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You are given that n is a positive integer. By expressing (x^2n)-1 as a product of factors, prove that (2^2n)-1 is divisible by 3.

X2n-1 = (xn+1)(xn-1) Therefore we can say 22n-1 = (2n+1)(2n-1) . As 2n is always even, a multiple of 3 is always either going t...

AL
Answered by Abraham L. Maths tutor
9791 Views

A circle has equation x^2 + y^2 - 8x - 10y + 5 = 0, find its centre and radius

To find the centre and radius of the circle, you need to get the equation into the form (x - a)2+ (y - b)2= r2. You can do this by rearranging to bring the x and y parts t...

MB
Answered by Martha B. Maths tutor
8405 Views

The volume of a cone is V = 1/3*pi*r^2*h. Make r the subject of the formula.

Answering the question by acknowledging the student understands what the question is actually asking. The subject of the formula sits by itself on one side of the equation and doesn't app...

AR
Answered by Alice-Kate R. Maths tutor
11818 Views

How should I revise for my A-level exams? What is the best preparation?

This is different for everyone, and the best way to learn the most effective way for revision is to implement this throughout the school year. Keep up to date with your notes and practice different types ...

Answered by History tutor
2245 Views

Given y=rootx + 4/rootx = 4, find the value of dy/dx when x=8, writing your answer in the form aroot2, where a is a rational number.

First, we will write out the equation, writing the root x values in a way that allows us to differentiate them. Root x can be written as x^1/2 and 4/rootx can be written as 4x^-1/2. Now we can differentia...

Answered by Maths tutor
13608 Views

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