Question Number 153808 by mathdanisur last updated on 10/Sep/21 $$\mathrm{If}\:\:\mathrm{0}<\mathrm{a}\leqslant\mathrm{b}<\mathrm{1}\:\:\mathrm{then}: \\ $$$$\underset{\:\boldsymbol{\mathrm{a}}} {\overset{\:\boldsymbol{\mathrm{b}}} {\int}}\underset{\:\boldsymbol{\mathrm{a}}} {\overset{\:\boldsymbol{\mathrm{b}}} {\int}}\underset{\boldsymbol{\mathrm{a}}} {\overset{\:\boldsymbol{\mathrm{b}}} {\int}}\left(\frac{\mathrm{1}\:-\:\mathrm{xyz}}{\mathrm{1}\:+\:\mathrm{xyz}}\right)^{\mathrm{3}} \mathrm{dxdydz}\:\geqslant\:\left(\underset{\boldsymbol{\mathrm{a}}} {\overset{\:\boldsymbol{\mathrm{b}}} {\int}}\frac{\mathrm{1}\:-\:\mathrm{x}^{\mathrm{3}} }{\mathrm{1}\:+\:\mathrm{x}^{\mathrm{3}} }\:\mathrm{dx}\right)^{\mathrm{3}} \\ $$…
Question Number 22739 by Tinkutara last updated on 22/Oct/17 $${If}\:\left(\mathrm{1}\:+\:{x}\right)^{{n}} \:=\:{C}_{\mathrm{0}} \:+\:{C}_{\mathrm{1}} {x}\:+\:{C}_{\mathrm{2}} {x}^{\mathrm{2}} \:+\:{C}_{\mathrm{3}} {x}^{\mathrm{3}} \\ $$$$+\:…\:+\:{C}_{{n}} {x}^{{n}} , \\ $$$${Prove}\:{that}\:\underset{\mathrm{0}\leqslant{i}<{j}\leqslant{n}} {\Sigma\Sigma}\left({i}\:+\:{j}\right){C}_{{i}} {C}_{{j}} \:=…
Question Number 22731 by selestian last updated on 22/Oct/17 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 22726 by math solver last updated on 22/Oct/17 Commented by math solver last updated on 24/Oct/17 $$\:{solve}\:{q}.\mathrm{8}? \\ $$ Commented by math solver…
Question Number 88252 by A8;15: last updated on 09/Apr/20 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 88251 by A8;15: last updated on 09/Apr/20 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 153780 by liberty last updated on 10/Sep/21 $$\:\lfloor\:\frac{\mathrm{125}}{\mathrm{12}}\:\rfloor\:=\mathrm{10}\:{or}\:\mathrm{11}\:? \\ $$ Answered by puissant last updated on 10/Sep/21 $$\lfloor\frac{\mathrm{125}}{\mathrm{12}}\rfloor=\lfloor\mathrm{10},\mathrm{41}\rfloor=\mathrm{10}.. \\ $$ Commented by liberty…
Question Number 88239 by A8;15: last updated on 09/Apr/20 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 22701 by selestian last updated on 22/Oct/17 Answered by ajfour last updated on 22/Oct/17 $${e}^{\left(\frac{\mathrm{sin}\:^{\mathrm{2}} {x}}{\mathrm{1}−\mathrm{sin}\:^{\mathrm{2}} {x}}\right)\mathrm{ln}\:\mathrm{2}} \:={e}^{\mathrm{ln}\:\mathrm{2}^{\mathrm{tan}\:^{\mathrm{2}} {x}} } \:=\mathrm{2}^{\mathrm{tan}\:^{\mathrm{2}} {x}} \\…
Question Number 88232 by A8;15: last updated on 09/Apr/20 Terms of Service Privacy Policy Contact: info@tinkutara.com