Question Number 206357 by hardmath last updated on 12/Apr/24 $$\mathrm{Find}: \\ $$$$\mathrm{1}\:+\:\mathrm{cos444}°\:−\:\mathrm{cos84}°\:+\:\mathrm{cot45}°\:=\:? \\ $$ Answered by MM42 last updated on 12/Apr/24 $$\mathrm{2}\:\checkmark \\ $$ Commented…
Question Number 206322 by MATHEMATICSAM last updated on 12/Apr/24 $$\mathrm{If}\:{abc}\:=\:\mathrm{1}\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that} \\ $$$$\:\frac{\mathrm{1}}{\mathrm{1}\:+\:{a}\:+\:{b}^{−\mathrm{1}} }\:+\:\frac{\mathrm{1}}{\mathrm{1}\:+\:{b}\:+\:{c}^{−\mathrm{1}} }\:+\:\frac{\mathrm{1}}{\mathrm{1}\:+\:{c}\:+\:{a}^{−\mathrm{1}} }\:=\:\mathrm{1} \\ $$ Commented by Rasheed.Sindhi last updated on 12/Apr/24 $${For}\:{similar}\:{question}\:{see}…
Question Number 206355 by mr W last updated on 12/Apr/24 $${if}\:{the}\:{sum}\:{of}\:{three}\:{positive}\:{real}\: \\ $$$${numbers}\:{is}\:{equal}\:{to}\:{their}\:{product}, \\ $$$${prove}\:{that}\:{at}\:{least}\:{one}\:{of}\:{the}\: \\ $$$${numbers}\:{is}\:{larger}\:{than}\:\mathrm{1}.\mathrm{7}. \\ $$ Answered by A5T last updated on…
Question Number 206339 by mnjuly1970 last updated on 12/Apr/24 $$ \\ $$$$\:\:\:\:\:{E}\:\subseteq\:{Y}\:\subseteq\:\left(\:{X}\:,\:{d}\:\right)\mid_{{metric}\:{space}} \\ $$$$\:\:\:\:{prove}\:\:{E}\:{is}\:{open}\:{in}\:{Y}\:{if}\:{and}\:\:{only}\:{if} \\ $$$$\:\:\:\:\:\:\:\exists\:{G}\:\left({open}\:{set}\:\right)\:{in}\:{X}\:\:{such}\:{that} \\ $$$$\:\:\:\:\:\:\:\:\:{E}\:=\:{G}\:\cap\:{Y}\:\:\:….\:\left({mathematical}\:{analysis}\:\left({I}\right)\right) \\ $$ Answered by Berbere last updated…
Question Number 206302 by ayietaamos last updated on 11/Apr/24 Answered by A5T last updated on 11/Apr/24 $${k}=\frac{{ln}\left(\frac{{T}}{\mathrm{3}{y}}\right)−\mathrm{1}}{\mathrm{2}} \\ $$ Answered by MATHEMATICSAM last updated on…
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…