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Further Mathematics

GCSE

A curve has equation y = ax^2 + 3x, when x= -1, the gradient of the curve is -5. Work out the value of a.

The gradient of a curve at a point is given by dy/dxDifferentiate the equationplug in the valuesdy/dx = 2ax + 3x = -1, dy/dx = -5-5 = 2a*-1 + 38 = 2aa = 4

Answered by Salma E. • Further Mathematics tutor

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Solve x^(-1/4) = 0.2

Get both sides in similar forms to make it easier to solve.1/x^1/4 = 1/5x^1/4 = 5x = 5⁴ = 625

Answered by Salma E. • Further Mathematics tutor

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The function f is given by f(x) = SQRT(2x − 5). Work out x when f(x) = 1.2

1.2 = SQRT(2x-5)square both sides1.2^2 = 2x -5 add 5 to both sides 1.2^2 + 5 = 2xdivide both sides by 2(1.2^2 + 5)/2 = x

Answered by Kieran Y. • Further Mathematics tutor

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express z(2+i)=(1+2i)^2 in the form z=x+iy

rearrange gives z = [(1+2i)^2]/(2+i)expanding (1+2i)^2 gives 4i-3 therefore this becomes (4i-3)/2+i multiply that by the conjugate (2-i)/(2-i) to give (11i-2)/5therefore z= -2/5 + 11i/5

Answered by Huy H. • Further Mathematics tutor

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Express (7+ √5)/(3+√5) in the form a + b √5, where a and b are integers.

(7+ √5)/(3+√5)Here, the denominator is not rational - (numbers like 2 and 3 are rational). A number with an irrational denominator isn't incorrect, it just isn't in the simplest form it can be in.To ratio...

Answered by Oscar G. • Further Mathematics tutor

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