Ifound this question in the sample assessment material of the igcse further pure maths.

the volume of a right circular cone is increasing at the rate of 45 cm3 s–1. the height of the cone is always three times the radius of the base of the cone. find the rate of increase of the radius of the base, in cms–1, when the radius of the cone is 4 cm. give your answer correct to 3 significant figures.

If the ratio of sum of the first m and n terms of an ap is m2 : n2 , show that the ratio of its mth and nth terms is (2m − 1) : (2n − 1).

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Grace is standing 18 feet from a lighthouse and kelly is standing 10 feet from grace. the angle that grace looks up to see the top of the lighthouse is 45°. the angle that kelly looks up to see the top of the lighthouse is y°. find the height, h, of the lighthouse. find the angle, rounded to the nearest tenth of a degree, in which kelly looks up to the top of the lighthouse. to the nearest tenth of a degree, find the value of x° . in two or more sentences, explain your calculations