Question Number 209023 by Spillover last updated on 30/Jun/24 Commented by Spillover last updated on 01/Jul/24 $${let}\:{u}=\frac{\mathrm{4}{x}}{\mathrm{1}+\mathrm{5}{x}}\:\:\:\:\:\:\frac{{du}}{{dx}}=\frac{\mathrm{4}}{\left(\mathrm{1}+\mathrm{5}{x}\right)^{\mathrm{2}} } \\ $$$$\frac{{d}}{{dx}}\left(\mathrm{tan}^{−\mathrm{1}} \frac{\mathrm{4}{x}}{\mathrm{1}+\mathrm{5}{x}}\right)=\frac{\frac{\mathrm{4}}{\left(\mathrm{1}+\mathrm{5}{x}\right)^{\mathrm{2}} }}{\mathrm{1}+\left(\frac{\mathrm{4}{x}}{\mathrm{1}+\mathrm{5}{x}}\right)^{\mathrm{2}} }=\frac{\mathrm{4}}{\mathrm{1}+\mathrm{10}{x}+\mathrm{25}{x}^{\mathrm{2}} } \\…
Question Number 209016 by Spillover last updated on 30/Jun/24 Answered by Spillover last updated on 02/Jul/24 Answered by Spillover last updated on 02/Jul/24 Terms of…
Question Number 208980 by lmcp1203 last updated on 30/Jun/24 $${please}\:.\:\:\:\:\:{find}\:\:\mathrm{2}^{\mathrm{11001}^{\mathrm{666}} } {mod}\:\mathrm{23}\:\:\:\:\:\:\:\:{thanks}. \\ $$ Answered by A5T last updated on 30/Jun/24 $$\mathrm{2}^{\mathrm{11001}^{\mathrm{666}} } {mod}\left(\mathrm{23}\right)\equiv\mathrm{2}^{\mathrm{11001}^{\mathrm{666}} \left[{mod}\:\phi\left(\mathrm{23}\right)\right]}…
Question Number 209015 by Spillover last updated on 30/Jun/24 Answered by Spillover last updated on 02/Jul/24 Answered by Spillover last updated on 02/Jul/24 Answered by…
Question Number 208976 by efronzo1 last updated on 30/Jun/24 Answered by mr W last updated on 30/Jun/24 $${say}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} ={u},\:{xy}={v} \\ $$$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} \geqslant\mathrm{2}\sqrt{{x}^{\mathrm{2}} {y}^{\mathrm{2}}…
Question Number 209041 by alcohol last updated on 30/Jun/24 Commented by alcohol last updated on 30/Jun/24 $${find}\:{r} \\ $$ Commented by mr W last updated…
Question Number 209036 by Tawa11 last updated on 30/Jun/24 There are 5 people in a school, 2 boys and 3girls, two students, are chosen at…
Question Number 209030 by Spillover last updated on 30/Jun/24 Answered by aleks041103 last updated on 30/Jun/24 $${moment}\:{generating}\:{function}\:{is} \\ $$$${m}\left({t}\right)=\underset{{k}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{{m}_{{k}} }{{k}!}{t}^{{k}} ={m}_{\mathrm{0}} +{m}_{\mathrm{1}} {t}+……
Question Number 209031 by Spillover last updated on 30/Jun/24 Answered by Spillover last updated on 07/Jul/24 $${f}\left({x}\right)=\begin{cases}{\frac{\mathrm{1}}{{n}}\:\:\:\:{x}=\mathrm{1},\mathrm{2},\mathrm{3},…..=\frac{\mathrm{1}}{{n}}\left[{e}^{{t}} +{e}^{\mathrm{2}{t}} +{e}^{\mathrm{3}{t}} +……..\right]}\\{\mathrm{0}\:\:{else}\:{where}}\end{cases} \\ $$$$\left({a}\right)\:{moment}\:{generating}\:{function} \\ $$$${M}_{{x}} \left({t}\right)={E}\left({e}^{{tx}}…
Question Number 208999 by Spillover last updated on 30/Jun/24 Answered by mr W last updated on 30/Jun/24 Commented by mr W last updated on 30/Jun/24…