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Question Number 210933 by mnjuly1970 last updated on 22/Aug/24 $$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$\:\:\:\:\:\:\mathrm{I}=\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}\:} \frac{\:{sin}\left(\:\mathrm{25}{x}\:\right)}{{sinx}}\:{dx}=? \\ $$$$ \\ $$$$ \\…
Question Number 210934 by hardmath last updated on 22/Aug/24 $$\mathrm{If}\:\:\:\frac{\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{ax}\:−\:\mathrm{18}}{\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{7x}\:+\:\mathrm{2b}}\:\:=\:\:\frac{\mathrm{x}\:−\:\mathrm{c}}{\mathrm{x}\:+\:\mathrm{5}} \\ $$$$\mathrm{Find}\:\:\:\boldsymbol{\mathrm{a}}\:+\:\boldsymbol{\mathrm{b}}\:+\:\boldsymbol{\mathrm{c}}\:=\:? \\ $$ Answered by A5T last updated on 22/Aug/24 $$\left({x}+\mathrm{5}\right)\left({x}\right)+\mathrm{2}\left({x}+\mathrm{5}\right)+\mathrm{2}{b}−\mathrm{10}\Rightarrow\mathrm{2}{b}−\mathrm{10}=\mathrm{0}\Rightarrow{b}=\mathrm{5} \\…
Question Number 210918 by VICHET last updated on 22/Aug/24 Answered by Frix last updated on 22/Aug/24 $$\mathrm{Let}\:{x}={t}+\mathrm{11} \\ $$$$\underset{{t}\rightarrow\mathrm{0}^{−} } {\mathrm{lim}}\:\frac{\mid{x}\mid}{{x}}\:=\underset{{t}\rightarrow\mathrm{0}^{−} } {\mathrm{lim}}\:\frac{−{x}}{{x}}\:=−\mathrm{1} \\ $$$$\underset{{t}\rightarrow\mathrm{0}^{+}…
Question Number 210935 by mr W last updated on 22/Aug/24 $${at}\:{what}\:{times},\:{if}\:{exist},\:{are}\:{the}\: \\ $$$${angles}\:{betwen}\:{the}\:{hour}\:{hand},\:{the} \\ $$$${minute}\:{hand}\:{and}\:{the}\:{second}\:{hand} \\ $$$${of}\:{a}\:{clock}\:{exactly}\:\mathrm{120}°? \\ $$$${assume}\:{that}\:{the}\:{hands}\:{of}\:{the}\:{clock} \\ $$$${move}\:{uniformly}. \\ $$ Answered by…
Question Number 210919 by RojaTaniya last updated on 22/Aug/24 Answered by mr W last updated on 22/Aug/24 $${yes},\:{we}\:{can}\:{design}\:{such}\:{two}\:{dices}. \\ $$$${the}\:{first}\:{one}\:{is}\:{a}\:{normal}\:{die} \\ $$$${with}\:{six}\:{faces}\:{which}\:{have}\:{digit}\: \\ $$$$\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4},\mathrm{5},\mathrm{6}\:{respectively}. \\…
Question Number 210895 by RojaTaniya last updated on 21/Aug/24 Answered by Rasheed.Sindhi last updated on 21/Aug/24 $${x}−\sqrt{\frac{\mathrm{10}}{{x}}}\:=\mathrm{11}\wedge\:{x}\in\mathbb{R}\Rightarrow{x}>\mathrm{0} \\ $$$$\: \\ $$$${x}−\sqrt{\frac{\mathrm{10}{x}}{{x}^{\mathrm{2}} }}\:=\mathrm{11} \\ $$$${x}−\frac{\sqrt{\mathrm{10}{x}}}{\mid{x}\mid}=\mathrm{11} \\…
Question Number 210906 by hardmath last updated on 21/Aug/24 $$\frac{\mathrm{19x}\:−\:\mathrm{x}^{\mathrm{2}} }{\mathrm{x}\:+\:\mathrm{1}}\:\centerdot\:\left(\mathrm{x}\:+\:\frac{\mathrm{19}\:−\:\mathrm{x}}{\mathrm{x}\:+\:\mathrm{1}}\right)\:=\:\mathrm{78} \\ $$$$\mathrm{find}:\:\:\boldsymbol{\mathrm{x}}\:=\:? \\ $$ Answered by Frix last updated on 21/Aug/24 $$\mathrm{Reconstructing}\:\mathrm{your}\:\mathrm{equation}: \\ $$$${x}=\frac{{a}}{\mathrm{2}}\pm\frac{\sqrt{{a}^{\mathrm{2}}…
Question Number 210917 by depressiveshrek last updated on 22/Aug/24 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{intersected}\:\mathrm{by}\:\mathrm{three} \\ $$$$\mathrm{circles}\:\mathrm{of}\:\mathrm{radius}\:\mathrm{1},\:\mathrm{centered}\:\mathrm{at}\:\mathrm{the} \\ $$$$\mathrm{origin},\:\mathrm{at}\:\left(\mathrm{1},\:\mathrm{0}\right)\:\mathrm{and}\:\left(\mathrm{1},\:\mathrm{1}\right)\:\mathrm{respectively}. \\ $$ Answered by mr W last updated on 22/Aug/24 Commented…