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 $${only}\:{if}\:{x}=\pm{y}.…
Question Number 206156 by cortano21 last updated on 08/Apr/24 Commented by mr W last updated on 08/Apr/24 $${what}\:{i}\:{think}\:{is}\:{clear}: \\ $$$${in}\:{the}\:{package}\:{there}\:{must}\:{be}\:{exactly} \\ $$$${one}\:{egg}.\:{there}\:{must}\:{be}\:{at}\:{least}\:{three} \\ $$$${lettuces}.\:{there}\:{must}\:{be}\:{at}\:{least}\:{one} \\…
Question Number 206157 by cortano21 last updated on 08/Apr/24 Commented by cortano21 last updated on 08/Apr/24 $$\:\:\:\:\:\cancel{\underline{\underbrace{ }}} \\ $$ Commented by A5T last updated…
Question Number 206155 by dimentri last updated on 08/Apr/24 $$\:\:\:\:\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 $$\mathrm{2}+\frac{\mathrm{2}}{{x}}=\frac{\mathrm{2}{x}+\mathrm{2}}{{x}}={a} \\ $$$$\mathrm{2}+\frac{\mathrm{2}}{{a}}=\mathrm{2}+\frac{{x}}{{x}+\mathrm{1}}=\frac{\mathrm{3}{x}+\mathrm{2}}{{x}+\mathrm{1}}={b} \\…
Question Number 206150 by Samuel12 last updated on 08/Apr/24 $$\mathrm{Calcul}\:\:\:\mid\mathrm{x}−\alpha\mid\:=\:????? \\ $$$$\:\:\bullet\:\:\:\:\:\:\mathrm{x}=−\mathrm{1}\:\:;\:\:\:\alpha\:\in\:\left[−\mathrm{1};\:−\frac{\mathrm{3}}{\mathrm{4}}\right] \\ $$$$\:\:\bullet\:\:\:\:\mathrm{x}=\mathrm{2}\:\:;\:\:\:\:\alpha\:\in\:\left[\mathrm{0}\:;\:\mathrm{3}\right]\:\:\:\:\:\:\:\mathrm{help}\:\mathrm{please}\:\: \\ $$ Answered by Frix last updated on 08/Apr/24 $$\mid{x}−\alpha\mid=\begin{cases}{{x}−\alpha;\:{x}−\alpha\geqslant\mathrm{0}}\\{−\left({x}−\alpha\right);\:{x}−\alpha<\mathrm{0}}\end{cases} \\…
Question Number 206151 by cortano21 last updated on 08/Apr/24 Answered by dimentri last updated on 08/Apr/24 $$\:\:\mathrm{x}=\mathrm{2}\Rightarrow\mathrm{f}\left(\mathrm{3}\right)=\mathrm{4}\: \\ $$$$\:\:\mathrm{x}=\mathrm{1}\Rightarrow\mathrm{f}\left(\mathrm{3}\right)=\:\mathrm{g}^{−\mathrm{1}} \left(\mathrm{1}\right) \\ $$$$\:\:\mathrm{g}\left(\mathrm{4}\right)=\:\mathrm{g}\left(\mathrm{f}\left(\mathrm{3}\right)\right)\:=\:\mathrm{g}\left(\mathrm{g}^{−\mathrm{1}} \left(\mathrm{1}\right)\right)\:=\:\mathrm{1} \\ $$…
Question Number 206177 by MATHEMATICSAM last updated on 08/Apr/24 $$\mathrm{Find}\:\mathrm{total}\:\mathrm{number}\:\mathrm{of}\:\mathrm{solutions}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{equation}\:\mathrm{sin}{x}\:=\:\mathrm{log}{x}. \\ $$ Answered by Frix last updated on 08/Apr/24 $$\mathrm{log}\:{x}\:=\mathrm{ln}\:{x}\:? \\ $$$$−\mathrm{1}\leqslant\mathrm{ln}\:{x}\:\leqslant\mathrm{1}\:\Leftrightarrow\:\mathrm{e}^{−\mathrm{1}} \leqslant{x}\leqslant\mathrm{e}…
Question Number 206178 by naka3546 last updated on 08/Apr/24 Commented by naka3546 last updated on 08/Apr/24 $$\mathrm{Evaluate}\:\mathrm{this}\:\mathrm{integral}\:\mathrm{by}\:\mathrm{interpreting}\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{areas}. \\ $$$$\underset{\mathrm{0}} {\int}^{\mathrm{35}} {g}\left({x}\right)\:{dx} \\ $$ Commented by…
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 $${x}=\sqrt{\frac{\sqrt{\mathrm{5}}+\mathrm{1}}{\:\sqrt{\mathrm{5}}−\mathrm{1}}}=\frac{\sqrt{\mathrm{5}}+\mathrm{1}}{\mathrm{2}}=\varphi \\ $$$${x}^{\mathrm{2}} ={x}+\mathrm{1}…
Question Number 206142 by universe last updated on 07/Apr/24 $$\:\:\:\:\mathrm{let}\:\:\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }+{p}\left({x}\right)\frac{{dy}}{{dx}}+{q}\left({x}\right){y}=\mathrm{0}\:,\:{x}\in\mathbb{R}\:\mathrm{where}\: \\ $$$$\:\:\:\:{p}\left({x}\right)\:\mathrm{and}\:{q}\left({x}\right)\:\mathrm{are}\:\mathrm{continuous}\:\mathrm{function}\:\mathrm{if} \\ $$$$\:\:\:\:{y}_{\mathrm{1}} =\:\mathrm{sin}{x}−\mathrm{2cos}{x}\:{and}\:{y}_{\mathrm{2}} \:=\:\mathrm{2sin}{x}\:+\mathrm{cos}{x} \\ $$$$\:\:\:\:\mathrm{are}\:{L}.{I}\:\left(\mathrm{linearly}\:\mathrm{independent}\right)\:\mathrm{solution} \\ $$$$\:\:\:\:\:\mathrm{then}\:\:\mid\mathrm{4}{p}\left(\mathrm{0}\right)+\mathrm{2}{q}\left(\mathrm{1}\right)\mid\:=\:?\:\:\: \\ $$ Answered…