Question Number 190395 by mr W last updated on 02/Apr/23 $${which}\:{is}\:{larger}, \\ $$$$\mathrm{2}^{\mathrm{234}} \:{or}\:\mathrm{5}^{\mathrm{100}} \:? \\ $$ Answered by aba last updated on 02/Apr/23 $$\mathrm{2}^{\mathrm{234}}…
Question Number 59316 by mr W last updated on 07/May/19 Answered by MJS last updated on 07/May/19 $${a}+{b}+{c}=\mathrm{25}\:\wedge\:{a},\:{b},\:{c}\:\in\mathbb{N}^{\bigstar} \:\Rightarrow\:\mathrm{1}\leqslant{a},\:{b},\:{c}\leqslant\mathrm{23} \\ $$$$\mathbb{S}=\left\{{n}\in\mathbb{N}^{\bigstar} \mid\mathrm{1}\leqslant{n}\leqslant\mathrm{23}\:\wedge\:\mathrm{mod}\left(\mathrm{360},\:{n}\right)=\mathrm{0}\right\}= \\ $$$$=\left\{\mathrm{1},\:\mathrm{2},\:\mathrm{3},\:\mathrm{4},\:\mathrm{5},\:\mathrm{6},\:\mathrm{8},\:\mathrm{9},\:\mathrm{10},\:\mathrm{12},\:\mathrm{15},\:\mathrm{18},\:\mathrm{20}\right\} \\…
Question Number 190339 by mr W last updated on 01/Apr/23 $${solve}\:{for}\:{x}\:\in\mathbb{R} \\ $$$$\sqrt{{x}−\mathrm{1}}+\sqrt{\mathrm{3}{x}−\mathrm{5}}+\sqrt{\mathrm{4}{x}−\mathrm{7}}=\mathrm{4}{x}−\mathrm{5} \\ $$ Answered by ajfour last updated on 01/Apr/23 $$\sqrt{{x}−\mathrm{1}}+\sqrt{\mathrm{3}{x}−\mathrm{5}}+\sqrt{\mathrm{4}{x}−\mathrm{7}} \\ $$$$\:\:=\frac{\mathrm{1}}{\mathrm{2}}\left({x}−\mathrm{1}+\mathrm{3}{x}−\mathrm{5}+\mathrm{4}{x}−\mathrm{7}\right)+\frac{\mathrm{3}}{\mathrm{2}}…
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Question Number 190192 by mr W last updated on 29/Mar/23 $${if}\:{a}>{b}>\mathrm{0},\:{find}\:{the}\:{minimum}\:{of} \\ $$$${a}^{\mathrm{2}} +\frac{\mathrm{1}}{\left({a}−{b}\right){b}}=? \\ $$ Commented by Frix last updated on 29/Mar/23 $$\mathrm{Minimum}=\mathrm{4}\:\mathrm{at}\:{a}=\sqrt{\mathrm{2}}\wedge{b}=\frac{\sqrt{\mathrm{2}}}{\mathrm{2}} \\…
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Question Number 189977 by cherokeesay last updated on 25/Mar/23 Answered by a.lgnaoui last updated on 26/Mar/23 $${the}\:\:{totale}\:{Area}: \\ $$$$\mathrm{2}\left(\mathrm{12}×\mathrm{3},\mathrm{5}+\mathrm{9}×\mathrm{3},\mathrm{5}\right)=\mathrm{147}{m}^{\mathrm{2}} \\ $$$${Area}\:{of}\:{windows}=\mathrm{21}{m}^{\mathrm{2}} \\ $$$${Area}\:{of}\:{tiles}=\mathrm{147}−\mathrm{21}=\mathrm{126}{m}^{\mathrm{2}} =\mathrm{126}×\mathrm{10}^{\mathrm{2}} {cm}^{\mathrm{2}}…
Question Number 189970 by Rupesh123 last updated on 25/Mar/23 Answered by Rasheed.Sindhi last updated on 25/Mar/23 $${x},{y},{x}+{y},{x}−{y}\:\in\mathbb{P}\:\:;\:{x},{y}=? \\ $$$$\bullet{If}\:\:{x}\:{and}\:{y}\:{were}\:{both}\:{odd}\:{primes} \\ $$$$\Rightarrow\mathrm{2}\:\mid\:\left({x}+{y}\right)\Rightarrow{x}+{y}\:\notin\mathbb{P}\:{or}\:{x}+{y}=\mathrm{2} \\ $$$${x}+{y}=\mathrm{2}\:{has}\:{no}\:{solution}\:{in}\:{prime} \\ $$$$\bullet{If}\:{x}={y}=\mathrm{2}\Rightarrow\:{x}+{y},{x}−{y}\:\notin\mathbb{P}…
Question Number 189901 by cherokeesay last updated on 23/Mar/23 Answered by BaliramKumar last updated on 24/Mar/23 $$\mathrm{4}.\:\left(\mathrm{i}\right)\:\mathrm{2}\left[\frac{\mathrm{1}}{\mathrm{2}}\:−\:\frac{\mathrm{1}}{\infty}\right]\:=\:\mathrm{2}\left[\frac{\mathrm{1}}{\mathrm{2}}\:−\:\mathrm{0}\right]\:=\:\mathrm{1} \\ $$ Answered by talminator2856792 last updated on…
Question Number 58804 by Tawa1 last updated on 30/Apr/19 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\:\mathrm{x}:\:\:\:\:\mathrm{4}\:\mathrm{cos}\:\mathrm{x}\:+\:\mathrm{3}\:\mathrm{sin}\:\mathrm{x}\:\:=\:\:\mathrm{2} \\ $$ Commented by MJS last updated on 30/Apr/19 $$\mathrm{generally} \\ $$$${a}\mathrm{cos}\:{x}\:+{b}\mathrm{sin}\:{x}\:={c} \\ $$$${x}=\mathrm{2arctan}\:{t} \\…