Question Number 190397 by pascal889 last updated on 02/Apr/23 Answered by som(math1967) last updated on 02/Apr/23 $$\:{x}^{{y}} ={y}^{{x}} \\ $$$$\Rightarrow{y}={x}^{\frac{{y}}{{x}}} \\ $$$$\left(\frac{{x}}{{y}}\right)^{\frac{{x}}{{y}}} \\ $$$$=\left(\frac{{x}}{{x}^{\frac{{y}}{{x}}} }\right)^{\frac{{x}}{{y}}}…
Question Number 190402 by Tinku Tara last updated on 02/Apr/23 $$\mathrm{v2}.\mathrm{272}\:\mathrm{fixes}\:\mathrm{some}\:\mathrm{issues}\:\mathrm{with}\:\mathrm{cursor} \\ $$$$\mathrm{position}\:\mathrm{while}\:\mathrm{writing}\:\mathrm{Right}\:\mathrm{to}\:\mathrm{Left} \\ $$$$\mathrm{Languages}\:\left(\mathrm{such}\:\mathrm{as}\:\mathrm{arabic}\right)\:\mathrm{using} \\ $$$$\mathrm{system}\:\mathrm{keyboard}. \\ $$ Commented by mr W last updated…
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Question Number 124824 by ZiYangLee last updated on 06/Dec/20 $$\mathrm{How}\:\mathrm{many}\:\mathrm{positive}\:\mathrm{four}-\mathrm{digits}\:\mathrm{integers} \\ $$$${abcd}\:\mathrm{satisfy}\:\mathrm{the}\:\mathrm{following}\:\mathrm{conditions}: \\ $$$$\left(\mathrm{i}\right)\:{abcd}\:\mathrm{is}\:\mathrm{divisible}\:\mathrm{hy}\:\mathrm{7}; \\ $$$$\left(\mathrm{ii}\right)\:\mathrm{When}\:\mathrm{the}\:\mathrm{first}\:\mathrm{and}\:\mathrm{the}\:\mathrm{last}\:\mathrm{digits} \\ $$$$\:\:\:\mathrm{are}\:\mathrm{interchanged},\:\mathrm{the}\:\mathrm{resulting}\:\mathrm{number} \\ $$$$\:\:\:{dbca}\:\mathrm{is}\:\mathrm{still}\:\mathrm{a}\:\mathrm{positive}\:\mathrm{four}-\mathrm{digits}\:\mathrm{number} \\ $$$$\:\:\:\mathrm{that}\:\mathrm{is}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{7}. \\ $$ Commented…
Question Number 190358 by Tinku Tara last updated on 01/Apr/23 $$\mathrm{The}\:\mathrm{latest}\:\mathrm{update}\:\mathrm{allows}\:\mathrm{you}\:\mathrm{to} \\ $$$$\mathrm{write}\:\mathrm{any}\:\mathrm{language}\:\mathrm{using}\:\mathrm{system} \\ $$$$\mathrm{keyboard}\:\mathrm{for}\:\mathrm{example} \\ $$$$\:\: \\ $$ Commented by mr W last updated…
Question Number 124819 by Ndala last updated on 06/Dec/20 $$\mathrm{5}^{{x}+\mathrm{2}} =\frac{\mathrm{594}}{\mathrm{5}} \\ $$$$\mathrm{5}^{{x}+\mathrm{3}} =\mathrm{594} \\ $$$$\left({x}+\mathrm{3}\right)\mathrm{log}\:_{\mathrm{5}} \mathrm{5}=\mathrm{log}\:_{\mathrm{5}} \mathrm{594} \\ $$$${x}+\mathrm{3}=\mathrm{log}\:_{\mathrm{5}} \mathrm{594}\rightarrow{x}=\mathrm{log}\:_{\mathrm{5}} \mathrm{594}−\mathrm{3} \\ $$ Commented…
Question Number 59273 by naka3546 last updated on 07/May/19 $${abc}\:\:=\:\:\mathrm{64} \\ $$$${a},\:{b},\:{c}\:\:\in\:\:\mathbb{R}^{+} \\ $$$${Find}\:\:{K}\:\:{that}\:\:{satisfy}\:\:{to}\:\:{the}\:\:{inequality}\:\:: \\ $$$$\:\:\:\:\:\frac{\left({a}\:+\:{b}\right)\:\sqrt{{ab}}\:\:+\:\:\left({b}\:+\:{c}\right)\:\sqrt{{bc}}\:\:+\:\:\left({c}\:+\:{a}\right)\:\sqrt{{ca}}}{\:\sqrt{{abc}}}\:\:\:\geqslant\:\:\sqrt{{a}}\:\:+\:\:\sqrt{{b}}\:\:+\:\:\sqrt{{c}}\:\:+\:\:{K}\:\:. \\ $$ Answered by tanmay last updated on 07/May/19…
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Question Number 59260 by naka3546 last updated on 07/May/19 Answered by mr W last updated on 07/May/19 $${white}=\mathrm{4}^{\mathrm{2}} \pi−\mathrm{3}^{\mathrm{2}} \pi+\mathrm{2}^{\mathrm{2}} \pi=\left(\mathrm{16}+\mathrm{4}−\mathrm{9}\right)\pi=\mathrm{11}\pi \\ $$$${blue}=\mathrm{6}^{\mathrm{2}} \pi−{white}=\left(\mathrm{36}−\mathrm{11}\right)\pi=\mathrm{25}\pi \\…
Question Number 190329 by yaslm last updated on 31/Mar/23 Commented by Frix last updated on 31/Mar/23 $$\mathrm{Because}\:\mathrm{everybody}\:\mathrm{here}\:\mathrm{is}\:\mathrm{clairvoyant}\:\mathrm{we} \\ $$$$\mathrm{know}\:\mathrm{Eqs}.\:\mathrm{12}.\mathrm{46},\:\mathrm{12}.\mathrm{47},\:\mathrm{12}.\mathrm{61}\:\&\:\mathrm{12}.\mathrm{62} \\ $$$$\mathrm{The}\:\mathrm{answers}\:\mathrm{are}\:\mathrm{given}\:\mathrm{in}\:{Bell},\:{Carson}\:\&\:{al}. \\ $$$$\left(\mathrm{1983}\right)\:\mathrm{on}\:\mathrm{page}\:\mathrm{436}\:\mathrm{Eq}.\:\mathrm{47}.\mathrm{38}\:\mathrm{for}\:{a}.,\:\mathrm{on}\:\mathrm{page} \\ $$$$\mathrm{214}\:\mathrm{Eq}.\:\mathrm{29}.\mathrm{4}\:\mathrm{for}\:{b}.\:\mathrm{and}\:\mathrm{in}\:{Yussuf}\:\left(\mathrm{1991}\right)\:\mathrm{on}…