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Further Mathematics
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The coefficient of the x^3 term in the expansion of (3x + a)^4 is 216. Find the value of a.

From the binomial theorem we know that the x^3 term in the expansion of the above expression must satisfy,
4C3 * (3x)^3 * a = 216x^3.
Hence, after multiplying out we must have,
108a * x^...

Answered by Adam B. Further Mathematics tutor
4955 Views

Why is it that when 'transformation A' is followed by 'transformation B', that the combined transformation is BA and not AB?

Remember that with matrix multiplication, "A times B" does not usually equal "B times A". If we take our 'matrix X' and transform it by 'matrix A'. We perform this transformation by ca...

Answered by JOE D. Further Mathematics tutor
6217 Views

Given a curve with parametric equations, x=acos^3(t) and y=asin^3(t), find the length of the curve between points A and B, where t=0 and t=2pi respectively.

The length of an arc between two points on a curve can be calculated in two ways; as the integral of ((dy/dx)^2 + 1)^1/2 between the values of the points, or as the integral of ((dy/dt)^2+(dx/dt)^2)^1/2 b...

Answered by Jack W. Further Mathematics tutor
3928 Views

Find the gradient of the line x^2 + 3x - 6 at the point (5,34)

Differentiate: 2x + 3.Substitute for x=5: 2(5) + 3Answer =13.

Answered by Dan D. Further Mathematics tutor
1496 Views

A parabola with equation y^2=4ax for constant a is translated by the vector (2,3) to give the curve C. The curve C passes through the point (4,7), what is the value of a?

Invert the translation of (2,3) to get the parabola passing through the point (4,7)-(2,3)=(2,4). This is the same as saying that y=4 when x=2, substitute this into your equation y^2=4ax to get a=2.This wi...

Answered by Gabriel V. Further Mathematics tutor
1903 Views

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