Question Number 210719 by lmcp1203 last updated on 17/Aug/24 $${find}\:\mathrm{63}!^{\mathrm{36}!} {mod}\mathrm{97}\:\:\:{thanks} \\ $$ Answered by A5T last updated on 19/Aug/24 $$\phi\left(\mathrm{97}\right)=\mathrm{96} \\ $$$$\mathrm{36}!\equiv\mathrm{0}\left({mod}\:\mathrm{96}\right)\Rightarrow\mathrm{36}!=\mathrm{96}{k} \\ $$$$\left(\mathrm{63}!,\mathrm{97}\right)=\mathrm{1}\Rightarrow\mathrm{63}!^{\mathrm{36}!}…
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Question Number 210723 by universe last updated on 17/Aug/24 $$\mathrm{the}\:\mathrm{volume}\:\mathrm{of}\:\mathrm{the}\:\mathrm{region}\:\mathrm{between}\:\mathrm{the}\: \\ $$$$\mathrm{planes}\:\mathrm{x}+\mathrm{y}+\mathrm{2z}=\mathrm{2}\:\mathrm{and}\:\mathrm{2x}+\mathrm{y}+\mathrm{z}\:=\:\mathrm{4}\:\mathrm{in}\: \\ $$$$\mathrm{the}\:\mathrm{first}\:\mathrm{octant}\:\mathrm{is} \\ $$ Answered by mr W last updated on 17/Aug/24 $${V}=\frac{\mathrm{1}}{\mathrm{6}}\left(\mathrm{2}×\mathrm{4}×\mathrm{4}−\mathrm{2}×\mathrm{2}×\mathrm{1}\right)=\frac{\mathrm{14}}{\mathrm{3}}…
Question Number 210685 by Tamukong last updated on 16/Aug/24 $${find} \\ $$$$\int\frac{\mathrm{1}}{{x}}{dx} \\ $$ Answered by Tinku Tara last updated on 16/Aug/24 $$\mathrm{ln}\:{x}\:+{C} \\ $$…
Question Number 210687 by shohruz last updated on 16/Aug/24 Commented by mr W last updated on 16/Aug/24 $${what}'{s}\:{the}\:{question}? \\ $$ Commented by Frix last updated…
Question Number 210677 by Safojon last updated on 16/Aug/24 Answered by BHOOPENDRA last updated on 16/Aug/24 $$\theta=\frac{{k}\pi}{\mathrm{7}\:},\mathrm{7}\theta={k}\pi\:\left({where}\:{k}=\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4}….{n}\right) \\ $$$$\mathrm{7}\theta=\pi\:\left({k}=\mathrm{1}\right) \\ $$$$\mathrm{4}\theta+\mathrm{3}\theta=\pi \\ $$$${tg}\mathrm{4}\theta=−{tg}\left(\mathrm{3}\theta\right)\:{let}\:{tg}={t} \\ $$$$\Rightarrow\:\frac{\mathrm{4}{t}−\mathrm{4}{t}^{\mathrm{3}}…
Question Number 210694 by ajfour last updated on 16/Aug/24 Answered by mr W last updated on 17/Aug/24 Commented by mr W last updated on 17/Aug/24…
Question Number 210695 by cherokeesay last updated on 16/Aug/24 Commented by A5T last updated on 17/Aug/24 Answered by mr W last updated on 17/Aug/24 Commented…
Question Number 210679 by peter frank last updated on 16/Aug/24 Answered by mr W last updated on 16/Aug/24 $${RH}_{\mathrm{16}°{C}} =\frac{\mathrm{273}.\mathrm{15}+\mathrm{16}}{\mathrm{273}.\mathrm{15}+\mathrm{20}}×\frac{\mathrm{17}.\mathrm{5}}{\mathrm{13}.\mathrm{6}}×\mathrm{36\%}\approx\mathrm{46\%} \\ $$ Commented by peter…
Question Number 210688 by BHOOPENDRA last updated on 16/Aug/24 $$ \\ $$In a convex quadrilateral ABCD, diagonals AC and BD intersect at E, while perpendicular…