Question Number 154649 by mathdanisur last updated on 20/Sep/21 $$\mathrm{if}\:\:\mathrm{n}\:\in\:\mathbb{N}^{>\mathrm{2}} \:\:\mathrm{prove}\:\mathrm{that} \\ $$$$\left[\left(\sqrt[{\mathrm{3}}]{\mathrm{n}}\:+\:\sqrt[{\mathrm{3}}]{\mathrm{n}\:+\:\mathrm{2}}\:\right)^{\mathrm{3}} \right]\:+\:\mathrm{1}\:=\:\mathrm{0}\:\left(\mathrm{mod}\:\mathrm{8}\right) \\ $$ Commented by MJS_new last updated on 20/Sep/21 $$\mathrm{just}\:\mathrm{a}\:\mathrm{try} \\…
Question Number 154651 by mathdanisur last updated on 20/Sep/21 $$\mathrm{let}\:\mathrm{be}\:\:\boldsymbol{\mathrm{A}}\:=\:\begin{pmatrix}{\mathrm{1}}&{\mathrm{1}}\\{\mathrm{0}}&{\mathrm{1}}\end{pmatrix}\:\:;\:\:\boldsymbol{\mathrm{B}}\:=\:\begin{pmatrix}{\mathrm{1}}&{\mathrm{0}}\\{\mathrm{1}}&{\mathrm{1}}\end{pmatrix} \\ $$$$\mathrm{find}\:\:\boldsymbol{\Omega}\:=\:\mathrm{e}^{\boldsymbol{\mathrm{A}}} \:\centerdot\:\left(\mathrm{e}^{\boldsymbol{\mathrm{B}}} \right)^{−\mathrm{1}} \\ $$$$\left(\mathrm{e}^{\boldsymbol{\mathrm{A}}} \:-\:\mathrm{exponential}\:\mathrm{matrix}\right) \\ $$ Answered by TheHoneyCat last updated on…
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Question Number 154647 by mathdanisur last updated on 20/Sep/21 $$\mathrm{f}\::\:\mathrm{Q}\:\rightarrow\:\mathrm{Q} \\ $$$$\mathrm{f}\left(\mathrm{x}\:+\:\mathrm{f}\left(\mathrm{y}\right)\right)\:=\:\mathrm{y}\:+\:\mathrm{f}\left(\mathrm{x}\right) \\ $$$$\forall\:\mathrm{x};\mathrm{y}\:\in\:\mathrm{Q} \\ $$ Answered by TheHoneyCat last updated on 20/Sep/21 $$\mathrm{I}\:\mathrm{demote}\:\mathrm{by}\:{f}^{{n}} \::\:{f}\circ…\circ{f}\:{n}\:\mathrm{times}…
Question Number 23566 by NECx last updated on 01/Nov/17 $$\left(\frac{{a}}{{b}}\right)^{\mathrm{log}\:{c}} .\left(\frac{{b}}{{c}}\right)^{\mathrm{log}\:{a}} .\left(\frac{{c}}{{a}}\right)^{\mathrm{log}\:{b}} =\mathrm{1}. \\ $$$$ \\ $$$${make}\:\frac{{logc}}{{c}}\:{the}\:{subject}\:{of}\:{formula} \\ $$ Commented by NECx last updated on…
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Question Number 89098 by askask last updated on 15/Apr/20 $${x}=^{\:\:{c}−\mathrm{1}} \sqrt{\frac{{ay}−{bz}}{{cdy}}} \\ $$$$ \\ $$$$\mathrm{If}\:{a}\:\mathrm{increases},\:\mathrm{what}\:\mathrm{happens}\:\mathrm{to}\:{x}? \\ $$$$\mathrm{Explain}\:\mathrm{your}\:\mathrm{answer}. \\ $$ Terms of Service Privacy Policy Contact:…
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Question Number 89086 by M±th+et£s last updated on 15/Apr/20 $${show}\:{that} \\ $$$$\sqrt[{\mathrm{3}}]{\frac{\mathrm{2}}{\mathrm{3}}−\frac{\mathrm{5}\sqrt{\mathrm{33}}}{\mathrm{18}}}+\sqrt[{\mathrm{3}}]{\frac{\mathrm{2}}{\mathrm{3}}+\frac{\mathrm{5}\sqrt{\mathrm{33}}}{\mathrm{18}}}=\mathrm{1} \\ $$ Commented by MJS last updated on 15/Apr/20 $$\mathrm{it}'\mathrm{s}\:\mathrm{wrong}. \\ $$ Terms…
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