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Given that y=ln([2x-1/2x=1]^1/2) , show that dy/dx= (1/2x-1)-(1/2x+1)

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. to ...
SF
Answered by Sam F. • Maths tutor
11337 Views

How do I work out probability when a random choice is repeated?

Before you try to work out the probability, establish the following answers from the question and jot them down. How many items are there in total? After something is chosen, is it put back before the next c...
NC
Answered by Naomi C. • Maths tutor
4075 Views

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
8001 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
4149 Views

Simplify 2a+6b-a+2b+3a

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 With b th...
TH
Answered by Tom H. • Maths tutor
5132 Views