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We want to make P = xy^2 into something more complicated, which only has Xs, and no Ys. 

Firstly, you need to remember that when there are two equations, the question will almost definitely involve...

One to one mapping means is that there's only one value you could insert into the function that would give you a certain output. f(x) = 2x+1 is an example of one to one mapping where 3, for example, is th...

First, we need to re-write it as e to the power something. The definition of log base e is that e^log(y) = y. We can put our expression into this equality too. So a^x = e^log(a^x), so we use log rules to ...

So in order to derive the quadratic equation we need to start with a quadratic that can represent any quadratic equation. Lets start with ax²+bx+c=0.

We will use the completing the squar...

So we have y = 0 and therefore x² - 6x - 16 =0 

This is then factorised to (x+2)(x-8) = 0 and therefore we have x = -2, x = -8

To find the gradient we need to find dy/dx

So...