Question Number 68676 by Rio Michael last updated on 14/Sep/19 $${Solve}\:{the}\:{equation} \\ $$$${tanh}^{−\mathrm{1}} \left(\frac{{x}−\mathrm{2}}{{x}+\mathrm{1}}\right)\:=\:{ln}\:\mathrm{2} \\ $$$${show}\:{that}\:{the}\:{set}\:\left\{\mathrm{1},\mathrm{2},\mathrm{4},\mathrm{8}\right\}\:\:{under}\:×_{\mathrm{15}} \:,{multiplication}\:{mod}\:\mathrm{15}\:\:{forms}\:{a}\:{group}. \\ $$ Commented by MJS last updated on…
Question Number 68675 by Rio Michael last updated on 14/Sep/19 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:{Express}\:{in}\:{partial}\:{fraction}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:{f}\left({x}\right)\:\equiv\:\frac{\mathrm{2}{x}^{\mathrm{3}} \:+\:{x}\:+\:\mathrm{2}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)\left({x}+\mathrm{1}\right)\left({x}−\mathrm{2}\right)}\:{x}\:\neq\:−\mathrm{1},\mathrm{2} \\ $$$${Hence}\:{or}\:{otherwise}\:\:{show}\:{that}\:\: \\ $$$$\:\int_{\mathrm{0}} ^{\mathrm{1}} {f}\left({x}\right)\:{dx}\:=\:−\frac{\mathrm{1}}{\mathrm{12}}\left[\:\mathrm{13}{ln}\:\mathrm{2}\:+\:\pi\right] \\ $$$$…
Question Number 68617 by Rio Michael last updated on 14/Sep/19 $${find}\:{the}\:{value}\:{of}\:{p}\:{given}\:{that} \\ $$$$\mathrm{3}^{{p}} \:×\:\mathrm{3}^{−\mathrm{1}} \:×\:\mathrm{5}\:×\:\mathrm{3}^{{p}−\mathrm{1}} \:=\:\mathrm{2}\:×\:\mathrm{3}^{\mathrm{4}} \\ $$ Commented by Rasheed.Sindhi last updated on 14/Sep/19…
Question Number 68609 by TawaTawa last updated on 14/Sep/19 Commented by TawaTawa last updated on 14/Sep/19 $$\mathrm{I}\:\mathrm{got}\:\mathrm{4m}/\mathrm{s}^{\mathrm{2}} \:\:\:\mathrm{in}\:\mathrm{number}\:\mathrm{14},\:\mathrm{please}\:\mathrm{help}\:\mathrm{me}\:\mathrm{check} \\ $$ Answered by mr W last…
Question Number 134135 by Agnibhoo last updated on 28/Feb/21 $$\mathrm{If}\:\mathrm{P}\:=\:\mathrm{2}\:+\:\frac{\mathrm{1}}{\mathrm{P}}\:\mathrm{then}\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{answer}\:\mathrm{of} \\ $$$$\mathrm{P}^{\mathrm{2}} \:−\:\frac{\mathrm{1}}{\mathrm{P}^{\mathrm{2}} }\:?\:\: \\ $$ Answered by Ñï= last updated on 28/Feb/21 $${p}^{\mathrm{2}} −\frac{\mathrm{1}}{{p}^{\mathrm{2}}…
Question Number 3062 by 123456 last updated on 04/Dec/15 $$\omega\left({z}\right)\:\left(\mathrm{Q3035}\right) \\ $$$$\mathrm{does} \\ $$$$\omega\left({z}\right)=\mathrm{0}\:\mathrm{for}\:{z}\in\mathbb{N}^{\ast} ? \\ $$ Commented by Filup last updated on 04/Dec/15 $$\mathrm{What}\:\mathrm{is}\:\mathbb{N}^{\ast}…
Question Number 134117 by ClarkeMelodyWenkeh last updated on 27/Feb/21 Answered by TheSupreme last updated on 28/Feb/21 $${A}=\mathrm{15} \\ $$$${B}=\mathrm{10} \\ $$$${A}\cup{B}={A}+{B}−{A}\cap{B}=\mathrm{20} \\ $$$${A}\cap{B}=\mathrm{15}+\mathrm{10}−\mathrm{20}=\mathrm{5} \\ $$$${p}\left({A}\cap{B}\right)=\frac{{A}\cap{B}}{{A}\cup{B}}=\frac{\mathrm{1}}{\mathrm{4}}…
Question Number 3044 by 123456 last updated on 03/Dec/15 $$\mathrm{random}\:\mathrm{question} \\ $$$$\mathrm{if}\:\mathrm{person}\:\mathrm{as}\:\mathrm{5}\:\mathrm{years}\:\mathrm{old}\:\mathrm{and}\:\left(\mathrm{s}\right)\mathrm{he}\:\mathrm{back} \\ $$$$\mathrm{10}\:\mathrm{years}\:\mathrm{in}\:\mathrm{time}\:\left(\mathrm{by}\:\mathrm{some}\:\mathrm{mean}\right) \\ $$$$\mathrm{would}\:\left(\mathrm{s}\right)\mathrm{he}\:\mathrm{have}\:−\mathrm{5}\:\mathrm{years}\:\mathrm{old}? \\ $$ Answered by Filup last updated on 03/Dec/15…
Question Number 3035 by 123456 last updated on 03/Dec/15 $$\omega\left({z}\right)=\underset{{n}\rightarrow\infty} {\mathrm{lim}}\frac{{n}^{{z}} \left[{z}+\left({z}+\mathrm{1}\right)+…+\left({z}+{n}\right)\right]}{{z}\left({z}+\mathrm{1}\right)\left({z}+\mathrm{2}\right)…\left({z}+{n}\right)} \\ $$$$\omega\left(\mathrm{1}\right)=? \\ $$ Commented by prakash jain last updated on 04/Dec/15 $${w}\left(\mathrm{1}\right)=\underset{{n}\rightarrow\infty}…
Question Number 134002 by Dwaipayan Shikari last updated on 26/Feb/21 $${What}\:{will}\:{be}\:{the}\:{minimum}\:{area}\:{of}\:{a}\:{heptagon}\:{inscribed}\:{in} \\ $$$${an}\:{unit}\:{square}? \\ $$ Commented by Dwaipayan Shikari last updated on 26/Feb/21 Answered by…