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If the gradient of PA is equal to the gradient of PB, then P must lie on the line through A AND B. Otherwise the gradients of PA and PB will be different (you can draw up a diagram to visualise this). So in essense, the locus of P is equation of the line through A and B (as P can lie anywhere on...

======================================================== T1 ENGG1000 Engineering Design...............78 DN T1 ENGG1811 Computing for Engineers..........86 HD T1 MATH1141 Higher Mathematics 1A............90 HD T1 PHYS1131 Higher Physics 1A................88 HD...

Find the derivative of the parabola at each poiints and then use the point-gradient formula to find the eqn of tangents y = 5/2 x^2 dy/dx = 5x at x = 2, dy/dx = 10 therefore, the eqn of tangent at (2,10) is y - 10 = 10(x-2) [rearrange into the general form] at x = -4/5, dy/dx = -4...

After all the scaling, also note that this mark is not just the exam mark, but the whole course (ie including the class tests, maple etc)

do the webstream gl mate

Re: HSC 2018 MX2 Integration Marathon an easier way is to just use the substitution u = sqrt(x) the integrand will be 2/sqrt(u^2+1), which is trivial to integrate (those usual log ones)

Yes, basically if you come first internally, then the assessment mark will be equal to the highest external in that subject from your school (which will be your exam mark if you get the highest external). So yes, if you come first internally, then your classmates wont affect your results at all...

woah so smart, thanks!

fun except for the goddamn lines to 891

Re: HSC 2018 MX2 Marathon Yes it should be (1 + \sqrt3 i)^{2n} + (1 - \sqrt3 i)^{2n} = 2^{2n + 1}

Re: HSC 2018 MX2 Marathon yes it's 4

Use the law of conservation of energy PE (initial) + KE (initial) = PE (final) + KE (final) -62.3 * 10^6 m + 1/2 mv^2 = -1.3 * 10^6 m + 0 (assuming the craft stops when it reaches point P then accelerates due to the moons gravity) solving for v, we get 11 kms^-1

ye basically do tons of practice questions where you apply the formula, and you'll automatically remember the formula and will get the hang of applying it without referring to any formula sheet or whatever Like the above post, understanding what's behind the formula also helps massively

Re: HSC 2018 MX2 Marathon http://community.boredofstudies.org/14/mathematics-extension-2/356905/question-7-ekmans-compilation.html#post7213476 for the working out of integrands clever solution if anyones interested

Re: HSC 2018 MX2 Marathon Are you sure you wrote the question right? Cause a and b are real numbers (-1+-√2) not complex numbers in the form a+ib (b=/=0) (assuming that's what you intended it to be)

Re: HSC 2018 MX2 Marathon A classic one $Simplify $ \sin(x)+\sin(2x) + \sin(3x) + ... + \sin(nx)

Re: HSC 2018 MX2 Marathon

Re: HSC 2018 MX2 Integration Marathon A nice one $ \noindent Evaluate $\int_{0}^{1}x\sqrt{x\sqrt[3]{x\sqrt[4]{x\sqrt[5]{x...}}}} $ d$x

oh yes my bad, forgot to square it and the pi smh forgot too much

$ \noindent Volume of revolution about the y-axis: $ \pi \int_{y_1}^{y_2} x^2 $ d$y \\ \\ $ So making $x$ the subject, we get $ x= e^{y} \\ \\ \therefore V=\pi \int_{1}^{3}e^{2y} $ d$y \\ \\= \left [ \frac{\pi}{2}e^{2y} \right ]_{1}^{3} \\ \\ = \frac{\pi}{2}e^2\left ( e^4-1 \right ) $ units$ ^3