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
$$\mathrm{10}+\mathrm{2}×\frac{\mathrm{3}}{\mathrm{4}}×\mathrm{10}+\mathrm{2}×\left(\frac{\mathrm{3}}{\mathrm{4}}\right)^{\mathrm{2}} ×\mathrm{10}+\mathrm{2}×\left(\frac{\mathrm{3}}{\mathrm{4}}\right)^{\mathrm{3}} ×\mathrm{10} \\ $$ $$=\mathrm{10}+\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\mathrm{2}×\left(\frac{\mathrm{3}}{\mathrm{4}}\right)^{{n}} ×\mathrm{10}=\mathrm{10}+\mathrm{20}\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(\frac{\mathrm{3}}{\mathrm{4}}\right)^{{n}} \\ $$ $$=\mathrm{10}+\mathrm{20}\frac{\frac{\mathrm{3}}{\mathrm{4}}}{\mathrm{1}−\frac{\mathrm{3}}{\mathrm{4}}}=\mathrm{10}+\mathrm{20}\left(\mathrm{3}\right)=\mathrm{70}{m} \\ $$
Commented bymathlove last updated on 19/Jan/23
$$ \\ $$ If you could explain a little about how we have a relationship, we would be grateful\\n
Answered by cortano1 last updated on 19/Jan/23
$${d}=\mid\frac{\mathrm{3}+\mathrm{4}}{\mathrm{3}−\mathrm{4}}\mid×\mathrm{10}\:{m}\:=\:\mathrm{70}\:{m} \\ $$
Commented bymathlove last updated on 19/Jan/23
$$ \\ $$ Give a little explanation from where you wrote four and three\\n