Question Number 136813 by mnjuly1970 last updated on 26/Mar/21 $$\:\:\:\:\: \\ $$$$\:\:\:……{advanced}\:\:\:\:{calculus}\left({I}\right)…. \\ $$$$\:\:\:\:{if}\::\: \\ $$$$\:\:\Omega=\int_{\frac{\pi}{\mathrm{4}}} ^{\:\frac{\pi}{\mathrm{2}}} \frac{{x}.{cos}\left(\mathrm{2}{x}\right).{cos}\left({x}\right)}{{sin}^{\mathrm{7}} \left({x}\right)}\:{dx}=\frac{{a}\pi}{\mathrm{90}} \\ $$$$\:\:\:{then}\:\:::\:\:{a}=??? \\ $$$$\:\: \\ $$$$\:\:\:\:…
Question Number 5742 by Rasheed Soomro last updated on 26/May/16 $$\bullet{Determine}\:{S} \\ $$$${S}={a}^{\mathrm{2}} +{ar}\left({a}+{r}\right)+{ar}^{\mathrm{2}} \left({a}+\mathrm{2}{r}\right)+…+{ar}^{{n}−\mathrm{1}} \left\{{a}+\left({n}−\mathrm{1}\right)\:{r}\right\}. \\ $$$$ \\ $$ Answered by Yozzii last updated…
Question Number 136815 by rs4089 last updated on 26/Mar/21 Answered by Dwaipayan Shikari last updated on 26/Mar/21 $${y}={e}^{\lambda{x}} \\ $$$${x}^{\mathrm{2}} \lambda^{\mathrm{2}} +{x}\lambda+\left({x}^{\mathrm{2}} −\frac{\mathrm{1}}{\mathrm{4}}\right)=\mathrm{0} \\ $$$$\Rightarrow\lambda=\frac{−{x}\pm\sqrt{{x}^{\mathrm{2}}…
Question Number 5738 by FilupSmith last updated on 26/May/16 $$\mathrm{I}'\mathrm{m}\:\mathrm{having}\:\mathrm{trouble}\:\mathrm{understanding}\:\mathrm{why}: \\ $$$$\mathrm{2}^{−\mathrm{1}} \equiv\mathrm{3}\left(\mathrm{mod}\:\mathrm{5}\right) \\ $$$$ \\ $$$$\mathrm{Can}\:\mathrm{someone}\:\mathrm{explain},\:\mathrm{please}?\:\mathrm{Thank}\:\mathrm{you}! \\ $$ Commented by Rasheed Soomro last updated…
Question Number 71273 by eriga last updated on 13/Oct/19 Commented by $@ty@m123 last updated on 13/Oct/19 $${Welcome}\:{Eriga}. \\ $$$${Pl}.\:{use}\:{EDITOR}\:{option} \\ $$$${instead}\:{of}\:{FORUM}\:{to}\:{type} \\ $$$${math}\:{related}\:{material}. \\ $$$$…
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Question Number 5734 by sanusihammed last updated on 25/May/16 $${Please}\:{show}\:{me}\:{an}\:{approach}\:{to}\:{solve}\:{this}… \\ $$$$ \\ $$$$\mathrm{2}^{{x}} \:=\:\mathrm{4}{x} \\ $$$$ \\ $$$${Find}\:{the}\:{value}\:{of}\:{x}\: \\ $$ Answered by prakash jain…
Question Number 136806 by mnjuly1970 last updated on 26/Mar/21 Answered by Dwaipayan Shikari last updated on 26/Mar/21 $$\mathrm{2}\int_{\mathrm{0}} ^{\infty} \frac{{sin}\left(\frac{\mathrm{1}}{{x}^{\mathrm{3}} }\right)}{\:\sqrt[{\mathrm{3}}]{{x}}}{dx}\:\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{1}}{{x}^{\mathrm{3}} }={u}\Rightarrow−\frac{\mathrm{3}}{{x}^{\mathrm{4}} }=\frac{{du}}{{dx}} \\ $$$$=\frac{\mathrm{2}}{\mathrm{3}}\int_{\mathrm{0}}…
Question Number 136803 by mnjuly1970 last updated on 26/Mar/21 $$\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:…..\mathscr{A}{dvanced}\:\:\:\:\blacktriangleleft………….\blacktriangleright\:\:\:\mathscr{C}{alculus}….. \\ $$$$\:\:\:\:\:\boldsymbol{\phi}=\int_{−\infty} ^{\:\infty} \frac{{sin}\left(\frac{\mathrm{1}}{{x}^{\mathrm{3}} }\right)}{{x}}{dx}=……??? \\ $$$$\:\:\:\:\:{solution}:: \\ $$$$\:\:\:\:\:\:\boldsymbol{\phi}\overset{\frac{\mathrm{1}}{{x}}\:={t}} {=}\:\mathrm{2}\int_{\mathrm{0}} ^{\:\infty} \frac{{sin}\left({t}^{\mathrm{3}} \right)}{\frac{\mathrm{1}}{{t}}}.\frac{{dt}}{{t}^{\mathrm{2}}…
Question Number 71265 by ajfour last updated on 13/Oct/19 Commented by ajfour last updated on 13/Oct/19 $${Find}\:{radius}\:{of}\:{yellow}\:{sphere}\:{x}, \\ $$$${that}\:{touches}\:{the}\:{other}\:{sphere}, \\ $$$${lateral}\:{surface}\:{of}\:{cone}\:{and}\: \\ $$$${cone}\:{cover}\:{plate}. \\ $$…