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Re: HSC 2012 Chemistry Marathon Natural systems require buffers in order to perform optimally preventing diseases and problems from arising. A buffer is an equimolar solution of weak acid and it's conjugate base that resists change in pH when small amounts of acid or base are added. A natural...

Space: 2. I'm unsure if i'm supposed to take AOB as a right angled triangle or not.. costheta = W/T_{OA} T_{OA} = W/costheta tantheta = T_{OA}/T_{OB} T_{OB} = W/(costheta x tantheta) = Wcosectheta N Motors and Generators: 1. Weight force at point P = 0.005 x 9.8 = 0.049N in to the page...

Re: HSC 2012 Chemistry Marathon Question:

1. Chemical equation 2. Calculate moles of each substance 3. Find whichever chemical is in excess 4. Find new concentration of hydrogen or hydroxide ions 5. Calculate new pH Following my steps: 1. HCl_{(aq)} + NaOH_{(aq)} \rightarrow NaCl_{(aq)} + H_2O_{(l)} 2. n_{HCl} = 0.1 \times 0.05 = 5...

\frac{1 - z}{1 + z} \times \frac{1 + \overline{z}}{1 + \overline{z}} = \frac{1 + \overline{z} - z - z\overline{z}}{1 + \overline{z} + z + z\overline{z}} = \frac{1 - |z|^2 - (z - \overline{z})}{1 + 2Re(z) + |z|^2} = \frac{-2iIm(z)}{2 + 2Re(z)} \therefore Re(\frac{1 - z}{1 + z}) = 0

y = \sqrt{2x} - 3 or y = \sqrt{2}x - 3 or y = \sqrt{2x - 3}

I'm not sure why, it's just what my tutor instilled in me :)

lol that's not what i meant. For e.g. \overrightarrow{OZ} = x + iy or \overrightarrow{OZ} = z

I thought you weren't allowed to combine vector notation with complex numbers..

Just for extra information, pH range of litmus is from 4.5 to 8.3 and changes from red to blue.

I'll join the fun soon, need to get some work done.

Initial eastward velocity is 0. Use Newton's 2nd law, F=ma to determine acceleration. Calculate the eastward velocity using v = u + at. Use vector addition to find resultant velocity. (pythagoras theorem to find the resultant speed and some trigonometry to find the angle) Use a = (v-u)/t...

27u^2 - 28u + 1 = 27u^2 - 27u - u + 1 = 27u(u - 1) - 1(u - 1) $Factorising out (u - 1)$ = (27u - 1)(u - 1)

Why don't you Spiral? :P

Remove the brackets, the -x and x cancel. Since 3/x^2, 2/x^2 and 5/x^2 have a common denominator, you can combine them, i.e. (3 + 2 - 5)/x^2 = 0 Now you're left with -1.

Misread it. Yeah you can use it, will give you the same answer and you just disregard t = 0 because that's when it is initially launched.

i) x^3 - 9xy^2z^2 $It doesn't look factorisable using any fancy methods like difference of two squares or two cubes or anything of the sort right now, so lets first take out a common factor between them two; x$ x(x^2 - 9y^2z^2) $ooh. a difference of two squares.$ x(x - 3yz)(x + 3yz)...

Re: 2012 HSC MX2 Marathon C: x^2 + y^2 = R^2 L: ax + by + c = 0 $i) For L to be tangent to C, the perpendicular distance from the centre of the circle (0,0) to L must equal to R$ \therefore |\frac{c}{\sqrt{a^2 + b^2}}| = R $Squaring both sides$ \frac{c^2}{a^2 + b^2} = R^2 \therefore...

1. cos2x = cosx 2cos^2x - 1 = cosx 2cos^2x - cosx - 1 = 0 $Apply quadratic formula or factorise to get solutions$ 2. tan^2x - 1 = 0 tan^2x = 1 tanx = \pm 1 tanx = 1 $ or $ tanx = -1 $Solve both for solutions$ 3. cos^2x - sinx = -1 (1 - sin^2x) - sinx = -1 sin^2x + sinx - 2 = 0...