Question Number 133590 by physicstutes last updated on 23/Feb/21 $$\mathrm{A}\:\mathrm{particle}\:\mathrm{performs}\:\mathrm{simple}\:\mathrm{harmonic}\:\mathrm{motion}\:\mathrm{between}\:\mathrm{two}\:\mathrm{points} \\ $$$$\mathrm{A}\:\mathrm{and}\:\mathrm{B}\:\mathrm{which}\:\mathrm{are}\:\mathrm{10}\:\mathrm{m}\:\mathrm{apart}\:\mathrm{on}\:\mathrm{a}\:\mathrm{horizontal}\:\mathrm{straight}\:\mathrm{line}. \\ $$$$\mathrm{When}\:\mathrm{the}\:\mathrm{particle}\:\mathrm{is}\:\mathrm{3}\:\mathrm{m}\:\mathrm{away}\:\mathrm{from}\:\mathrm{the}\:\mathrm{centre},\:\mathrm{O},\:\mathrm{of}\:\mathrm{the}\:\mathrm{line}\:\mathrm{AB}, \\ $$$$\mathrm{its}\:\mathrm{speed}\:\mathrm{is}\:\mathrm{8}\:\mathrm{ms}^{−\mathrm{1}} .\:\mathrm{Find}\:\mathrm{the}\:\mathrm{least}\:\mathrm{time}\:\mathrm{required}\:\mathrm{for}\:\mathrm{the} \\ $$$$\mathrm{particle}\:\mathrm{to}\:\mathrm{move}\:\mathrm{from}\:\mathrm{B}\:\mathrm{to}\:\mathrm{the}\:\mathrm{midpoint}\:\mathrm{of}\:\mathrm{OA}. \\ $$ Answered by mr W…
Question Number 2514 by 123456 last updated on 21/Nov/15 $$\mathrm{is}\:\mathrm{there}\:\mathrm{a}\:\mathrm{function} \\ $$$${f}:\mathbb{R}^{\mathrm{2}} \rightarrow\mathbb{R} \\ $$$$\mathrm{such}\:\mathrm{that} \\ $$$${f}\left[{x},{f}\left({x},{y}\right)\right]={f}\left[{f}\left({x},{y}\right),{y}\right]={f}\left({x},{y}\right) \\ $$$$? \\ $$ Answered by prakash jain…
Question Number 133587 by bemath last updated on 23/Feb/21 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{exact}\:\mathrm{value}\:\mathrm{of}\:\mathrm{cos}\:\mathrm{12}°\:. \\ $$ Answered by Dwaipayan Shikari last updated on 23/Feb/21 $${sin}\frac{\pi}{\mathrm{60}}={sin}\frac{\pi}{\mathrm{10}}{cos}\frac{\pi}{\mathrm{12}}−{sin}\frac{\pi}{\mathrm{12}}{cos}\frac{\pi}{\mathrm{10}} \\ $$$$=\frac{\sqrt{\mathrm{5}}−\mathrm{1}}{\mathrm{4}}.\frac{\sqrt{\mathrm{2}+\sqrt{\mathrm{3}}}}{\mathrm{2}}−\frac{\sqrt{\mathrm{10}−\mathrm{2}\sqrt{\mathrm{5}}}}{\mathrm{4}}.\frac{\sqrt{\mathrm{2}+\sqrt{\mathrm{3}}}}{\mathrm{2}} \\ $$$$=\frac{\mathrm{1}}{\mathrm{16}}\left(\left(\sqrt{\mathrm{5}}−\mathrm{1}\right)\left(\sqrt{\mathrm{6}}−\sqrt{\mathrm{2}}\right)−\left(\sqrt{\mathrm{6}}+\sqrt{\mathrm{2}}\right)\sqrt{\mathrm{10}−\mathrm{2}\sqrt{\mathrm{5}}}\right)…
Question Number 68046 by mhmd last updated on 03/Sep/19 Answered by mind is power last updated on 03/Sep/19 $$\frac{{d}\left({e}^{\frac{{sin}\left(\mathrm{2}{x}\right)}{\mathrm{2}}} \right)}{{dx}}={cos}\left(\mathrm{2}{x}\right){e}^{{sin}\left({x}\right){cos}\left({x}\right)} \\ $$$$\int\frac{{e}^{{sin}\left({x}\right){cos}\left({x}\right)} {cos}\left(\mathrm{2}{x}\right)}{\mathrm{1}+{e}^{{sin}\left(\mathrm{2}{x}\right)} }{dx} \\…
Question Number 133583 by bemath last updated on 23/Feb/21 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{cos}\:\mathrm{x}−\mathrm{1}+\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{2}}−\frac{\mathrm{x}^{\mathrm{4}} }{\mathrm{24}}}{\mathrm{x}^{\mathrm{6}} } \\ $$ Answered by EDWIN88 last updated on 23/Feb/21 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}−\frac{\mathrm{x}^{\mathrm{2}}…
Question Number 68043 by mhmd last updated on 03/Sep/19 $$\int_{\pi/\mathrm{2}} ^{\pi} {e}^{{cosx}} \sqrt{\mathrm{1}−{e}^{{cosx}} }\:{sinx}\:{dx} \\ $$ Commented by mathmax by abdo last updated on 03/Sep/19…
Question Number 133579 by mr W last updated on 23/Feb/21 Commented by mr W last updated on 23/Feb/21 $$\mathrm{hope}\:\mathrm{you}\:\mathrm{are}\:\mathrm{doing}\:\mathrm{well}\:\mathrm{sir}… \\ $$ Commented by EDWIN88 last…
Question Number 68040 by mathmax by abdo last updated on 03/Sep/19 $${find}\:{f}\left({a}\right)\:=\int_{\mathrm{1}} ^{\mathrm{2}} {arctan}\left({x}+\frac{{a}}{{x}}\right){dx}\:\:{and} \\ $$$${calculate}\:{f}^{'} \left({a}\right)\:{at}\:{form}\:{of}\:{integral} \\ $$ Commented by mathmax by abdo last…
Question Number 68041 by A8;15: last updated on 03/Sep/19 Commented by mr W last updated on 03/Sep/19 $${see}\:{Q}#\mathrm{67386} \\ $$ Terms of Service Privacy Policy…
Question Number 2504 by 123456 last updated on 21/Nov/15 $${f}\left({x},{y}\right)={f}\left({x},{y}−{x}\right) \\ $$$${f}\left({x},{y}\right)={f}\left({y},{x}\right) \\ $$$${f}\left(\mathrm{0},{y}\right)={y}^{\mathrm{2}} \\ $$$$\mathrm{does} \\ $$$${g}\left({x}\right):={f}\left({x},{x}\right) \\ $$$${g}\left(−{x}\right)\overset{?} {=}{g}\left({x}\right) \\ $$$${f}\left(\mathrm{10},\mathrm{5}\right)=? \\ $$…