A ball is thrown vertically up from the ground, rises to a height of 10 metres and then falls and bounces. At each bounce it rises vertically to four-fifths of the height from which it fell. Write down the original height to which the ball was thrown and then, without multiplying them out, expressions for the height to which the ball will rise after one bounce, two bounces and eleven bounces. Use an appropriate formula to calculate, to the nearest centimetre, the total distance travelled by the ball from the first throw to the twelfth impact with the ground

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