Question Number 34877 by NECx last updated on 12/May/18 $$\mathrm{4}\:{couples}\:{are}\:{to}\:{take}\:{a}\:{photograph} \\ $$$${with}\:{a}\:{newly}\:{wedded}\:{couple}\:{in}\:{a} \\ $$$${wedding}\:{party}.{In}\:{how}\:{many}\:{ways} \\ $$$${can}\:{this}\:{be}\:{done}\:{if}: \\ $$$$\left.{i}\right){the}\:{celebrated}\:{couple}\:{must}\:{stand} \\ $$$${in}\:{the}\:{middle} \\ $$$$\left.{ii}\right){each}\:{couple}\:{must}\:{stand}\:{next}\:{to} \\ $$$${each}\:{other} \\…
Question Number 99985 by Rio Michael last updated on 24/Jun/20 $$\mathrm{A}\:\mathrm{certain}\:\mathrm{wire}\:\mathrm{has}\:\mathrm{length}\:\mathrm{4}.\mathrm{5}\:\mathrm{cm}\:\mathrm{and}\:\mathrm{mass}\:\mathrm{12}.\mathrm{3}\:\mathrm{g},\:\:\mathrm{with}\:\mathrm{an} \\ $$$$\mathrm{electrical}\:\mathrm{resistance}\:\mathrm{of}\:\mathrm{1}.\mathrm{1}\:\mathrm{m}\Omega.\:\mathrm{this}\:\mathrm{wire}\:\mathrm{falls}\:\mathrm{through}\:\mathrm{a}\:\mathrm{horizontal} \\ $$$$\mathrm{magnetic}\:\mathrm{field}\:\:\mathrm{with}\:\mathrm{flux}\:\mathrm{density}\:\mathrm{of}\:\mathrm{0}.\mathrm{35}\:\mathrm{T}.\:\mathrm{As}\:\mathrm{his}\:\mathrm{wire}\:\mathrm{falls}\:\mathrm{its}\:\mathrm{ends} \\ $$$$\mathrm{slide}\:\mathrm{smoothly}\:\mathrm{between}\:\mathrm{two}\:\mathrm{rails}\:\mathrm{connected}\:\mathrm{by}\:\mathrm{a}\:\mathrm{wire}\:\mathrm{with}\:\mathrm{negligible} \\ $$$$\mathrm{internal}\:\mathrm{resistance}.\:\mathrm{Calculate}\:\mathrm{the}\:\mathrm{magnitude}\:\mathrm{of}\:\mathrm{the}\:\mathrm{terminal}\:\mathrm{energy} \\ $$$$\mathrm{resistance},\:\mathrm{neglecting}\:\mathrm{the}\:\mathrm{resistance}\:\mathrm{of}\:\mathrm{the}\:\mathrm{rails}. \\ $$ Terms of…
Question Number 34410 by Tinkutara last updated on 05/May/18 $${Prove}\:{that}\:\frac{\left({n}^{\mathrm{2}} \right)!}{\left({n}!\right)^{{n}+\mathrm{1}} }\:{is}\:{always}\:{an}\:{integer} \\ $$$${for}\:{n}\in{N}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 99905 by Rio Michael last updated on 23/Jun/20 Commented by Rio Michael last updated on 23/Jun/20 $$\mathrm{P}\:\mathrm{and}\:{Q}\:\mathrm{are}\:\mathrm{two}\:\mathrm{identical}\:\mathrm{straight}\:\mathrm{cables}\:\mathrm{each}\:\mathrm{of}\:\mathrm{electrical}\:\mathrm{resistance}\:\mathrm{20}.\mathrm{0}\Omega. \\ $$$$\mathrm{placed}\:\mathrm{4}.\mathrm{8}\:\mathrm{cm}\:\mathrm{apart}\:\mathrm{in}\:\mathrm{air}.\: \\ $$$$\left(\mathrm{a}\right)\:\mathrm{find}\:\mathrm{the}\:\mathrm{current}\:\mathrm{through}\:\mathrm{each}\:\mathrm{cable} \\ $$$$\left(\mathrm{b}\right)\:\mathrm{draw}\:\mathrm{the}\:\mathrm{magnetic}\:\mathrm{field}\:\mathrm{pattern}\:\mathrm{in}\:\mathrm{the}\:\mathrm{region}\:\mathrm{between}\:{P}\:\mathrm{and}\:{Q}…
