Question Number 206160 by MATHEMATICSAM last updated on 08/Apr/24 $$\mathrm{If}\:{x}\:\mathrm{and}\:{y}\:\mathrm{are}\:\mathrm{real}\:\mathrm{numbers}\:\mathrm{then}\:\mathrm{is}\:\mathrm{it} \\ $$$$\mathrm{possible}\:\mathrm{that}\:\mathrm{sec}\theta\:=\:\frac{\mathrm{2}{xy}}{{x}^{\mathrm{2}} \:+\:{y}^{\mathrm{2}} }\:? \\ $$ Commented by mr W last updated on 08/Apr/24 $${only}\:{if}\:{x}=\pm{y}.…
Question Number 206155 by dimentri last updated on 08/Apr/24 $$\:\:\:\:\mathrm{x}\:=\:\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{x}}}}}} \\ $$$$\:\:\:\mathrm{find}\:\mathrm{x}.\: \\ $$ Answered by MM42 last updated on 08/Apr/24 $$\mathrm{2}+\frac{\mathrm{2}}{{x}}=\frac{\mathrm{2}{x}+\mathrm{2}}{{x}}={a} \\ $$$$\mathrm{2}+\frac{\mathrm{2}}{{a}}=\mathrm{2}+\frac{{x}}{{x}+\mathrm{1}}=\frac{\mathrm{3}{x}+\mathrm{2}}{{x}+\mathrm{1}}={b} \\…
Question Number 206108 by MATHEMATICSAM last updated on 07/Apr/24 $$\mathrm{If}\:{x}\:=\:\sqrt{\frac{\sqrt{\mathrm{5}}\:+\:\mathrm{1}}{\:\sqrt{\mathrm{5}}\:−\:\mathrm{1}}}\:\mathrm{then}\:{x}^{\mathrm{12}} \:=\:? \\ $$ Answered by mr W last updated on 07/Apr/24 $${x}=\sqrt{\frac{\sqrt{\mathrm{5}}+\mathrm{1}}{\:\sqrt{\mathrm{5}}−\mathrm{1}}}=\frac{\sqrt{\mathrm{5}}+\mathrm{1}}{\mathrm{2}}=\varphi \\ $$$${x}^{\mathrm{2}} ={x}+\mathrm{1}…
Question Number 206104 by cortano21 last updated on 07/Apr/24 $$\:\:\:\:\downharpoonleft\underline{\:} \\ $$ Answered by dimentri last updated on 07/Apr/24 $$\:\:\mathrm{7}^{−\mathrm{a}} =\:\mathrm{3}^{−\mathrm{b}} =\:\mathrm{2}^{−\mathrm{c}} =\mathrm{5}^{−\mathrm{d}} =\:\mathrm{m} \\…
Question Number 206129 by hardmath last updated on 07/Apr/24 Answered by MaruMaru last updated on 07/Apr/24 $${constant}\:\mathcal{C}\:??? \\ $$$${is}\:{it}\:{potter}\:{const}??? \\ $$$$ \\ $$https://ko.m.wikipedia.org/wiki/%ED%8F%AC%ED%84%B0_%EC%83%81%EC%88%98 Commented by…
Question Number 206074 by MATHEMATICSAM last updated on 06/Apr/24 $$\left({x}_{\mathrm{1}} \:−\:{x}_{\mathrm{2}} \:+\:{x}_{\mathrm{3}} \right)^{\mathrm{2}} \:=\:{x}_{\mathrm{2}} \left({x}_{\mathrm{4}} \:+\:{x}_{\mathrm{5}} \:−\:{x}_{\mathrm{2}} \right) \\ $$$$\left({x}_{\mathrm{2}} \:−\:{x}_{\mathrm{3}} \:+\:{x}_{\mathrm{4}} \right)^{\mathrm{2}} \:=\:{x}_{\mathrm{3}} \left({x}_{\mathrm{5}}…
Question Number 206066 by hardmath last updated on 06/Apr/24 $$\mathrm{Find}: \\ $$$$\frac{\mathrm{3}}{\mathrm{4}}\:\centerdot\:\frac{\mathrm{8}}{\mathrm{9}}\:\centerdot\:\frac{\mathrm{15}}{\mathrm{16}}\:\centerdot\:…\:\centerdot\:\frac{\mathrm{120}}{\mathrm{121}}\:=\:? \\ $$ Answered by mr W last updated on 06/Apr/24 $$\underset{{n}=\mathrm{2}} {\overset{\mathrm{11}} {\prod}}\frac{{n}^{\mathrm{2}}…
Question Number 206063 by MATHEMATICSAM last updated on 06/Apr/24 $$\mathrm{If}\:\left({x}\:+\:\sqrt{\mathrm{1}\:+\:{x}^{\mathrm{2}} }\right)\left({y}\:+\:\sqrt{\mathrm{1}\:+\:{y}^{\mathrm{2}} }\right)\:=\:\mathrm{1}\:\mathrm{then} \\ $$$$\mathrm{find}\:\left({x}\:+\:{y}\right)^{\mathrm{2}} . \\ $$ Answered by mr W last updated on 06/Apr/24…
Question Number 206082 by hardmath last updated on 06/Apr/24 $$\mathrm{If}\:\:\:\mathrm{cos}\boldsymbol{\alpha}\:=\:\mathrm{sin}\boldsymbol{\alpha}\:+\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}} \\ $$$$\mathrm{Find}\:\:\:\mathrm{sin2}\boldsymbol{\alpha}\:=\:? \\ $$ Answered by MATHEMATICSAM last updated on 29/Apr/24 $$\mathrm{cos}\alpha\:=\:\mathrm{sin}\alpha\:+\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}} \\ $$$$\Rightarrow\:\mathrm{cos}\alpha\:−\:\mathrm{sin}\alpha\:=\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}} \\…
Question Number 206025 by cortano12 last updated on 05/Apr/24 $$\:\:\:\:\:\mathrm{2}^{\mathrm{2024}} \:=\:{x}\:\left({mod}\:\mathrm{10}\right)\: \\ $$ Answered by BaliramKumar last updated on 05/Apr/24 $$\mathrm{Find}\:\mathrm{unit}\:\mathrm{digit} \\ $$$$\mathrm{2}^{\mathrm{2024}} \:=\:\mathrm{2}^{\mathrm{4k}\:+\:\mathrm{4}} \:=\:\mathrm{2}^{\mathrm{4}}…