Question Number 193853 by York12 last updated on 21/Jun/23 $$ \\ $$$$\boldsymbol{{Let}}\:\boldsymbol{{n}}\:\&\:\boldsymbol{{k}}\:\boldsymbol{{be}}\:\boldsymbol{{positive}}\:\boldsymbol{{integers}}\:\boldsymbol{{and}}\:\boldsymbol{{let}} \\ $$$$\boldsymbol{{S}}\:\boldsymbol{{be}}\:\boldsymbol{{a}}\:\boldsymbol{{set}}\:\boldsymbol{{of}}\:\boldsymbol{{n}}\:\boldsymbol{{points}}\:\boldsymbol{{in}}\:\boldsymbol{{The}}\:\boldsymbol{{plane}}\:\boldsymbol{{such}}\:\boldsymbol{{that}}\:: \\ $$$$\boldsymbol{{For}}\:\boldsymbol{{any}}\:\boldsymbol{{point}}\:\boldsymbol{{P}}\:\boldsymbol{{of}}\:\boldsymbol{{S}}\:\boldsymbol{{there}}\:\boldsymbol{{are}}\:\boldsymbol{{at}}\:\boldsymbol{{least}}\:\boldsymbol{{K}}\:\boldsymbol{{points}}\:\boldsymbol{{of}}\:\boldsymbol{{S}}\:\boldsymbol{{Equidistant}}\:\boldsymbol{{from}}\:\boldsymbol{{p}} \\ $$$$\boldsymbol{{Prove}}\:\boldsymbol{{that}}\:\boldsymbol{{k}}<\frac{\mathrm{1}}{\mathrm{2}}+\sqrt{\mathrm{2}\boldsymbol{{n}}} \\ $$ Terms of Service Privacy Policy…
Question Number 193756 by Shlock last updated on 19/Jun/23 Answered by talminator2856792 last updated on 19/Jun/23 $$\:\:\mathrm{7}\left(\mathrm{7}{a}\:+\:{b}\right)\:+\:{c}\:=\:\mathrm{7}\left(\mathrm{40}\right)\:+\:\mathrm{6} \\ $$$$\:\: \\ $$$$\:\:\rightarrow\:{c}\:=\:\mathrm{6}\:\left(\mathrm{mod}\:\mathrm{7}\right) \\ $$$$\:\:\rightarrow\:{c}\:=\:\mathrm{6} \\ $$$$\:\:…
Question Number 193760 by York12 last updated on 19/Jun/23 $${prove}\:{that} \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}×\frac{\mathrm{3}}{\mathrm{4}}×\frac{\mathrm{5}}{\mathrm{6}}×\frac{\mathrm{7}}{\mathrm{8}}×\frac{\mathrm{9}}{\mathrm{10}}…×\frac{\mathrm{99}}{\mathrm{100}}>\frac{\mathrm{1}}{\mathrm{13}}\:\:\: \\ $$ Answered by MM42 last updated on 19/Jun/23 $${can}\:{br}\:{show}\::\:\underset{{i}=\mathrm{1}} {\overset{{n}} {\prod}}\:\frac{\mathrm{2}{i}−\mathrm{1}}{\mathrm{2}{i}}\:>\:\frac{\mathrm{11}}{\mathrm{10}\sqrt{\mathrm{4}{n}+\mathrm{1}}} \\…
Question Number 193449 by Mingma last updated on 14/Jun/23 Commented by Frix last updated on 14/Jun/23 $$\mathrm{The}\:\mathrm{remainder}\:\mathrm{of}\:\mathrm{10}^{{n}} −\mathrm{1}\:\mathrm{divided}\:\mathrm{by}\:\mathrm{625} \\ $$$$\mathrm{is}\:\mathrm{624}\:\mathrm{for}\:{n}\geqslant\mathrm{4} \\ $$ Commented by Mingma…
Question Number 193438 by Mingma last updated on 14/Jun/23 Answered by qaz last updated on 14/Jun/23 $${log}_{\mathrm{3}} \left(\mathrm{9}{x}−\mathrm{3}\right)=\mathrm{1}+{log}_{\mathrm{3}} \left(\mathrm{3}{x}−\mathrm{1}\right)\:\:\:\:\:,{log}_{\mathrm{3}} \left({x}−\frac{\mathrm{1}}{\mathrm{3}}\right)={log}_{\mathrm{3}} \left(\mathrm{3}{x}−\mathrm{1}\right)−\mathrm{1} \\ $$$${log}_{\mathrm{3}} \left(\mathrm{3}{x}−\mathrm{1}\right)={y} \\…
Question Number 193435 by Mingma last updated on 14/Jun/23 Commented by maths_plus last updated on 14/Jun/23 $$\mathrm{i}\:\mathrm{want}\:\mathrm{to}\:\mathrm{known}\:… \\ $$ Answered by qaz last updated on…
Question Number 193280 by Mingma last updated on 09/Jun/23 Answered by AST last updated on 09/Jun/23 $$\mathrm{1000}\overset{\_\_\_\_} {{def}}+\overset{\_\_\_\_} {{abc}}=\mathrm{6000}\overset{\_\_\_\_} {{abc}}+\mathrm{6}\overset{\_\_\_\_} {{def}}\Rightarrow\frac{{def}}{{abc}}=\frac{\mathrm{5999}}{\mathrm{994}}=\frac{\mathrm{857}}{\mathrm{142}} \\ $$$$\Rightarrow\overset{\_\_\_\_\_\_\_\_} {{abcdef}}=\mathrm{142857} \\…
Question Number 193180 by BaliramKumar last updated on 06/Jun/23 $$\mathrm{If}\:{a}\:+\:{b}\:=\:\mathrm{1001}\:\&\:\mathrm{HCF}\left({a},\:{b}\right)\:=\:\mathrm{13}\: \\ $$$$\mathrm{then}\:\mathrm{how}\:\mathrm{many}\:\mathrm{set}\:\mathrm{of}\:{a}\:\&\:{b}. \\ $$ Answered by Subhi last updated on 06/Jun/23 $${a}\:=\:\mathrm{13}{k} \\ $$$${b}\:=\:\mathrm{13}{m} \\…
Question Number 131054 by benjo_mathlover last updated on 01/Feb/21 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{first}\:\mathrm{four}\:\mathrm{terms}\:\mathrm{in}\:\mathrm{the}\:\mathrm{series}\: \\ $$$$\mathrm{expansion}\:\mathrm{of}\:\frac{\mathrm{1}}{\mathrm{3x}+\mathrm{5}}\:\mathrm{ascending}\:\mathrm{power} \\ $$$$\mathrm{x}\:\mathrm{and}\:\mathrm{state}\:\mathrm{the}\:\mathrm{set}\:\mathrm{of}\:\mathrm{values}\:\mathrm{of}\:\mathrm{x}\:\mathrm{for} \\ $$$$\mathrm{which}\:\mathrm{this}\:\mathrm{expansion}\:\mathrm{is}\:\mathrm{valid}\:. \\ $$ Answered by EDWIN88 last updated on 01/Feb/21…
Question Number 131010 by Boucatchou last updated on 31/Jan/21 $$\:\:\:\:\:\:{Determine}\:\:{integers}\:\:{a},\:{b}\:{such}\:{that}\:\:\begin{cases}{{a}+{b}=\mathrm{182}}\\{{a}\vee{b}=\mathrm{13}}\end{cases} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com