Higher Plus

In a circle theorem proof, a step uses the fact that the exterior angle of a cyclic quadrilateral is being found. State the reason being quoted.

A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 3/14. Work out r.

On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2. How many more values are in the wider class?

A block has mass 900 g (to the nearest 10 g) and volume 23 cm³ (to the nearest cm³). Work out the upper bound of its density, to 2 decimal places.A block has mass 900 g (to the nearest 10 g) and volume 23 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.

Use the iteration x(n+1) = cube root of (11x(n) + 9) with x(0) = 1. Work out x(1) to 3 decimal places.