Question Number 194884 by cortano12 last updated on 18/Jul/23 $$\:\:\:\:\:\:{x}!\:=\:\mathrm{6}!.\:\mathrm{7}!\: \\ $$$$\:\:\:\:\:\:{x}^{\mathrm{2}} \:=?\: \\ $$ Answered by AST last updated on 18/Jul/23 $$=\mathrm{7}!×\left(\mathrm{2}×\mathrm{3}\right)×\mathrm{5}×\mathrm{4}×\mathrm{3}×\mathrm{2}×\mathrm{1}= \\ $$$$\mathrm{7}!×\left(\mathrm{4}×\mathrm{2}\right)×\left(\mathrm{3}×\mathrm{3}\right)×\left(\mathrm{5}×\mathrm{2}\right)=\mathrm{10}!={x}!\Rightarrow{x}^{\mathrm{2}}…
Question Number 194887 by Mastermind last updated on 18/Jul/23 $$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{Inverse}\:\mathrm{laplace}\:\mathrm{transform}\:\mathrm{of} \\ $$$$\frac{\mathrm{S}\:+\:\mathrm{2}}{\mathrm{S}^{\mathrm{2}} \:+\mathrm{4S}\:+\:\mathrm{7}} \\ $$$$ \\ $$$$\mathrm{Urgent}! \\ $$ Answered by Dwan last updated on…
Question Number 194881 by tri26112004 last updated on 18/Jul/23 $${Give}\:\bigtriangleup{ABC}\: \\ $$$${Proof}:\:{sin}\:{A}\:+\:{sin}\:{B}\:+\:{sin}\:{C}\:>\:\mathrm{2} \\ $$ Answered by Frix last updated on 19/Jul/23 $$\mathrm{It}'\mathrm{s}\:\mathrm{not}\:\mathrm{true}. \\ $$$$\mathrm{0}<\mathrm{sin}\:{A}\:+\mathrm{sin}\:{B}\:+\mathrm{sin}\:{C}\:\:\leqslant\frac{\mathrm{3}\sqrt{\mathrm{3}}}{\mathrm{2}} \\…
Question Number 194861 by cherokeesay last updated on 17/Jul/23 Answered by horsebrand11 last updated on 17/Jul/23 $$\:\:\mathrm{let}\:\mathrm{the}\:\mathrm{side}\:\mathrm{length}\:\mathrm{of}\:\mathrm{the}\:\mathrm{small} \\ $$$$\:\:\mathrm{square}\:\mathrm{be}\:\mathrm{p}. \\ $$$$\:\:\left(\mathrm{1}+\mathrm{p}\right)^{\mathrm{2}} \:+\:\mathrm{p}^{\mathrm{2}} \:=\:\left(\sqrt{\mathrm{2}}\:\right)^{\mathrm{2}} \\ $$$$\:\:\mathrm{2p}^{\mathrm{2}}…
Question Number 194847 by cortano12 last updated on 17/Jul/23 $$\:\:\:\:\:\:\underbrace{\:} \\ $$ Commented by Tinku Tara last updated on 17/Jul/23 $${z}=?,\:\mathrm{without}\:\mathrm{knowing}\:{z}\:\mathrm{you}\:\mathrm{cannot} \\ $$$$\mathrm{find}\:{n} \\ $$…
Question Number 194846 by dimentri last updated on 17/Jul/23 $$\:\:\:\:\:\:\underbrace{\:} \\ $$ Answered by som(math1967) last updated on 17/Jul/23 $$\:{x}=\frac{\sqrt[{\mathrm{3}}]{\mathrm{10}+\mathrm{6}\sqrt{\mathrm{3}}}\left(\sqrt{\mathrm{3}}−\mathrm{1}\right)}{\:\sqrt{\mathrm{5}+\mathrm{1}+\mathrm{2}\sqrt{\mathrm{5}}}−\sqrt{\mathrm{5}}} \\ $$$${x}=\frac{\sqrt[{\mathrm{3}}]{\mathrm{3}\sqrt{\mathrm{3}}+\mathrm{3}.\mathrm{3}+\mathrm{3}\sqrt{\mathrm{3}}+\mathrm{1}}\left(\sqrt{\mathrm{3}}−\mathrm{1}\right)}{\:\sqrt{\left(\sqrt{\mathrm{5}}+\mathrm{1}\right)^{\mathrm{2}} }−\sqrt{\mathrm{5}}} \\ $$$${x}=\frac{\sqrt[{\mathrm{3}}]{\left(\sqrt{\mathrm{3}}\right)^{\mathrm{3}}…
Question Number 194869 by sonukgindia last updated on 17/Jul/23 Answered by Frix last updated on 17/Jul/23 $$−{x}^{\mathrm{2}^{−{x}^{\mathrm{4}} } } =−{x}^{\mathrm{4}^{−{x}^{\mathrm{2}} } } \\ $$$${x}^{\left(\mathrm{1}/\mathrm{2}\right)^{{x}^{\mathrm{4}} }…
Question Number 194853 by horsebrand11 last updated on 17/Jul/23 Answered by cortano12 last updated on 17/Jul/23 $$\:\:\:\underbrace{\Subset} \\ $$ Commented by horsebrand11 last updated on…
Question Number 194868 by Erico last updated on 17/Jul/23 $$\mathrm{Prove}\:\mathrm{that}\:\forall{n}\in\mathrm{IN} \\ $$$$\underset{\:\mathrm{0}} {\int}^{\:\mathrm{1}} {t}\:{sin}^{\mathrm{2}{n}} \left({lnt}\right){dt}=\:\frac{\mathrm{1}}{\mathrm{1}−{e}^{−\mathrm{2}\pi} }\:\underset{\:\mathrm{0}} {\int}^{\:\pi} {e}^{−\mathrm{2}{t}} {sin}^{\mathrm{2}{n}} \left({t}\right){dt} \\ $$ Answered by witcher3…
Question Number 194852 by mustafazaheen last updated on 17/Jul/23 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\mathrm{cosx}\right)^{\mathrm{log}\left(\mathrm{x}\right)} =? \\ $$$$ \\ $$ Answered by MM42 last updated on 17/Jul/23…