Question Number 190480 by aba last updated on 03/Apr/23 $$\mathrm{Proof}\:\mathrm{that}\:\left(\sqrt{\mathrm{2}}\right)^{\sqrt{\mathrm{2}}} \in\mathbb{R}\backslash\mathrm{Q} \\ $$ Answered by mehdee42 last updated on 04/Apr/23 $${lem}:\:{if}\:\:{p}\notin{Q}\Rightarrow\sqrt{{p}}\notin{Q} \\ $$$${clim}:\:\mathrm{2}^{\sqrt{\mathrm{2}}} \notin{Q} \\…
Question Number 59400 by hhghg last updated on 09/May/19 $$\left(\mathrm{4}^{\mathrm{6}} \right)^{\mathrm{2}} \\ $$ Answered by Pranay last updated on 09/May/19 $$\mathrm{4}^{\mathrm{12}\:=\:} \mathrm{16777216} \\ $$ Terms…
Question Number 124932 by aurpeyz last updated on 07/Dec/20 Answered by som(math1967) last updated on 07/Dec/20 $$\mathrm{Equivalent}\:\mathrm{capacitance} \\ $$$$\frac{\mathrm{1}}{\mathrm{C}}=\frac{\mathrm{1}}{\mathrm{4}+\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}=\frac{\mathrm{3}}{\mathrm{6}} \\ $$$$\mathrm{C}=\mathrm{2}\mu\mathrm{F} \\ $$$$\mathrm{charge}\:=\mathrm{12}×\mathrm{2}=\mathrm{24}×\mathrm{10}^{−\mathrm{6}} \mathrm{coulomb} \\…
Question Number 190464 by alcohol last updated on 03/Apr/23 $$\begin{cases}{{u}_{{n}+\mathrm{1}} \:=\:{u}_{{n}} −\mathrm{3}\:}\\{{v}_{{n}+\mathrm{1}} \:=\:\mathrm{4}{v}_{{n}} }\end{cases}\::\:{u}_{\mathrm{0}} \:=\:{v}_{\mathrm{0}} \:=\:\mathrm{1} \\ $$$${w}_{{n}} \:=\:\frac{\mathrm{1}−{u}_{{n}} }{{v}_{{n}} } \\ $$$$−\:{show}\:{that}\:{w}_{{n}} \:{is}\:{bounded} \\…
Question Number 124931 by ZiYangLee last updated on 07/Dec/20 $$\mathrm{If}\:\mathrm{3}^{\mathrm{2019}} +{k}\:\mathrm{is}\:\mathrm{a}\:\mathrm{multiple}\:\mathrm{of}\:\mathrm{11},\: \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{smallest}\:\mathrm{positive}\:\mathrm{integer}\:{k}. \\ $$ Answered by MJS_new last updated on 07/Dec/20 $$\mathrm{3}^{\mathrm{0}} =\mathrm{11}{n}+\mathrm{1} \\…
Question Number 190459 by mathlove last updated on 03/Apr/23 $$ \\ $$hi me tinko Tara Hello, when I use my mobile keyboard, the writing is…
Question Number 190452 by vishal1234 last updated on 03/Apr/23 $$\int\frac{{cos}^{\mathrm{1}.\mathrm{5}} {x}−{sin}^{\mathrm{1}.\mathrm{5}} {x}}{\:\sqrt{{sinx}\:{cosx}}}\:{dx} \\ $$$$=\:\int\frac{{cos}^{\frac{\mathrm{3}}{\mathrm{2}}} {x}}{{sin}^{\mathrm{1}/\mathrm{2}} {x}\:{cos}^{\mathrm{1}/\mathrm{2}} {x}}{dx}−\int\frac{{sin}^{\frac{\mathrm{3}}{\mathrm{2}}} {x}}{{sin}^{\mathrm{1}/\mathrm{2}} {x}\:{cos}^{\mathrm{1}/\mathrm{2}} {x}}\:{dx} \\ $$$$=\:\int\:\frac{{cosx}}{{sin}^{\mathrm{1}/\mathrm{2}} {x}}\:{dx}\:−\:\int\:\frac{{sinx}}{{cos}^{\mathrm{1}/\mathrm{2}} {x}}\:{dx} \\…
Question Number 190449 by MathsFan last updated on 03/Apr/23 $$ \\ $$John stands at 10m from a mango tree while Philip stands between John and…
Question Number 59377 by jimful last updated on 09/May/19 $$\mathrm{Find}\:\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}+\mathrm{2n}+\mathrm{3n}^{\mathrm{2}} +\mathrm{4n}^{\mathrm{3}} }{\mathrm{3}^{\mathrm{n}} } \\ $$ Answered by tanmay last updated on 09/May/19 $${S}=\underset{{n}=\mathrm{1}}…
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