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    What does it mean to have irrational and complex powers?

    In exponentiation, we are told that raising something to an integral power (n, say) means multiplying it with itself a total of n times, if n is non-negative. And we also learn fairly early on that should the exponent be negative, then a^{-n}=\frac{1}{a^n}. We even extend this to the...
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    Thoughts on Latin

    What were your thoughts on this year's Latin exam?
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    Best of Luck Team BOS 2014

    harrypotterfan had a similar thread but seems to have deleted it O_O. Anyway, good luck Team BOS 2014 - the only and the best! *Inserts motivational, stirring speech* Edit: Motivational, stirring speech has arrived. Many of us have been around here for a year or more, the rest of us for...
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    On combinatorial arguments

    Hello BOS denizens :). Do you know whether the HSC allows for combinatorial proofs when dealing with binomial coefficient identities? e.g. Proving that \sum_{k=1}^{n}k \binom{n}{k}=n\cdot2^{n-1} We can model this as creating a committee of size k people with a single chairperson, from a...
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    Combinatorics Inclusion-exclusion principle

    Hello, I'd like to request some assistance with understanding a worked example from Terry Lee's Fundamental Maths. Find the number of ways you can arrange A, A, B, B, C, C such that no two identical letters are together. What he did was calculate total number of ways- 90. then he calculated: -...
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    Circle Geometry

    Hello again BOS denizens, I'd like to enquire as to validity of my proof. In the diagram shown, the angles marked in red are equal. I want to prove that the quadrilateral ABCD is cyclic. So what I did was produce a circle around triangle ABC, since all triangles are cyclic. Then I said, since...
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    Permutations and combnations: groups of equal size

    Hi BOS denizens, I'd just like to ask, why is it then when one divides a group of people into x smaller groups of equal size, they divide the total number of ways by x factorial? E.g. dividing 12 people into 3 groups of 4 gives \frac{\binom{12}{4}\binom{8}{4}}{3!} Why does one divide by 6...
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    Module B Speeches Essay

    Hi all. If it would not be too much trouble, could someone here (preferably a non-2014 HSC student) glance over my speeches essay for me?
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    Globalisation Case Study

    Hello, I was just wondering, if it would not be too much trouble, could someone glance over a case study essay for me? Many thanks =)
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    Statistics

    Hello everyone (:. I've recently taken a bit of an interest in statistics, and I was wondering, are there any good websites that could be used for learning statistics? the one i'm currently using is onlinestatbook.com, which has a textbook pdf, but since I've just started learning statistics...
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    Curve sketching

    Hello everyone =). I was just wondering, is graphing a very big topic for extension 2 mathematics? I'm not struggling with it or anything, I just hate curve sketching in general. Thank you all in advance :).
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    Manganese dioxide

    Hi people, I just did this prac in chemistry today involving the use of a catalyst (manganese dioxide) in the decomposition of hydrogen peroxide into water and oxygen. I was just wondering, how come after the MnO2 pellets are added to the solution and the reaction takes place, it looks like they...
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    Help! Fail kid here

    Ok so theoretically I left my retainer at home. What are the chances that my teeth will still fit in it after 5 weeks and what's the recommended treatment?
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    Animal Farm

    Hey guys, I know that I'm only in Yr10 and thus this thread should probs be somewhere else, but the best English people frequent this place more. So, anyways, can anyone tell me how the use of anthropomorphism in Animal Farm allows the readers to relate to them?
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