Question Number 67881 by mr W last updated on 01/Sep/19 $${find}\:{all}\:{x},{y}\:\in{R}\:{such}\:{that} \\ $$$$\left({x}+{yi}\right)^{\mathrm{2019}} ={x}−{yi} \\ $$ Answered by mind is power last updated on 01/Sep/19…
Question Number 2344 by 123456 last updated on 17/Nov/15 $${f}\left({z}\right){e}^{\mathrm{1}−{z}} ={f}\left(\mathrm{1}−{z}\right)\pi^{{z}} \mathrm{sin}\:\left(\pi{z}\right) \\ $$$${f}\left({z}\right)={z}^{\mathrm{2}} ,\Re\left({z}\right)\geqslant\mathrm{1}/\mathrm{2} \\ $$$${f}\left({z}\right)=\mathrm{0},{z}=?? \\ $$ Commented by Yozzi last updated on…
Question Number 133412 by EDWIN88 last updated on 22/Feb/21 $$\mathrm{What}\:\mathrm{are}\:\mathrm{the}\:\mathrm{last}\:\mathrm{two}\:\mathrm{digits}\:\mathrm{of}\:\mathrm{2}^{\mathrm{222}} −\mathrm{1}\:? \\ $$ Answered by liberty last updated on 22/Feb/21 $$\mathrm{2}^{\mathrm{10}} =\mathrm{1024}\equiv\mathrm{24}\:\left(\mathrm{mod}\:\mathrm{100}\right) \\ $$$$\mathrm{2}^{\mathrm{20}} \equiv\mathrm{24}^{\mathrm{2}}…
Question Number 2341 by Rasheed Soomro last updated on 17/Nov/15 $${For}\:{what}\:{conditions} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\left({i}\right)\:{x}^{{y}^{{z}} } <\left({x}^{{y}} \right)^{{z}} \:\:? \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\left({ii}\right)\:{y}^{{x}^{{z}} } <\left({x}^{{y}} \right)^{{z}} \:? \\ $$…
Question Number 2340 by Yozzi last updated on 18/Nov/15 $${Prove}\:{that},\:\forall{m}\in\mathbb{Z}^{+} , \\ $$$$\underset{{r}=\mathrm{1}} {\overset{{m}} {\prod}}\Gamma\left({x}+\frac{{r}−\mathrm{1}}{{m}}\right)={m}^{\frac{\mathrm{1}}{\mathrm{2}}−{mx}} \left(\mathrm{2}\pi\right)^{\frac{{m}−\mathrm{1}}{\mathrm{2}}} \Gamma\left({mx}\right). \\ $$$$\left\{\Gamma\left({x}\right)=\int_{\mathrm{0}} ^{\infty} {t}^{{x}−\mathrm{1}} {e}^{−{t}} {dt},\:{x}>\mathrm{0}\right\} \\ $$…
Question Number 67871 by rrebo5637@gmail.com last updated on 01/Sep/19 $$\mathrm{8}=\mathrm{4x} \\ $$$$\mathrm{x}=? \\ $$ Commented by Prithwish sen last updated on 01/Sep/19 $$\mathrm{2} \\ $$…
Question Number 2334 by Syaka last updated on 16/Nov/15 $$\int\frac{{dx}}{\left({x}^{\mathrm{2}} \:+\:\mathrm{3}{x}\:+\:\mathrm{9}\right)\sqrt{{x}^{\mathrm{2}} \:+\:\mathrm{5}{x}\:+\:\mathrm{7}}\:}\:\:=\:? \\ $$ Commented by prakash jain last updated on 16/Nov/15 $${x}^{\mathrm{2}} +\mathrm{5}{x}+\mathrm{7}=\left({x}+\frac{\mathrm{5}}{\mathrm{2}}\right)^{\mathrm{2}} +\frac{\mathrm{3}}{\mathrm{4}}…
Question Number 133400 by Engr_Jidda last updated on 21/Feb/21 $${fine}\:{the}\:{solution}\:{of}\:{the}\:{differential} \\ $$$${equation}\:{y}^{\mathrm{2}} +\mathrm{9}{y}=\mathrm{9}{sec}^{\mathrm{2}} \mathrm{3}{x},\:\mathrm{0}<{x}<\frac{\pi}{\mathrm{2}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 133403 by Engr_Jidda last updated on 21/Feb/21 $${verify}\:{that}\:\varrho^{{x}} \:{and}\:{x}\:{are}\:{the}\:{solution} \\ $$$${of}\:{the}\:{homogeneous}\:{equation}\:{corresponding} \\ $$$${to}\:\left(\mathrm{1}−{x}\right){y}^{\mathrm{2}} +{xy}^{\mathrm{1}} −{y}=\mathrm{2}\left({x}−\mathrm{1}\right)^{\mathrm{2}} \varrho^{{x}\:} ,\:\mathrm{0}<{x}<\mathrm{1} \\ $$$${and}\:{find}\:{the}\:{general}\:{solution}. \\ $$ Terms of…
Question Number 2329 by 123456 last updated on 16/Nov/15 $${a}_{{n}} =\left(−\mathrm{1}\right)^{{n}} \left(\lfloor\frac{{n}}{\mathrm{9}}\rfloor+\mathrm{1}\right) \\ $$$$\underset{{n}\geqslant\mathrm{0}} {\sum}{a}_{{n}} =? \\ $$$${b}_{{n}} =\frac{\left({a}_{{n}} −\mathrm{1}\right)\left(\mathrm{9}−{a}_{{n}} \right)}{{n}+\mathrm{1}} \\ $$$$\underset{{n}\geqslant\mathrm{0}} {\sum}{b}_{{n}} =?…