Question Number 209316 by klipto last updated on 06/Jul/24 $$\boldsymbol{\mathrm{if}}\:\:\mathrm{2}\boldsymbol{\mathrm{n}}^{\mathrm{2}} +\mathrm{3}\boldsymbol{\mathrm{n}}^{\mathrm{3}} =\boldsymbol{\mathrm{n}}! \\ $$$$\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{n}} \\ $$ Answered by A5T last updated on 07/Jul/24 $${n}\left(\mathrm{2}+\mathrm{3}{n}\right)=\left({n}−\mathrm{1}\right)! \\…
Question Number 209318 by essaad last updated on 06/Jul/24 Answered by Frix last updated on 06/Jul/24 $$\mathrm{We}\:\mathrm{know}\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\:\frac{\mathrm{1}}{{k}}\:=\infty \\ $$$${k}>\mathrm{1}:\:\frac{\mathrm{1}}{\:\sqrt{{k}}}>\frac{\mathrm{1}}{\:{k}}\:\Rightarrow\:\underset{{k}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{\:\sqrt{{k}}}\:>\underset{{k}=\mathrm{1}} {\overset{\infty}…
Question Number 209281 by Tawa11 last updated on 06/Jul/24 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{r},\:\mathrm{if}\:\:\overset{\mathrm{10}} {\:}\mathrm{C}_{\mathrm{r}} \:\:=\:\:\overset{\mathrm{10}} {\:}\mathrm{C}_{\mathrm{2r}\:\:+\:\:\mathrm{1}} \\ $$ Commented by klipto last updated on 06/Jul/24 $$\:\:\:\:\:\:\:^{\boldsymbol{\mathrm{n}}} \boldsymbol{\mathrm{C}}_{\mathrm{r}} =^{\mathrm{n}}…
Question Number 209314 by SonGoku last updated on 06/Jul/24 Commented by SonGoku last updated on 06/Jul/24 $$\mathrm{How}\:\mathrm{to}\:\mathrm{find}\:\mathrm{the}\:\mathrm{of}\:\mathrm{this}\:\mathrm{polygon}? \\ $$ Commented by mr W last updated…
Question Number 209246 by Erico last updated on 05/Jul/24 $$\mathrm{Find}\:\mathrm{f}\left(\mathrm{x}\right)=\underset{\:\mathrm{0}} {\int}^{\:\mathrm{x}} \frac{\mathrm{dt}}{\mathrm{t}+\mathrm{e}^{\mathrm{f}\left(\mathrm{t}\right)} } \\ $$ Answered by mr W last updated on 06/Jul/24 $${f}\left({x}\right)=\int_{\mathrm{0}} ^{{x}}…
Question Number 209272 by Tawa11 last updated on 05/Jul/24 Commented by Tawa11 last updated on 05/Jul/24 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{shaded}\:\mathrm{area}. \\ $$ Answered by A5T last updated on…
Question Number 209240 by Jubr last updated on 05/Jul/24 $${If}\:\:{x}\:\:+\:\:\frac{\mathrm{49}}{{x}\:+\:\mathrm{48}}\:\:=\:\:−\:\mathrm{34} \\ $$$${find}\:\:\left(\mathrm{2}{x}\:+\:\mathrm{83}\right)^{\mathrm{3}} \:+\:\frac{\mathrm{1}}{\left(\mathrm{2}{x}\:+\:\mathrm{83}\right)^{\mathrm{3}} } \\ $$ Answered by som(math1967) last updated on 05/Jul/24 $${x}+\mathrm{48}+\frac{\mathrm{49}}{{x}+\mathrm{48}}=−\mathrm{34}+\mathrm{48} \\…
Question Number 209241 by mr W last updated on 05/Jul/24 Answered by A5T last updated on 05/Jul/24 Commented by A5T last updated on 05/Jul/24 $$\sqrt{{a}^{\mathrm{2}}…
Question Number 209263 by hardmath last updated on 05/Jul/24 $$ \\ $$6 different letters were written to 6 different people and 6 different envelopes were…
Question Number 209228 by universe last updated on 04/Jul/24 Answered by Frix last updated on 04/Jul/24 $$\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\left(\mathrm{cos}\:{x}\:+\mathrm{sin}\:{x}\right)^{{n}} {dx}=\sqrt{\mathrm{2}}\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\mathrm{sin}^{{n}} \:\left({x}+\frac{\pi}{\mathrm{4}}\right)\:{dx}= \\ $$$$=\sqrt{\mathrm{2}}\underset{\frac{\pi}{\mathrm{4}}}…