Question Number 61322 by Tawa1 last updated on 31/May/19 Answered by MJS last updated on 02/Jun/19 $$\mathrm{the}\:\mathrm{cuboid}\:\mathrm{with}\:\mathrm{the}\:\mathrm{greatest}\:\mathrm{volume}\:\mathrm{at}\:\mathrm{a} \\ $$$$\mathrm{given}\:\mathrm{surface}\:\mathrm{is}\:\mathrm{a}\:\mathrm{cube} \\ $$$$ \\ $$$${S}\mathrm{urface}=\mathrm{2}{a}^{\mathrm{2}} +\mathrm{4}{ab}=\mathrm{216}\:\Rightarrow\:{b}=\frac{\mathrm{54}}{{a}}−\frac{{a}}{\mathrm{2}} \\…
Question Number 61320 by behi83417@gmail.com last updated on 31/May/19 $$\boldsymbol{\mathrm{solve}}\:\boldsymbol{\mathrm{for}}\:\boldsymbol{\mathrm{x}}: \\ $$$$\:\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{x}}^{\mathrm{4}} −\boldsymbol{\mathrm{x}}=\mathrm{12} \\ $$ Answered by MJS last updated on 31/May/19 $$\mathrm{no}\:“\mathrm{beautiful}''\:\mathrm{solution} \\ $$$${x}_{\mathrm{1}}…
Question Number 126854 by sdfg last updated on 24/Dec/20 Answered by mathmax by abdo last updated on 24/Dec/20 $$\mathrm{h}\rightarrow\mathrm{r}^{\mathrm{2}} \:+\mathrm{k}^{\mathrm{2}} =\mathrm{0}\:\Rightarrow\mathrm{r}^{\mathrm{2}} =−\mathrm{k}^{\mathrm{2}} \:\Rightarrow\mathrm{r}\:=\overset{−} {+}\mathrm{ik}\:\Rightarrow\mathrm{y}_{\mathrm{h}} =\mathrm{ae}^{\mathrm{ikx}}…
Question Number 192388 by sudipmoi last updated on 16/May/23 Answered by aleks041103 last updated on 22/May/23 $${p}>\mathrm{0} \\ $$$$\int_{\mathrm{1}} ^{\:\infty} \frac{{sin}\left({x}\right){dx}}{{x}^{{p}} }=\left[−\frac{{cos}\left({x}\right)}{{x}^{{p}} }\right]_{\mathrm{1}} ^{\infty} −\int_{\mathrm{1}}…
Question Number 61318 by Tawa1 last updated on 31/May/19 Answered by tanmay last updated on 01/Jun/19 $$\overset{\rightarrow} {{V}}_{{train}\:{w}.{r}.{t}\:{ground}} =\left(\frac{\mathrm{64000}}{\mathrm{3600}}\right){m}/{s}\:\overset{\rightarrow} {{i}}=\left(\frac{\mathrm{160}}{\mathrm{9}}\right){m}/{s}\:\overset{\rightarrow} {{i}} \\ $$$$\overset{\rightarrow} {{V}}_{{rain}\:{w}.{r}.{t}\:{ground}} =\mathrm{5}{m}/{s}\:\left(−\overset{\rightarrow}…
Give-the-function-x-2-7x-8-0-have-two-roots-x-1-and-x-2-No-solving-the-function-Find-x-1-3-x-2-2023-
Question Number 192390 by TUN last updated on 16/May/23 $${Give}\:{the}\:{function}: \\ $$$${x}^{\mathrm{2}} −\mathrm{7}{x}−\mathrm{8}=\mathrm{0} \\ $$$${have}\:{two}\:{roots}\:{x}_{\mathrm{1}\:} {and}\:{x}_{\mathrm{2}} \\ $$$${No}\:{solving}\:{the}\:{function}\: \\ $$$${Find}:\:{x}_{\mathrm{1}} ^{\mathrm{3}} +{x}_{\mathrm{2}} +\mathrm{2023} \\ $$…
Question Number 192387 by cortano12 last updated on 16/May/23 $$\:\mathrm{Simplify}\: \\ $$$$\:\sqrt{\mathrm{2}\left(\mathrm{1}+\sqrt{\mathrm{4}+\left(\frac{\mathrm{2017}^{\mathrm{4}} −\mathrm{1}}{\mathrm{2017}^{\mathrm{2}} }\right)^{\mathrm{2}} }\right)}\: \\ $$$$\:\mathrm{is}\:….\: \\ $$ Answered by a.lgnaoui last updated on…
Question Number 126848 by mohammad17 last updated on 24/Dec/20 Answered by mathmax by abdo last updated on 24/Dec/20 $$\mid\mathrm{z}−\mathrm{1}+\mathrm{i}\mid=\mathrm{1}\:\:\:\mathrm{put}\:\mathrm{z}=\mathrm{x}+\mathrm{iy}\:\Rightarrow \\ $$$$\mid\mathrm{z}−\mathrm{1}+\mathrm{i}\mid=\mid\mathrm{x}+\mathrm{iy}−\mathrm{1}+\mathrm{i}\mid=\mid\mathrm{x}−\mathrm{1}+\mathrm{i}\left(\mathrm{y}+\mathrm{1}\right)\mid=\sqrt{\left(\mathrm{x}−\mathrm{1}\right)^{\mathrm{2}} \:+\left(\mathrm{y}+\mathrm{1}\right)^{\mathrm{2}} } \\ $$$$\mid\mathrm{z}−\mathrm{1}+\mathrm{i}\mid=\mathrm{1}\:\Rightarrow\left(\mathrm{x}−\mathrm{1}\right)^{\mathrm{2}}…
Question Number 61313 by Tony Lin last updated on 31/May/19 $$\left.{how}\:{to}\:{calculate}\:\underset{{n}\rightarrow+\infty} {\mathrm{lim}0}.\mathrm{05}^{\mathrm{0}.\mathrm{05}^{\mathrm{0}.\mathrm{05}^{.^{.^{.\mathrm{0}.\mathrm{05}} } } } } \right\}{n} \\ $$$${in}\:{a}\:{simple}\:{and}\:{fast}\:{way}? \\ $$ Commented by mr W…
Question Number 126845 by mnjuly1970 last updated on 24/Dec/20 $$\:\:\:\:\:\:\:\:\:\:\:…\:{calculus}\:\:\left(\mathrm{I}\right)… \\ $$$$\:\:\:\:{prove}\:::\: \\ $$$$\:\:\:\:\:\:\:{i}::\:\:\lfloor\mathrm{2}{x}\rfloor\overset{?} {=}\lfloor{x}\rfloor+\lfloor{x}+\frac{\mathrm{1}}{\mathrm{2}}\rfloor \\ $$$$\:\:\:\:\:\:\:{ii}::\:\lfloor\mathrm{3}{x}\rfloor=\lfloor{x}\rfloor+\lfloor{x}+\frac{\mathrm{1}}{\mathrm{3}}\rfloor+\lfloor{x}+\frac{\mathrm{2}}{\mathrm{3}}\rfloor \\ $$$$ \\ $$ Answered by floor(10²Eta[1]) last…