Question Number 43374 by peter frank last updated on 10/Sep/18 $$\mathrm{A}\:\mathrm{drawer}\:\mathrm{contains}\:\mathrm{5}\:\mathrm{brown}\:\mathrm{socks}\:\mathrm{and}\:\mathrm{4} \\ $$$$\mathrm{blue}\:\mathrm{socks}\:\mathrm{well}\:\mathrm{mixed}.\:\mathrm{A}\:\mathrm{man}\:\mathrm{reaches} \\ $$$$\mathrm{the}\:\mathrm{drawer}\:\mathrm{and}\:\mathrm{pulls}\:\mathrm{out}\:\mathrm{2}\:\mathrm{socks}\:\mathrm{at} \\ $$$$\mathrm{random}.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that} \\ $$$$\mathrm{they}\:\mathrm{match}? \\ $$ Answered by tanmay.chaudhury50@gmail.com last…
Question Number 43344 by peter frank last updated on 10/Sep/18 $$\mathrm{The}\:\mathrm{number}\:\mathrm{1},\:\mathrm{2},\:\mathrm{3},\:…,\:{n}\:\:\mathrm{are}\:\mathrm{arranged} \\ $$$$\mathrm{in}\:\mathrm{a}\:\mathrm{random}\:\mathrm{order}.\:\mathrm{The}\:\mathrm{probability} \\ $$$$\mathrm{that}\:\mathrm{the}\:\mathrm{digits}\:\mathrm{1},\:\mathrm{2},\:\mathrm{3},\:…,\:{k}\:\left({k}>{n}\right)\:\mathrm{appears} \\ $$$$\mathrm{as}\:\mathrm{neighbours}\:\mathrm{is} \\ $$ Commented by MrW3 last updated on…
Question Number 108790 by saorey0202 last updated on 19/Aug/20 $$\mathrm{The}\:\mathrm{values}\:\mathrm{of}\:\theta\:\mathrm{lying}\:\mathrm{between}\:\mathrm{0}\:\mathrm{and} \\ $$$$\frac{\pi}{\mathrm{2}}\:\mathrm{and}\:\mathrm{satisfying}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\begin{vmatrix}{\mathrm{1}+\mathrm{sin}^{\mathrm{2}} \theta}&{\:\:\mathrm{cos}^{\mathrm{2}} \theta}&{\mathrm{4}\:\mathrm{sin}\:\mathrm{4}\theta}\\{\:\:\:\mathrm{sin}^{\mathrm{2}} \theta}&{\mathrm{1}+\mathrm{cos}^{\mathrm{2}} \theta}&{\mathrm{4}\:\mathrm{sin}\:\mathrm{4}\theta}\\{\:\:\:\mathrm{sin}^{\mathrm{2}} \theta}&{\:\:\:\mathrm{cos}^{\mathrm{2}} \theta}&{\mathrm{1}+\mathrm{sin}^{\mathrm{4}} \theta}\end{vmatrix}=\mathrm{0}\:\:\mathrm{are} \\ $$ Commented by…
Question Number 43180 by gunawan last updated on 08/Sep/18 $$\mathrm{The}\:\mathrm{smallest}\:\mathrm{and}\:\mathrm{the}\:\mathrm{largest}\:\mathrm{values}\:\mathrm{of} \\ $$$$\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{1}−{x}}{\mathrm{1}+{x}}\right)\:,\:\:\mathrm{0}\leqslant\:{x}\:\leqslant\:\mathrm{1}\:\:\mathrm{are} \\ $$ Commented by maxmathsup by imad last updated on 08/Sep/18 $${let}\:\varphi\left({x}\right)={arctan}\left(\frac{\mathrm{1}−{x}}{\mathrm{1}+{x}}\right)\:\:\:{with}\:{x}\in\left[\mathrm{0},\mathrm{1}\right]\:{changement}\:{x}\:={cos}\theta\:{give}…
Question Number 43179 by gunawan last updated on 08/Sep/18 $$\mathrm{The}\:\mathrm{solution}\:\mathrm{of} \\ $$$$\mathrm{sin}^{−\mathrm{1}} \left(\frac{\mathrm{2}{a}}{\mathrm{1}+{a}^{\mathrm{2}} }\right)−\mathrm{cos}^{−\mathrm{1}} \left(\frac{\mathrm{1}−{b}^{\mathrm{2}} }{\mathrm{1}+{b}^{\mathrm{2}} }\right)=\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{2}{x}}{\mathrm{1}−{x}^{\mathrm{2}} }\right)\:\mathrm{is} \\ $$ Answered by tanmay.chaudhury50@gmail.com last…
