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The gradient of a curve at a point is given by dy/dxDifferentiate the equationplug in the valuesdy/dx = 2ax + 3x = -1, dy/dx = -5-5 = 2a*-1 + 38 = 2aa = 4

Get both sides in similar forms to make it easier to solve.1/x^1/4 = 1/5x^1/4 = 5x = 5⁴ = 625

1.2 = SQRT(2x-5)square both sides1.2^2 = 2x -5 add 5 to both sides 1.2^2 + 5 = 2xdivide both sides by 2(1.2^2 + 5)/2 = x

rearrange gives z = [(1+2i)^2]/(2+i)expanding (1+2i)^2 gives 4i-3 therefore this becomes (4i-3)/2+i multiply that by the conjugate (2-i)/(2-i) to give (11i-2)/5therefore z= -2/5 + 11i/5

(7+ √5)/(3+√5)Here, the denominator is not rational - (numbers like 2 and 3 are rational). A number with an irrational denominator isn't incorrect, it just isn't in the simplest form it can be in.To ratio...