Question Number 2748 by Rasheed Soomro last updated on 26/Nov/15 $${Show}\:{that}\:\frac{\mathrm{3}^{\mathrm{2}{n}+\mathrm{1}} +\mathrm{5}^{\mathrm{2}{n}+\mathrm{1}} }{\mathrm{8}}\:{is}\:{an}\:{integer}\:{for}\:{n}\in\mathbb{Z}^{+} \:. \\ $$ Answered by prakash jain last updated on 26/Nov/15 $${f}\left({n}\right)=\mathrm{3}^{\mathrm{2}{n}+\mathrm{1}}…
Question Number 68280 by mezihloic last updated on 08/Sep/19 $${given}\:{that}\:\mathrm{432}_{{n}} −\mathrm{413}_{{n}} =\mathrm{11}_{\mathrm{10}} .{find}\:{the}\:{value}\:{of}\:{n} \\ $$ Commented by TawaTawa last updated on 08/Sep/19 $$\mathrm{4}\:×\:\mathrm{n}^{\mathrm{2}} \:+\:\mathrm{3}\:×\:\mathrm{n}^{\mathrm{1}} \:+\:\mathrm{2}\:×\:\mathrm{n}^{\mathrm{0}}…
Question Number 133818 by bramlexs22 last updated on 24/Feb/21 $$\mathrm{An}\:\mathrm{urn}\:\mathrm{contains}\:\mathrm{24}\:\mathrm{balls}\::\:\mathrm{6}\:\mathrm{white}\:,\:\mathrm{6}\:\mathrm{black},\: \\ $$$$\mathrm{6}\:\mathrm{green}\:,\:\mathrm{and}\:\mathrm{6}\:\mathrm{red}.\:\mathrm{If}\:\mathrm{4}\:\mathrm{balls}\: \\ $$$$\mathrm{are}\:\mathrm{drawn}\:\mathrm{at}\:\mathrm{random}\:\mathrm{with}\:\mathrm{replacement} \\ $$$$.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that} \\ $$$$\mathrm{at}\:\mathrm{least}\:\mathrm{3}\:\mathrm{different}\:\mathrm{colors}\:\mathrm{are}\: \\ $$$$\mathrm{represented}\:\mathrm{in}\:\mathrm{the}\:\mathrm{sample}\:? \\ $$ Terms of Service…
Question Number 68278 by TawaTawa last updated on 08/Sep/19 Commented by mr W last updated on 08/Sep/19 $${it}\:{is}\:{to}\:{see}\:{that}\:{the}\:{crocodile}\:{takes} \\ $$$$\mathrm{0}.\mathrm{5}\:{seconds}\:{for}\:\mathrm{1}\:{meter}\:{in}\:{water}\:{and} \\ $$$$\mathrm{0}.\mathrm{4}\:{seconds}\:{for}\:\mathrm{1}\:{meter}\:{on}\:{land}.\:{is} \\ $$$${this}\:{true}?\:{because}\:{i}\:{thought}\:{a}\:{crocodile} \\…
Question Number 68272 by peter frank last updated on 08/Sep/19 Answered by Kunal12588 last updated on 08/Sep/19 $${H}_{{max}} ={maximum}\:{height} \\ $$$${R}={horizontal}\:{range} \\ $$$${H}_{{max}} ={h}=\frac{{u}_{{y}} ^{\mathrm{2}}…
Question Number 68270 by ~ À ® @ 237 ~ last updated on 08/Sep/19 $$\:{Prove}\:{that}\:\:{if}\:\:{Li}_{\mathrm{2}} \left({x}\right)=\underset{{n}=\mathrm{1}} {\sum}\:\frac{{x}^{{n}} }{{n}^{\mathrm{2}} }\:\:\:{then} \\ $$$$\forall\:{x}\:\:{Li}_{\mathrm{2}} \left({x}\right)+{Li}_{\mathrm{2}} \left(\mathrm{1}−{x}\right)\:=\:\frac{\pi^{\mathrm{2}} }{\mathrm{6}}\:−{ln}\left({x}\right){ln}\left(\mathrm{1}−{x}\right)\:\: \\…
Question Number 2735 by prakash jain last updated on 25/Nov/15 $$\mathrm{Does}\:\mathrm{the}\:\mathrm{following}\:\mathrm{series}\:\mathrm{converge}? \\ $$$$\underset{{i}=\mathrm{1}} {\overset{\infty} {\sum}}\mid\frac{\mathrm{sin}\:{i}}{{i}}\mid \\ $$ Commented by Filup last updated on 26/Nov/15 $$\mathrm{There}\:\mathrm{is}\:\mathrm{a}\:\mathrm{limit}…
Question Number 133804 by mr W last updated on 24/Feb/21 Commented by Dwaipayan Shikari last updated on 24/Feb/21 $${Beautiful}\:{fractals}… \\ $$ Commented by bramlexs22 last…
Question Number 68271 by ~ À ® @ 237 ~ last updated on 08/Sep/19 $$\:\:{Find}\:\:{J}=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{W}\left(−{ulnu}\right)}{{ulnu}}\:{du}\:\:\:\:{when}\:\:{W}\:{is}\:{the}\:{lambert}\:{function} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 68260 by aliesam last updated on 08/Sep/19 $${find}\:{f}\left({x}\right)\:{if}\: \\ $$$${f}\left(\frac{\mathrm{1}}{{x}}\right)+{f}\left(\mathrm{1}−{x}\right)={x} \\ $$ Commented by Prithwish sen last updated on 08/Sep/19 $$\mathrm{Put}\:\mathrm{x}=\:\frac{\mathrm{1}}{\mathrm{x}}\:\Rightarrow\mathrm{f}\left(\mathrm{x}\right)+\mathrm{f}\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{x}}\right)=\frac{\mathrm{1}}{\mathrm{x}}……\left(\mathrm{i}\right) \\ $$$$\mathrm{Putx}=\:\frac{\mathrm{x}}{\mathrm{x}−\mathrm{1}}\Rightarrow\mathrm{f}\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{x}}\right)+\mathrm{f}\left(\frac{\mathrm{1}}{\mathrm{1}−\mathrm{x}}\right)=\frac{\mathrm{x}}{\mathrm{x}−\mathrm{1}}…..\left(\mathrm{ii}\right)…