Question Number 66420 by Rio Michael last updated on 14/Aug/19 $${solve}\:{the}\:{differential}\:{equation} \\ $$$$\:\mathrm{2}\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }\:+\:\frac{{dy}}{{dx}}\:−\:{e}^{−{x}} \:=\:\mathrm{4} \\ $$ Commented by mathmax by abdo last updated…
Question Number 66421 by Rio Michael last updated on 14/Aug/19 $${show}\:{that}\:{for}\:{a}\:{given}\:{complex}\:{number}\:{z} \\ $$$$\:{z}^{{n}} \:=\:{r}^{{n}} \:\left({cosn}\theta\:+\:{isinn}\theta\right)\: \\ $$ Answered by MJS last updated on 14/Aug/19 $${z}={r}\left(\mathrm{cos}\:\theta\:+\mathrm{i}\:\mathrm{sin}\:\theta\right)={r}\mathrm{e}^{\mathrm{i}\theta}…
Question Number 131953 by SLVR last updated on 10/Feb/21 $$ \\ $$ Commented by SLVR last updated on 10/Feb/21 Terms of Service Privacy Policy Contact:…
Question Number 66418 by 888 last updated on 14/Aug/19 $${what}\:{operation}\:{on}\:{interger}\:{used}\:{in}\:\mathrm{9}\left(\mathrm{7}.\mathrm{8}\right)=\left(\mathrm{9}.\mathrm{7}\right).\mathrm{8}?? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 883 by 112358 last updated on 12/Apr/15 $${How}\:{many}\:{even}\:{numbers}\: \\ $$$${between}\:\mathrm{3000}\:{and}\:\mathrm{7000}\:{can}\:{be} \\ $$$${formed}\:{using}\:{the}\:{digits}\: \\ $$$$\mathrm{2},\mathrm{3},\mathrm{4},\mathrm{5},\mathrm{6}\:{and}\:\mathrm{8}\:{if}\:{repetition} \\ $$$${of}\:{digits}\:{is}\:{not}\:{allowed}? \\ $$ Answered by prakash jain last…
Question Number 880 by arnav last updated on 11/Apr/15 $${Solve} \\ $$$$\frac{{x}+\mathrm{3}}{{x}−\mathrm{3}}<\mathrm{1} \\ $$ Answered by 123456 last updated on 11/Apr/15 $$\frac{{x}+\mathrm{3}}{{x}−\mathrm{3}}−\mathrm{1}<\mathrm{0} \\ $$$$\frac{{x}+\mathrm{3}−{x}+\mathrm{3}}{{x}−\mathrm{3}}<\mathrm{0} \\…
Question Number 66412 by aliesam last updated on 14/Aug/19 $${if} \\ $$$$ \\ $$$${f}\left({x}\right)={ln}\left({x}+\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}\right) \\ $$$$ \\ $$$${find} \\ $$$$ \\ $$$${f}^{−\mathrm{1}} \left({x}\right)=? \\…
Question Number 877 by sagarwal last updated on 07/Apr/15 $$\mathrm{An}\:\mathrm{8}×\mathrm{8}\:\mathrm{checkerboard}\:\mathrm{is}\:\mathrm{to}\:\mathrm{be}\:\mathrm{coloured} \\ $$$$\mathrm{with}\:\mathrm{6}\:\mathrm{colors}\:\:\mathrm{in}\:\mathrm{a}\:\mathrm{way}\:\mathrm{that}\:\mathrm{no}\:\mathrm{2}\:\mathrm{adjacent} \\ $$$$\mathrm{cells}\:\left(\mathrm{sharing}\:\mathrm{side}\right)\:\mathrm{have}\:\mathrm{the}\:\mathrm{same}\:\mathrm{color}.\:\mathrm{In}\:\mathrm{how} \\ $$$$\mathrm{many}\:\mathrm{ways}\:\mathrm{can}\:\mathrm{it}\:\mathrm{be}\:\mathrm{done}. \\ $$ Commented by 123456 last updated on 12/Apr/15…
Question Number 66413 by hmamarques1994@gmail.com last updated on 14/Aug/19 $$\: \\ $$$$\:\:\sqrt{\mathrm{8}+\boldsymbol{\mathrm{log}}_{\mathrm{6}} \left(\boldsymbol{\mathrm{x}}!\right)}+\sqrt{\mathrm{17}−\boldsymbol{\mathrm{log}}_{\boldsymbol{\mathrm{x}}!} \left(\mathrm{6}\right)}\:=\:\mathrm{7} \\ $$$$\: \\ $$ Answered by MJS last updated on 14/Aug/19…
Question Number 874 by 123456 last updated on 08/Apr/15 $${f}:\mathbb{R}\rightarrow\mathbb{R} \\ $$$${g}:\mathbb{R}\rightarrow\mathbb{R} \\ $$$${f}\left({x}\right)={g}\left({x}\right)−{f}\left(−{x}\right) \\ $$$${g}\left({x}\right)={f}\left({x}\right)+{g}\left(−{x}\right) \\ $$$${f}\left({x}\right)=? \\ $$$${g}\left({x}\right)=? \\ $$$${f}\left({x}\right)+{g}\left({x}\right)=? \\ $$$$\boldsymbol{{f}}\left(\boldsymbol{{x}}\right)\overset{?} {=}\boldsymbol{{f}}\left(−\boldsymbol{{x}}\right)…