oh sorry I forgot about that. In this case you would start by finding exactly where the ball is at a height of 30m (there will be two times - a diagram may help). Then, knowing that the trajectory of the ball is a concave down parabola, you can deduce when the ball is at a height of less than...

Note that the ball will hit the net if and only if the net is placed within the ball's horizontal range.