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Re: HSC 2016 MX2 Combinatorics Marathon New question: Prove that: \sum_{r=0}^{n} \left[\binom{n}{r}\cdot \sum_{s=0}^{n-r}\binom{n-r}{s} 2^{n-r-s}\right] = 4^n

Re: HSC 2016 MX2 Combinatorics Marathon You should be able to justify the 2^n without summing a series.

Once you see that one of the roots is i, it is much easier to use sum or product of roots than to use the quadratic formula.

Re: HSC 2016 MX2 Combinatorics Marathon We don't actually need to worry about the other letters at all. They aren't relevant to the problem. The number of ways of choosing the positions for the Rs is 9C3. The number of such positions satisfying the condition is 7 (123, 234, 345, ..., 789)...

Actually .... that statement has a ring of truth to it. Extension 2 exams are just widdle baby 4 unit exams.

Since the course hasn't been called "4 unit" for SIXTEEN years, why doesn't this get renamed to "Extension 2"? It is like Sydney Grammar who still officially refer to Year 12 as "Sixth Form" FORTY years after it changed.

The point is that I was asked to justify why religion is BS. If someone is permitted to say 'other religions are BS simply because mine is correct', then I should be permitted to say 'ALL religions are BS because my view of the universe (a purely scientific one) is correct. The fact of the...

I thought I'd resurrect this comment (from page 5 of this thread). I want to see what people would say to counteract this type of thinking. How are people like this who are clearly very intelligent in other respects somehow missing the deeper meaning and beauty of mathematics? (For me, although...

You clearly didn't understand the point of my question. I wasn't claiming or implying that the big 3 religions are derived from Zoroastrianism (neither am I saying they are not - it just wasn't my point here). My question was basically - do you think Zoroastrianism is BS? I also asked you to...

Just to make sure you are aware of an issue that wasn't brought out by the other questions, graph |y| = x^3 - 1

Any EARLIER Fibonacci number. It wouldn't make any sense without that word.

The locus of its centre ......... as what changes?

Re: MX2 2016 Integration Marathon They have been asked indirectly in older HSC exams, where the functions C(x) and S(x) were defined in terms of exponentials, and the various properties required to be derived.

What is your opinion on the existence of the Zoroastrian god Ahura Mazda? Assuming you believe it doesn't exist, explain why. (Without referring to your own religion)

In Linear Algebra, matrix multiplication is equivalent to function composition. If a matrix M represents a function f, then M^2 represents f^2, but M^2 is a multiplication and f^2 is a composition. The composition power notation is regular used in Linear Algebra, but only on generic...

Alternatively: Solve the equation |2x-6|=x+3 first. Then graph y=|2x-6| and y=x+3 on the same axes, showing the x values of the points of intersection found in your algebraic solution. Then use the graph to solve the inequality. It is essentially the same thing, but many people find it less...

I hope you remove your colander in class.

Moved on? I hope that doesn't mean you've taken the BS on board.

Re: HSC 2016 4U Marathon A downwards force is not a "lateral" force. Edit - yes, I know what you mean now.

Re: HSC 2016 4U Marathon Alternative solution without directly using the triangle inequality: Let z = r cis theta and substitute. Rearrange to write cos^2 theta in terms of r. Then using the fact that 0 <= cos^2 theta <= 1, solve the resulting inequality to find the range for r^2 and...