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    HSC 2016 MX1 Marathon (archive)

    Re: HSC 2016 3U Marathon The reason for that is to account for the rotational symmetry of the seating in tables. It's standard required knowledge for 3U perms and combs for circular arrangements.
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    HSC 2016 MX1 Marathon (archive)

    Re: HSC 2016 3U Marathon The term posted for Ambility's no. of ways to seat people in the 5-seat table is incorrect. Can anyone explain what was the reasoning behind Ambility's expression for that, and why it is not quite right? (Just focus on the numerator.)
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    HSC 2016 MX1 Marathon (archive)

    Re: HSC 2016 3U Marathon wu345's answer is correct. It would be an instructive exercise to find the flaw with the method posted by Ambility.
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    HSC 2016 MX1 Marathon (archive)

    Re: HSC 2016 3U Marathon What was your solution?
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    Proving determinant properties

    $\noindent Recall that the determinant of the conjugate of a matrix is the conjugate of the determinant of that matrix. (Also transpose and conjugate are interchangeable for a matrix). Also, determinant of a transpose is the determinant of the original matrix.$ $\noindent Hence $\det...
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    Year 10 Mathematics in Vietnam

    What if the HSC syllabus changes a lot in that time?
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    MedEntry workshop trial exam - disappointed with percentiles

    studyandstudyandyeah said they'd be hapy to pay "any price you set", so you could just set a price tag of like $1 billion :p.
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    HSC 2016 Maths Marathon (archive)

    Re: HSC 2016 2U Marathon Paradoxica intended it as a mathematical joke. The actual answer is of course ex + c.
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    Cambridge HSC MX1 Textbook Marathon/Q&A

    Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread Oops, no, it's correct, I realise I misread the Q., the acceleration was 4 at x = 2; I accidentally did it at x = 4. So I got a different value for n. The actual value for n would be sqrt(2).
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    Using determinants

    Not really sure. I might have a search later about it. Someone used it last year I remember reading on the 2015 HSC 4U Exam Thoughts thread for a Q. about showing area independent of theta. I'm pretty sure they'll know what you're doing if you use determinants at least, (unlike some school...
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    Using determinants

    OK This one they basically want us to prove what I said about the determinant being (twice the) the triangle area (signed). A proof of this may be found here: https://people.richland.edu/james/lecture/m116/matrices/area.html . Here's a proof using trapezia...
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    Using determinants

    Oh yes, that was a typo (I copy-pasted your determinant but forgot to change those last entries). I'll fix it up.
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    Using determinants

    Incidentally, that determinant is twice the (signed) area of the triangle formed by the three points A, B, C. Knowledge of this determinant formula for triangle areas makes some HSC conics Q's really easy to do (the ones like 'show the area is independent of theta' etc.).
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    Using determinants

    $\noindent Since they're collinear, remember that $\overrightarrow{AB}$ is a multiple of $\overrightarrow{AC}$, so this imposes some conditions on the coordinates.$ $\noindent We don't need to expand it either. We can just row-reduce a tiny bit. Doing $R_2 \to R_2 - R_2$ and $R_3 \to R_3 -...
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    Cambridge HSC MX1 Textbook Marathon/Q&A

    Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread I doubt they'd ask it in the HSC without providing a conversion rate though, so don't worry.
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    Cambridge HSC MX1 Textbook Marathon/Q&A

    Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread Yeah they're the same. I think you need to use the fact that AP is one inch and convert it to feet. From Google, 1 inch = 0.0833333 foot = 5/60 foot = 1/12 foot. This means viewing everything with origin A, the equation of...
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    Cambridge HSC MX1 Textbook Marathon/Q&A

    Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread Which part do you need help with? Just finding the volume? Once we've found that, multiplying it by 0.25 will give us the mass in tons.
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    Proving determinant properties

    The induction method was just to prove the thing about determinant of triangular matrices being the product of diagonal elements. If you're allowed to assume that, then you don't need to prove it, so no induction needed. Then the only thing needed to be proved was that the diagonal elements of...
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    Cambridge HSC MX1 Textbook Marathon/Q&A

    Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread Yeah. You only need to take one of them to find n.
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    Proving determinant properties

    After reading through your solution carefully (before I'd only glanced at it), I see you were almost there. To finish it off, notice that ujk = 0 whenever k < j, due to triangular matrix condition. This means the only potentially non-zero term in the sum at the end will be when k = j, i.e...
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