Question Number 212723 by ajfour last updated on 22/Oct/24 Commented by ajfour last updated on 22/Oct/24 $${Find}\:\:{R}_{{min}} \\ $$ Answered by mr W last updated…
Question Number 212716 by MrGaster last updated on 22/Oct/24 $$ \\ $$$$\:\:\:\:\:\:\:\mathrm{cos}\frac{\pi}{\mathrm{7}}+\mathrm{cos}\frac{\mathrm{3}\pi}{\mathrm{7}}+\mathrm{cos}\frac{\mathrm{5}\pi}{\mathrm{7}}=? \\ $$ Answered by golsendro last updated on 22/Oct/24 Terms of Service Privacy…
Question Number 212719 by Spillover last updated on 22/Oct/24 Answered by A5T last updated on 22/Oct/24 Commented by A5T last updated on 22/Oct/24 $${a}=\mathrm{2}\left(\frac{\pi}{\mathrm{6}}−\frac{{sin}\mathrm{60}°}{\mathrm{2}}\right)=\mathrm{2}\left(\frac{\pi}{\mathrm{6}}−\frac{\sqrt{\mathrm{3}}}{\mathrm{4}}\right)=\frac{\pi}{\mathrm{3}}−\frac{\sqrt{\mathrm{3}}}{\mathrm{2}} \\…
Question Number 212745 by RoseAli last updated on 22/Oct/24 Answered by mehdee7396 last updated on 22/Oct/24 $${lim}_{{x}\rightarrow\mathrm{0}} \left(\frac{\mathrm{1}+{tanx}}{\mathrm{1}−{tanx}}−\mathrm{1}\right)×\frac{\mathrm{1}}{{sinx}} \\ $$$$={lim}_{{x}\rightarrow\mathrm{0}} \left(\frac{\mathrm{2}{tanx}}{\mathrm{1}−{tanx}}\right)×\frac{\mathrm{1}}{{sinx}} \\ $$$$={lim}_{{x}\rightarrow\mathrm{0}} \left(\frac{\mathrm{2}}{\mathrm{1}−{tanx}}\right)×\frac{\mathrm{1}}{{cosx}}=\mathrm{2} \\…
Question Number 212741 by mathocean1 last updated on 22/Oct/24 $${a},\:{b},{c}\:\in\:\mathbb{N}^{\ast} \\ $$$$ \\ $$$${Show}\:{that}\:{ab}<{c}\:\Rightarrow\:{a}+{b}\leqslant{c} \\ $$$$ \\ $$ Answered by A5T last updated on 22/Oct/24…
Question Number 212736 by RojaTaniya last updated on 22/Oct/24 Answered by efronzo1 last updated on 22/Oct/24 $$\:\:\:\:\frac{\mathrm{x}}{\mathrm{4}}\:=\:\frac{\mathrm{9}}{\mathrm{15}}\:\Rightarrow\mathrm{x}=\frac{\mathrm{12}}{\mathrm{5}} \\ $$$$\:\:\:\:\frac{\mathrm{y}}{\mathrm{5}}=\:\frac{\mathrm{9}}{\mathrm{15}}\Rightarrow\mathrm{y}=\:\mathrm{3} \\ $$$$\:\:\:\:\:\frac{\mathrm{z}}{\mathrm{6}}=\:\frac{\mathrm{9}}{\mathrm{15}}\:\Rightarrow\mathrm{z}=\frac{\mathrm{18}}{\mathrm{5}} \\ $$ Commented by…
Question Number 212686 by mr W last updated on 21/Oct/24 $${in}\:{how}\:{many}\:{ways}\:{can}\:{a}\:{teacher} \\ $$$${divide}\:{his}\:\mathrm{10}\:{studens}\:{into}\:\mathrm{4}\:{groups} \\ $$$${such}\:{that}\:{each}\:{group}\:{has}\:{at}\:{least}\:\mathrm{2}\: \\ $$$${students}? \\ $$ Commented by Spillover last updated on…
Question Number 212714 by Mingma last updated on 21/Oct/24 Answered by mr W last updated on 22/Oct/24 Commented by mr W last updated on 22/Oct/24…
Question Number 212711 by RojaTaniya last updated on 21/Oct/24 $$\:{f}\left({x}\right)=\frac{\mathrm{1}}{\mathrm{1}−{x}} \\ $$$$\:{y}={f}\left({x}\right),\:{z}={f}\left({y}\right),\:{f}\left({z}\right)=? \\ $$ Answered by MATHEMATICSAM last updated on 21/Oct/24 $${y}\:=\:{f}\left({x}\right)\:=\:\frac{\mathrm{1}}{\mathrm{1}\:−\:{x}} \\ $$$${f}\left({y}\right)\:=\:{f}\left(\frac{\mathrm{1}}{\mathrm{1}\:−\:{x}}\right)\:=\:\frac{\mathrm{1}}{\mathrm{1}\:−\:\frac{\mathrm{1}}{\mathrm{1}\:−\:{x}}}\:=\:\frac{\mathrm{1}\:−\:{x}}{−\:{x}}\:=\:\frac{{x}\:−\:\mathrm{1}}{{x}} \\…
Question Number 212673 by golsendro last updated on 21/Oct/24 $$\:\:\:\: \\ $$ Answered by Frix last updated on 21/Oct/24 $$\sqrt{\mathrm{2}{x}+\mathrm{3}}={x}^{\mathrm{2}} −{x}−\mathrm{3} \\ $$$$\mathrm{Squaring}\:\&\:\mathrm{transforming} \\ $$$$\:\:\:\:\:\left[\mathrm{introduces}\:\mathrm{false}\:\mathrm{solutions}!\right]…