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Question Number 185222 by mathlove last updated on 18/Jan/23

$$$$ A ball falls from a height of 10m and lands on the ground 75% of each time it falls, it gets up again; of the What is the total distance traveled by the ball? (a) 35m b) 40m c) 70m d) 75m\n

Answered by Ar Brandon last updated on 19/Jan/23

$$10+2\times \frac{3}{4}\times 10+2\times {\left(\frac{3}{4}\right)}^2\times 10+2\times {\left(\frac{3}{4}\right)}^3\times 10$$ $$=10+\underset{n=1}{\sum ^{\mathrm{\infty }}}2\times {\left(\frac{3}{4}\right)}^n\times 10=10+20\underset{n=1}{\sum ^{\mathrm{\infty }}}{\left(\frac{3}{4}\right)}^n$$ $$=10+20\frac{\frac{3}{4}}{1-\frac{3}{4}}=10+20\left(3\right)=70m$$

Commented bymathlove last updated on 19/Jan/23

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Answered by cortano1 last updated on 19/Jan/23

$$d=\mid \frac{3+4}{3-4}\mid \times 10m=70m$$

Commented bymathlove last updated on 19/Jan/23

$$$$ Give a little explanation from where you wrote four and three\n

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