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For this question we have to use the chain rule. The chain rule is dy/dx (the differential you are looking for) = du/dx (the differential of u with respect to x) * dy/du(the differential of y with respect...

y=ln([2x-1/2x=1]^1/2)- can be written as y= [0.5ln(2x-1)]-[0.5ln(2x+1)] due to laws of logs. Take first term -- (0.5ln(2x-1)) and substitute 2x-1 for u. so u=2x-1 and y=0.5lnu Now dy/du=1/2u and du/dx=2. ...

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...

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...