Question Number 108453 by gospelkenny last updated on 17/Aug/20 $$\mathrm{If}\:\:{R}=\left(\mathrm{7}+\mathrm{4}\sqrt{\mathrm{3}}\right)^{\mathrm{2}{n}} \:=\:{I}+{f},\:\mathrm{where}\:{I}\:\in\:{N} \\ $$$$\mathrm{and}\:\:\:\mathrm{0}<{f}<\mathrm{1},\:\mathrm{then}\:{R}\left(\mathrm{1}−{f}\right)\:\mathrm{equals} \\ $$ Answered by 1549442205PVT last updated on 17/Aug/20 $$\mathrm{Set}\:\mathrm{Q}=\left(\mathrm{7}−\mathrm{4}\sqrt{\mathrm{3}}\right)^{\mathrm{2n}} \Rightarrow\sqrt{\mathrm{RQ}}=\left[\left(\mathrm{7}+\mathrm{4}\sqrt{\mathrm{3}}\right)^{\mathrm{n}} \left(\mathrm{7}−\mathrm{4}\sqrt{\mathrm{3}}\right)^{\mathrm{n}}…
Question Number 108407 by ZiYangLee last updated on 16/Aug/20 $$\mathrm{The}\:\mathrm{sides}\:\mathrm{AB},\:\mathrm{BC},\:\mathrm{CA}\:\mathrm{of}\:\mathrm{a}\:\mathrm{triangleABC} \\ $$$$\mathrm{have}\:\mathrm{3},\:\mathrm{4}\:\mathrm{and}\:\mathrm{5}\:\mathrm{interior}\:\mathrm{points}\:\mathrm{respectively} \\ $$$$\mathrm{on}\:\mathrm{them}.\:\mathrm{The}\:\mathrm{total}\:\mathrm{number}\:\mathrm{of}\:\mathrm{triangles} \\ $$$$\mathrm{that}\:\mathrm{can}\:\mathrm{be}\:\mathrm{constructed}\:\mathrm{by}\:\mathrm{using}\:\mathrm{these} \\ $$$$\mathrm{points}\:\mathrm{as}\:\mathrm{vertices}\:\mathrm{is} \\ $$ Answered by mbertrand658 last updated…
Question Number 42728 by RANGAM kumar last updated on 01/Sep/18 $$\mathrm{If}\:{A}=\begin{bmatrix}{\:\:\:\mathrm{cos}\:{x}}&{\mathrm{sin}\:{x}}\\{−\mathrm{sin}\:{x}}&{\mathrm{cos}\:{x}}\end{bmatrix}\:\mathrm{and}\: \\ $$$${A}\:\mathrm{adj}\:{A}\:=\:{k}\begin{bmatrix}{\mathrm{1}}&{\mathrm{0}}\\{\mathrm{0}}&{\mathrm{1}}\end{bmatrix},\:\mathrm{then}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{k}\:\mathrm{is} \\ $$ Answered by math1967 last updated on 01/Sep/18 $${adjA}=\begin{bmatrix}{{cosx}}&{{sinx}}\\{−{sinx}}&{{cosx}}\end{bmatrix}^{{t}} =\begin{bmatrix}{{cosx}}&{−{sinx}}\\{{sinx}}&{{cosx}}\end{bmatrix} \\…
Question Number 42684 by 1996ajaykmar@email.com last updated on 31/Aug/18 $$\mathrm{The}\:\mathrm{coefficient}\:\mathrm{of}\:{x}^{\mathrm{4}} \:\mathrm{in}\:\mathrm{the}\:\mathrm{expansion}\:\mathrm{of} \\ $$$$\left(\frac{{x}}{\mathrm{2}}\:−\:\frac{\mathrm{3}}{{x}^{\mathrm{2}} }\right)^{\mathrm{10}} \:\mathrm{is} \\ $$ Commented by maxmathsup by imad last updated on…
Question Number 42668 by bbnnftm833 last updated on 31/Aug/18 $$\mathrm{If} \\ $$$$\mid{a}\:\mathrm{sin}^{\mathrm{2}} \theta+{b}\:\mathrm{sin}\:\theta\:\mathrm{cos}\:\theta+{c}\:\mathrm{cos}^{\mathrm{2}} \theta−\frac{\mathrm{1}}{\mathrm{2}}\left({a}−{c}\right)\mid \\ $$$$\:\:\:\leqslant\:\frac{\mathrm{1}}{\mathrm{2}}\:{k},\:\mathrm{then}\:{k}^{\mathrm{2}} \:\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$ Terms of Service Privacy Policy Contact:…