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Re: HSC 2015 3U Marathon It's actually not that bad once you do the substitution. I found it in a Stanford Math Tournament, but they gave it without the substitution.

Re: HSC 2015 3U Marathon $Evaluate $\int^{\infty}_{e^{e^e}}~\frac{\mathrm{d}x}{x(\ln{x})(\ln{(\ln{x})})(\ln{(\ln{(\ln{x})})})^{\frac{4}{3}}} $ using the substitution $u=\ln{(\ln{(\ln{x})})}$.

Re: HSC 2015 3U Marathon Skipping the first step: \begin{align*}\textup{2. Assume true for }n&=k \\(1+x)^k&=\binom{k}{0} + \binom{k}{1}x + \binom{k}{2}x^2 +...+ \binom{k}{k}x^k \\\end{align*} \begin{align*}\textup{3. Prove true for }n&=k+1 \\\textup{RTP: }(1+x)^{k+1}&=\binom{k+1}{0} +...

3 marks. It is question 24(c) of the 2006 HSC Economics paper.

Because the first investment, placed in at the start of the 5 years, has been in the bank account for 60 months at the end. By that time, it will have compounded 60 months worth of interest. "policy matures..." refers to when the savings policy has reached the end of its term and Ester is able...

(i) The first investment is the $250 that is initially deposited. You are meant to find out the value of this $250 once it has been in the bank for 60 months (5 years = 60 months). (i)) You should be familiar with how to write out the amount (An) of money in the bank account after n months...

ii) This graph (lets call it v(t)), is the velocity function. The gradient of this function represents acceleration. So to find when acceleration is zero, you find the stationary points of this graph (the velocity function), which can be found by letting v'(t)=0. v'(t) is the same as f''(x), if...

re: HSC Chemistry Marathon Archive a) Petroleum -> Fractional distillation -> Cracking of long chain hydrocarbons -> ethene undergoes a substitution reaction to form phenylethene -> phenylethene monomers take part in an addition polymerisation reaction to form polystyrene Is that enough for 3...

There have been a lot of threads on this. Read this one: http://community.boredofstudies.org/17/chemistry/317689/cyclohexene-bromine-water-prac.html and also this http://community.boredofstudies.org/239/production-materials/234351/cyclohexene-bromine-water.html#post4891519

Right now I'm using the Uni Jetstream SX-217. Prefer using the uni-ball Vision RT though.

The normal domain for ln(x) is x>0. In this case, we have ln[tan(x)], so we require tan(x)>0 over the domain 0≤x≤2π. Might be easier to find for what values of x this inequality holds true if you draw a graph of tan(x).

Split the inequality into two parts: 4x \leq 15 and 15 \leq -9x . Now simplify those and graph the solution to both of those on a number line.

The first and second lines are not linked. I was just stating what 'a' was equal to. The change of base rule is: \log_a{b}=\frac{\log_m{a}}{\log_m{b}} Did you get the second question?

First one requires you to manipulate the terms and use log laws to get log10(2) in terms of log5(8): \begin{align*}\log_5{8}&=a \\\log_{10}{2}&=\frac{\log_5{2}}{\log_5{10}} \\&=\frac{\log_5{2}}{\log_5{5}+\log_5{2}}...

Regret doing Biology. Human body stuff is interesting, but all the plants stuff not so much. Should've have done engineering studies or PDHPE instead I think. Sent from my SM-G900I using Tapatalk

Re: HSC 2015 3U Marathon Several people started with $400 each and played a game with the following unusual rules. Each player pays $10 to the house at the beginning of each round. During each round, one active player is declared the loser, and he distributes all of his money in equal amounts...

Re: HSC 2015 3U Marathon $Evaluate $ \frac{100}{\log_2{100!}}+\frac{100}{\log_3{100!}}+\frac{100}{\log_4{100!}}+...+\frac{100}{\log_{100}{100!}}.

Re: HSC 2015 3U Marathon Triangle ABC is inscribed within a semi-circle with diameter AB as shown. The area of triangle ABC is equal to 2/9 of the area of the semi-circle. Find the size of the smallest angle in triangle ABC to the nearest degree.

Re: HSC 2015 3U Marathon Ah okay I see what you mean. From the answer I'm pretty sure they intend for you to use the first method you've quoted.

Re: HSC 2015 3U Marathon The answer is: 2/3.