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let x1 = 0, y1 = 0 in (0,0) and let x2 = 8 and y2 = 8 in (8,8). To find the gradient, we would do (y2 - y1)/(x2-x1) = 1. To find the length, we would do the square root of the following: (y2-y1)^2 + (y2-y...

y = 1/2x^3 - 9x^3/2 + 8/x + 30y = 1/2x^3 - 9x^3/2 + 8x-1 + 30dy/dx = 3/2x^2 - 27/2x^1/2 - 8x^-2 + 0dy/dx = 3/2x^2 - 27/2x^1/2 - 8/x^2substitute x=4 into equation for yy = 1/2(4)^3 - 9(4)^3 + 8/4 +30y = 32...

When learning new content, I know it is really intimidating seeing how many new formulas and equations are needed to answer questions, however I also know how easy it is to get on top of it all! My main p...

5cos³x = 5cosxFirstly -5cosx from both sides and divide through by 5We have:cos³x-cosx = 0We can factorise this:cosx(cos²x - 1) = 0 For this to be true either:cosx = 0 or ...

(4-x)^-1/2 = (4 (1 - x/4))^-1/2 = 1/2 (1 - x/4)^-1/2 = 1/2 ( 1 + x/8 + 3x²/128 + ...) = 1/2 + x/16 + 3x²/256 + ...Therefore the first three ter...