Question Number 3044 by 123456 last updated on 03/Dec/15 $$\mathrm{random}\:\mathrm{question} \\ $$$$\mathrm{if}\:\mathrm{person}\:\mathrm{as}\:\mathrm{5}\:\mathrm{years}\:\mathrm{old}\:\mathrm{and}\:\left(\mathrm{s}\right)\mathrm{he}\:\mathrm{back} \\ $$$$\mathrm{10}\:\mathrm{years}\:\mathrm{in}\:\mathrm{time}\:\left(\mathrm{by}\:\mathrm{some}\:\mathrm{mean}\right) \\ $$$$\mathrm{would}\:\left(\mathrm{s}\right)\mathrm{he}\:\mathrm{have}\:−\mathrm{5}\:\mathrm{years}\:\mathrm{old}? \\ $$ Answered by Filup last updated on 03/Dec/15…
Question Number 3035 by 123456 last updated on 03/Dec/15 $$\omega\left({z}\right)=\underset{{n}\rightarrow\infty} {\mathrm{lim}}\frac{{n}^{{z}} \left[{z}+\left({z}+\mathrm{1}\right)+…+\left({z}+{n}\right)\right]}{{z}\left({z}+\mathrm{1}\right)\left({z}+\mathrm{2}\right)…\left({z}+{n}\right)} \\ $$$$\omega\left(\mathrm{1}\right)=? \\ $$ Commented by prakash jain last updated on 04/Dec/15 $${w}\left(\mathrm{1}\right)=\underset{{n}\rightarrow\infty}…
Question Number 134002 by Dwaipayan Shikari last updated on 26/Feb/21 $${What}\:{will}\:{be}\:{the}\:{minimum}\:{area}\:{of}\:{a}\:{heptagon}\:{inscribed}\:{in} \\ $$$${an}\:{unit}\:{square}? \\ $$ Commented by Dwaipayan Shikari last updated on 26/Feb/21 Answered by…
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…