Question Number 153040 by mnjuly1970 last updated on 04/Sep/21 $$ \\ $$$$\:{prove}\:{that}.. \\ $$$$ \\ $$$$\Omega\:=\int_{\mathrm{0}} ^{\:\infty} \frac{\:{sin}\:\left({x}\:\right)}{{sinh}\left({x}\right)}{dx}\:=\frac{\pi}{\mathrm{2}}\:{tanh}\:\left(\frac{\pi}{\mathrm{2}}\right)\:\: \\ $$ Terms of Service Privacy Policy…
Question Number 21970 by j.masanja06@gmail.com last updated on 07/Oct/17 $${integrate} \\ $$$$\int{sec}^{\mathrm{3}} {xdx} \\ $$ Answered by Tikufly last updated on 07/Oct/17 $$\:\int\mathrm{sec}^{\mathrm{3}} {xdx}=\int\:\left(\mathrm{sec}{x}\right)\left(\mathrm{sec}^{\mathrm{2}} {x}\right){dx}…
Question Number 87504 by M±th+et£s last updated on 04/Apr/20 $${solve}\: \\ $$$$\frac{{dy}}{{dx}}=\mathrm{2}\left(\frac{\mathrm{2}+{y}}{\mathrm{1}+{x}+{y}}\right)^{\mathrm{2}} \\ $$ Answered by TANMAY PANACEA. last updated on 04/Apr/20 $${i}\:{think} \\ $$$$\frac{{dy}}{{dx}}=\mathrm{2}\left(\frac{{x}+{y}}{\mathrm{1}+{x}+{y}}\right)^{\mathrm{2}}…
Question Number 87505 by Ar Brandon last updated on 04/Apr/20 Commented by MJS last updated on 04/Apr/20 $$\mathrm{the}\:\mathrm{same}\:\mathrm{old}\:\mathrm{question}\:\mathrm{the}\:\mathrm{1}.\mathrm{000}.\mathrm{000}.\mathrm{000th} \\ $$$$\mathrm{time}. \\ $$$$\mathrm{the}\:\mathrm{cable}\:\mathrm{hangs}\:\mathrm{down}\:\mathrm{40}\:\mathrm{meters}\:\mathrm{from}\:\mathrm{each} \\ $$$$\mathrm{pole}.\:\mathrm{if}\:\mathrm{the}\:\mathrm{cable}\:\mathrm{is}\:\mathrm{80}\:\mathrm{meters}\:\mathrm{long},\:\mathrm{there}'\mathrm{s} \\…
Question Number 21967 by Tinkutara last updated on 07/Oct/17 $$\mathrm{A}\:\mathrm{block}\:\mathrm{is}\:\mathrm{tied}\:\mathrm{with}\:\mathrm{a}\:\mathrm{thread}\:\mathrm{of}\:\mathrm{length}\:{l} \\ $$$$\mathrm{and}\:\mathrm{moved}\:\mathrm{in}\:\mathrm{a}\:\mathrm{horizontal}\:\mathrm{circle}\:\mathrm{on}\:\mathrm{a} \\ $$$$\mathrm{rough}\:\mathrm{table}.\:\mathrm{Coefficient}\:\mathrm{of}\:\mathrm{friction} \\ $$$$\mathrm{between}\:\mathrm{block}\:\mathrm{and}\:\mathrm{table}\:\mathrm{is}\:\mu\:=\:\mathrm{0}.\mathrm{2}. \\ $$$$\mathrm{Find}\:\mathrm{tan}\:\theta,\:\mathrm{where}\:\theta\:\mathrm{is}\:\mathrm{the}\:\mathrm{angle} \\ $$$$\mathrm{between}\:\mathrm{acceleration}\:\mathrm{and}\:\mathrm{frictional} \\ $$$$\mathrm{force}\:\mathrm{at}\:\mathrm{the}\:\mathrm{instant}\:\mathrm{when}\:\mathrm{speed}\:\mathrm{of} \\ $$$$\mathrm{particle}\:\mathrm{is}\:{v}\:=\:\sqrt{\mathrm{1}.\mathrm{6}{lg}} \\…
Question Number 87503 by M±th+et£s last updated on 04/Apr/20 $$\int\frac{{x}^{\mathrm{2}} }{\mathrm{1}+{x}^{\mathrm{5}} }{dx} \\ $$ Commented by MJS last updated on 04/Apr/20 $${x}^{\mathrm{5}} +\mathrm{1}=\left({x}+\mathrm{1}\right)\left({x}^{\mathrm{2}} −\frac{\mathrm{1}−\sqrt{\mathrm{5}}}{\mathrm{2}}{x}+\mathrm{1}\right)\left({x}^{\mathrm{2}} −\frac{\mathrm{1}+\sqrt{\mathrm{5}}}{\mathrm{2}}+\mathrm{1}\right)…
Question Number 153039 by ZiYangLee last updated on 04/Sep/21 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{x}\left({e}^{{x}} +\mathrm{1}\right)−\mathrm{2}\left({e}^{{x}} −\mathrm{1}\right)}{{x}^{\mathrm{3}} }\:=\:? \\ $$ Answered by puissant last updated on 04/Sep/21 $$={lim}_{{x}\rightarrow\mathrm{0}} \frac{{x}\left(\mathrm{1}+{x}+\frac{{x}^{\mathrm{2}}…
Question Number 21965 by j.masanja06@gmail.com last updated on 07/Oct/17 $${integrate} \\ $$$$\int{sin}^{\mathrm{3}} {xdx} \\ $$ Answered by Tikufly last updated on 07/Oct/17 $$\:\:=\int\:\left(\mathrm{sin}^{\mathrm{2}} {x}\right)\mathrm{sin}{xdx} \\…
Question Number 153038 by 7770 last updated on 04/Sep/21 Answered by mr W last updated on 04/Sep/21 $${say}\:{BC}={DC}={AD}=\mathrm{1} \\ $$$${BD}=\mathrm{2}×\mathrm{1}×\mathrm{sin}\:\mathrm{24}=\mathrm{2}\:\mathrm{sin}\:\mathrm{24} \\ $$$$\mathrm{96}−\frac{\mathrm{180}−\mathrm{48}}{\mathrm{2}}=\mathrm{30} \\ $$$$\angle{A}=\alpha \\…
Question Number 21964 by chernoaguero@gmail.com last updated on 07/Oct/17 Answered by ibraheem160 last updated on 07/Oct/17 $$\mathrm{y}=\mathrm{x}^{\mathrm{2}} \left(\mathrm{2x}−\mathrm{5}\right)^{\mathrm{4}} \\ $$$$\frac{\mathrm{du}}{\mathrm{dx}}=\mathrm{2x},\:\:\frac{\mathrm{dv}}{\mathrm{dx}}=\mathrm{8}\left(\mathrm{2x}−\mathrm{5}\right)^{\mathrm{3}} \\ $$$$\: \\ $$$$\frac{\mathrm{dy}}{\mathrm{dx}}=\mathrm{u}\frac{\mathrm{dv}}{\mathrm{dx}}+\mathrm{v}\frac{\mathrm{du}}{\mathrm{dx}} \\…