Question Number 215134 by RoseAli last updated on 29/Dec/24 Answered by Ghisom last updated on 29/Dec/24 $$\int\sqrt{{x}−\sqrt{{x}^{\mathrm{2}} −\mathrm{4}}}{dx}= \\ $$$$\:\:\:\:\:\left[{t}=\sqrt{{x}−\sqrt{{x}^{\mathrm{2}} −\mathrm{4}}}\:\rightarrow\:{dx}=−\frac{\mathrm{2}\sqrt{{x}^{\mathrm{2}} −\mathrm{4}}}{{t}}{dt}\right] \\ $$$$=\int\left({t}^{\mathrm{2}} −\frac{\mathrm{4}}{{t}^{\mathrm{2}}…
Question Number 215114 by issac last updated on 29/Dec/24 Answered by TonyCWX08 last updated on 29/Dec/24 $$\oint={Integral}\:{over}\:{a}\:{closed}\:{path} \\ $$$$\subset\int\int\supset={Integral}\:{over}\:{a}\:{closed}\:{surface} \\ $$$$\subset\int\int\int\supset={Integral}\:{over}\:{a}\:{closed}\:{region}\:{in}\:\mathrm{3}{D}\:{space}. \\ $$ Answered by…
Question Number 215141 by cherokeesay last updated on 29/Dec/24 Answered by aleks041103 last updated on 30/Dec/24 $${eqn}:\:\left({x}−{s}\right)^{\mathrm{2}} +{y}^{\mathrm{2}} ={r}^{\mathrm{2}} \\ $$$${the}\:{following}\:{systems}\:{must}\:{have}\:{one}\:{soln} \\ $$$$\begin{cases}{{y}=\sqrt{{x}}}\\{\left({x}−{s}\right)^{\mathrm{2}} +{y}^{\mathrm{2}} ={r}^{\mathrm{2}}…
Question Number 215126 by mr W last updated on 29/Dec/24 Commented by Ghisom last updated on 29/Dec/24 $${L}\:\mathrm{must}\:\mathrm{be}\:\mathrm{horizontal}\:\mathrm{for}\:{r}\:\rightarrow\:\mathrm{max} \\ $$$$\mathrm{or}\:\mathrm{am}\:\mathrm{I}\:\mathrm{missing}\:\mathrm{something}? \\ $$ Commented by mr…
Question Number 215137 by hardmath last updated on 29/Dec/24 $$\mathrm{If}\:\:\:\overline {\mathrm{ab}}\:+\:\overline {\mathrm{ba}}\:=\:\mathrm{n}^{\mathrm{2}} \\ $$$$\mathrm{Find}\:\:\:\mathrm{max}\left(\mathrm{a}\centerdot\mathrm{b}\right)\:−\:\mathrm{min}\left(\mathrm{a}\centerdot\mathrm{b}\right)\:=\:? \\ $$ Answered by mahdipoor last updated on 29/Dec/24 $${ab}+{ba}=\mathrm{11}\left({a}+{b}\right)=\mathrm{11}^{\mathrm{2}} ={n}^{\mathrm{2}}…
Question Number 215086 by mahdijebraili last updated on 28/Dec/24 Answered by MathematicalUser2357 last updated on 28/Dec/24 $$\mathrm{Here}'\mathrm{s}\:\mathrm{the}\:\mathrm{answer}\:\mathrm{as}\:\mathrm{a}\:\mathrm{drawing}: \\ $$$$ \\ $$ Terms of Service Privacy…
Question Number 215081 by MrGaster last updated on 28/Dec/24 $$ \\ $$$$\mathrm{prove}: \\ $$$$ \\ $$$$\int_{\mathrm{0}} ^{\infty} \frac{\left(\mathrm{ln}\left({x}/\left(\mathrm{1}+{x}\right)\right)^{\mathrm{4}} \mathrm{ln}\left({x}^{\mathrm{3}} \left(\mathrm{1}+{x}\right)^{\mathrm{17}} \right.\right.}{\mathrm{1}+{x}}{dx}=−\mathrm{240}\zeta\left(\mathrm{3}\right)^{\mathrm{2}} \\ $$$$ \\ $$…
Question Number 215092 by BaliramKumar last updated on 28/Dec/24 Commented by BaliramKumar last updated on 28/Dec/24 $${I}\:{want}\:{to}\:{find}\:{the}\:{value}\:{of}\:\boldsymbol{{a}}\:{and}\:\boldsymbol{{b}} \\ $$ Commented by BaliramKumar last updated on…
Question Number 215094 by ajfour last updated on 28/Dec/24 Commented by ajfour last updated on 28/Dec/24 A question discussed Statics+Geometry https://youtu.be/vktsHDGgBlw?si=z6XC7xw6G8m6XjrS Commented by mr W last updated on 28/Dec/24…
Question Number 215089 by golsendro last updated on 28/Dec/24 $$\:\:\mathrm{log}\:_{\mathrm{2}} \:\mathrm{x}\:+\:\mathrm{log}\:_{\mathrm{3}} \:\left(\mathrm{x}+\mathrm{1}\right)\:=\:\mathrm{5}\: \\ $$$$\:\mathrm{x}\:=\:? \\ $$ Answered by efronzo1 last updated on 28/Dec/24 $$\:\:\:\mathrm{log}\:_{\mathrm{3}} \left(\mathrm{x}+\mathrm{1}\right)−\mathrm{2}\:=\:\mathrm{3}−\mathrm{log}\:_{\mathrm{2}}…