Question Number 4234 by Filup last updated on 04/Jan/16 $${n},\:{m}\in\mathbb{Z} \\ $$$${n}!={n}\left({n}−\mathrm{1}\right)\left({n}−\mathrm{2}\right)… \\ $$$$ \\ $$$$\mathrm{if}\:{n}!={m}\:\mathrm{where}\:\mathrm{we}\:\mathrm{know}\:\mathrm{the}\:\mathrm{value} \\ $$$${m}\:\mathrm{but}\:\mathrm{not}\:{n},\:\mathrm{can}\:\mathrm{we}\:\mathrm{solve}\:\mathrm{for}\:{n}? \\ $$ Commented by prakash jain last…
Question Number 135300 by bobhans last updated on 12/Mar/21 $$\left(\sqrt{\mathrm{2}}\:+\sqrt{\mathrm{3}}\:+\mathrm{1}\right)\left(\sqrt{\mathrm{2}}\:−\sqrt{\mathrm{3}}\:+\mathrm{1}\right)\left(\sqrt{\mathrm{2}}\:+\sqrt{\mathrm{3}}−\mathrm{1}\right)\left(\sqrt{\mathrm{2}}−\sqrt{\mathrm{3}}−\mathrm{1}\right)=? \\ $$ Answered by Olaf last updated on 12/Mar/21 $$\left(\sqrt{\mathrm{2}}+\sqrt{\mathrm{3}}+\mathrm{1}\right)\left(\sqrt{\mathrm{2}}−\sqrt{\mathrm{3}}−\mathrm{1}\right)\:=\:\mathrm{2}−\left(\sqrt{\mathrm{3}}+\mathrm{1}\right)^{\mathrm{2}} \\ $$$$=\:−\mathrm{2}−\mathrm{2}\sqrt{\mathrm{3}}\:=\:−\mathrm{2}\left(\mathrm{1}+\sqrt{\mathrm{3}}\right) \\ $$$$\left(\sqrt{\mathrm{2}}+\sqrt{\mathrm{3}}−\mathrm{1}\right)\left(\sqrt{\mathrm{2}}−\sqrt{\mathrm{3}}+\mathrm{1}\right)\:=\:\mathrm{2}−\left(\sqrt{\mathrm{3}}−\mathrm{1}\right)^{\mathrm{2}} \\…
Question Number 4232 by Yozzii last updated on 03/Jan/16 Commented by Yozzii last updated on 04/Jan/16 $${I}'{m}\:{experiencing}\:{difficulty}\: \\ $$$${to}\:{solve}\:{the}\:\mathrm{2}{nd}\:{part}\:{without}\:{use}\:{of}\:{a}\:{theorem} \\ $$$${I}\:{posted}\:{sometime}\:{ago},\:{and}\: \\ $$$${generating}\:{functions}. \\ $$…
Question Number 135298 by Ahmed1hamouda last updated on 12/Mar/21 Answered by mr W last updated on 12/Mar/21 $$\mathrm{1} \\ $$$${z}={x}+{yi} \\ $$$$\frac{\mathrm{1}}{{z}}=\frac{\mathrm{1}}{{x}+{yi}}=\frac{{x}−{yi}}{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} } \\…
Question Number 135285 by mnjuly1970 last updated on 11/Mar/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:{pre}−{calculus} \\ $$$$\:\:{if}\:\:\:\:\:\:\:{log}_{\mathrm{48}} ^{\mathrm{72}} +{log}_{\mathrm{54}} ^{\mathrm{12}} \:={k}\: \\ $$$$\:\:\:\:\:\:{then}\:\:{log}_{\:\mathrm{12}} ^{\:\mathrm{27}} \:\:=??? \\ $$$$\:\:\:\:\:\:\:\: \\ $$ Answered…
Question Number 69738 by Therealsincro last updated on 27/Sep/19 $${Sarah}\:{dances}\:{everyday}\:{of}\:{the}\:{week}, \\ $$$${including}\:{saturdays}\:{and}\:{sundays}. \\ $$$${In}\:{november}\:\mathrm{2018},\:{Sarah}\:{had}\:{to}\:{miss} \\ $$$${a}\:{few}\:{days}.\:{To}\:{control}\:{her}\:{absences} \\ $$$${she}\:{marks}\:{the}\:{day}\:{she}\:{missed}\:{class} \\ $$$${with}\:{a}\:\boldsymbol{{x}}\:{on}\:{the}\:{calendar}. \\ $$$${She}\:{marked}\:{the}\:\mathrm{5}{th},\:\mathrm{21}{st}\:{and}\:\mathrm{27}{th} \\ $$$${of}\:{november}. \\…
Question Number 69741 by ajfour last updated on 27/Sep/19 Commented by mr W last updated on 27/Sep/19 Commented by mr W last updated on 27/Sep/19…
Question Number 4176 by Yozzii last updated on 31/Dec/15 Commented by Yozzii last updated on 31/Dec/15 $${If}\:{it}'{s}\:{hard}\:{to}\:{read},\:{the}\:{info} \\ $$$${reads}\:{x}\geqslant{b}>\mathrm{0}. \\ $$ Commented by prakash jain…
Question Number 135230 by benjo_mathlover last updated on 11/Mar/21 $${A}\:{hockey}\:{team}\:{plays}\:{in}\:{an}\:{arena}\:{that} \\ $$$${has}\:{a}\:{seating}\:{capacity}\:{of}\:\mathrm{15},\mathrm{000} \\ $$$${spectators}.\:{With}\:{the}\:{ticket}\:{price} \\ $$$${seat}\:{at}\:\$\mathrm{14},\:{average}\:{attendance} \\ $$$${at}\:{recent}\:{games}\:{has}\:{been}\:\mathrm{9500}. \\ $$$${A}\:{market}\:{survey}\:{indicates}\:{that} \\ $$$${for}\:{each}\:{dollar}\:{the}\:{ticket}\:{price} \\ $$$${is}\:{lowered}\:,{the}\:{average}\:{attendance} \\…
Question Number 69681 by ajfour last updated on 26/Sep/19 Commented by ajfour last updated on 26/Sep/19 $${Q}.\mathrm{69496}\:\:\:\left({A}\:{try}..\right) \\ $$ Commented by ajfour last updated on…