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If I have a reocurring decimal I use a special trick to work it out as a fraction. The trick is to try and cancel out the reocurring bit by multiplying by 10 several times and then using subtractio...

Multiples that equal 20: 1 and 20, 2 and 10, 4 and 5Which of these multiples add/subtract to give -9?= -4 and -5Therefore answer is:(x-4)(x-5)=0x= 4 or x= 5

Drawing a diagram for this would show that the height of the tree above us is given by tan(63)*15, so the total height is this added to 1.6 m. This gives a height of 31 m.

Stationary points are points at which the gradient of the curve is zero. The gradient is given by dy/dx so we start by computing this using product rule to give us dy/dx=-sin²x+cos²x...

There are two stages to this integral. Stage 1: Notice that there is a quadratic inside a square root in the denominator. We wish to look for a substitution which will reduce this problem...