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 $$\:\sqrt{\left(\mathrm{10}−\mathrm{x}\right)\left(\mathrm{10}+\mathrm{x}\right)}\:+\sqrt{\left(\mathrm{8}−\mathrm{x}\right)\left(\mathrm{8}+\mathrm{x}\right)}\:=\:\mathrm{12}…
Question Number 196115 by sonukgindia last updated on 18/Aug/23 Answered by Rasheed.Sindhi last updated on 18/Aug/23 $${xy}+\mathrm{66}{x}−\mathrm{88}{y}−\mathrm{88}×\mathrm{66}=\mathrm{23333}−\mathrm{88}×\mathrm{66} \\ $$$${x}\left({y}+\mathrm{66}\right)−\mathrm{88}\left({y}+\mathrm{66}\right)=\mathrm{17525} \\ $$$$\left({x}−\mathrm{88}\right)\left({y}+\mathrm{66}\right)=\mathrm{5}^{\mathrm{2}} ×\mathrm{701}\: \\ $$$$\begin{cases}{\underset{{x}=\mathrm{89}\:} {{x}−\mathrm{88}=\mathrm{1}}\:\wedge\:\underset{{y}=\mathrm{23267}}…
Question Number 196111 by sonukgindia last updated on 18/Aug/23 Answered by mahdipoor last updated on 18/Aug/23 $$\Rightarrow\Rightarrow\Rightarrow\Rightarrow\:{if}\:{n}\leqslant{x}\:\Rightarrow \\ $$$$\Sigma=\left({x}−\mathrm{1}\right)+…+\left({x}−{n}\right)={nx}−\frac{{n}^{\mathrm{2}} +{n}}{\mathrm{2}}= \\ $$$${x}^{\mathrm{2}} −\left({n}+\mathrm{1}\right){x}+\left(\frac{{n}^{\mathrm{2}} +\mathrm{2}{n}+\mathrm{5}}{\mathrm{4}}\right) \\…