math

when a ball falls vertically off a table it rebounds 75% of its height after each bounce. if it travels a total of 490 cm, how high was the table top above the floor

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  1. did you make a sketch

    Let the height of the table be x cm
    I see the ball doing this

    x + 2x(.75) + 2x(.75)^2 + 2x(.75)^3 + ... = 490

    x + 2x[.75 + .75^2 + .75^3 + ...] = 490

    the sequence inside my square brackets is an infinite series with a=.75 and r=.75
    A∞ = a/(1-r) = .75/(.25) = 3

    so x + 2x(3) = 490
    x = 70
    so the table is 70 cm high.

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