Question Number 206048 by MATHEMATICSAM last updated on 05/Apr/24 $$\mathrm{Prove}\:\mathrm{that}\:\mathrm{2}^{\mathrm{sin}^{\mathrm{2}} \theta} \:+\:\mathrm{2}^{\mathrm{cos}^{\mathrm{2}} \theta} \:\geqslant\:\mathrm{2}\sqrt{\mathrm{2}}. \\ $$ Answered by A5T last updated on 05/Apr/24 $$\mathrm{2}^{{sin}^{\mathrm{2}} \theta}…
Question Number 205993 by otchereabdullai@gmail.com last updated on 04/Apr/24 $$\:{Given}\:{that}\:\left(\mathrm{3}−\sqrt{{n}}\right)^{\mathrm{2}} ={m}−\mathrm{6}\sqrt{\mathrm{2}}\:{where} \\ $$$${m},{n}\:{are}\:{positive}\:{integers}\:{find}\:{m}−{n} \\ $$ Answered by A5T last updated on 04/Apr/24 $$\mathrm{9}+{n}−\mathrm{6}\sqrt{{n}}={m}−\mathrm{6}\sqrt{\mathrm{2}}\:\Rightarrow\mathrm{9}+{n}={m}\:\wedge\:{n}=\mathrm{2}\Rightarrow{m}−{n}=\mathrm{9} \\ $$…
Question Number 205988 by cortano12 last updated on 04/Apr/24 $$\:\:{Given}\:{f}\left({x}+\mathrm{1}\right)=\mathrm{2}^{{f}\left({x}\right)} .{f}\left(\mathrm{1}\right) \\ $$$$\:\:{and}\:{f}\left(\mathrm{1}\right)=\:\mathrm{16}\: \\ $$$$\:\:{then}\:{f}\left(\mathrm{2016}\right)=? \\ $$ Answered by Berbere last updated on 04/Apr/24 $${f}\left(\mathrm{2}\right)=\mathrm{2}^{\mathrm{20}}…
Question Number 205990 by MATHEMATICSAM last updated on 04/Apr/24 $$\mathrm{If}\:{x}\:=\:\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}\:\mathrm{then}\:\frac{\sqrt{\mathrm{1}\:+\:{x}}\:+\:\sqrt{\mathrm{1}\:−\:{x}}}{\:\sqrt{\mathrm{1}\:+\:{x}}\:−\:\sqrt{\mathrm{1}\:−\:{x}}}\:=\:? \\ $$ Answered by cortano12 last updated on 04/Apr/24 $$\:\frac{\left(\sqrt{\mathrm{1}+{x}}\:+\sqrt{\mathrm{1}−{x}}\:\right)^{\mathrm{2}} }{\mathrm{2}{x}}\:=\:\frac{\mathrm{2}+\mathrm{2}\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}{\mathrm{2}{x}}\: \\ $$$$\:=\:\frac{\mathrm{1}}{{x}}\:+\:\sqrt{\frac{\mathrm{1}}{{x}^{\mathrm{2}} }−\mathrm{1}}\:…
Question Number 206007 by SANOGO last updated on 04/Apr/24 $$\left({E},<,>\:\right):\:\:\:{prouve} \\ $$$$<{x},{y}>=\frac{\mathrm{1}}{\mathrm{4}}\underset{{k}={o}} {\overset{\mathrm{3}} {\sum}}{i}^{{k}} \mid\mid{x}\:+\:{i}^{{k}} {y}\mid\mid^{\mathrm{2}} \\ $$ Commented by Berbere last updated on 04/Apr/24…
Question Number 206003 by mnjuly1970 last updated on 04/Apr/24 Answered by Berbere last updated on 04/Apr/24 $$\Omega=\int_{\mathrm{0}} ^{\infty} \frac{{e}^{−{x}} }{{x}^{\mathrm{2}} }\left(\mathrm{1}−{cos}\left({x}\right)\right){dx} \\ $$$$\Omega\left({a}\right)=\int_{\mathrm{0}} ^{\infty} \frac{{e}^{−{x}}…
Question Number 205919 by Red1ight last updated on 03/Apr/24 $$\mathrm{write}\:\mathrm{the}\:\mathrm{following}\:\mathrm{recursive}\:\mathrm{function}\:\mathrm{in}\:\mathrm{explicit}\:\mathrm{form} \\ $$$${f}\left(\mathrm{1}\right)=\mathrm{1} \\ $$$${f}\left({n}+\mathrm{1}\right)=\left({n}+\mathrm{1}\right){f}\left({n}\right)+{n}! \\ $$ Answered by Tinku Tara last updated on 03/Apr/24 $${f}\left({n}\right)=\left({n}\right){f}\left({n}−\mathrm{1}\right)+\left({n}−\mathrm{1}\right)!…
Question Number 205941 by cortano12 last updated on 03/Apr/24 $$\:\:\:\mathrm{2}+\frac{\mathrm{2}}{\mathrm{2}−\frac{\mathrm{2}}{\mathrm{2}+\frac{\mathrm{2}}{\mathrm{2}−\frac{\mathrm{2}}{\mathrm{2}+\frac{\mathrm{2}}{\mathrm{3}}}}}}\:=?\: \\ $$$$\: \\ $$ Answered by mr W last updated on 03/Apr/24 $$\mathrm{2}+\frac{\mathrm{2}}{\mathrm{2}−\frac{\mathrm{2}}{\mathrm{2}+\frac{\mathrm{2}}{\mathrm{2}−\frac{\mathrm{2}}{\mathrm{2}+\frac{\mathrm{2}}{\mathrm{3}}}}}} \\ $$$$=\mathrm{2}+\frac{\mathrm{2}}{\mathrm{2}−\frac{\mathrm{2}}{\mathrm{2}+\frac{\mathrm{2}}{\mathrm{2}−\frac{\mathrm{3}}{\mathrm{4}}}}}…
Question Number 205975 by Tinku Tara last updated on 03/Apr/24 $$\mathrm{As}\:\mathrm{reported}\:\mathrm{some}\:\mathrm{users}\:\mathrm{uploaded} \\ $$$$\mathrm{wrong}\:\mathrm{pictures}. \\ $$$$\mathrm{Priviledge}\:\mathrm{of}\:\mathrm{following}\:\mathrm{users}\:\mathrm{are} \\ $$$$\mathrm{now}\:\mathrm{elevated}\:\mathrm{so}\:\mathrm{that}\:\mathrm{they}\:\mathrm{can}\:\mathrm{delete} \\ $$$$\mathrm{any}\:\mathrm{post}. \\ $$$$ \\ $$$$\mathrm{mr}\:\mathrm{W} \\ $$$$\mathrm{Rasheed}\:\mathrm{Sindhi}…
Question Number 205938 by mokys last updated on 03/Apr/24 $$\frac{{dx}}{{dt}}=\:{y}+\mathrm{4}{z}\:….\left(\mathrm{1}\right) \\ $$$$\frac{{dy}}{{dt}}\:=\:{z}−{x}…..\left(\mathrm{2}\right) \\ $$$$\frac{{dz}}{{dt}}\:=\:{x}\:−\:{y}….\left(\mathrm{3}\right) \\ $$$${solve}\:{the}\:{sistem}\:{by}\:{operator}\:\left(\:{elemination}\:{method}\:\right) \\ $$$$ \\ $$$$ \\ $$ Terms of Service…