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u are right, sorry

Nice

m(gradient P) = 1/t .: m(gradient Q) = -t (as normal Q is perpendicular to normal P) y = \frac{x^2}{4a} \frac{dy}{dx} = \frac{x}{2a} We know that the gradient of normal Q is -t \therefore -t = \frac{x}{2a} \therefore x = -2at Sub this back into parabola as it lies on it and u get...

thats overkill lol

Find a connection between the point x and y by means of squaring, using perfect square factorisation, etc (its so hard to explain the way of thinking for this question without giving it away)

yeh sometimes depending on my fear i would say "therefore the locus of R is the parabola ______ with focus (__,__)"

In locus they always tell u to find a point, in this case it is R(-apq(p+q), a^2 (p^2 + pq + q^2 +2)) From part (ii), we got pq = -1 (because PQ is focal chord) Now lets write out R x = -apq(p+q) x = a(p+q) (as pq = -1) y = a^2(p^2 + pq + q^2 +2) y = a^2(p^2 + q^2 + 1) We need to get...

yeh it does haha, sorry, my lack of clearness caused ambiguity

before anything happens, forget about that weird "top curve-lower curve theory" For 0 \leq x \leq \frac{\pi}{2}, graph y = sinx and y = -cosx If u wanna find the area between these curves, get a blue and red pen. Colour the area under the curve y= sinx blue, and the area under the curve y =...

nah lol, it was my way of explaining to her which would be the top curve if u had the graph (or drew it)

Common sense y = x^2 + 2 y = x^2 Which one is the top curve? i.e. which graph within the domain given/found will appear on top (or having more larger y-values for each corresponding x-value)

Re: HSC 2013 4U Marathon Multiply them?

Re: HSC 2013 2U Marathon so the ladder is extendable?

Well done Menomaths!

Re: MX2 Integration Marathon yep Nice, more methods are great Yes!

Re: MX2 Integration Marathon ahhh

Re: MX2 Integration Marathon $By graphing: e^{x^2} > 2 - e^{-x^2} \\ \\ ~~~~~~~~~~~\therefore e^{x^2}+e^{-x^2} >2 \\ \\ \therefore $\int_0^1\left ( e^{x^2}+e^{-x^2} \right )dx >\int_0^12dx \\ \\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~=2 Question: $Show that $\int \frac{dx}{1+cosx}dx = tan\left (...

Say i do this course and pick a major - psychology, is this the same as bachelor of psychology? (like what i learn and future jobs)

Re: HSC 2013 4U Marathon Can i let polynomial P(x) be P(x) = \sum_{k=0}^{n}a_kx^k with roots a_1, ...,a_n?

re: HSC Chemistry Marathon Archive i greatly simplified the question and gave the student a name lol (oh so maybe u didnt get an ethanol-mass calculation question)