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Question Number 84792 by M±th+et£s last updated on 16/Mar/20 $${a},{b},{c}\geqslant\mathrm{0} \\ $$$${a}+{b}+{c}=\mathrm{3} \\ $$$${show}\:{that} \\ $$$$\sqrt[{\mathrm{3}}]{{a}}\:+\sqrt[{\mathrm{3}}]{{b}}\:+\sqrt[{\mathrm{3}}]{{c}}\geqslant{ab}+{bc}+{ca} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
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…
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 $$\left.\mathrm{1}\right)\:\mathrm{33}\boldsymbol{\mathrm{x}}\:\:\equiv\:\:\mathrm{48}\:\left(\mathrm{mod}\:\mathrm{654}\right)…
Question Number 19250 by Tinkutara last updated on 07/Aug/17 $$\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 $$\mathrm{yes},\:\mathrm{so}\:\mathrm{do}\:\mathrm{i}\:\mathrm{think}. \\ $$$$\mathrm{but}\:\mathrm{if}\:{z}=−\mathrm{1}\:?!…
Question Number 150326 by mathdanisur last updated on 11/Aug/21 $$\mathrm{Find}\:\:\boldsymbol{\mathrm{ax}}^{\mathrm{5}} +\boldsymbol{\mathrm{by}}^{\mathrm{5}} \:\:\mathrm{if}\:\mathrm{the}\:\mathrm{real}\:\mathrm{numbers} \\ $$$$\boldsymbol{\mathrm{a}},\boldsymbol{\mathrm{b}},\boldsymbol{\mathrm{x}}\:\:\mathrm{and}\:\:\boldsymbol{\mathrm{y}}\:\:\mathrm{satisf}\:\mathrm{the}\:\mathrm{equations}: \\ $$$$\mathrm{ax}\:+\:\mathrm{by}\:=\:\mathrm{3} \\ $$$$\mathrm{ax}^{\mathrm{2}} \:+\:\mathrm{by}^{\mathrm{2}} \:=\:\mathrm{7} \\ $$$$\mathrm{ax}^{\mathrm{3}} \:+\:\mathrm{by}^{\mathrm{3}} \:=\:\mathrm{16} \\…
Question Number 84785 by john santu last updated on 16/Mar/20 $$\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…
Question Number 19247 by 99 last updated on 07/Aug/17 Commented by NEC last updated on 08/Aug/17 $${please}\:{type}\:{it}\:{so}\:{we}\:{can}\:{see}\:{it} \\ $$$${clearly}. \\ $$$$ \\ $$ Commented by…
Question Number 84782 by mr W last updated on 16/Mar/20 $${Find}\:{the}\:{last}\:{three}\:{digits}\:{of}\:\mathrm{2019}^{\mathrm{2019}} . \\ $$ Commented by jagoll last updated on 16/Mar/20 $$\mathrm{19}^{\mathrm{2019}} \:=\:\left(\mathrm{18}+\mathrm{1}\right)^{\mathrm{2019}} \\ $$$$=\:\underset{\mathrm{i}=\mathrm{1}}…
Question Number 19245 by Tinkutara last updated on 07/Aug/17 $$\mathrm{Let}\:{f}\left({x}\right)\:\mathrm{be}\:\mathrm{a}\:\mathrm{quadratic}\:\mathrm{polynomial} \\ $$$$\mathrm{with}\:\mathrm{integer}\:\mathrm{coefficients}\:\mathrm{such}\:\mathrm{that}\:{f}\left(\mathrm{0}\right) \\ $$$$\mathrm{and}\:{f}\left(\mathrm{1}\right)\:\mathrm{are}\:\mathrm{odd}\:\mathrm{integers}.\:\mathrm{Prove}\:\mathrm{that} \\ $$$$\mathrm{the}\:\mathrm{equation}\:{f}\left({x}\right)\:=\:\mathrm{0}\:\mathrm{does}\:\mathrm{not}\:\mathrm{have}\:\mathrm{an} \\ $$$$\mathrm{integer}\:\mathrm{solution}. \\ $$ Commented by RasheedSindhi last updated…