Question Number 139639 by bemath last updated on 30/Apr/21 $$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{reflection}\:\mathrm{of}\:\mathrm{the}\: \\ $$$$\mathrm{point}\:\left(\mathrm{2},\mathrm{2}\right)\:\mathrm{in}\:\mathrm{the}\:\mathrm{line}\:\mathrm{x}+\mathrm{2y}\:=\:\mathrm{4}? \\ $$ Commented by bramlexs22 last updated on 30/Apr/21 $$\mathrm{Let}\:\mathrm{P}\left(\mathrm{2},\mathrm{2}\right)\:\&\:\mathrm{P}'\left(\mathrm{a},\mathrm{b}\right)\:\mathrm{is}\:\mathrm{the}\:\mathrm{reflectional} \\ $$$$\mathrm{image}\:\mathrm{of}\:\mathrm{P}\:\mathrm{in}\:\mathrm{L}. \\…
Question Number 8564 by tawakalitu last updated on 16/Oct/16 Commented by ridwan balatif last updated on 16/Oct/16 $$\mathrm{let}:\:\mathrm{V}'=\mathrm{V}_{\mathrm{o}} −\mathrm{4}\:,\:\:\:\mathrm{with}\:\mathrm{V}_{\mathrm{o}} \:\mathrm{is}\:\mathrm{speed}\:\mathrm{that}\:\mathrm{we}\:\mathrm{want}\:\mathrm{to}\:\mathrm{count}\:\mathrm{it} \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathrm{t}^{'} \:=\mathrm{t}+\mathrm{2} \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathrm{S}\:=\mathrm{240}\:\mathrm{km}…
Question Number 8560 by FilupSmith last updated on 16/Oct/16 $$\frac{{n}}{\mathrm{2}^{{k}} }={m},\:\:\:\:\:\:\:{n},{m},{k}\in\mathbb{Z} \\ $$$$\mathrm{For}\:\mathrm{any}\:\mathrm{integer}\:{n},\:\mathrm{how}\:\mathrm{many}\:\mathrm{times} \\ $$$$\mathrm{can}\:\mathrm{you}\:\mathrm{divide}\:\mathrm{it}\:\mathrm{by}\:\mathrm{2},\:\mathrm{such}\:\mathrm{that}\:\mathrm{the} \\ $$$$\mathrm{result}\:\mathrm{is}\:\mathrm{always}\:\mathrm{a}\:\mathrm{whole}\:\mathrm{number}. \\ $$$$\: \\ $$$$\mathrm{e}.\mathrm{g}.\:\mathrm{120} \\ $$$$\mathrm{160}/\mathrm{2}=\mathrm{80} \\ $$$$\mathrm{80}/\mathrm{2}=\mathrm{40}…
Question Number 8558 by Sopheak last updated on 16/Oct/16 Commented by FilupSmith last updated on 16/Oct/16 $${S}_{{n}} =\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{{k}^{\mathrm{4}} }{\left(\mathrm{2}{k}−\mathrm{1}\right)\left(\mathrm{2}{k}+\mathrm{1}\right)} \\ $$$$\frac{\mathrm{1}}{\left(\mathrm{2}{k}−\mathrm{1}\right)\left(\mathrm{2}{k}+\mathrm{1}\right)}=\frac{{A}}{\mathrm{2}{k}−\mathrm{1}}+\frac{{B}}{\mathrm{2}{k}+\mathrm{1}} \\ $$$$\mathrm{1}={A}\left(\mathrm{2}{k}+\mathrm{1}\right)+{B}\left(\mathrm{2}{k}−\mathrm{1}\right)…
Question Number 8554 by Sopheak last updated on 16/Oct/16 $${Problem}\:.\mathrm{15} \\ $$$${Find}\:{the}\:{sum}\:{of} \\ $$$${S}=\:\frac{\mathrm{3}}{\mathrm{1}!+\mathrm{2}!+\mathrm{3}!}+\frac{\mathrm{4}}{\mathrm{2}!+\mathrm{3}!+\mathrm{4}!}+\frac{\mathrm{5}}{\mathrm{3}!+\mathrm{4}!+\mathrm{5}!}+…+\frac{\mathrm{2016}}{\mathrm{2014}!+\mathrm{2015}!+\mathrm{2016}!} \\ $$$$\: \\ $$ Commented by Yozzias last updated on 16/Oct/16…
Question Number 8553 by Sopheak last updated on 16/Oct/16 Commented by Yozzias last updated on 16/Oct/16 $$\frac{\mathrm{1}}{\mathrm{n}!}−\frac{\mathrm{1}}{\left(\mathrm{n}+\mathrm{1}\right)!}=\frac{\mathrm{1}}{\mathrm{n}!}\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{n}+\mathrm{1}}\right)=\frac{\mathrm{1}}{\mathrm{n}!}\left(\frac{\mathrm{n}+\mathrm{1}−\mathrm{1}}{\mathrm{n}+\mathrm{1}}\right)=\frac{\mathrm{n}}{\mathrm{n}!\left(\mathrm{n}+\mathrm{1}\right)}=\frac{\mathrm{n}}{\left(\mathrm{n}+\mathrm{1}\right)!} \\ $$ Answered by Yozzias last updated on…
Question Number 74087 by mr W last updated on 19/Nov/19 $$\left({Q}\mathrm{73828}\right) \\ $$$${prove}\:{that}\:{no}\:{cube}\:{exists}\:{whose}\:{corners} \\ $$$${are}\:{located}\:{on}\:{all}\:{faces}\:{of}\:{an}\:{other}\:{cube}. \\ $$ Commented by mr W last updated on 18/Nov/19…
Question Number 8550 by tawakalitu last updated on 15/Oct/16 Answered by ridwan balatif last updated on 16/Oct/16 Commented by tawakalitu last updated on 16/Oct/16 $$\mathrm{Wow}.\:\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir}.…
Question Number 139619 by I want to learn more last updated on 29/Apr/21 Answered by mr W last updated on 30/Apr/21 $${P}={pressure} \\ $$$${V}={volume}\:{of}\:{gas}\:\left({air}\right) \\…
Question Number 8545 by Rishabh#1 last updated on 15/Oct/16 $$\mathrm{18}:\mathrm{48}\:::\:\mathrm{180}:? \\ $$$$\mathrm{Answer}\:\mathrm{optioms} \\ $$$$\mathrm{a}.\:\mathrm{392}\:\mathrm{b}.\:\mathrm{294}\:\mathrm{c}.\mathrm{230} \\ $$ Commented by Rishabh#1 last updated on 16/Oct/16 $$\mathrm{Answer}\:\mathrm{given}\:\mathrm{is}\:\mathrm{294}.\:\mathrm{I}\:\mathrm{am}\:\mathrm{not} \\…