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Re: HSC 2013 4U Marathon A nice circle geo question \\$Two circles with centres O and P and radii r and s (where r $<$ s) respectively touch externally at T. ABC and ADE are common tangents to the two circles.\\\\a) Show that A, O, T and P are collinear\\b) Show that AO = $\frac{r(r+s)}{s-r}

Re: HSC 2013 4U Marathon A nice circle geo question \\$Two circles with centres O and P and radii r and s (where r $<$ s) respectively touch externally at T. ABC and ADE are common tangents to the two circles.\\\\a) Show that A, O, T and P are collinear\\b) Show that AO= $\frac{r(r+s)}{s-r}

Re: HSC 2013 4U Marathon http://community.boredofstudies.org/showthread.php?t=298062 nice word for word copied questions...

Re: HSC 2013 3U Marathon Thread \int \frac{1-\sqrt{x}}{1-\sqrt[4]{x}}\; dx\\\\=\int \frac{\left ( 1-\sqrt[4]{x} \right )\left ( 1+\sqrt[4]{x} \right )}{1-\sqrt[4]{x}}\; dx\\\\=\int \left ( 1+\sqrt[4]{x} \right )dx\\\\=x+\frac{4}{5}x^{\frac{5}{4}}+c

Re: HSC 2013 4U Marathon if the roots are real but one's negative and the other positive? but then technically it can be -pi too

Re: HSC 2013 4U Marathon 0, since if all the coefficients are real, the roots must occur in conjugate pairs, therefore the arguments will be in opposite in sign? edit: oh right it can also be pi as well

Re: HSC 2013 4U Marathon damn I think I missed all the shortcuts :(

Re: HSC 2013 4U Marathon Edit: cbb to latex, will scan solution

Re: HSC 2013 4U Marathon did you get something like 2x^3+3x^2+8=0? just wanted to check, probably made heaps of sillies along the way.

Re: HSC 2013 4U Marathon you don't say :p this thread is now called the "realisenothing and sy123 marathon thread" heh

so short haha

Yeah I know another person with those exact same marks, such a beast :p

It's the distance between P and A_i all squared so it doesn't matter the order? It just looks nicer but not necessary I guess. I'll redo this again since I rushed it

Sorry for the messiness, might have missed out some lines or something edit: new solution

m8 coroneos is where it's at

^lol that's not classical... although Zimmer does make epic movie soundtracks!

+1

Every year your school has at LEAST 30% of students getting ATARs of over 99+, so you should be aiming to be in the top 30% of your grade OVERALL. However it's not as simple when it comes to determining ranks in individual subjects due to scaling, cohort strength/teachers etc. Don't forget...

bump!

couldn't be bothered to type out "+1" lol