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White paint costs £2.80 per litre. Blue paint costs £3.50 per litre. White paint and blue paint are mixed in the ratio 3 : 2 Work out the cost of 18 litres of the mixture.

To work out how many litres of white and blue paint is needed, use the ratio 3:2. To find the specifc ratio for 18 litres, of paint: 2+3=5, 18/5=3.6 so (3:2) 3.6 becomes 10.8:7.2 (check 10.8+7.2=18). So to d...
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Answered by Aidan D. • Maths tutor
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Using the equation cos(a+b) = cos(a)cos(b) - sin(a)sin(b) or otherwise, show that cos(2x) = 2cos^2(x) - 1.

First let a = b = x such that: cos(a + b) = cos(a)cos(b) - sin(a)sin(b) becomes: cos(x + x) = cos(x)cos(x) - sin(x)sin(x) Leading to: cos(2x) = cos 2 (x) - sin 2 (x) Using the fact that sin 2 (y) + cos 2 (y)...
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Answered by Benjamin H. • Maths tutor
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Give the definition simple harmonic motion and write down the defining equation for such motion stating the meaning of any symbols involved.

Simple harmonic motion is defined as a form of periodic motion in which a point or body oscillates in such a way that the acceleration of the point or body is directly proportional to its displacement from t...
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Answered by Benjamin H. • Physics tutor
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How does Charlotte Bronte present Jane Eyre as a strong female character?

Jane's strong character is best seen in the context of her gender as she shows traits that trangress and push the boundaries of those expected of Victorian women. She is fiercely independent and she is fearl...
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How does an increase in temperature affect the rate of a chemical reaction?

An increase in temperature will increse the rate of a chemical reaction, and a decrease in temperature will decrese the rate. This is because the hotter the reactant particles are, the more kinetic energy th...
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