Question Number 139525 by TOTTI last updated on 28/Apr/21 Commented by mr W last updated on 29/Apr/21 $$=\mathrm{log}_{\sqrt{{x}}} \:\left(\sqrt{{x}}\right)^{\mathrm{2}} =\mathrm{3}^{\mathrm{1}/\mathrm{3}} \\ $$$$=\mathrm{2log}_{\sqrt{{x}}} \:\sqrt{{x}}=\mathrm{3}^{\mathrm{1}/\mathrm{3}} \\ $$$$\Rightarrow\mathrm{2}=\mathrm{3}^{\mathrm{1}/\mathrm{3}}…
Question Number 139524 by mnjuly1970 last updated on 28/Apr/21 $$\:\:\:\:\:\:\:\:\:\:\:\:……{advanced}\:\:{calculus}….. \\ $$$$\:\:\:\:\:\:\:\:\:{prove}\:\:{that}: \\ $$$$\:{i}::\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\infty} \left(\frac{\mathrm{1}}{\mathrm{2}}{e}^{−\mathrm{2}{x}} −\frac{\mathrm{1}}{\mathrm{1}+{e}^{{x}} }\right)\frac{\mathrm{1}}{{x}}\:{dx}={log}\left(\frac{\mathrm{1}}{\:\sqrt{\pi}}\:\right) \\ $$$$\:{ii}::\int_{\mathrm{0}} ^{\:\infty} \left(\frac{\mathrm{1}}{\mathrm{2}}−\frac{\mathrm{1}}{\mathrm{1}+{e}^{−{x}} }\right)\frac{{e}^{−\mathrm{2}{x}} }{{x}}{dx}={log}\left(\frac{\sqrt{\pi}}{\mathrm{2}}\right) \\…
Question Number 8452 by tawakalitu last updated on 11/Oct/16 Commented by 123456 last updated on 12/Oct/16 $$\mathrm{sin}\:{x}+\mathrm{cos}\:{x}=\frac{\mathrm{1}}{\mathrm{2}} \\ $$$${a}=\mathrm{sin}\:{x},{b}=\mathrm{cos}\:{x} \\ $$$${a}+{b}=\frac{\mathrm{1}}{\mathrm{2}} \\ $$$${a}^{\mathrm{2}} +{b}^{\mathrm{2}} =\mathrm{1}…
Question Number 139521 by mnjuly1970 last updated on 28/Apr/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:#\:\:\:{nice}\:…\:{calculus}# \\ $$$$\:\:\:\:\:\:\:\:{if}\:\:\:\:\left({pq}\right)^{{sin}^{\mathrm{2}} \left({x}\right)} +\left({pq}\right)^{{cos}^{\mathrm{2}} \left({x}\right)} ={p}+{q} \\ $$$$\:\:\:\:\:\:\:\:\:\:{then}\:\:\:\:{tan}\left({x}\right)=? \\ $$ Answered by qaz last updated…
Question Number 73982 by mhmd last updated on 17/Nov/19 $${if}\:{p}_{{r}} ^{{n}} =\mathrm{49}\:,\:{c}_{{r}} ^{{n}} =\mathrm{196}\:{find}\:{the}\:{valve}\:{of}\:{r}\:{and}\:{n}? \\ $$$${pleas}\:{sir}\:{help}\:{me} \\ $$ Commented by som(math1967) last updated on 17/Nov/19…
Question Number 73983 by mhmd last updated on 17/Nov/19 $${if}\:{p}_{{r}} ^{{n}} =\mathrm{49}\:,\:{c}_{{r}} ^{{n}} =\mathrm{196}\:{find}\:{the}\:{valve}\:{of}\:{r}\:{and}\:{n}? \\ $$$${pleas}\:{sir}\:{help}\:{me} \\ $$ Answered by $@ty@m123 last updated on 17/Nov/19…
Question Number 73974 by Raxreedoroid last updated on 17/Nov/19 $$\mathrm{Prove}\:\mathrm{this}\:\mathrm{equation} \\ $$$$\frac{\mathrm{2}^{{x}−\mathrm{1}} \left({x}−\frac{\mathrm{1}}{\mathrm{2}}\right)!}{\frac{\mathrm{1}}{\mathrm{2}}!}=\frac{\left(\mathrm{2}{x}−\mathrm{1}\right)!}{\mathrm{2}^{{x}−\mathrm{1}} \left({x}−\mathrm{1}\right)!} \\ $$ Answered by mind is power last updated on 17/Nov/19…
Question Number 139505 by bemath last updated on 28/Apr/21 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{greatest}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x}^{\mathrm{2}} \mathrm{y}^{\mathrm{3}} \: \\ $$$$\mathrm{when}\:\mathrm{3x}+\mathrm{4y}=\mathrm{5} \\ $$ Commented by mr W last updated on 28/Apr/21 $$\mathrm{3}{x}+\mathrm{4}{y}=\mathrm{5}\:\Rightarrow{y}\in\left(−\infty,\infty\right)…
Question Number 139506 by I want to learn more last updated on 28/Apr/21 Commented by I want to learn more last updated on 28/Apr/21 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{double}\:\mathrm{line}\:\mathrm{angle}.…
Question Number 139501 by aliibrahim1 last updated on 28/Apr/21 Answered by mr W last updated on 28/Apr/21 $$\left({x}+\mathrm{3}{i}\right)^{\mathrm{100}} =−\mathrm{1}={e}^{\left(\mathrm{2}{k}+\mathrm{1}\right)\pi{i}} \\ $$$${x}_{{k}} +\mathrm{3}{i}={e}^{\frac{\left(\mathrm{2}{k}+\mathrm{1}\right)\pi}{\mathrm{100}}{i}} \\ $$$${x}_{{k}} ={e}^{\frac{\left(\mathrm{2}{k}+\mathrm{1}\right)\pi}{\mathrm{100}}{i}}…