Question Number 212514 by ajfour last updated on 16/Oct/24 Answered by mr W last updated on 18/Oct/24 Commented by mr W last updated on 17/Oct/24…
Question Number 212515 by efronzo1 last updated on 16/Oct/24 $$\:\:\mathrm{The}\:\mathrm{numbers}\:\mathrm{of}\:\mathrm{pairs}\:\mathrm{of}\:\mathrm{natural}\: \\ $$$$\:\:\:\mathrm{numbers}\:\left(\mathrm{x},\mathrm{y}\right)\:\mathrm{with}\:\mathrm{x},\mathrm{y}\:\leqslant\:\mathrm{33}\:\mathrm{that}\: \\ $$$$\:\:\:\mathrm{satisfy}\:\mathrm{5}\:\mid\:\mathrm{3}^{\mathrm{x}^{\mathrm{y}−\mathrm{1}} } \:+\:\mathrm{2}^{\mathrm{y}^{\mathrm{2x}} } \:\mathrm{is}\:…\: \\ $$$$\:\:\left(\mathrm{A}\right)\:\mathrm{295}\:\:\:\:\left(\mathrm{B}\right)\:\mathrm{296}\:\:\:\:\:\:\:\left(\mathrm{C}\right)\:\mathrm{297}\:\:\:\:\:\:\left(\mathrm{D}\right)\:\mathrm{298}\:\:\:\left(\mathrm{E}\right)\:\mathrm{299} \\ $$ Commented by A5T…
Question Number 212508 by hardmath last updated on 15/Oct/24 Commented by hardmath last updated on 15/Oct/24 $$\mathrm{Find}: \\ $$$$ \\ $$Find the modulus of the…
Question Number 212506 by hardmath last updated on 15/Oct/24 $$\mathrm{Find}:\:\:\:\:\:\:\sqrt[{\mathrm{4}}]{−\:\frac{\mathrm{18}}{\mathrm{1}\:+\:\boldsymbol{\mathrm{i}}\:\sqrt{\mathrm{3}}}} \\ $$ Answered by Frix last updated on 15/Oct/24 $$−\frac{\mathrm{18}}{\mathrm{1}+\sqrt{\mathrm{3}}\mathrm{i}}=−\frac{\mathrm{9}}{\mathrm{2}}+\frac{\mathrm{9}\sqrt{\mathrm{3}}}{\mathrm{2}}\mathrm{i}=\mathrm{9e}^{\mathrm{i}\frac{\mathrm{2}\pi}{\mathrm{3}}} \\ $$$$\left(\mathrm{9e}^{\mathrm{i}\frac{\mathrm{2}\pi}{\mathrm{3}}} \right)^{\frac{\mathrm{1}}{\mathrm{4}}} =\sqrt{\mathrm{3}}\mathrm{e}^{\mathrm{i}\frac{\pi}{\mathrm{6}}} =\frac{\mathrm{3}}{\mathrm{2}}+\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}\mathrm{i}…
Question Number 212500 by ajfour last updated on 15/Oct/24 $${Can}\:{we}\:{exactly}\:{find}\:{r}_{{max}} \left({a}\right). \\ $$$${r}^{\mathrm{2}} +\frac{\mathrm{2}{rt}}{{a}}\left({t}+\mathrm{2}\sqrt{{ar}}\right)={t}^{\mathrm{2}} \:\:\:\:\forall\:{t}\:{is}\:{parameter} \\ $$ Answered by mr W last updated on 15/Oct/24…
Question Number 212503 by peter frank last updated on 15/Oct/24 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 212496 by efronzo1 last updated on 15/Oct/24 $$\:\mathrm{If}\:\mathrm{1}.\mathrm{1}!+\mathrm{3}.\mathrm{2}!+…+\left(\mathrm{2n}−\mathrm{1}\right).\mathrm{n}!\: \\ $$$$\:=\:\mathrm{a}.\left(\mathrm{n}+\mathrm{1}\right)!+\mathrm{b}\left(\mathrm{1}!+\mathrm{2}!+…+\left(\mathrm{n}+\mathrm{1}\right)!\right)+\mathrm{c}\: \\ $$$$\:\mathrm{for}\:\mathrm{a},\mathrm{b},\mathrm{c}\:\mathrm{integers}\:\mathrm{number} \\ $$$$\:\mathrm{find}\:\mathrm{2a}−\mathrm{b}+\mathrm{3c}\: \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 212497 by MrGaster last updated on 15/Oct/24 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 212498 by ChantalYah last updated on 15/Oct/24 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 212499 by efronzo1 last updated on 15/Oct/24 $$\:\:\mathrm{Given}\:\mathrm{a},\mathrm{b},\mathrm{c}\:\mathrm{and}\:\mathrm{d}\:\mathrm{are}\:\mathrm{reals}\: \\ $$$$\:\mathrm{numbers}\:\mathrm{such}\:\mathrm{that}\: \\ $$$$\:\:\:\:\begin{cases}{\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} =\mathrm{10}}\\{\mathrm{c}^{\mathrm{2}} +\mathrm{d}^{\mathrm{2}} =\mathrm{10}\:}\\{\mathrm{ab}+\mathrm{cd}=\mathrm{0}}\end{cases} \\ $$$$\:\:\mathrm{Find}\:\mathrm{ac}\:+\:\mathrm{bd}. \\ $$ Answered by ajfour…