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BOACDE

The diagram shows a triangle OAB. The point C is the mid-point of OA. The point D lies on CB such that CD : DB = 2 : 3.

→OC = c→CB = b

The point E lies on AB such that →OE = λ→OD and →AE = μ→AB, where λ and μ are scalars.

Find two expressions for →OE, each in terms of b, c and a scalar, and hence find AE : EB. [8]

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CALCULATORMedium

[Maximum mark: 5]

A bouncy ball is dropped out of a second story classroom window, 5 m off the ground. Every time the ball hits the ground it bounces 89 % of its previous height.

(a)  Find the height the ball reaches after the 2nd bounce.

[2]

(b)  Find the total distance the ball has travelled when it hits the ground for the 5th time.

[3]
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