Question Number 76061 by tw000001 last updated on 23/Dec/19 $$\mathrm{What}'\mathrm{s}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of} \\ $$$$\frac{\mathrm{13}{a}+\mathrm{13}{b}+\mathrm{2}{c}}{\mathrm{2}{a}+\mathrm{2}{b}}+\frac{\mathrm{24}{a}−{b}+\mathrm{13}{c}}{\mathrm{2}{b}+\mathrm{2}{c}}+\frac{−{a}+\mathrm{24}{b}+\mathrm{13}{c}}{\mathrm{2}{a}+\mathrm{2}{c}}? \\ $$$$\left({a},{b},{c}\:\mathrm{are}\:\mathrm{positive}\:\mathrm{numbers}.\right) \\ $$$$\mathrm{I}\:\mathrm{think}\:\mathrm{nobody}\:\mathrm{can}\:\mathrm{solve}\:\mathrm{this}. \\ $$ Answered by MJS last updated on 23/Dec/19…
Question Number 76048 by peter frank last updated on 22/Dec/19 $$\int{e}^{{x}^{\mathrm{2}} } {dx} \\ $$ Answered by Crabby89p13 last updated on 23/Dec/19 $${Actually}\:{there}\:{is}\:{no}\:{elementary} \\ $$$${function}\:{that}\:{describes}\:{the}\:{integral}\:{of}…
Question Number 10515 by ABD last updated on 15/Feb/17 $$\mathrm{2}^{{a}} =\mathrm{6}^{\frac{{x}}{{x}+{y}}\:} \:\:\:.\mathrm{3}^{{a}} \:=\mathrm{6}^{\frac{{y}}{{x}+{y}}} \:\Rightarrow\mathrm{8}^{\frac{{y}}{{x}}+\mathrm{1}} =? \\ $$ Answered by mrW1 last updated on 15/Feb/17 $$\mathrm{2}^{{a}}…
Question Number 141578 by Khalmohmmad last updated on 20/May/21 $$\int\sqrt{\mathrm{1}+\frac{\mathrm{1}}{{x}}}{dx}=? \\ $$ Answered by bramlexs22 last updated on 20/May/21 $$\:\int\:\frac{\sqrt{\mathrm{1}+{x}}}{\:\sqrt{{x}}}\:{dx}\: \\ $$$$\:{let}\:\sqrt{\mathrm{1}+{x}}\:=\:{u}\:\Rightarrow{x}={u}^{\mathrm{2}} −\mathrm{1}\: \\ $$$${dx}\:=\:\mathrm{2}{u}\:{du}\:…
Question Number 10493 by ABD last updated on 14/Feb/17 $$\frac{\mathrm{1}}{\mathrm{2}!}+\frac{\mathrm{2}}{\mathrm{3}!}+\frac{\mathrm{3}}{\mathrm{4}!}+\frac{\mathrm{4}}{\mathrm{5}!}+…+\frac{\mathrm{17}}{\mathrm{18}!}=? \\ $$ Answered by mrW1 last updated on 14/Feb/17 $${since}\:\frac{{n}}{\left({n}+\mathrm{1}\right)!}=\frac{\mathrm{1}}{{n}!}−\frac{\mathrm{1}}{\left({n}+\mathrm{1}\right)!} \\ $$$$\frac{\mathrm{1}}{\mathrm{2}!}+\frac{\mathrm{2}}{\mathrm{3}!}+\frac{\mathrm{3}}{\mathrm{4}!}+\frac{\mathrm{4}}{\mathrm{5}!}+…+\frac{\mathrm{17}}{\mathrm{18}!} \\ $$$$=\left(\frac{\mathrm{1}}{\mathrm{1}!}−\frac{\mathrm{1}}{\mathrm{2}!}\right)+\left(\frac{\mathrm{1}}{\mathrm{2}!}−\frac{\mathrm{1}}{\mathrm{3}!}\right)+\left(\frac{\mathrm{1}}{\mathrm{3}!}−\frac{\mathrm{1}}{\mathrm{4}!}\right)+\centerdot\centerdot\centerdot+\left(\frac{\mathrm{1}}{\mathrm{17}!}−\frac{\mathrm{1}}{\mathrm{18}!}\right) \\…
Question Number 10492 by ABD last updated on 14/Feb/17 $$\mathrm{3}^{{logx}} −\mathrm{2}^{{logx}−\mathrm{1}} =\mathrm{2}^{{logx}+\mathrm{1}} −\mathrm{2}×\mathrm{3}^{{logx}−\mathrm{1}} \Rightarrow{x}=? \\ $$ Answered by mrW1 last updated on 14/Feb/17 $$\mathrm{3}^{{logx}} −\frac{\mathrm{2}^{\mathrm{log}\:{x}}…
Question Number 76009 by Rio Michael last updated on 22/Dec/19 $${hiw}\:{do}\:{i}\:{solve} \\ $$$$\mathrm{2}^{{x}} \:=\:\mathrm{4}{x}? \\ $$ Answered by mr W last updated on 22/Dec/19 $$\mathrm{2}^{{x}}…
Question Number 10470 by ABD last updated on 13/Feb/17 Answered by sandy_suhendra last updated on 13/Feb/17 $$\mathrm{squares}\:\mathrm{1}×\mathrm{1}=\mathrm{8}^{\mathrm{2}} =\mathrm{64} \\ $$$$\mathrm{squares}\:\mathrm{2}×\mathrm{2}=\mathrm{7}^{\mathrm{2}} =\mathrm{49} \\ $$$$\mathrm{squares}\:\mathrm{3}×\mathrm{3}=\mathrm{6}^{\mathrm{2}} =\mathrm{36} \\…
Question Number 76003 by mivheal last updated on 22/Dec/19 $$\mathrm{22}+\mathrm{2} \\ $$ Answered by 21042004 last updated on 22/Dec/19 $$\mathrm{So}\:\mathrm{simple}: \\ $$$$\mathrm{22}+\mathrm{2}=\mathrm{24} \\ $$ Terms…
Question Number 10464 by ABD last updated on 10/Feb/17 Answered by mrW1 last updated on 10/Feb/17 $${for}\:\mid{x}−\mathrm{2}\mid=\mathrm{0}\:\Rightarrow{x}=\mathrm{2},\:\mid\mathrm{3}{x}−\mathrm{8}\mid=\mathrm{2} \\ $$$${for}\:\mid\mathrm{3}{x}−\mathrm{8}\mid=\mathrm{0}\:\Rightarrow{x}=\frac{\mathrm{8}}{\mathrm{3}},\:\mid{x}−\mathrm{2}\mid=\frac{\mathrm{2}}{\mathrm{3}}<\mathrm{2} \\ $$$${A}_{{max}} =\frac{\mathrm{24}}{\frac{\mathrm{2}}{\mathrm{3}}+\mathrm{0}}=\mathrm{36} \\ $$ Terms…