Question Number 165385 by SLVR last updated on 31/Jan/22 $${Number}\:{of}\:\:{ways}..{n}\: \\ $$$${differrnt}\:\:{things}\:{be}\:{distributed} \\ $$$${in}\:{r}\:{identical}\:{boxes}\:{so}\:{as} \\ $$$$\left.\mathrm{1}\right){empty}\:{box}\:{is}\:{allowed} \\ $$$$\left.\mathrm{2}\right){empty}\:{box}\:{not}\:{allowed} \\ $$$${Number}\:{of}\:{ways}…{n}\:{identical} \\ $$$${things}\:{be}\:{distributed}\:{to}\:{r} \\ $$$${identical}\:{boxes}\:{so}\:{as} \\…
Question Number 165376 by MikeH last updated on 31/Jan/22 $$\mathrm{Verify}\:\mathrm{wether}\:{f}\:\mathrm{is}\:\mathrm{invertible}\: \\ $$$${f}\:\left({x}\right)\:=\:\left(\mathrm{1}+\mathrm{2}{x}\right)^{\mathrm{3}} \\ $$ Answered by Rasheed.Sindhi last updated on 31/Jan/22 $${f}\:\left({x}\right)\:=\:\left(\mathrm{1}+\mathrm{2}{x}\right)^{\mathrm{3}} \\ $$$${y}=\left(\mathrm{1}+\mathrm{2}{x}\right)^{\mathrm{3}} \\…
Question Number 165361 by MikeH last updated on 31/Jan/22 $$\mathrm{Obtain}\:\mathrm{a}\:\mathrm{general}\:\mathrm{formula}\:\mathrm{for} \\ $$$$\mathrm{the}\:\mathrm{sequence} \\ $$$$\:\frac{\mathrm{2}}{\mathrm{3}},\frac{\mathrm{4}}{\mathrm{5}},\frac{\mathrm{8}}{\mathrm{9}},\frac{\mathrm{16}}{\mathrm{17}},\frac{\mathrm{32}}{\mathrm{33}},… \\ $$$$\mathrm{assuming}\:\mathrm{the}\:\mathrm{sequence}\:\mathrm{continues}\:\mathrm{in}\:\mathrm{that} \\ $$$$\mathrm{pattern}. \\ $$ Commented by MJS_new last updated…
Question Number 164996 by Mathematification last updated on 24/Jan/22 Answered by mr W last updated on 25/Jan/22 $${AB}={x}_{\mathrm{1}} +{x}_{\mathrm{2}} \\ $$$${AB}=\sqrt{\left(\mathrm{3}+\mathrm{2}\right)^{\mathrm{2}} −\left(\mathrm{3}−\mathrm{2}\right)^{\mathrm{2}} }+\sqrt{\left(\mathrm{2}+\mathrm{1}.\mathrm{5}\right)^{\mathrm{2}} −\left(\mathrm{4}.\mathrm{5}−\mathrm{2}\right)^{\mathrm{2}} }…
Question Number 99194 by bemath last updated on 19/Jun/20 Answered by bramlex last updated on 19/Jun/20 $${suppose}\:{probability}\:{win}\:{or}\:{draw}\:{or}\:{lose}\:{are} \\ $$$${same}\:{is}\:\frac{\mathrm{1}}{\mathrm{3}} \\ $$$${not}\:{to}\:{lose}\:{in}\:{those}\:{three}\:{matches}\: \\ $$$${case}\left(\mathrm{1}\right)\:\left(\mathrm{3}{w}\right)\Rightarrow\left(\frac{\mathrm{1}}{\mathrm{3}}\right)^{\mathrm{3}} =\:\frac{\mathrm{1}}{\mathrm{27}} \\…
Question Number 164588 by ArielVyny last updated on 19/Jan/22 $${soit}\:{K}\:{un}\:{corps};\:{pour}\:{toute}\:{permutation} \\ $$$$\sigma\:{de}\:{S}_{{n}} ,\:{on}\:{note}\:{P}\left(\sigma\right)\:{sa}\:{matrice}\:{dans}\:{la}\:{base} \\ $$$${canonique}\:{de}\:{K}^{{n}} . \\ $$$${montrer}\:{que}\:{deux}\:{permutations}\:\sigma_{\mathrm{1}} \:{et}\:\sigma_{\mathrm{2}} \:{sont} \\ $$$${conjugues}\:{dans}\:{S}_{{n}} \:{si}\:{et}\:{seulement}\:{si}\: \\ $$$${P}\left(\sigma_{\mathrm{1}}…