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(1) 5(3x - 2y) = 14 -2ax 15x - 10y = 14 - 2ax (2) 15x +2ax -10y = 14 15x + 2ax = 10y + 14
(3) x(15 + 2a) = 10y + 14 x = (10y + 14) / (15 + 2a)
To asking us to make x the subject of a fo...

(a) let A be (x1,y1) and B be (x2,y2), Gradient = m = (y2-y1)/(x2-x1) m = (4- -5)/(-1-2) = 9/(-3) = -3 Gradient = -3
(b) equation of a straight line line: y = mx + c => y1 = ...

Let's take for example the integral 5x²(x³-4)⁴dx. This is very difficult and not at all nice to expand in terms of x, so we can effectively "create" a new variab...

AB = B - A = (4,3,-6)- (2,0,-1) = (2 , 3 , -5)BC = C - B = (9,3,-4) - (4,3,-6) = (5, 0 , 2)
If perpendicular "AB dot BC" should equal zeroAB dot BC = (2,3,-5) dot (5,0,2) = (2x5) + (3x0) + ...

think of it in the form of Ax^2 +Bx +C. Most of the GCSE examples will have A as zero so we will ignore the A. To factorise this you need to find what two numbers multiply to make C and adds to make B. In...