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A man travels 360m along a straight road. He walks for the first 120m at 1.5ms-1, runs the next 180m at 4.5ms-1, and then walks the final 60m at 1.5ms-1. A women travels the same route, in the same time. At what time does the man overtake the women?

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 must b...
JG
Answered by James G. • Maths tutor
8073 Views

Solve $\color{orange}{a}x^2 - \color{blue}{b}x + \color{green}{c} = 0$

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}{b...
MC
Answered by Maciej C. • Maths tutor
4212 Views

Solve 8(4^x ) – 9(2^x ) + 1 = 0

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 a simple quadrat...
DS
Answered by Daljit S. • Maths tutor
9848 Views

Find the stationary points on the curve y = x^3 + 3x^2 - 9x - 4

A stationary point is where the gradient is exactly zero - the curve is neither increasing or decreasing. This means that we need to differentiate y to find dy/dx and then set this equal to 0. Doing this, us...
RR
Answered by Richard R. • Maths tutor
17292 Views

By writing tan x as sin x cos x , use the quotient rule to show that d dx ðtan xÞ ¼ sec2 x .

First write tanx as sinx/cosx as it is always helpful to use what additional information the question gives you. It says we must use the quotient rule to calculate the result so it is also a good idea to wri...
DB
Answered by Daniel B. • Maths tutor
7785 Views