Recent content by jyu

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    HSC Extension 2 Mathematics Predictions / Thoughts

    check the revised version
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    Hardest geometry question in history answered by student trivially............ How?

    Suppose that PQR is a 50-60-70 (respectively) triangle with an interior point X. Let angle PXR = s and angle QXR = t. Find (in terms of s and t) the three angles of any triangle with side lengths equal to PX, QX and RX.
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    Nice proof

    False statement (the sum on the right has x terms), because x is not necessarily a natural number. If x are natural numbers, x^2 is not differentiable.
  4. J

    Hard Binomial Theorem Question - HELP

    a^n=3b, na^(n-1)=6b, 0.5n(n-1)a^(n-2)=5b a=3, b=243, n=6
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    I tried k=sqrt(3.5), plotted x and y intercepts and alpha, they are not collinear.
  7. J


    There is only one real x such that P(x)=0. Not three real xs. Meaning of root.
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    Exactly one real root and no complex roots when k=+/-1. For other real values of k, there are 3 roots according to the Fundamental Theorem of Algebra, one must be real according to the Conjugate Roots Theorem.
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    If k=1, z^3-3z^2+3z-1=(z-1)^3, if k=-1, z^3+3z^2+3z+1=(z+1)^3, .: exactly one real root each. I think you need to review your question.
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    HSC 2018-2019 MX2 Integration Marathon

    Re: HSC 2018 MX2 Integration Marathon Try replacing both e^x with e^(x^2).
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    HSC Physics Marathon 2013-2015 Archive

    re: HSC Physics Marathon Archive The reaction force as in Newton's third law.
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    HSC 2015 MX1 Marathon (archive)

    Re: HSC 2015 3U Marathon h=\frac{-\sqrt{2}+\sqrt{10}}{4}d