Question Number 213485 by tri26112004 last updated on 06/Nov/24 $${prove}\:{that} \\ $$$$\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{2}} }+…+\frac{\mathrm{1}}{\mathrm{2021}^{\mathrm{2}} }<\frac{\mathrm{25}}{\mathrm{36}} \\ $$ Answered by mr W last updated on 06/Nov/24…
Question Number 213486 by a.lgnaoui last updated on 06/Nov/24 $$\:\:\boldsymbol{\mathrm{x}}^{\mathrm{5}} +\mathrm{5}\boldsymbol{\mathrm{x}}−\frac{\mathrm{6}}{\boldsymbol{\mathrm{x}}}=\mathrm{0}\:\:\:\:\:\:\boldsymbol{\mathrm{x}}? \\ $$ Answered by Frix last updated on 06/Nov/24 $${x}^{\mathrm{6}} +\mathrm{5}{x}^{\mathrm{2}} −\mathrm{6}=\mathrm{0} \\ $$$$\left({x}^{\mathrm{6}}…
Question Number 213482 by efronzo1 last updated on 06/Nov/24 Answered by A5T last updated on 06/Nov/24 $$\mathrm{3}\mid{Y}\Rightarrow\mathrm{8}+{c}+\mathrm{2}+\mathrm{3}+{d}\equiv\mathrm{0}\left({mod}\:\mathrm{3}\right)\Rightarrow{c}+{d}\equiv\mathrm{2}\left({mod}\:\mathrm{3}\right) \\ $$$$\mathrm{3}\mid{X}\Rightarrow\mathrm{9}\mid{Y}\::\: \\ $$$$\mathrm{3}+\mathrm{1}+{a}+\mathrm{5}+{b}\equiv\mathrm{0}\left({mod}\:\mathrm{3}\right)\Rightarrow\mathrm{8}+{c}+\mathrm{2}+\mathrm{3}+{d}\equiv\mathrm{0}\left({mod}\:\mathrm{9}\right) \\ $$$$\Rightarrow{a}+{b}\equiv\mathrm{0}\left({mod}\:\mathrm{3}\right)\Rightarrow{c}+{d}\equiv\mathrm{5}\left({mod}\:\mathrm{9}\right) \\ $$$$\mathrm{3}\mid{X}\Rightarrow{c}+{d}=\mathrm{5}\Rightarrow{a}+{b}=\mathrm{0},\mathrm{3},\mathrm{6},\mathrm{9}\:\wedge\:{c}+{d}=\mathrm{5}…
Question Number 213451 by issac last updated on 06/Nov/24 $$\int\:\:\frac{\mathrm{1}}{{z}^{\mathrm{6}} −\mathrm{1}}\:\mathrm{d}{z}=?? \\ $$ Answered by Frix last updated on 06/Nov/24 $$\int\frac{{dz}}{{z}^{\mathrm{6}} −\mathrm{1}}=\underset{{k}=\mathrm{1}} {\overset{\mathrm{4}} {\sum}}{I}_{{k}} \\…
Question Number 213504 by Spillover last updated on 06/Nov/24 Answered by A5T last updated on 06/Nov/24 $${psin}^{\mathrm{2}} {x}−{q}\left(\mathrm{1}−{sin}^{\mathrm{2}} {x}\right)={p}−{q} \\ $$$${psin}^{\mathrm{2}} {x}−{q}+{qsin}^{\mathrm{2}} {x}={p}−{q} \\ $$$${sin}^{\mathrm{2}}…
Question Number 213436 by mr W last updated on 05/Nov/24 Answered by A5T last updated on 05/Nov/24 Commented by mr W last updated on 05/Nov/24…
Question Number 213439 by Ari last updated on 05/Nov/24 Commented by BaliramKumar last updated on 06/Nov/24 $${l}\:{and}\:{b}\:=\:? \\ $$$$\mathrm{If}\:\mathrm{square}\:\:\:\:=\:\lceil\frac{\sqrt{\mathrm{2000}}}{\mathrm{7}}\rceil^{\mathrm{2}} =\:\mathrm{49} \\ $$$$ \\ $$ Commented…
Question Number 213423 by efronzo1 last updated on 05/Nov/24 $$\:\:\lfloor\:\frac{\mathrm{1}}{\mathrm{2}}\mathrm{x}−\mathrm{1}\rfloor\:+\:\lfloor\:\frac{\mathrm{2}}{\mathrm{2}}\mathrm{x}−\mathrm{2}\rfloor+\lfloor\frac{\mathrm{3}}{\mathrm{2}}\mathrm{x}−\mathrm{3}\rfloor+…+\lfloor\frac{\mathrm{100}}{\mathrm{2}}\mathrm{x}−\mathrm{100}\rfloor\:\leqslant\mathrm{10100} \\ $$$$\:\:\mathrm{for}\:\mathrm{x}\:\mathrm{non}\:\mathrm{negative}\:\mathrm{integers}. \\ $$$$\:\:\:\mathrm{find}\:\mathrm{the}\:\mathrm{possible}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x} \\ $$ Answered by golsendro last updated on 05/Nov/24 $$\:\:\:\underline{ }…
Question Number 213435 by mnjuly1970 last updated on 14/Nov/24 $$ \\ $$$$\:\:\:\:\:\:\:{A}\:\in\:\mathrm{M}_{\mathrm{2}×\mathrm{2}} \:\:,{and}\:,{det}\:\left({A}\right)\neq\mathrm{0}\::\:\:\:{A}^{\mathrm{3}} \:=\:{A}^{\mathrm{2}} \:+\:{A} \\ $$$$\:\:\:\:\:\:\:\:\Rightarrow\:\:{det}\:\left(\:{A}\:−\mathrm{2}{I}\:\right)=? \\ $$$$\:\:\:\:\:\: \\ $$ Terms of Service Privacy…
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