Question Number 196160 by peter frank last updated on 19/Aug/23 Commented by mr W last updated on 19/Aug/23 $${without}\:{a}\:{diagram}\:{other}\:{people}\:{can}'{t} \\ $$$${understand}\:{what}\:{you}\:{mean}\:{with} \\ $$$${water}\:{mark},\:{liquid}\:{mark}\:{etc}. \\ $$…
Question Number 196094 by leicianocosta last updated on 18/Aug/23 Answered by dimentri last updated on 18/Aug/23 $$\left(\mathrm{1}\right)\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(\frac{\mathrm{2}^{\mathrm{3}\left({n}−\mathrm{1}\right)} }{\mathrm{3}^{\mathrm{2}{n}} }\right)=\:\frac{\mathrm{1}}{\mathrm{9}}+\frac{\mathrm{8}}{\mathrm{81}}+\frac{\mathrm{64}}{\mathrm{729}}+\ldots \\ $$$$\:\:\:\:\:\:=\:\frac{\frac{\mathrm{1}}{\mathrm{9}}}{\mathrm{1}−\frac{\mathrm{8}}{\mathrm{9}}}\:=\:\mathrm{1}\: \\ $$…
Question Number 196145 by Erico last updated on 18/Aug/23 $$\mathrm{Calculer}\:\underset{\:\frac{\mathrm{1}}{\alpha}} {\int}^{\:+\infty} {e}^{−\alpha{t}^{\mathrm{2}} +\mathrm{2}{t}} {dt} \\ $$ Answered by Mathspace last updated on 20/Aug/23 $${t}=\frac{\mathrm{1}}{\alpha}+{x}\:\Rightarrow \\…
Question Number 196143 by mr W last updated on 18/Aug/23 $${say}\:{you}\:{have}\:\mathrm{3}\:\left({different}\right)\:{books} \\ $$$${about}\:{mathematics},\:\mathrm{4}\:\left({different}\right) \\ $$$${books}\:{about}\:{physics}\:{and}\:\mathrm{5}\:\left({different}\right) \\ $$$${books}\:{about}\:{chemistry}.\:{in}\:{how}\:{many} \\ $$$${ways}\:{can}\:{you}\:{arrange}\:{them}\:{in}\:{a}\:{shelf} \\ $$$${such}\:{that}\:{no}\:{two}\:{books}\:{from}\:{the}\:{same} \\ $$$${subject}\:{are}\:{adjacent}? \\ $$…
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Question Number 196134 by sonukgindia last updated on 18/Aug/23 Answered by AST last updated on 18/Aug/23 $$\left[{log}\left({x}\right)+{log}\left({y}\right)\right]^{\mathrm{2}} −\mathrm{2}{log}\left({x}\right){log}\left({y}\right)=\mathrm{2}{log}\left({xy}\right) \\ $$$$\Rightarrow\left[{log}\left({xy}\right)\right]^{\mathrm{2}} =\mathrm{2}\left[{log}\left({xy}\right)+{log}\left({x}\right){log}\left({y}\right)\right]…\left({i}\right) \\ $$$${Let}\:\left[{log}\left({xy}\right)\right]={t};\left({i}\right)\Rightarrow{t}^{\mathrm{2}} −\mathrm{2}{t}=\mathrm{2}{log}\left({x}\right){log}\left({y}\right) \\…
Question Number 196121 by sniper237 last updated on 18/Aug/23 $${In}\:{forest}\:,\:{a}\:{hunter}\:{obstains}\:{that} \\ $$$${Every}\:{morning}\:{a}\:{snake}\:{eats}\:{a}\:{mouse} \\ $$$${Every}\:{afternoon}\:{a}\:{scorpion}\:{kills}\:{a}\:{snake} \\ $$$${Every}\:{night}\:{a}\:{mouse}\:{corrodes}\:{a}\:{scorpion} \\ $$$${The}\:\mathrm{8}^{{th}} \:{day}\:{morning}\:,\:{there}\:{remains} \\ $$$${Only}\:{one}\:{of}\:{them}\:,\:{a}\:{mouse} \\ $$$$ \\ $$$${How}\:{many}\:{were}\:{they},\:{in}\:{each}\:{species}?…
Question Number 196117 by sonukgindia last updated on 18/Aug/23 Answered by Rasheed.Sindhi last updated on 18/Aug/23 $${m}^{\mathrm{2}} \left(\mathrm{1}+\mathrm{3}{n}^{\mathrm{2}} \right)−\mathrm{10}\left(\mathrm{3}{n}^{\mathrm{2}} +\mathrm{1}\right)=\mathrm{517}−\mathrm{10} \\ $$$$\left({m}^{\mathrm{2}} −\mathrm{10}\right)\left(\mathrm{3}{n}^{\mathrm{2}} +\mathrm{1}\right)=\mathrm{507} \\…
Question Number 196119 by mr W last updated on 18/Aug/23 $${solve} \\ $$$$\sqrt{\mathrm{100}−{x}^{\mathrm{2}} }+\sqrt{\mathrm{64}−{x}^{\mathrm{2}} }=\mathrm{12} \\ $$ Answered by cortano12 last updated on 18/Aug/23 $$\:\sqrt{\left(\mathrm{10}−\mathrm{x}\right)\left(\mathrm{10}+\mathrm{x}\right)}\:+\sqrt{\left(\mathrm{8}−\mathrm{x}\right)\left(\mathrm{8}+\mathrm{x}\right)}\:=\:\mathrm{12}…