Question Number 193626 by SaRahAli last updated on 17/Jun/23 Answered by MM42 last updated on 17/Jun/23 $${x}=\sqrt{\mathrm{2}} \\ $$$$\Rightarrow\left(\sqrt{\mathrm{2}}\right)^{\left(\sqrt{\mathrm{2}}\right)^{\mathrm{8}} } =\left(\sqrt{\mathrm{2}}\right)^{\mathrm{16}} =\mathrm{256}\:\:\&\:\:\left(\sqrt{\mathrm{2}}\right)^{\left(\sqrt{\mathrm{2}}\right)^{\mathrm{2}} } =\left(\sqrt{\mathrm{2}}\right)^{\mathrm{2}} =\mathrm{2}…
Question Number 193618 by Brianodhiambo last updated on 17/Jun/23 $${x}^{{log}_{\mathrm{2}} {x}} =\mathrm{256} \\ $$ Answered by aba last updated on 17/Jun/23 $$\mathrm{x}^{\mathrm{log}_{\mathrm{2}} \left(\mathrm{x}\right)} =\mathrm{256}\:\Rightarrow\:\mathrm{x}^{\mathrm{log}_{\mathrm{2}} \left(\mathrm{x}\right)}…
Question Number 193617 by SaRahAli last updated on 17/Jun/23 Answered by witcher3 last updated on 17/Jun/23 $$\mathrm{x}\left(\mathrm{x}−\mathrm{3}\right)=\mathrm{x}^{\mathrm{2}} −\mathrm{3x} \\ $$$$\left(\mathrm{x}−\mathrm{1}\right)\left(\mathrm{x}−\mathrm{2}\right)=\mathrm{x}^{\mathrm{2}} −\mathrm{3x}+\mathrm{2} \\ $$$$\mathrm{t}=\mathrm{x}^{\mathrm{2}} −\mathrm{3x} \\…
Question Number 193611 by aba last updated on 17/Jun/23 $$\mathrm{2}\sqrt{\mathrm{4}}\:\boldsymbol{\div}\:\mathrm{2}\sqrt{\mathrm{4}}\:=? \\ $$ Answered by Skabetix last updated on 17/Jun/23 $${if}\:{it}\:{is}\:\left(\mathrm{2}\sqrt{}\mathrm{4}\right)/\left(\mathrm{2}\sqrt{}\mathrm{4}\right)=\mathrm{1} \\ $$$${else}\:\mathrm{2}×\sqrt{}\mathrm{4}/\mathrm{2}\:×\sqrt{}\mathrm{4}\:=\:\mathrm{2}\:×\:\mathrm{2}/\mathrm{2}\:×\:\mathrm{2}\:=\mathrm{2}×\mathrm{1}×\mathrm{2}=\mathrm{4} \\ $$$$ \\…
Question Number 193670 by mokys last updated on 17/Jun/23 $${show}\:{that}\:\int_{{c}} \:{e}^{\frac{\mathrm{1}}{{z}^{\mathrm{2}} }} \:{dz}\:=\:\mathrm{0}\:{when}\:\mid{z}\mid\:<\mathrm{1} \\ $$ Commented by mokys last updated on 17/Jun/23 $$????? \\ $$…
Question Number 193664 by 073 last updated on 17/Jun/23 Commented by 073 last updated on 17/Jun/23 $$\mathrm{prove}\:\mathrm{that} \\ $$ Commented by 073 last updated on…
Question Number 193585 by York12 last updated on 16/Jun/23 $$ \\ $$$${There}\:{exists}\:{a}\:{unique}\:{positive}\:{integer}\:{a}\:{for} \\ $$$${which}\:{The}\:{sum}\:{u}\:\:=\:\underset{{n}=\mathrm{1}} {\overset{\mathrm{2023}} {\sum}}\lfloor\frac{{n}^{\mathrm{2}} −{na}}{\mathrm{5}}\rfloor\:{is}\:{an}\:{integer} \\ $$$${trictly}\:{between}\:−\mathrm{1000}\:\&\:\mathrm{1000}\:{find}\:{a}+{u}. \\ $$ Answered by York12 last…
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Question Number 193504 by aba last updated on 15/Jun/23 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}x}^{\mathrm{x}^{\mathrm{x}} } =? \\ $$ Commented by Frix last updated on 15/Jun/23 $$\mathrm{0} \\ $$…
Question Number 193494 by aba last updated on 15/Jun/23 $$\boldsymbol{\mathrm{Let}}\:\boldsymbol{\mathrm{n}}\:\boldsymbol{\mathrm{be}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{fixed}}\:\boldsymbol{\mathrm{positive}}\:\boldsymbol{\mathrm{integer}}\:\boldsymbol{\mathrm{such}}\:\boldsymbol{\mathrm{that}} \\ $$$$\mathrm{sin}\left(\frac{\pi}{\mathrm{2n}}\right)+\mathrm{cos}\left(\frac{\boldsymbol{\pi}}{\mathrm{2n}}\right)=\frac{\sqrt{\mathrm{n}}}{\mathrm{2}} \\ $$$$\boldsymbol{\mathrm{Then}}\:\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{n}} \\ $$ Commented by maths_plus last updated on 15/Jun/23 $$\mathrm{cool} \\…