Question Number 133988 by Dwaipayan Shikari last updated on 26/Feb/21 $$\left(\mathrm{2}+\frac{\pi}{{e}}\right)\left(\frac{\mathrm{17}}{\mathrm{16}}+\frac{\pi}{\mathrm{4}{e}}\right)\left(\frac{\mathrm{82}}{\mathrm{81}}+\frac{\pi}{\mathrm{9}{e}}\right)\left(\frac{\mathrm{257}}{\mathrm{256}}+\frac{\pi}{\mathrm{16}{e}}\right)… \\ $$ Commented by Olaf last updated on 26/Feb/21 $$\mathrm{P}\:=\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\prod}}\left(\frac{?+\mathrm{1}}{?}+\frac{\pi}{{n}^{\mathrm{2}} {e}}\right) \\…
Question Number 2851 by 123456 last updated on 28/Nov/15 $${x}^{\mathrm{2}} ={x}+{x}+{x}+\centerdot\centerdot\centerdot+{x}\:\left({x}\:\mathrm{times}\right) \\ $$$$\mathrm{taking}\:\mathrm{derivate} \\ $$$$\mathrm{2}{x}=\mathrm{1}+\mathrm{1}+\mathrm{1}+\centerdot\centerdot\centerdot+\mathrm{1}\:\left({x}\:\mathrm{times}\right) \\ $$$$\mathrm{2}{x}={x}\:\left({x}\neq\mathrm{0}\right) \\ $$$$\mathrm{2}=\mathrm{1} \\ $$$$\mathrm{where}\:\mathrm{the}\:\mathrm{problem}? \\ $$ Commented by…
Question Number 133838 by I want to learn more last updated on 24/Feb/21 Commented by mr W last updated on 25/Feb/21 $${it}\:{is}\:{not}\:{clear}\:{what}\:{is}\:{meant}.\:{is}\:{the} \\ $$$${lineman}\:\mathrm{4}.\mathrm{6}\:{away}\:{from}\:{the}\:{goalposts} \\…
Question Number 68278 by TawaTawa last updated on 08/Sep/19 Commented by mr W last updated on 08/Sep/19 $${it}\:{is}\:{to}\:{see}\:{that}\:{the}\:{crocodile}\:{takes} \\ $$$$\mathrm{0}.\mathrm{5}\:{seconds}\:{for}\:\mathrm{1}\:{meter}\:{in}\:{water}\:{and} \\ $$$$\mathrm{0}.\mathrm{4}\:{seconds}\:{for}\:\mathrm{1}\:{meter}\:{on}\:{land}.\:{is} \\ $$$${this}\:{true}?\:{because}\:{i}\:{thought}\:{a}\:{crocodile} \\…
Question Number 133722 by I want to learn more last updated on 23/Feb/21 Answered by mr W last updated on 23/Feb/21 $${x}=\mathrm{28}\left(\mathrm{tan}\:\mathrm{40}−\mathrm{tan}\:\mathrm{20}\right) \\ $$ Answered…
Question Number 133708 by Dwaipayan Shikari last updated on 23/Feb/21 $$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{cos}\left(\left(\pi+{e}\right){n}\right)}{{n}^{\mathrm{4}} } \\ $$ Answered by mindispower last updated on 24/Feb/21 $$\underset{{n}\geqslant\mathrm{1}} {\sum}\frac{{sin}\left({nx}\right)}{{n}}={Im}\:\underset{{n}\geqslant\mathrm{1}}…
Question Number 133692 by Dwaipayan Shikari last updated on 23/Feb/21 $$\frac{{sin}\mathrm{1}}{{e}}−\frac{{sin}\left(\mathrm{2}\right)}{\mathrm{2}{e}^{\mathrm{2}} }+\frac{{sin}\left(\mathrm{3}\right)}{\mathrm{3}{e}^{\mathrm{3}} }−\frac{{sin}\left(\mathrm{4}\right)}{\mathrm{4}{e}^{\mathrm{4}} }+…={tan}^{−\mathrm{1}} \left(\frac{{sin}\left(\mathrm{1}\right)}{{cos}\left(\mathrm{1}\right)+{e}}\right) \\ $$ Commented by Dwaipayan Shikari last updated on 23/Feb/21…
Question Number 2524 by 123456 last updated on 21/Nov/15 $${f}:\mathbb{R}^{\mathrm{2}} \rightarrow\mathbb{R} \\ $$$${f}\left({x},{y}\right)={x}^{\mathrm{2}} −{y}^{\mathrm{2}} \:\:\:\:\:\:\:\:\:\:{y}\geqslant\mathrm{0} \\ $$$${f}\left({x},{y}\right)={x}^{\mathrm{2}} +{y}^{\mathrm{2}} \:\:\:\:\:\:\:\:\:\:{y}\leqslant\mathrm{0} \\ $$$$\mathrm{find} \\ $$$$\left({x},{y}\right)\:\mathrm{for}\:\mathrm{min}\:{f}\left({x},{y}\right) \\ $$$$\left({x},{y}\right)\:\mathrm{for}\:{f}\left({x},{y}\right)=\mathrm{1}…
Question Number 133590 by physicstutes last updated on 23/Feb/21 $$\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…