Question Number 207985 by efronzo1 last updated on 02/Jun/24 Answered by mr W last updated on 02/Jun/24 $${say}\:{AC}={s}={AB}={CB} \\ $$$${AP}^{\mathrm{2}} ={s}×{AM}\:\Rightarrow{AP}=\sqrt{{s}×{AM}} \\ $$$${CP}^{\mathrm{2}} ={s}×{CN}\:\Rightarrow{CP}=\sqrt{{s}×{CN}} \\…
Question Number 207986 by Thomaseinstein last updated on 02/Jun/24 $$\left({x}−\mathrm{3}\right)^{\sqrt{{x}−\mathrm{3}\:}} \:\:=\:\mathrm{3} \\ $$ Answered by Frix last updated on 02/Jun/24 $${x}−\mathrm{3}>\mathrm{0} \\ $$$$\sqrt{{x}−\mathrm{3}}\:\mathrm{ln}\:\left({x}−\mathrm{3}\right)\:=\mathrm{3} \\ $$$${x}=\mathrm{3}+\mathrm{e}^{\mathrm{2}{t}}…
Question Number 208011 by necx122 last updated on 02/Jun/24 Commented by necx122 last updated on 02/Jun/24 $${If}\:{the}\:{ratio}\:{of}\:<{ARS}\::\:<{BRT}\:=\:\mathrm{9}:\mathrm{4}, \\ $$$${find}\:{the}\:{ratio}\:{of}\:{area}\:{ABC}\::\:{area}\:{ARS} \\ $$ Commented by A5T last…
Question Number 208037 by hardmath last updated on 02/Jun/24 $$\mathrm{Find}:\:\:\:\mathrm{2}\:\mathrm{log}_{\sqrt{\mathrm{5}}} \:\:\mathrm{sin}\:\frac{\pi}{\mathrm{7}}\:\centerdot\:\mathrm{log}_{\sqrt{\boldsymbol{\mathrm{sin}}\:\frac{\boldsymbol{\pi}}{\mathrm{7}}}} \:\:\mathrm{5}\:\:=\:\:? \\ $$ Answered by mr W last updated on 02/Jun/24 $$=\mathrm{2}×\frac{\mathrm{log}\:\left(\mathrm{sin}\:\frac{\pi}{\mathrm{7}}\right)}{\frac{\mathrm{log}\:\mathrm{5}}{\mathrm{2}}}×\frac{\mathrm{log}\:\mathrm{5}}{\frac{\mathrm{log}\:\left(\mathrm{sin}\:\frac{\pi}{\mathrm{7}}\right)}{\mathrm{2}}} \\ $$$$=\mathrm{8}×\frac{\cancel{\mathrm{log}\:\left(\mathrm{sin}\:\frac{\pi}{\mathrm{7}}\right)}}{\cancel{\mathrm{log}\:\mathrm{5}}}×\frac{\cancel{\mathrm{log}\:\mathrm{5}}}{\cancel{\mathrm{log}\:\left(\mathrm{sin}\:\frac{\pi}{\mathrm{2}}\right)}}…
Question Number 208034 by ali009 last updated on 02/Jun/24 Commented by ali009 last updated on 02/Jun/24 $${how}\:{that}\:{can}\:{be}\:{proved}? \\ $$ Answered by Frix last updated on…
Question Number 208003 by efronzo1 last updated on 02/Jun/24 Answered by A5T last updated on 02/Jun/24 Commented by A5T last updated on 02/Jun/24 $${PM}=\frac{\mathrm{18}}{{s}};{Let}\:{line}\:{through}\:{Q}\:{parallel}\:{to}\:{KN}\:{meet} \\…
Question Number 207980 by mnjuly1970 last updated on 01/Jun/24 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:{In}\:\:\:{A}\overset{\Delta} {{B}C}\::\:\:{B}=\:\mathrm{90}^{\:\mathrm{o}} \: \\ $$$$\:\mathrm{BB}'\:\:\bot\:\mathrm{CC}'\:\left(\:\mathrm{BB}'\:{and}\:\mathrm{CC}'\:{are}\:{medians}\right) \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\Rightarrow\:\:\:\:\frac{\boldsymbol{{m}}_{\boldsymbol{{c}}} }{\boldsymbol{{m}}_{\boldsymbol{{a}}} \:}\:=\:? \\ $$$$\boldsymbol{{note}}:\:\:\mid\:\mathrm{CC}'\:\mid\:=\:\boldsymbol{{m}}_{\boldsymbol{{c}}} \:\:,\:\mid\mathrm{AA}'\mid=\:\boldsymbol{{m}}_{\boldsymbol{{a}}}…
Question Number 207979 by Tawa11 last updated on 01/Jun/24 generate nth term for the sequence: 1, 1, 1, 2, 3, 5, 9, 18, 35, 75…
Question Number 207963 by efronzo1 last updated on 01/Jun/24 $$\:\:\:\underline{\underbrace{\lessdot}} \\ $$ Commented by Frix last updated on 01/Jun/24 $$\mathrm{You}\:\mathrm{can}\:\mathrm{only}\:\mathrm{approximate}.\:\mathrm{I}\:\mathrm{get} \\ $$$${x}\approx\mathrm{1}.\mathrm{31430946414} \\ $$ Terms…
Question Number 207954 by solihin last updated on 01/Jun/24 $$\:\underline{\boldsymbol{{x}}} \\ $$ Commented by MathematicalUser2357 last updated on 02/Jun/24 $${I}\:{see}\:\underline{\boldsymbol{{x}}}\:{in}\:{tinku}\:{tara} \\ $$ Answered by AliJumaa…