Question Number 224393 by fantastic last updated on 07/Sep/25 $${there}\:{is}\:{a}\:{number}\: \\ $$$${when}\:{the}\:{digits}\:{of}\:{the}\:{number} \\ $$$${are}\:{suffled}\:{randomly}\:{a}\:{new} \\ $$$${number}\:{is}\:{generated}\:{which} \\ $$$${is}\:{double}\:{of}\:{the}\:{first}\:{number} \\ $$$${The}\:{question}\:{is} \\ $$$${what}\:{is}\:{the}\:{smallest}\:{number} \\ $$$${which}\:{satisfies}\:{the}\:{rules}?? \\…
Question Number 224380 by fantastic last updated on 06/Sep/25 $${Please}\:{some}\:{geometry}\:{Q} \\ $$$${Living}\:{an}\:{inactive}\:{live}\:{for} \\ $$$${several}\:{days}… \\ $$ Commented by Tawa11 last updated on 08/Sep/25 Commented by…
Question Number 224381 by infinityaction last updated on 06/Sep/25 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 224382 by fantastic last updated on 06/Sep/25 $${Q}\mathrm{224176}. \\ $$$${Sir}\:{can}\:{this}\:{be}\:{solved}\:{without} \\ $$$${using}\:{trigonometry}?? \\ $$$${If}\:{not}\:{can}\:{you}\:{please}\:{show}\:{me} \\ $$$${the}\:{way}\:{which}\:{uses}\:{trig}.{the}\:{least}?? \\ $$ Commented by Frix last updated…
Question Number 224360 by Tawa11 last updated on 05/Sep/25 Find the equation of the circle which touches the circles x² + y² – 2x +…
Question Number 224373 by Nicholas666 last updated on 05/Sep/25 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{Show}}\:\boldsymbol{\mathrm{that}}\:; \\ $$$$\:\:\:\:\:\mathcal{I}\:=\:\underset{\:\:\mathrm{0}} {\overset{\:\:\mathrm{1}} {\int}}\underset{\:\:\mathrm{0}} {\overset{\:\mathrm{1}} {\int}}\:\:\frac{\mathrm{ln}\left(\mathrm{1}+\sqrt{{xy}}\right)\:\mathrm{ln}\left(\mathrm{1}+\:\sqrt{\frac{\mathrm{1}−{x}}{\mathrm{1}−{y}}}\right)}{\:\sqrt{\mathrm{1}−{x}}\:\:\sqrt{\mathrm{1}−{y}}\:\:\left({x}+{y}\right)}\:\:{dxdy}\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\mathcal{I}\:=\:\zeta\left(\mathrm{3}\right)−\frac{\mathrm{70}}{\mathrm{351}}−\frac{\mathrm{280}}{\mathrm{351}}\:\mathrm{ln}\:\mathrm{2}−\frac{\mathrm{40}}{\mathrm{117}}\:\mathrm{ln}^{\mathrm{2}} \:\mathrm{2}\:+\frac{\mathrm{412}}{\mathrm{351}}\:\mathrm{ln}^{\mathrm{3}} \:\mathrm{2}\:+\:\frac{\mathrm{167}}{\mathrm{2106}}\:\pi^{\mathrm{2}} \:\mathrm{ln}\:\mathrm{2}\:\:\:\:\:\:\:\:\:\:\: \\ $$$$…
Question Number 224358 by fantastic last updated on 05/Sep/25 Commented by fantastic last updated on 05/Sep/25 Answered by mr W last updated on 05/Sep/25 $${tension}\:{between}\:{m}_{\mathrm{2}}…
Question Number 224335 by kin last updated on 04/Sep/25 Answered by mingski last updated on 04/Sep/25 $$=\frac{\mathrm{2}×\mathrm{3}×\mathrm{9}}{\mathrm{3}}−\mathrm{6}×\mathrm{3}−\left(\frac{\mathrm{2}×\mathrm{2}×\mathrm{4}}{\mathrm{3}}−\mathrm{6}×\mathrm{2}\right) \\ $$$$=\mathrm{18}−\mathrm{18}−\left(\frac{\mathrm{16}}{\mathrm{3}}−\mathrm{18}\right) \\ $$$$=\frac{\mathrm{38}}{\mathrm{3}} \\ $$ Terms of…
Question Number 224342 by Rojarani last updated on 04/Sep/25 Answered by mingski last updated on 04/Sep/25 $${x}^{\mathrm{2}} −{x}−\mathrm{1000}\sqrt{\mathrm{1}+\mathrm{8000}{x}}=\mathrm{1000} \\ $$$${x}^{\mathrm{2}} −{x}=\mathrm{1000}\left(\mathrm{1}+\sqrt{\mathrm{1}+\mathrm{8000}{x}}\right) \\ $$$${x}\left({x}−\mathrm{1}\right)=\mathrm{1000}\left(\mathrm{1}+\sqrt{\mathrm{1}+\mathrm{8000}{x}}\right) \\ $$$$\mathrm{Then}\:\mathrm{guess}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x}.…
Question Number 224336 by wongb1506 last updated on 04/Sep/25 Answered by som(math1967) last updated on 04/Sep/25 $${let}\:{EC}={x},\:\angle{BEC}=\alpha \\ $$$$\therefore\angle{AED}=\mathrm{180}−\mathrm{60}−\alpha=\mathrm{120}−\alpha \\ $$$$\:\frac{\mathrm{4}}{{x}}={sin}\alpha\Rightarrow\frac{\mathrm{1}}{{x}}=\frac{\mathrm{sin}\:\alpha}{\mathrm{4}} \\ $$$$\:\:\frac{\mathrm{3}}{{x}}={sin}\left(\mathrm{120}−\alpha\right)\Rightarrow\frac{\mathrm{1}}{{x}}=\frac{{sin}\left(\mathrm{120}−\alpha\right)}{\mathrm{3}} \\ $$$$\therefore\:\frac{{sin}\alpha}{\mathrm{4}}=\frac{{sin}\left(\mathrm{120}−\alpha\right)}{\mathrm{3}}…