Question Number 155562 by 0731619 last updated on 02/Oct/21 Commented by tabata last updated on 02/Oct/21 $$\boldsymbol{{Solve}}\:::\:\sqrt{\boldsymbol{{x}}}\:+\:\boldsymbol{{y}}\:=\:\mathrm{5}\:\:,\:\sqrt{\boldsymbol{{y}}}\:+\:\boldsymbol{{x}}\:=\:\mathrm{3}\: \\ $$$$ \\ $$$$\boldsymbol{{Solution}}:: \\ $$$$ \\ $$$$\boldsymbol{{let}}:\:\boldsymbol{{a}}^{\mathrm{2}}…
Question Number 90013 by ar247 last updated on 20/Apr/20 $$−{p}^{\mathrm{2}} +\mathrm{2027}=−{q}^{\mathrm{2}} \\ $$$${p}+{q}=? \\ $$ Commented by mr W last updated on 21/Apr/20 $${p}^{\mathrm{2}} −{q}^{\mathrm{2}}…
Question Number 155537 by SANOGO last updated on 01/Oct/21 Answered by amin96 last updated on 01/Oct/21 $$\left.\mathrm{1}\right)\:\:{y}={x}^{{r}} \:\:\:\frac{{dy}}{{dx}}={rx}^{{r}−\mathrm{1}\:\:\:\:} \:\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }=\:\left\{{r}^{\mathrm{2}} −{r}\right\}{x}^{{r}−\mathrm{2}} \\ $$$${x}^{\mathrm{2}} ×\left({r}^{\mathrm{2}}…
Question Number 24456 by gopikrishnan005@gmail.com last updated on 18/Nov/17 $${The}\:{product}\:{of}\:{a}\:{monomial}\:{by}\:{a}\:{binomial}\:{is}\:{a} \\ $$ Answered by $@ty@m last updated on 18/Nov/17 $${binomial}. \\ $$$${Example}: \\ $$$${x}\left({y}+{z}\right) \\…
Question Number 155524 by aliyn last updated on 01/Oct/21 $$\boldsymbol{{how}}\:\boldsymbol{{can}}\:\boldsymbol{{convert}}\:\boldsymbol{{the}}\:\boldsymbol{{interval}}\:\boldsymbol{{of}}\:\boldsymbol{{the}}\:\boldsymbol{{intigral}}\: \\ $$$$\int_{\mathrm{0}} ^{\:\mathrm{1}} \boldsymbol{{f}}\left(\boldsymbol{{x}}\right)\:\boldsymbol{{dx}}\:\boldsymbol{{to}}\:\boldsymbol{{the}}\:\boldsymbol{{interval}}\:\int_{\mathrm{0}} ^{\:\infty} \:\boldsymbol{{f}}\left(\boldsymbol{{x}}\right)\:\boldsymbol{{dx}}\:? \\ $$ Commented by tabata last updated on 01/Oct/21…
Question Number 155527 by ZiYangLee last updated on 01/Oct/21 $$\mathrm{If}\:{f}\left(\mathrm{tan}^{\mathrm{2}} \:\frac{\theta}{\mathrm{2}}\right)=\:\frac{\mathrm{2}}{\mathrm{1}+\mathrm{cos}\:\theta}\:,\:\mathrm{find}\:{f}\left(\mathrm{sin}\:\frac{\theta}{\mathrm{2}}\right). \\ $$ Answered by Ar Brandon last updated on 01/Oct/21 $${f}\left(\mathrm{tan}^{\mathrm{2}} \frac{\vartheta}{\mathrm{2}}\right)=\frac{\mathrm{2}}{\mathrm{1}+\mathrm{cos}\vartheta} \\ $$$${f}\left(\frac{\mathrm{sin}^{\mathrm{2}}…
Question Number 155510 by VIDDD last updated on 01/Oct/21 Answered by puissant last updated on 04/Oct/21 $$\:{I}=\sqrt{{log}_{\sqrt{\mathrm{2}}} \sqrt{\sqrt{\mathrm{2}}×\mathrm{2}^{\frac{\mathrm{1}}{\mathrm{4}}} }+\:{log}_{\sqrt[{\mathrm{4}}]{\mathrm{2}}} \sqrt[{\mathrm{4}}]{\mathrm{2}^{\frac{\mathrm{3}}{\mathrm{4}}} }} \\ $$$$\Rightarrow\:{I}=\sqrt{{log}_{\sqrt{\mathrm{2}}} \mathrm{2}^{\frac{\mathrm{3}}{\mathrm{8}}} +\:{log}_{\sqrt[{\mathrm{4}}]{\mathrm{2}}}…
Question Number 155496 by mathocean1 last updated on 01/Oct/21 $${Given}\:{I}_{{n}} =\underset{{n}\pi} {\overset{\left({n}+\mathrm{1}\right)\pi} {\int}}{e}^{−{x}} {sinx}\:{dx}\:,\:{n}\in\mathbb{N}. \\ $$$$\mathrm{1}.\:{Find}\:{a}\:{relation}\:{between}\:{I}_{{n}+\mathrm{1}} {and}\:{I}_{{n}} . \\ $$ Answered by ArielVyny last updated…
Question Number 155488 by SANOGO last updated on 01/Oct/21 Answered by puissant last updated on 01/Oct/21 $${Q}=\int_{{a}} ^{{b}} \frac{{f}\left({x}\right)}{{f}\left({x}\right)+{f}\left({a}+{b}−{x}\right)}{dx}\:\:\left(\mathrm{1}\right) \\ $$$${u}={a}+{b}−{x}\:\rightarrow\:{x}={a}+{b}−{u}\:\rightarrow\:{dx}=−{du} \\ $$$$\Rightarrow\:{Q}=\int_{{b}} ^{{a}} \frac{{f}\left({a}+{b}−{u}\right)}{{f}\left({a}+{b}−{u}\right)+{f}\left({u}\right)}\left(−{du}\right)…
Question Number 155450 by SANOGO last updated on 30/Sep/21 Answered by Kamel last updated on 30/Sep/21 $${L}=\underset{{n}\rightarrow+\infty} {{lim}e}^{\frac{\mathrm{2}}{\mathrm{2}{n}}\underset{{k}=\mathrm{1}} {\overset{\mathrm{2}{n}−\mathrm{1}} {\sum}}{Ln}\left({sin}\left(\frac{{k}\pi}{\mathrm{2}{n}}\right)\right)} ={e}^{\mathrm{2}\int_{\mathrm{0}} ^{\mathrm{1}} {Ln}\left({sin}\left(\pi{x}\right)\right){dx}} ={e}^{−\mathrm{2}{Ln}\left(\mathrm{2}\right)} =\frac{\mathrm{1}}{\mathrm{4}}…