Question Number 49851 by Saorey last updated on 11/Dec/18 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 180923 by Shrinava last updated on 19/Nov/22 Answered by aleks041103 last updated on 20/Nov/22 $${Forbenius}:\:{A},{B},{C}\in{M}_{{n}} \left(\mathbb{F}\right) \\ $$$${rk}\left({abc}\right)+{rk}\left({b}\right)\geqslant{rk}\left({ab}\right)+{rk}\left({bc}\right) \\ $$$${b}={A} \\ $$$${a}={A}^{\mathrm{3}} \\…
Question Number 180896 by mr W last updated on 18/Nov/22 $${find}\:{the}\:{maximum}\:{of}\:\underset{{i}=\mathrm{1}} {\overset{\mathrm{100}} {\sum}}\mathrm{sin}^{\mathrm{3}} \:{x}_{{i}} \\ $$$${if}\:\underset{{i}=\mathrm{1}} {\overset{\mathrm{100}} {\sum}}\mathrm{sin}\:{x}_{{i}} =\mathrm{0}. \\ $$ Commented by mr W…
Question Number 180894 by depressiveshrek last updated on 18/Nov/22 $${x}^{\mathrm{3}} +{x}=\mathrm{1} \\ $$$${x}^{\mathrm{8}} +\mathrm{3}{x}^{\mathrm{3}} =? \\ $$ Commented by Rasheed.Sindhi last updated on 19/Nov/22 $$\mathcal{T}{he}\:{solutions}/{answers}\:\left({complete}\right.…
Question Number 49823 by pieroo last updated on 11/Dec/18 $$\mathrm{Complete}\:\mathrm{the}\:\mathrm{square}\:\mathrm{in}\:\mathrm{the}\:\mathrm{expression} \\ $$$$\mathrm{y}^{\mathrm{2}} +\mathrm{8y}+\mathrm{9k}\:\mathrm{and}\:\mathrm{hence}\:\mathrm{find}\:\mathrm{the}\:\mathrm{value} \\ $$$$\mathrm{of}\:\mathrm{k}\:\mathrm{that}\:\mathrm{makes}\:\mathrm{it}\:\mathrm{a}\:\mathrm{perfect}\:\mathrm{square}. \\ $$ Answered by ajfour last updated on 11/Dec/18 $$\left({y}+\mathrm{4}\right)^{\mathrm{2}}…
Question Number 180889 by mr W last updated on 18/Nov/22 $${the}\:{average}\:{of}\:\mathrm{10}\:{numbers}\:{is}\:\mathrm{5}.\:{the} \\ $$$${sum}\:{of}\:{their}\:{squares}\:{is}\:\mathrm{5000}.\:{how}\: \\ $$$${large}\:{can}\:{the}\:{largest}\:{number}\:{among} \\ $$$${them}\:{at}\:{most}\:{be}\:{and}\:{how}\:{small}\:{can}\: \\ $$$${the}\:{smallest}\:{number}\:{among}\:{them} \\ $$$${at}\:{most}\:{be}? \\ $$ Commented by…
Question Number 180873 by Shrinava last updated on 18/Nov/22 $$\mathrm{If}\:\:\:\mathrm{a},\mathrm{b},\mathrm{c}<\mathrm{0}\:\:\:\mathrm{and}\:\:\:\mathrm{abc}\left(\mathrm{a}+\mathrm{b}+\mathrm{c}\right)=\mathrm{64} \\ $$$$\mathrm{Then}\:\mathrm{find}\:\mathrm{min}\:\mathrm{of}\:\:\:\mathrm{P}=\mathrm{2a}+\mathrm{b}+\mathrm{c} \\ $$ Commented by mr W last updated on 18/Nov/22 $${please}\:{check}\:{the}\:{question}.\:{since} \\ $$$${a},{b},{c}<\mathrm{0},\:{P}\:{has}\:{maximum},\:{not}\:{min}.…
Question Number 115333 by zakirullah last updated on 25/Sep/20 Commented by zakirullah last updated on 25/Sep/20 $${solve}\:{only}\:{Q}\left(\mathrm{5},\mathrm{6}\right) \\ $$ Commented by bemath last updated on…
Question Number 115325 by zakirullah last updated on 25/Sep/20 Commented by mohammad17 last updated on 25/Sep/20 $$\left.{Q}\mathrm{5}/{i}\right) \\ $$$$ \\ $$$${z}^{\mathrm{2}} +{z}+\mathrm{3}=\mathrm{0}\Rightarrow{z}=\frac{−{b}\pm\sqrt{{b}^{\mathrm{2}} −\mathrm{4}{ac}}}{\mathrm{2}{a}}\Rightarrow{z}=\frac{−\mathrm{1}\pm{i}\sqrt{\mathrm{11}}}{\mathrm{2}} \\ $$$$\therefore{z}=−\frac{\mathrm{1}}{\mathrm{2}}−\frac{\sqrt{\mathrm{11}}}{\mathrm{2}}{i}\:\:,\:{z}=−\frac{\mathrm{1}}{\mathrm{2}}+\frac{\sqrt{\mathrm{11}}}{\mathrm{2}}{i}…
Question Number 180856 by Shrinava last updated on 18/Nov/22 $$\mathrm{find}\:\mathrm{all}\:\mathrm{values}\:\mathrm{of}\:\:\mathrm{m}\in\mathbb{R}\:\:\mathrm{such}\:\mathrm{that}\:\mathrm{the}\:\mathrm{equation}: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\boldsymbol{\mathrm{x}}} \:\frac{\mathrm{arctan}\boldsymbol{\mathrm{y}}}{\mathrm{y}}\:\mathrm{dy}\:=\:\mathrm{mx} \\ $$$$\mathrm{has}\:\mathrm{two}\:\mathrm{real}\:\mathrm{roots}:\:\:\:\mathrm{x}_{\mathrm{1}} \in\left(−\infty;\mathrm{0}\right)\:,\:\mathrm{x}_{\mathrm{2}} \in\left(\mathrm{0};\infty\right) \\ $$ Answered by mr W last…