Question Number 64698 by Rio Michael last updated on 20/Jul/19 Commented by Rio Michael last updated on 20/Jul/19 $${the}\:{figure}\:{above}\:{shows}\:{a}\:{wood}\:{of}\:{mass}\:\mathrm{50}{kg}\:{held}\:{by}\:{a}\:{rope}\: \\ $$$${which}\:{is}\:{inclined}\:{at}\:\mathrm{30}°\:{to}\:{the}\:{wood}\:{and}\:{supported}\:{by}\:{a}\:{wall}. \\ $$$${calculate}\:{the}\:{tension}\:{in}\:{the}\:{rope} \\ $$$$\:\:\:\left({take}\:{g}\:=\:\mathrm{10}{ms}^{−\mathrm{2}}…
Question Number 64697 by Rio Michael last updated on 20/Jul/19 $${i}\:{need}\:{some}\:{help}\:{here}.\: \\ $$$$\:{An}\:{object}\:{of}\:{mass}\:\:\:{m}\:\:\:{falls}\:{from}\:{a}\:{height}\:\:{h}_{\mathrm{1}} \:{and}\:{rebound} \\ $$$${to}\:{a}\:{height}\:{of}\:{h}_{\mathrm{2}} .\:{write}\:{an}\:{expression}\:{for}\:{its}\:{momentum}. \\ $$ Answered by peter frank last updated…
Question Number 130226 by stelor last updated on 23/Jan/21 $$\mathrm{please}\:\mathrm{I}\:\mathrm{need}\:\mathrm{help}… \\ $$$$\int\left(\frac{\mathrm{e}^{{x}} +\mathrm{1}}{\mathrm{e}^{\mathrm{2x}} +\mathrm{1}}\right){dx} \\ $$ Answered by Lordose last updated on 23/Jan/21 $$\Omega\:\overset{\mathrm{u}=\mathrm{e}^{\mathrm{x}} }…
Question Number 64688 by peter frank last updated on 20/Jul/19 Answered by mr W last updated on 20/Jul/19 $${M}_{\mathrm{0}} ={original}\:{mass} \\ $$$$−{u}\frac{{dm}}{{dt}}={m}\frac{{dv}}{{dt}} \\ $$$$−{u}\int_{{M}_{\mathrm{0}} }…
Question Number 64687 by aliesam last updated on 20/Jul/19 Commented by mathmax by abdo last updated on 21/Jul/19 $${let}\:{A}\:=\int\:\:\:\frac{{e}^{\frac{−{cos}\left(\mathrm{2}{x}\right)}{\mathrm{2}}} }{{sin}^{\mathrm{2}} {x}}\:{dx}\:\Rightarrow\:{A}\:=\int\:\:\:\frac{{e}^{−\frac{{cos}\left(\mathrm{2}{x}\right)}{\mathrm{2}}} }{\frac{\mathrm{1}−{cos}\left(\mathrm{2}{x}\right)}{\mathrm{2}}}\:{dx} \\ $$$$=\:\mathrm{2}\:\int\:\:\:\frac{{e}^{−\frac{{cos}\left(\mathrm{2}{x}\right)}{\mathrm{2}}} }{\mathrm{1}−{cos}\left(\mathrm{2}{x}\right)}{dx}\:\:\:{changement}\:{cos}\left(\mathrm{2}{x}\right)\:={t}\:{give}\:\mathrm{2}{x}={argch}\left({t}\right)…
Question Number 130223 by Study last updated on 23/Jan/21 $${li}\underset{{x}\rightarrow\overset{−} {\mathrm{5}}} {{m}lo}\underset{\frac{\mathrm{2}}{\mathrm{3}}} {{g}}\left(\mathrm{3}{x}−\mathrm{15}\right)=? \\ $$ Answered by EDWIN88 last updated on 23/Jan/21 $$\underset{{x}\rightarrow\mathrm{5}^{−} } {\mathrm{lim}}\:\mathrm{log}\:_{\mathrm{2}/\mathrm{3}}…
Question Number 64686 by ajfour last updated on 20/Jul/19 Answered by ajfour last updated on 20/Jul/19 $${Let}\:{B}\:{be}\:{origin}\:\:{and}\:{x}\:{axis}\:{along} \\ $$$${BC}. \\ $$$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} ={c}^{\mathrm{2}} \\ $$$$\left({x}−{a}\right)^{\mathrm{2}}…
Question Number 130221 by bramlexs22 last updated on 23/Jan/21 $$\mathrm{Prove}\:\mathrm{that}\:\mathrm{tan}\:\mathrm{2A}=\frac{\mathrm{2tan}\:\mathrm{A}}{\mathrm{1}−\mathrm{tan}\:^{\mathrm{2}} \mathrm{A}} \\ $$ Answered by EDWIN88 last updated on 23/Jan/21 $$\mathrm{by}\:\mathrm{De}'\mathrm{Moivre}\:\mathrm{theorem}\: \\ $$$$\mathrm{cos}\:\mathrm{2A}+{i}\:\mathrm{sin}\:\mathrm{2}{A}\:=\:\left(\mathrm{cos}\:\mathrm{A}+{i}\:\mathrm{sin}\:\mathrm{A}\right)^{\mathrm{2}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\left(\mathrm{cos}^{\mathrm{2}}…
Question Number 130214 by Lordose last updated on 23/Jan/21 $$\int\frac{\mathrm{u}^{\mathrm{2}} }{\left(\mathrm{1}+\mathrm{u}^{\mathrm{2}} \right)^{\mathrm{2}} }\mathrm{du} \\ $$ Answered by liberty last updated on 23/Jan/21 $$\mathrm{J}=\int\:\frac{\left(\mathrm{u}^{\mathrm{2}} +\mathrm{1}\right)−\mathrm{1}}{\left(\mathrm{1}+\mathrm{u}^{\mathrm{2}} \right)^{\mathrm{2}}…
Question Number 64677 by mathmax by abdo last updated on 20/Jul/19 $${let}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} {lnt}\:{ln}\left(\mathrm{1}−{xt}\right){dt}\:\:\:{with}\:\mid{x}\mid<\mathrm{1} \\ $$$$\left.\mathrm{1}\right){determine}\:{a}\:{explicit}\:{form}\:{for}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{also}\:{g}\left({x}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{tlnt}}{\mathrm{1}−{xt}}{dt} \\ $$$$\left.\mathrm{3}\right)\:{give}\:{f}^{\left({n}\right)} \left({x}\right)\:{at}\:{form}\:{of}\:{integral} \\ $$$$\left.\mathrm{4}\right)\:{calculate}\:\int_{\mathrm{0}}…