Question Number 189710 by Mastermind last updated on 20/Mar/23
Answered by aleks041103 last updated on 20/Mar/23
$${V}\left(\mathrm{12}\right)={V}\left(\mathrm{21}\right)−{V}\left(\mathrm{21}−\mathrm{15}\right)={V}\left(\mathrm{21}\right)−{V}\left(\mathrm{6}\right) \\ $$$${V}\left(\mathrm{12}\right)=\mathrm{2}{V}\left(\mathrm{6}\right) \\ $$$$\Rightarrow\frac{\mathrm{3}}{\mathrm{2}}{V}\left(\mathrm{12}\right)={V}\left(\mathrm{21}\right)\Rightarrow{V}\left(\mathrm{12}\right)=\frac{\mathrm{2}}{\mathrm{3}}{V}\left(\mathrm{21}\right) \\ $$$$\Rightarrow{the}\:{water}\:{is}\:\frac{\mathrm{2}}{\mathrm{3}}\:{of}\:{the}\:{bottle} \\ $$$$\boldsymbol{{Note}}\:\mathrm{1}:\:{V}\left({x}\right)\:{is}\:{the}\:{volume}\:{of}\:{water}\:{for}\: \\ $$$${x}\:{cm}\:{of}\:{water}\:{in}\:{the}\:{bottle}\:{the}\:{right}\:{way}\:{up}. \\ $$$$\boldsymbol{{Note}}\:\mathrm{2}:\:{We}\:{suppose}\:{that}\:{for}\:{x}\leqslant\mathrm{12}{cm} \\ $$$${the}\:{bottle}\:{is}\:{cyllindrical}\:{and}\:{so} \\ $$$${V}\left({x}\right)\:{is}\:{linear}\:{for}\:{x}<\mathrm{12}{cm}. \\ $$
Answered by mr W last updated on 20/Mar/23
$${from}\:{picture}\:\mathrm{1}:\:\mathrm{12}\:{cm}\:{water} \\ $$$${from}\:{picture}\:\mathrm{2}:\:\mathrm{6}\:{cm}\:{air} \\ $$$$\Rightarrow{volume}\:{of}\:{water}\:{is}\:\mathrm{2}\:{times}\:{of} \\ $$$${the}\:{volume}\:{of}\:{air} \\ $$$$\Rightarrow\:{in}\:{the}\:{bottle}\:\mathrm{2}/\mathrm{3}\:{is}\:{water}\:{and} \\ $$$$\mathrm{1}/\mathrm{3}\:{is}\:{air}. \\ $$
Answered by manolex last updated on 21/Mar/23
