Question Number 194877 by SajaRashki last updated on 18/Jul/23 $${without}\:{calculator}\:{Prove}:\:\sqrt[{\mathrm{6}}]{\pi^{\mathrm{5}} +\pi^{\mathrm{4}} }<{e} \\ $$ Commented by SajaRashki last updated on 24/Jul/23 $${without}\:{calculator}\:{Prove}:\:\sqrt[{\mathrm{6}}]{\pi^{\mathrm{5}} +\pi^{\mathrm{4}} }<{e} \\…
Question Number 194888 by Abdullahrussell last updated on 18/Jul/23 Answered by aleks041103 last updated on 18/Jul/23 $${The}\:{combined}\:{ages}\:{of}\:{Mary}\:{and}\:{Ann}\:{is}\:\mathrm{44}\:{years}. \\ $$$$\left(\:{M}\left({t}_{\mathrm{1}} \right)+{A}\left({t}_{\mathrm{1}} \right)=\mathrm{44}\:\right) \\ $$$${Mary}\:{is}\:{twice}\:{as}\:{old}\:{as}\:{Ann}\:{was} \\ $$$$\left(\:{M}\left({t}_{\mathrm{1}}…
Question Number 194884 by cortano12 last updated on 18/Jul/23 $$\:\:\:\:\:\:{x}!\:=\:\mathrm{6}!.\:\mathrm{7}!\: \\ $$$$\:\:\:\:\:\:{x}^{\mathrm{2}} \:=?\: \\ $$ Answered by AST last updated on 18/Jul/23 $$=\mathrm{7}!×\left(\mathrm{2}×\mathrm{3}\right)×\mathrm{5}×\mathrm{4}×\mathrm{3}×\mathrm{2}×\mathrm{1}= \\ $$$$\mathrm{7}!×\left(\mathrm{4}×\mathrm{2}\right)×\left(\mathrm{3}×\mathrm{3}\right)×\left(\mathrm{5}×\mathrm{2}\right)=\mathrm{10}!={x}!\Rightarrow{x}^{\mathrm{2}}…
Question Number 194846 by dimentri last updated on 17/Jul/23 $$\:\:\:\:\:\:\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}}} \\ $$$${x}=\frac{\sqrt[{\mathrm{3}}]{\mathrm{3}\sqrt{\mathrm{3}}+\mathrm{3}.\mathrm{3}+\mathrm{3}\sqrt{\mathrm{3}}+\mathrm{1}}\left(\sqrt{\mathrm{3}}−\mathrm{1}\right)}{\:\sqrt{\left(\sqrt{\mathrm{5}}+\mathrm{1}\right)^{\mathrm{2}} }−\sqrt{\mathrm{5}}} \\ $$$${x}=\frac{\sqrt[{\mathrm{3}}]{\left(\sqrt{\mathrm{3}}\right)^{\mathrm{3}}…
Question Number 194853 by horsebrand11 last updated on 17/Jul/23 Answered by cortano12 last updated on 17/Jul/23 $$\:\:\:\underbrace{\Subset} \\ $$ Commented by horsebrand11 last updated on…
Question Number 194851 by Guriya last updated on 17/Jul/23 $$\boldsymbol{\mathrm{Name}}\:\:\:\boldsymbol{\mathrm{Zainab}}\:\boldsymbol{\mathrm{Bibi}} \\ $$$$\boldsymbol{\mathrm{BC}}\mathrm{200400692} \\ $$$$\boldsymbol{\mathrm{A}}\mathrm{ssignmeng}\:\mathrm{No}#\mathrm{2}\: \\ $$$$\boldsymbol{\mathrm{Mth}}\:\mathrm{621} \\ $$$$\mathrm{solution}.. \\ $$$$\mathrm{a}_{\mathrm{n}} =\frac{\left(\mathrm{n}− \right)!}{\left(\mathrm{n}+ \right)^{\mathrm{2}} } \\…
Question Number 194844 by sniper237 last updated on 16/Jul/23 $$\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} +\left({x}+\mathrm{3}\right)^{\mathrm{2}} =\left({x}^{\mathrm{2}} +{ax}+{b}\right)\left({x}^{\mathrm{2}} +{cx}+{d}\right) \\ $$$${Find}\:{a},{b},{c},{d}. \\ $$ Answered by Frix last updated on…
Question Number 194809 by dimentri last updated on 16/Jul/23 $$\:\:\:\:{If}\:{f}\left({x}\right)={ax}^{\mathrm{2}} −\mathrm{5}{x}+\mathrm{3}\:{and}\: \\ $$$$\:\:\:{g}\left({x}\right)=\mathrm{3}{x}−\mathrm{3}\:{intersection}\:{at} \\ $$$$\:{points}\:\left(\mathrm{1},{h}\right)\:{and}\:\left(\mathrm{3},{t}\right). \\ $$$$\:\:{Find}\:\:\underline{ } \\ $$ Answered by horsebrand11 last updated…
Question Number 194837 by mr W last updated on 16/Jul/23 $${for}\:{x}>\mathrm{0}\:{find}\:{the}\:{minimum}\:{of}\:{the} \\ $$$${function}\:{f}\left({x}\right)={x}^{\mathrm{3}} +\frac{\mathrm{5}}{{x}}. \\ $$ Answered by Frix last updated on 16/Jul/23 $${f}'\left({x}\right)=\mathrm{0} \\…
Question Number 194808 by York12 last updated on 15/Jul/23 $$ \\ $$$${suppose}\:{a},{b},{c}\:{are}\:{positive}\:{real}\:{numbers} \\ $$$${prove}\:{the}\:{inequality} \\ $$$$\left(\frac{{a}+{b}}{\mathrm{2}}\right)\left(\frac{{b}+{c}}{\mathrm{2}}\right)\left(\frac{{c}+{a}}{\mathrm{2}}\right)\geqslant\left(\frac{{a}+{b}+{c}}{\mathrm{3}}\right)\sqrt[{\mathrm{3}}]{\left({abc}\right)^{\mathrm{2}} } \\ $$ Commented by York12 last updated on…