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Re: The p00n thread Yea some of friends did this too

Re: The p00n thread ~Chit Chat Thread~ Don't bother studying 3U, just do 4U and 3U comes naturally

Re: The p00n thread why would you need to memorize that Also that list is redundant, you dont need conj(z1 - z2) = conj(z1) - cong(z2) and you dont need conj(z1/z2) = conj(z1)/conj(z2)

Thank you very much for your response, I will try to investigate the Mathematics/Chemistry dual major option though, I will probably need to contact the faculty of engineering for a more specific response.

Yes you can do this, it is what is said on the website, I can do a double degree which is 5 years but my plan and circumstances find it not very preferable Can anyone help or will I need to contact the Dean

Re: HSC 2014 4U Marathon \\ $Let$ \ \ f(x) \ \ $be a continuous concave up function where$ \ \ a \leq x \leq b \\ \\ $i) Show that$ \\ \\ \frac{f(a) + f(b)}{2} \geq f \left(\frac{a+b}{2} \right) \\ \\ $ii) Hence show that$ \\ \\ \left(\sin^2 \alpha + \csc^2 \alpha \right)^2 + (\cos^2 \alpha +...

Re: HSC 2014 4U Marathon Yea the expression is incorrect, here is a hint: u_k = \binom{n}{k} w_{n-k} $Let$ \ \ w_m \ \ $be the number of ways to arrange$ \ m \ $objects such that each object is NOT in its original spot$ Note that w_m \neq m! \ $since this doesn't guarentee each object...

Hello, I am considering doing a Bachelor of Science (Advanced Mathematics) for 3 years before undertaking a Masters in Engineering for another 1.5 years. According to the USYD Masters of Engineering site, I can do a Bachelor of Science degree before doing a Masters in Engineering provided...

Re: HSC 2014 4U Marathon Well we get x^2(4A^2B - AC^2) = -DC^2 x^2 = \frac{-DC^2}{4A^2B - AC^2} = \frac{DC^2}{AC^2 - 4A^2B} In order for the RHS to be positive, the numerator and denominator either both need to be positive ort both be negative, since hte numerator is always positive...

Re: HSC 2014 4U Marathon The idea is spot on, my algebra was though y= -(2A/C) x Ax^2 + B \frac{4A^2x^2}{C^2} + Cx \frac{-2A}{C}x + D = 0 \\ \\ x^2(\frac{4A^2B}{C^2}- A) = -D and thus \frac{4A^2B}{C^2} - A \leq 0

Re: HSC 2014 4U Marathon This can fall under graphs \\ $An implicit curve is sketched in the$ \ xy \ $plane with the equation$ \\ \\ Ax^2 + By^2 + Cxy + D = 0 \ \ \ \ \ $With$ \ \ A,B,C,D > 0 \\ \\ $Show that in order for the curve to be an ellipse then$ \ \ \ \ C^2 \geq 4AB

Re: HSC 2014 4U Marathon Actually I made a mistake in my working, the limit does not exist, my bad

Re: HSC 2014 4U Marathon Well done on the first solution is correct, but, are you sure that your result for the limit is correct? I am getting a different result Also the inqeualities posted are way too hard for HSC level inequalities, HSC level is easy

Re: HSC 2014 4U Marathon \\ $Evaluate$ \\ \\ \lim_{n \to \infty} \frac{1}{n} \sum_{k=1}^n \cos(k) The above 4 questions are able to be done with only Complex Numbers and Polynomials knowledge.

Re: HSC 2014 4U Marathon \\ $Two polynomials with real co-efficients are such that$ \ \ \ P(x) = Q(x) \ \ \ $for real values of$ \ x \\ \\ $Show that$ \ \ P(x) = Q(x) \ \ $for complex values of$ \ x

Re: HSC 2014 4U Marathon \\ $Suppose that there exists a polynomial such that$ \\ \\ P(x-1) + P(x+1) = 2P(x) \\ $show that$ \ P(x) \ $can only have a degree of at most 1$

Re: HSC 2014 4U Marathon \\ $Find all solutions real or complex to the equations$ \\ \\ x+y+z = 3 \\ x^2+y^2+z^2=3 \\ x^3+y^3+z^3=3

Re: HSC 2014 4U Marathon \\ $Prove for positive$ \ a,b,c \\ \\ \sqrt{\frac{2a}{a+b}} + \sqrt{\frac{2b}{b+c}} + \sqrt{\frac{2c}{c+a}} \leq 3

Re: HSC 2014 4U Marathon \\ $The roots of the polynomial$ \\ \\ P(x) = x^3 - \alpha x^2 + \beta x - \gamma \\ \\ $are$ \ \ \alpha , \beta , \gamma \\ \\ $Find$ \ \alpha, \beta, \gamma

Re: HSC 2014 4U Marathon \\ $Let$ \ \ \ a, \ b , \ p, \ q > 0 \ \ \ \ $and$ \ \ \ \frac{1}{p} + \frac{1}{q} = 1 \\ \\ $Prove that$ \ \ \frac{a^p}{p} + \frac{b^q}{q} \geq ab