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Category: Algebra

If-x-y-and-z-are-positive-integers-then-determine-the-smallest-positive-integer-N-x-y-z-xy-yz-zx-which-is-bigger-than-2022-

Question Number 150346 by mathdanisur last updated on 11/Aug/21 $$\mathrm{If}\:\:\boldsymbol{\mathrm{x}};\boldsymbol{\mathrm{y}}\:\mathrm{and}\:\boldsymbol{\mathrm{z}}\:\mathrm{are}\:\mathrm{positive}\:\mathrm{integers},\:\mathrm{then} \\ $$$$\mathrm{determine}\:\mathrm{the}\:\mathrm{smallest}\:\mathrm{positive}\:\mathrm{integer} \\ $$$$\boldsymbol{\mathrm{N}}=\mathrm{x}+\mathrm{y}+\mathrm{z}+\mathrm{xy}+\mathrm{yz}+\mathrm{zx},\:\mathrm{which}\:\mathrm{is} \\ $$$$\mathrm{bigger}\:\mathrm{than}\:\mathrm{2022}. \\ $$ Commented by Rasheed.Sindhi last updated on 12/Aug/21…

ultimately-Q-149894-boils-down-to-finding-s-max-s-min-h-scos-pi-6-2-k-ssin-pi-6-2-r-2-

Question Number 150331 by ajfour last updated on 11/Aug/21 $${ultimately}\:\:{Q}.\mathrm{149894}\:\:{boils}\: \\ $$$${down}\:{to}\:{finding}\:{s}_{{max}} ,\:{s}_{{min}} \:\forall \\ $$$$\:\:\:\:\left\{{h}−{s}\mathrm{cos}\:\left(\theta−\frac{\pi}{\mathrm{6}}\right)\right\}^{\mathrm{2}} \\ $$$$+\left\{{k}−{s}\mathrm{sin}\:\left(\theta+\frac{\pi}{\mathrm{6}}\right)\right\}^{\mathrm{2}} ={r}^{\mathrm{2}} \\ $$$$ \\ $$ Terms of…

1-33x-48-mod-654-2-5-1000-000-x-mod-41-Find-x-

Question Number 150327 by mathdanisur last updated on 11/Aug/21 $$\left.\mathrm{1}\right)\:\mathrm{33}\boldsymbol{\mathrm{x}}\:\:\equiv\:\:\mathrm{48}\:\left(\mathrm{mod}\:\mathrm{654}\right) \\ $$$$\left.\mathrm{2}\right)\:\mathrm{5}^{\mathrm{1000}\:\mathrm{000}} \:\:\equiv\:\:\boldsymbol{\mathrm{x}}\:\left(\mathrm{mod}\:\mathrm{41}\right) \\ $$$$\mathrm{Find}\:\:\boldsymbol{\mathrm{x}}=? \\ $$ Answered by Rasheed.Sindhi last updated on 11/Aug/21 $$\left.\mathrm{1}\right)\:\mathrm{33}\boldsymbol{\mathrm{x}}\:\:\equiv\:\:\mathrm{48}\:\left(\mathrm{mod}\:\mathrm{654}\right)…

Why-arg-z-arg-z-2kpi-k-Z-Shouldn-t-it-be-always-0-

Question Number 19250 by Tinkutara last updated on 07/Aug/17 $$\mathrm{Why}\:\mathrm{arg}\left({z}\right)\:+\:\mathrm{arg}\left(\bar {{z}}\right)\:=\:\mathrm{2}{k}\pi,\:{k}\:\in\:{Z}? \\ $$$$\mathrm{Shouldn}'\mathrm{t}\:\mathrm{it}\:\mathrm{be}\:\boldsymbol{\mathrm{always}}\:\mathrm{0}? \\ $$ Commented by ajfour last updated on 07/Aug/17 $$\mathrm{yes},\:\mathrm{so}\:\mathrm{do}\:\mathrm{i}\:\mathrm{think}. \\ $$$$\mathrm{but}\:\mathrm{if}\:{z}=−\mathrm{1}\:?!…

Find-ax-5-by-5-if-the-real-numbers-a-b-x-and-y-satisf-the-equations-ax-by-3-ax-2-by-2-7-ax-3-by-3-16-ax-4-by-4-42-

Question Number 150326 by mathdanisur last updated on 11/Aug/21 $$\mathrm{Find}\:\:\boldsymbol{\mathrm{ax}}^{\mathrm{5}} +\boldsymbol{\mathrm{by}}^{\mathrm{5}} \:\:\mathrm{if}\:\mathrm{the}\:\mathrm{real}\:\mathrm{numbers} \\ $$$$\boldsymbol{\mathrm{a}},\boldsymbol{\mathrm{b}},\boldsymbol{\mathrm{x}}\:\:\mathrm{and}\:\:\boldsymbol{\mathrm{y}}\:\:\mathrm{satisf}\:\mathrm{the}\:\mathrm{equations}: \\ $$$$\mathrm{ax}\:+\:\mathrm{by}\:=\:\mathrm{3} \\ $$$$\mathrm{ax}^{\mathrm{2}} \:+\:\mathrm{by}^{\mathrm{2}} \:=\:\mathrm{7} \\ $$$$\mathrm{ax}^{\mathrm{3}} \:+\:\mathrm{by}^{\mathrm{3}} \:=\:\mathrm{16} \\…

at-what-time-is-the-short-clock-and-long-hour-hand-form-an-angle-of-180-degrees-

Question Number 84785 by john santu last updated on 16/Mar/20 $$\mathrm{at}\:\mathrm{what}\:\mathrm{time}\:\mathrm{is}\:\mathrm{the}\:\mathrm{short}\:\mathrm{clock}\: \\ $$$$\mathrm{and}\:\mathrm{long}\:\mathrm{hour}\:\mathrm{hand}\:\mathrm{form}\:\mathrm{an}\: \\ $$$$\mathrm{angle}\:\mathrm{of}\:\mathrm{180}\:\mathrm{degrees}? \\ $$ Commented by mr W last updated on 16/Mar/20…