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Given an integral of a function parametrized with respect to an integer index n, prove a given recursive identity and use this to evaluate the integral for a specific value of n.

This exercise is interesting as it combines a variety of concepts fundamental to integration and maths in general. It also allows to introduce the student to the idea of recursion , very often used to solve ...
MC
Answered by Marco C. • Maths tutor
3078 Views

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.

X 2n -1 = (x n +1)(x n -1) Therefore we can say 2 2n -1 = (2 n +1)(2 n -1) . As 2 n is always even, a multiple of 3 is always either going to be 1 above or 1 below it, e.g. 3 is one below 4 and 9 is 1 above ...
AL
Answered by Abraham L. • Maths tutor
10151 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 = r 2 . You can do this by rearranging to bring the x and y parts together, and completing the sq...
MB
Answered by Martha B. • Maths tutor
8825 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 appear at all on the ot...
AR
Answered by Alice-Kate R. • Maths tutor
12479 Views

X is inversely proportional to Y. When X=4, Y=9. If Y=6, what is the value of X?

There are a few steps to this question. Before we can work out our value of X we will have to figure out an equation that links X and Y.Now if X were proportional to Y, then as X got bigger so would Y.We can...
AW
Answered by Andrew W. • Maths tutor
6930 Views