Question Number 218187 by Mingma last updated on 01/Apr/25 Answered by efronzo1 last updated on 01/Apr/25 $$\mathrm{5}.\mathrm{1}\::\:\frac{\mathrm{k}}{\mathrm{5}}\:=\:\frac{\mathrm{2}}{\mathrm{3}}\:\Rightarrow\mathrm{k}=\frac{\mathrm{10}}{\mathrm{3}}\: \\ $$$$\:\mathrm{5}.\mathrm{2}\::\:\mathrm{6}+\mathrm{5k}=\mathrm{0}\:\Rightarrow\mathrm{k}=−\frac{\mathrm{6}}{\mathrm{5}} \\ $$ Terms of Service Privacy…
Question Number 218214 by ajfour last updated on 01/Apr/25 $${Q}\:\mathrm{214876}\:{always}\:{displsyed}\:{on}\:{sort}\:{by} \\ $$$$\:{recent}\:{activity},\:{its}\:{been}\:{months}\:{likethis}.. \\ $$ Commented by Tinku Tara last updated on 01/Apr/25 Looks like it is only considering question till year 2024. Will fix. Also Mr W the code for gif upload is also pending. Will fix these by end of the month. Commented by…
Question Number 218208 by Marzuk last updated on 01/Apr/25 $${This}\:{question}\:{is}\:{really}\:{important} \\ $$$${Prove}\:{or}\:{disprove}\:{that} \\ $$$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{3}^{{n}} {m}+\mathrm{3}^{{n}−\mathrm{1}} }{\mathrm{2}^{\lceil\frac{{n}}{\mathrm{2}}\rceil} }\:+\:\frac{\mathrm{3}^{{n}−\mathrm{1}} }{\mathrm{2}^{{n}} }\: \\ $$$$\:{the}\:{limit}\:{exists}\:{for}\:{m}\:\in\:{N}\:\backslash{B} \\ $$$${where}\:{B}\:=\:\left\{{n}\:\mid\:{log}_{\mathrm{2}} \left({n}\right)\:\in\:{N}\:\right\}…
Question Number 218169 by vile last updated on 31/Mar/25 $${P}\left(\mathrm{5},\mathrm{6}\right)=\frac{\mathrm{15}!}{\left(\mathrm{15}−\mathrm{6}\right)}\:=\:\frac{\mathrm{15}!}{\mathrm{9}!}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\frac{\mathrm{15}×\mathrm{14}×\mathrm{131}×\mathrm{2}×\mathrm{11}×\mathrm{10}×\mathrm{9}×\mathrm{8}×\mathrm{7}×\mathrm{6}×\mathrm{5}×\mathrm{4}×\mathrm{3}×\mathrm{2}×\mathrm{1}}{\mathrm{9}×\mathrm{8}×\mathrm{7}×\mathrm{6}×\mathrm{5}×\mathrm{4}×\mathrm{3}×\mathrm{2}×} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\mathrm{15}×\mathrm{14}×\mathrm{13}×\mathrm{12}×\mathrm{11}×\mathrm{10} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\mathrm{3},\mathrm{603},\mathrm{600} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$ Terms of Service Privacy Policy…
Question Number 218165 by hardmath last updated on 31/Mar/25 $$\lambda\:>\:\mathrm{0} \\ $$$$\mathrm{x}\:,\:\mathrm{y}\:,\:\mathrm{z}\:\in\:\mathrm{C} \\ $$$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{system}:\:\:\:\begin{cases}{\mathrm{xy}\:=\:\mathrm{z}^{\mathrm{2}} \:+\:\mathrm{2}\lambda\mathrm{z}\:−\:\lambda\mathrm{x}\:−\:\lambda\mathrm{y}}\\{\mathrm{yz}\:=\:\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{2}\lambda\mathrm{x}\:−\:\lambda\mathrm{y}\:−\:\lambda\mathrm{z}\:\:\:\:\:\:\:\:}\\{\mathrm{zx}\:=\:\mathrm{y}^{\mathrm{2}} \:+\:\mathrm{2}\lambda\mathrm{y}\:−\:\lambda\mathrm{z}\:−\:\lambda\mathrm{x}}\end{cases} \\ $$ Answered by mr W last updated…
Question Number 218162 by Ismoiljon_008 last updated on 31/Mar/25 $$\:\:\: \\ $$$$\:\:\:{Each}\:{edge}\:{of}\:{a}\:{parallelepiped}\:{is}\:\mathrm{1}\:{cm}\:{long}. \\ $$$$\:\:\:{At}\:{one}\:{of}\:{its}\:{vertices},\:{all}\:{three}\:{face}\:{angles} \\ $$$$\:\:\:{are}\:{acute},\:{and}\:{each}\:{measures}\:\mathrm{2}\alpha. \\ $$$$\:\:\:{Find}\:{the}\:{volume}\:{of}\:{the}\:{parallepiped}. \\ $$$$\:\:\:{Help}\:{me},\:\:{please} \\ $$ Answered by mr…
Question Number 218163 by hardmath last updated on 31/Mar/25 $$\mathrm{Find}:\:\:\:\int\:\frac{\mathrm{x}}{\:\sqrt{\mathrm{48}\:−\:\mathrm{2x}\:−\:\mathrm{x}^{\mathrm{2}} }}\:\mathrm{dx}\:=\:? \\ $$ Answered by efronzo1 last updated on 31/Mar/25 $$\:\mathrm{I}=\:\int\:\frac{\mathrm{x}}{\:\sqrt{\mathrm{49}−\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{2}} }}\:\mathrm{dx} \\ $$$$\:\mathrm{x}+\mathrm{1}\:=\:\mathrm{7sin}\:\:\mathrm{u}\: \\…
Question Number 218184 by hardmath last updated on 31/Mar/25 $$−\:\mathrm{2025}\:\::\:\:\mathrm{7} \\ $$$$\mathrm{Residue}\:=\:? \\ $$ Answered by MrGaster last updated on 05/Apr/25 $$−\mathrm{2025}=\mathrm{7}\left(−\mathrm{290}\right)+\mathrm{5} \\ $$ Commented…
Question Number 218185 by hardmath last updated on 31/Mar/25 $$\mathrm{Find}: \\ $$$$\underset{\boldsymbol{\mathrm{n}}\rightarrow\infty} {\mathrm{lim}}\:\mathrm{sin}\:\left(\mathrm{n}\pi\:\sqrt{\mathrm{n}^{\mathrm{2}} \:+\:\mathrm{2n}\:+\:\mathrm{2}\centerdot\left(\mathrm{k}\:+\:\mathrm{1}\right)}\right)\:=\:? \\ $$$$\mathrm{k}\:\in\:\mathbb{Z}\:-\:\mathrm{fixed} \\ $$ Answered by vnm last updated on 01/Apr/25…
Question Number 218153 by Rojarani last updated on 31/Mar/25 $$\:{x}+{y}\:=\mathrm{12} \\ $$$$\:{minimum}\:{value}\:{of} \\ $$$$\:\sqrt{{x}^{\mathrm{2}} +\mathrm{4}}\:+\sqrt{{y}^{\mathrm{2}} +\mathrm{9}}\:=? \\ $$ Answered by mr W last updated on…