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a-b-c-d-R-a-b-c-d-1-Prove-that-abc-bcd-cda-dab-1-27-176-27-abcd-

Question Number 58462 by naka3546 last updated on 23/Apr/19 $${a},\:{b},\:{c},\:{d}\:\:\in\:\:\mathbb{R}^{+} \\ $$$${a}\:+\:{b}\:+\:{c}\:+\:{d}\:\:=\:\:\mathrm{1} \\ $$$${Prove}\:\:{that}\:\:: \\ $$$${abc}\:+\:{bcd}\:+\:{cda}\:+\:{dab}\:\:\leqslant\:\:\frac{\mathrm{1}}{\mathrm{27}}\:\:+\:\:\frac{\mathrm{176}}{\mathrm{27}}\:{abcd} \\ $$ Answered by tanmay last updated on 24/Apr/19…

tan-x-39-3-cosx-

Question Number 123971 by Khalmohmmad last updated on 29/Nov/20 $$\mathrm{tan}\:{x}=−\frac{\sqrt{\mathrm{39}}}{\mathrm{3}} \\ $$$$\mathrm{cos}{x}=? \\ $$ Commented by mr W last updated on 29/Nov/20 $$\mathrm{tan}\:{x}<\mathrm{0} \\ $$$$\Rightarrow\frac{\pi}{\mathrm{2}}<{x}<\pi\:\Rightarrow\mathrm{cos}\:{x}<\mathrm{0}…

A-1-2-3-2-3-1-3-2-1-det-M-3-3-T-

Question Number 123970 by Khalmohmmad last updated on 29/Nov/20 $${A}=\begin{bmatrix}{\mathrm{1}\:\:\:\mathrm{2}\:\:\:\:\:\mathrm{3}}\\{\mathrm{2}\:\:\:\mathrm{3}\:\:\:\:\:\mathrm{1}}\\{\mathrm{3}\:\:\:\:\mathrm{2}\:\:\:\:\mathrm{1}}\end{bmatrix} \\ $$$${det}\left({M}_{\mathrm{3}×\mathrm{3}} \right)^{{T}} =? \\ $$ Commented by MJS_new last updated on 29/Nov/20 $$\mathrm{det}\:{M}^{{T}} \:=\mathrm{det}\:{M}…

A-1-2-3-2-3-1-3-2-1-det-M-3-3-

Question Number 123965 by Khalmohmmad last updated on 29/Nov/20 $${A}=\begin{bmatrix}{\mathrm{1}\:\:\:\mathrm{2}\:\:\:\:\:\mathrm{3}}\\{\mathrm{2}\:\:\:\mathrm{3}\:\:\:\:\:\mathrm{1}}\\{\mathrm{3}\:\:\:\:\mathrm{2}\:\:\:\:\mathrm{1}}\end{bmatrix} \\ $$$${det}\left({M}_{\mathrm{3}×\mathrm{3}} \right)=? \\ $$ Commented by MJS_new last updated on 29/Nov/20 $$\begin{vmatrix}{{a}}&{{b}}&{{c}}\\{{d}}&{{e}}&{{f}}\\{{g}}&{{h}}&{{i}}\end{vmatrix}={aei}+{bfg}+{cdh}−\left({afh}+{bdi}+{ceg}\right) \\ $$…