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A is the point with coordinates (5, 9) B is the point with coordinates (d, 15) The gradient of the line AB is 3 Work out the value of d.

A straight line equation is defined as y=mx+c where m is the gradient and c is the intercept. Since the gradient is already said to be 3 we can substitute this in to mean the equation for AB is y=3x+c. Since...
TA
Answered by Tarun A. • Maths tutor
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Find all solutions of the equation in the interval [0, 2π]. 5 cos^3 x = 5 cos x

5cos 3 x = 5cosxFirstly -5cosx from both sides and divide through by 5We have:cos 3 x-cosx = 0We can factorise this:cosx(cos 2 x - 1) = 0 For this to be true either:cosx = 0 or cos 2 x = 1for cosx = 0This oc...
GC
Answered by Georgiana C. • Maths tutor
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Block 1 is 24mm long. Block 2 is 32mm long. Vignesh joins some type 1 blocks together to make a straight row. He then joins some type 2 blocks together to make a straight row of the same length. (a) Write down the shortest possible length of this row.

96mm (a) Express 24 and 32 as prime numbers (explained in interview)(b) Use this to find the LCM (lowest common multiple) (c) Don't forget units!
VO
Answered by Vera O. • Maths tutor
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Factorise x^2 +6x + 8

Firstly list two numbers that add to 6 and right them down e.g. 4 and 2.Secondly list two numbers that multiply to form 8 e.g. 8 and 1 or 4 and 2.The numbers that appear in both solutions will therefore be t...
EM
Answered by Euan M. • Maths tutor
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Find the first three terms in the expansion of (4-x)^(-1/2) in ascending powers of x.

(4-x) -1/2 = (4 (1 - x/4)) -1/2 = 1/2 (1 - x/4) -1/2 = 1/2 ( 1 + x/8 + 3x 2 /128 + ...) = 1/2 + x/16 + 3x 2 /256 + ...Therefore the first three terms are 1/2 + x/16 + 3x 2 /256
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