Question Number 72718 by Rio Michael last updated on 01/Nov/19 $${given}\:{that}\: \\ $$$$\:{a}\:\equiv\:{b}\left({mod}\:{n}\right)\: \\ $$$${show}\:{that}\:{a}^{{k}} \:\equiv\:{b}^{{k}} \:\left({mod}\:{n}\right) \\ $$ Commented by prof Abdo imad last…
Question Number 138254 by mey3nipaba last updated on 11/Apr/21 Commented by Rasheed.Sindhi last updated on 11/Apr/21 $$\mathrm{40} \\ $$ Commented by Dwaipayan Shikari last updated…
Question Number 138249 by sahnaz last updated on 11/Apr/21 $$\mathrm{li}\underset{\mathrm{n}\rightarrow\mathrm{0}} {\mathrm{m}}\frac{\mathrm{2}^{\mathrm{n}+\mathrm{1}} +\mathrm{3}^{\mathrm{n}+\mathrm{2}} +\mathrm{4}^{\mathrm{n}+\mathrm{3}} }{\mathrm{2}^{\mathrm{n}} +\mathrm{3}^{\mathrm{n}} +\mathrm{4}^{\mathrm{n}} } \\ $$ Answered by mathmax by abdo last…
Question Number 138248 by sahnaz last updated on 11/Apr/21 $$\mathrm{x}^{\mathrm{x}+\mathrm{4}} =\mathrm{32} \\ $$ Commented by mr W last updated on 11/Apr/21 $${no}\:{exact}\:{solution}! \\ $$$${x}\approx\mathrm{1}.\mathrm{8149} \\…
Question Number 7178 by aftab ahmad last updated on 14/Aug/16 Commented by aftab ahmad last updated on 14/Aug/16 $$\boldsymbol{{Very}}\:\boldsymbol{{nice}}\:\boldsymbol{{approach}}\:\boldsymbol{{sir}}..\boldsymbol{{T}}{h}\boldsymbol{{anks}}\:\boldsymbol{{a}}\:\boldsymbol{{lot}}. \\ $$ Commented by Yozzia last…
Question Number 138250 by sahnaz last updated on 11/Apr/21 $$\left(\mathrm{x}^{\mathrm{2}} −\mathrm{10x}+\mathrm{6}\right)^{\mathrm{x}−\mathrm{2}} >\mathrm{1} \\ $$ Answered by bobhans last updated on 11/Apr/21 $$\left({x}^{\mathrm{2}} −\mathrm{10}{x}+\mathrm{6}\right)^{{x}−\mathrm{2}} \:>\:\left({x}^{\mathrm{2}} −\mathrm{10}{x}+\mathrm{6}\right)^{\mathrm{0}}…
Question Number 138240 by bobhans last updated on 11/Apr/21 $$\:\left({x}−\mathrm{1}\right)\frac{{dy}}{{dx}}\:+{xy}\:=\:\mathrm{2}{xe}^{−{x}} \\ $$ Answered by EDWIN88 last updated on 11/Apr/21 $$\:\frac{{dy}}{{dx}}\:+\:\frac{{x}}{{x}−\mathrm{1}}\:{y}\:=\:\frac{\mathrm{2}{x}}{{e}^{{x}} \left({x}−\mathrm{1}\right)} \\ $$$${put}\:{IF}\:=\:{e}^{\int\:\frac{{x}}{{x}−\mathrm{1}}\:{dx}} \:=\:{e}^{\int\:\frac{{x}−\mathrm{1}+\mathrm{1}}{{x}−\mathrm{1}}\:{dx}} ={e}^{{x}+\mathrm{ln}\:\left({x}−\mathrm{1}\right)}…
Question Number 7168 by Tawakalitu. last updated on 14/Aug/16 $${I}\:{have}\:{five}\:{envelopes}\:{numbered}\:\mathrm{3},\mathrm{4},\mathrm{5},\mathrm{6},\mathrm{7}\:{all}\:{hidden}\:{in}\:{a} \\ $$$${box},\:{i}\:{picked}\:{an}\:{envelope}\:.\:\:{If}\:{its}\:{prime}\:{then}\:{i}\:{get}\:{the}\: \\ $$$${square}\:{of}\:{that}\:{number}\:{in}\:{Naira}.\:{Otherwise}\:\left({without}\:\right. \\ $$$$\left.{replacement}\right)\:{i}\:{picked}\:{another}\:{envelope}\:{and}\:{then}\:{get}\:{the} \\ $$$${sum}\:{of}\:{the}\:{squares}\:{of}\:{the}\:{two}\:{numbers}\:{picked}\:\left({in}\:{Naira}\right) \\ $$$${what}\:{is}\:{the}\:{chance}\:{of}\:{me}\:{getting}\:\:{N}\mathrm{25}\:\:? \\ $$$$ \\ $$ Commented…
Question Number 138236 by mohammad17 last updated on 11/Apr/21 $${prove}\:{that}\: \\ $$$$ \\ $$$$\frac{{e}^{−\mathrm{2}{y}} }{\mathrm{1}+{e}^{−\mathrm{2}{y}} }<\mid{tan}\left({z}\right)\:−\:{i}\mid<\frac{{e}^{−\mathrm{2}{y}} }{\mathrm{1}−{e}^{−\mathrm{2}{y}} }\:\:\:,{y}>\mathrm{0} \\ $$$$ \\ $$$${how}\:{can}\:{solve}\:{this}\:? \\ $$ Commented…
Question Number 7165 by Tawakalitu. last updated on 15/Aug/16 $$\mathrm{30}\:{teams}\:{participated}\:{in}\:{the}\:{football}\:{tournament}\:.\:{At}\:{the}\: \\ $$$${end}\:{of}\:{the}\:{competition}\:{it}\:{turned}\:{out}\:{that}\:{in} \\ $$$${Any}\:{group}\:{of}\:{three}\:\:{teams}\:{it}\:{is}\:{possible}\:{to}\:{single}\:{out}\:{two} \\ $$$${teams}\:{which}\:{score}\:{equal}\:{point}\:{in}\:{three}\:{games}.\: \\ $$$${within}\:{this}\:{group}\:\left(\mathrm{3}\:{points}\:{are}\:{given}\:{for}\:{the}\:{victory},\:\right. \\ $$$$\left.\mathrm{1}\:{point}\:{for}\:{the}\:{draw}\:,\:\mathrm{0}\:{point}\:{for}\:{the}\:{defeat}\:\right).\: \\ $$$${what}\:{is}\:{the}\:{least}\:{possible}\:{number}\:{of}\:{draws}\:{that}\:{can}\:{occur} \\ $$$${in}\:{such}\:{a}\:{tournament}\:? \\…