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Further Mathematics

A Level

Does the following matrix A = (2 2 // 3 9) (upper row then lower row) have an inverse? If the matrix A^2 is applied as a transformation to a triangle T, by what factor will the area of the triangle change under the transformation?

The answer to the first part is that the matrix does have an inverse. This is found by finding the determinant of the matrix from the formula ad - bc (for some matrix ( a b // c d ) ) to get the ...

Answered by Calum O. • Further Mathematics tutor

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Split x^4/[(x^2+4)*(x-2)^2] into partial fractions and hence differentiate it

The answer to this question will be explained during the interview session

Answered by Arhant S. • Further Mathematics tutor

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Where does Euler's Formula come from?

Euler's Formula is: e^ix = cos(x) + isin(x)

This identity comes from the Maclaurin expansion of the exponential function. The resulting maclaurin series is a power series in x with odd te...

Answered by Luke K. • Further Mathematics tutor

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Integrate x^2sin(x) between -pi and pi

It is possible to solve this question using integration by parts. However, we note that sin(x) is an odd function, meaning that sin(-x) = -sin(x). Thus x²sin(x) is also an odd function. This me...

Answered by Harry L. • Further Mathematics tutor

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How far is the point (7,4,1) from the line that passes through the points (6,4,1) and (6,3,-1)?

To begin with, we should find the equation of the line. To do this we appoint a position vector and a direction vector. The position vector can simply be one of the two points we are give, i.e. (6,4,1). T...

Answered by Rebecca H. • Further Mathematics tutor

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