Question Number 18655 by Tinkutara last updated on 26/Jul/17 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{odd}\:\mathrm{integers} \\ $$$$\mathrm{between}\:\mathrm{30},\mathrm{000}\:\mathrm{and}\:\mathrm{80},\mathrm{000}\:\mathrm{in}\:\mathrm{which}\:\mathrm{no} \\ $$$$\mathrm{digit}\:\mathrm{is}\:\mathrm{repeated}. \\ $$ Commented by mrW1 last updated on 27/Jul/17 $$\mathrm{let}'\mathrm{s}\:\mathrm{say}\:\mathrm{the}\:\mathrm{number}\:\mathrm{is}\:\mathrm{XZZZY} \\…
Question Number 18652 by Tinkutara last updated on 26/Jul/17 $$\mathrm{Show}\:\mathrm{that}\:\mathrm{for}\:\mathrm{any}\:\mathrm{natural}\:\mathrm{number}\:{n}, \\ $$$$\mathrm{the}\:\mathrm{fraction}\:\frac{\mathrm{21}{n}\:+\:\mathrm{4}}{\mathrm{14}{n}\:+\:\mathrm{3}}\:\mathrm{is}\:\mathrm{in}\:\mathrm{its}\:\mathrm{lowest}\:\mathrm{term}. \\ $$ Answered by diofanto last updated on 27/Jul/17 $$\mathrm{Lets}\:\mathrm{prove}\:\mathrm{by}\:\mathrm{contradiction}. \\ $$$$\mathrm{Suppose}\:\mathrm{there}\:\mathrm{is}\:{d}\:>\:\mathrm{1}\:\mathrm{such}\:\mathrm{that} \\…
Question Number 18498 by Tinkutara last updated on 22/Jul/17 $$\mathrm{How}\:\mathrm{many}\:\mathrm{times}\:\mathrm{is}\:\mathrm{digit}\:\mathrm{0}\:\mathrm{written}\:\mathrm{when} \\ $$$$\mathrm{listing}\:\mathrm{all}\:\mathrm{numbers}\:\mathrm{from}\:\mathrm{1}\:\mathrm{to}\:\mathrm{3333}? \\ $$ Commented by richard last updated on 23/Jul/17 $${do}\:{you}\:{want}\:{how}\:{many}\:{zeros}\:{there}\:{are}\:{between}\:\mathrm{1}\:{and}\:\mathrm{3333},\:{or}\:{how}\:{many}\:{times}\:{the}\:“\mathrm{0}''\:{appears},\:{independently}\:{of}\:{the}\:{amount}\:{of}\:{zeros}? \\ $$ Answered…
Question Number 83891 by bagjamath last updated on 07/Mar/20 $$ \\ $$$$ \\ $$$$\mathrm{1111}^{\mathrm{2019}} \:\mathrm{mod}\:\mathrm{11111}=….? \\ $$ Commented by MJS last updated on 08/Mar/20 $$\mathrm{you}\:\mathrm{are}\:\mathrm{right},\:\mathrm{I}\:\mathrm{misread}\:\mathrm{1111}^{\mathrm{2019}}…
Question Number 18135 by Tinkutara last updated on 15/Jul/17 $$\mathrm{Let}\:{x}\:\mathrm{be}\:\mathrm{the}\:\mathrm{LCM}\:\mathrm{of}\:\mathrm{3}^{\mathrm{2002}} \:−\:\mathrm{1}\:\mathrm{and} \\ $$$$\mathrm{3}^{\mathrm{2002}} \:+\:\mathrm{1}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{last}\:\mathrm{digit}\:\mathrm{of}\:{x}. \\ $$ Commented by mrW1 last updated on 15/Jul/17 $$\mathrm{0} \\…
Question Number 148951 by EDWIN88 last updated on 01/Aug/21 $${Let}\:{complex}\:{number}\:{z}=\left({a}+\mathrm{cos}\:\theta\right)+\left(\mathrm{2}{a}−\mathrm{sin}\:\theta\right){i}\:. \\ $$$${If}\:\mid{z}\mid\:\leqslant\mathrm{2}\:{for}\:{any}\:\theta\in{R}\:{then}\:{the} \\ $$$${range}\:{of}\:{real}\:{number}\:{a}\:{is}\:\_\_\_ \\ $$ Answered by iloveisrael last updated on 01/Aug/21 Answered by…
Question Number 83289 by Cmr 237 last updated on 29/Feb/20 $$\:\:{solve} \\ $$$$\boldsymbol{{log}}_{\left(\mathrm{24}\boldsymbol{{sinx}}\right)} \left(\mathrm{24}\boldsymbol{{cosx}}\right)=\frac{\mathrm{3}}{\mathrm{2}} \\ $$ Answered by TANMAY PANACEA last updated on 29/Feb/20 $$\frac{{ln}\mathrm{24}{cosx}}{{ln}\mathrm{24}{sinx}}=\frac{\mathrm{3}}{\mathrm{2}}…
Question Number 17446 by Tinkutara last updated on 05/Jul/17 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{integer}\:\mathrm{closest}\:\mathrm{to} \\ $$$$\mathrm{100}\left(\mathrm{12}\:−\:\sqrt{\mathrm{143}}\right). \\ $$ Commented by ajfour last updated on 06/Jul/17 $$\mathrm{100}\left(\mathrm{12}−\sqrt{\mathrm{143}}\right)=\frac{\mathrm{100}}{\mathrm{12}+\sqrt{\mathrm{143}}} \\ $$$$\:\:\approx\frac{\mathrm{100}}{\mathrm{24}}\:\approx\:\mathrm{4}.\mathrm{2}\: \\…
Question Number 17303 by RasheedSoomro last updated on 03/Jul/17 $$\mathrm{What}\:\mathrm{are}\:\mathrm{next}\:\mathrm{three}\:\mathrm{numbers} \\ $$$$\mathrm{in}\:\mathrm{the}\:\mathrm{following}\:\mathrm{sequence}: \\ $$$$\mathrm{4},\mathrm{6},\mathrm{12},\mathrm{18},\mathrm{30},\mathrm{42},\mathrm{60},… \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 17272 by RasheedSoomro last updated on 03/Jul/17 $$\mathrm{Determine}\:\mathrm{two}\:\mathrm{distinct}\:\mathrm{primes}\:\:\:\mathrm{p}\:\:\:\mathrm{and}\:\:\:\mathrm{q}\: \\ $$$$\mathrm{such}\:\mathrm{that}: \\ $$$$\left(\mathrm{i}\right)\:\mathrm{p}+\mathrm{q}+\mathrm{1},\mathrm{p}+\mathrm{q}−\mathrm{1},\frac{\mathrm{p}+\mathrm{q}}{\mathrm{2}}\:\in\:\mathbb{P}\:\left(\mathrm{All}\:\mathrm{primes}\right)? \\ $$$$\left(\mathrm{ii}\right)\:\mathrm{p}+\mathrm{q}+\mathrm{1},\mathrm{p}+\mathrm{q}−\mathrm{1},\frac{\mathrm{p}+\mathrm{q}}{\mathrm{2}},\frac{\mathrm{p}−\mathrm{q}}{\mathrm{2}}\:\in\:\mathbb{P}\:\left(\mathrm{All}\:\mathrm{primes}\right)? \\ $$ Commented by prakash jain last updated on…