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Re: If I roll a marble down a ramp and of the edge of a bench or something why does . do they have the same radius?

arg(z1/z2) = 日1-日2 arg(z1/z2) = arg(z1) - arg(z2)

wtf we didnt learn that until high school

well you don't add/multiply fractions either in primary school the question is just to test your mathematical ability. it doesn't necessarily need to be a primary school problem.

x = 1 or 2 for the positive case not sure if the negative case is possible to solve, apart from doing approximations

1-2k>1/2 2k<1/2 k<1/4 k2<1/16 8k2<1/2 1-2k>8k2 (1-2k)/k2 > 8 assuming 0 < k < 0.25 is what you meant

a) 8! -> just order the 8 people b)4!*4!*2 -> order each of the 4 girls and boys, multiply by 2 since either girls or boys could be in the odd/even spots c) first view the 2 girls as one person -> this gives 7! ways. but the 2 girls can order themselves in 2! ways, so 7!*2! d) now, we firstly...

you could just say w3 = 1 (w3)2 = 1 (w2)3 = 1 so w2 is also a cube root of unity

^except that the -2's have been turned into -2's 4^{-2}\times6^3\times8^4\times12^{-2} \\ = 2^{-4}\times 2^3\times 3^3\times 2^{12}\times 2^{-4}\times 3^{-2}\\ = 2^7 \times 3\\ = 384

well yeah. if it's impossible to solve the question otherwise, just assume it's regular

hey piitb you should take spare drink bottles in case other people forget them then you can make new friends as well :) i wish you good luck :) :) :) :) :) :) :) :) :) :) :) :) :)

lol this was in the other thread y" = 8, for all x values. then you integrate and evaluate constants

there will be 2 answers, since it's an even power (you can factor out the -1) like how (x+1)2 = (-x-1)2

woah what's going on there it's using difference of two squares (a2+b2)2 - 2ab = (a2+b2 + sqrt{2ab})(a2+b2 - sqrt{2ab})

+4y12 same as the normal simpson's rules, but using the areas

there's your mistake D = 1 + 3 - 1/6 = +3 5/6 this gives f(2) = 20.5

maybe if I rephrase the question it would help? y" = 8 when x=1, y' = 0 when x=1, y=3 fine the equation of y. (it's just integrating and evaluating constants)

yeah, use substitution/reverse chain rule

sorry, i subbed the wrong value of t into the expression I think y = 4x2 - 8x + 7 would be the solution to the second one. i don't complete get the question though (the way it's worded maybe?)

why do the questions you have use partial derivatives? since those aren't dealt with in HSC maths I'll just use the usual notation: \frac{dx}{d t} = (t-3)^2\\ \int \frac{dx}{d t} dt = \int (t-3)^2dt\\ \int dx = \frac {1}{3}(t-3)^3 + C\\ x = \frac {1}{3}(t-3)^3 + C when t = 0, x = 7 7 =...