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4. A(x-2)^2 + B(x-2) + C =Ax^2 - 4Ax +4A +Bx - 2B +C = Ax^2 - (4A+B)x + (c- 2B) Equating coefficients A = 3 4A + B = 0 B = -12 C-2B = -5 C = -29 5) tan is -ve and sin is positive so theta is in the second quadrant tan = opp/adj = 3/10 hypotenuse = rt109 cos theta = adj/hyp = 10/rt109 =...

1. (5x+1)(x-2) 2. 3/(2rt3-5) = 3(2rt3+5)/-13 = -6rt3/13 - 15/13 a = -6 b =-15 3) 2/(2x^2-x-1) - 6/(4x^2-1) = 2/[(2x+1)(x-1)] - 6/[(2x+1)(2x-1)] = [2(2x-1) - 6(2x+1)]/[(2x+1)(2x-1)(x-1)] = (4x-2-12x-6)/[(2x+1)(2x-1)(x-1)] = -(8x+4)/[(2x+1)(2x-1)(x-1)] = -4/([2x-1)(x-1)]

The factorised form is simplest.

I find it easier to use the table and just do them in groups of three eg x 1 2 3 4 5 y 1 4 9 16 25 ...1 4 1 .........1 4 1 so then multiply by h/3 = 1/3 ((1 + 4*4 + 9) + (9 + 4*16 + 25)) 100 posts :)

over the real numbers - eg (x^2 +1) rather than (x-i)(x+i)

d/dx(x^2 - 3x - 4) = 2x - 3 For st. pts d/dx = 0 2x - 3 = 0 x = 1.5 The second derivative = 2 which means the curve is concave up for all values of x, which means the stationary pt is a minimum stationary point. The turning point is not a point of inflexion - parabolas don't have them. For...

1. What year did/will you complete year 12? 2006. 2. Do You have the internet at home? Broadband. 3. How many hours per week would you spend on the internet? About ten 4. How much of that time would be for educational reasons and how much would be for personel use? 9 for...

He's just used the identity sin 2x = 2sinxcosx

Originally posted by Ragerunner in the SAM forum

I think that may be because it is harder to get the high marks in standard - hardly anyone gets bands five and six.

(a+bi)^2 = 6i a^2 - b^2 = 0 + or - a = + or - b 2ab = 6 ab = 3 a = +/- sqrt 3 b = +/- sqrt 3 so sqrt of 6i = +/- (sqrt 3 + sqrt3i)

We did this from our text book - boat against + with the current vs boat across the current. This relates to the Michelson-Morley experiment in that they attempted to measure the speed of light with and against the aether and compare it to the speed across the aether. hsc.csu.edu.au is a...

= d/dx 2(2x+3)^-4 = 2 x -4 x 2 (2x+3)^-5 = -16(2x+3)^-5 =-16/(2x+3)^5 Have more confidence in yourself!

3) Ways of getting 45 or more (4,5) + (5,5) (5,4) + (5,5) (5,5) + (4,5) (5,5) + (5,4) (5,5) + (5,5) Total no. possibilities = 1/36 * 1/36 = 1/1296 so P of getting 45 or more = 5/1296 so P getting less than 45 = 1291/1296

2a) After one sock is picked out there are seven socks left in the drawer, one of which is the same as the one already drawn. Therefore the probability of the second sock being the same as the first is 1/7. b) 6/7 * 4/6 (two different socks will give a pair in the third draw) = 4/7 c)...

1a) 1/3 * 1/4+ 1/3 * 1/4 = 1/6 b) 1 - (2/3 * 3/4) = 1/2

It is dependant on the refractive index of the substance - the metre is the distance light can travel in 1/c seconds in a vacuum

True, but that's a 3U topic.

You need to multiply by 3 as there are 3 different ways of getting 2 sixes. So 3*1/6*1/6*5/6 = 15/216 + (1/6)^3 = 16/216

Didn't you learn that in the waves topic in yr11?