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In order to answer this question we will break it down into several pieces. Firstly, using physical arguments, can we narrow down which interval the man must overtake the women? After some thought, it mus...

Generally, quadratic equation of the form $\color{orange}{a}x^2 - \color{blue}{b}x + \color{green}{c} = 0$ where $\color{orange}{a} \neq 0$ can be solve by evaluating $$\color{brown}{\Delta} = \color{blue...

Look for the corresponding letters to each number. So, as an example those with a. remember that the + or - before it tells us whether it is to be added or subtracted

There are 2a-a+3a so that = 4a...

At first this equation seems tricky, but we can perform a clever substitution to simplify it. We notice that if let y = 2^x, then we can rewrite this as:

8(y^2) - 9y + 1 = 0

This now becomes...

This question relies on knowledge of algebraic expressions and highest common factors.

What is the highest common factor which goes into the expressions 8y and 4y^2.

The answer is 4y. This i...