Question Number 200821 by Calculusboy last updated on 24/Nov/23 Answered by shunmisaki007 last updated on 24/Nov/23 $$\mathrm{ln}\left(\mathrm{10}!\right) \\ $$$$=\mathrm{ln}\left(\mathrm{10}\centerdot\mathrm{9}\centerdot\mathrm{8}\centerdot\mathrm{7}\centerdot\mathrm{6}\centerdot\mathrm{5}\centerdot\mathrm{4}\centerdot\mathrm{3}\centerdot\mathrm{2}\centerdot\mathrm{1}\right) \\ $$$$=\mathrm{ln}\left(\left(\mathrm{2}\centerdot\mathrm{5}\right)\centerdot\mathrm{3}^{\mathrm{2}} \centerdot\mathrm{2}^{\mathrm{3}} \centerdot\mathrm{7}\centerdot\left(\mathrm{2}\centerdot\mathrm{3}\right)\centerdot\mathrm{5}\centerdot\mathrm{2}^{\mathrm{2}} \centerdot\mathrm{3}\centerdot\mathrm{2}\centerdot\mathrm{1}\right) \\…
Question Number 200823 by mathlove last updated on 24/Nov/23 $${cos}\mathrm{20}\centerdot{cos}\mathrm{40}+{cos}^{\mathrm{2}} \mathrm{80}=? \\ $$ Answered by som(math1967) last updated on 24/Nov/23 $$\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{2}{cos}\mathrm{20}{cos}\mathrm{40}+\mathrm{2}{cos}^{\mathrm{2}} \mathrm{80}\right) \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}}\left({cos}\mathrm{20}+{cos}\mathrm{60}+\mathrm{1}+{cos}\mathrm{160}\right) \\…
Question Number 200833 by Mastermind last updated on 24/Nov/23 $$\mathrm{Advance}\:\mathrm{question} \\ $$$$ \\ $$$$\mathrm{A}\:\mathrm{phone}\:\mathrm{mistakenly}\:\mathrm{got}\:\mathrm{locked}\:\mathrm{with}\:\mathrm{the}\: \\ $$$$\mathrm{pattern}\:\mathrm{of}\:\:\mathrm{3}\:×\:\mathrm{3}\:\mathrm{form},\:\mathrm{in}\:\mathrm{how}\:\mathrm{many}\:\mathrm{attempts} \\ $$$$\mathrm{person}\:\mathrm{can}\:\mathrm{try}\:\mathrm{before}\:\mathrm{he}\:\mathrm{can}\:\mathrm{eventually}\:\mathrm{get} \\ $$$$\mathrm{it}\:\mathrm{right}\:? \\ $$$$ \\ $$$$\mathrm{Thank}\:\mathrm{you} \\…
Question Number 200834 by Rasheed.Sindhi last updated on 24/Nov/23 $${Show}\:{that}\:\:\:\overline {\:\:{abc}\:}+\overline {\:{bca}\:}+\overline {\:{cab}\:} \\ $$$${is}\:{divisible}\:{by}\:\mathrm{37} \\ $$ Answered by AST last updated on 24/Nov/23 $$\mathrm{111}\left({a}+{b}+{c}\right)\:{is}\:{a}\:{multiple}\:{of}\:\mathrm{37}…
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Question Number 200792 by sonukgindia last updated on 23/Nov/23 Commented by Frix last updated on 23/Nov/23 $$\mathrm{Do}\:\mathrm{you}\:\mathrm{know}\:\mathrm{the}\:\mathrm{answer}? \\ $$$$\mathrm{Is}\:\mathrm{it}\:\mathrm{63}.\mathrm{77\%}? \\ $$ Commented by sonukgindia last…
Question Number 200761 by a.lgnaoui last updated on 23/Nov/23 $$\boldsymbol{\mathrm{Determiner}}\:\:\boldsymbol{\mathrm{r}}\:\:\mathrm{et}\:\:\boldsymbol{\mathrm{R}}\:\:\left({voir}\:{figure}\:\right) \\ $$$$\:\mathrm{Sachant}\:\mathrm{aue}:\measuredangle\boldsymbol{\mathrm{C}}=\mathrm{120}\:\::\boldsymbol{{AB}}=\mathrm{12} \\ $$ Commented by a.lgnaoui last updated on 23/Nov/23 Commented by mr W…
Question Number 200795 by mathlove last updated on 23/Nov/23 $$\underset{{x}\rightarrow{sin}\mathrm{1}} {\mathrm{lim}}\:\frac{\mathrm{1}−{x}^{\mathrm{2}} }{\mathrm{1}+{cosx}}=? \\ $$ Answered by witcher3 last updated on 23/Nov/23 $$\mathrm{x}\rightarrow\frac{\mathrm{1}−\mathrm{x}^{\mathrm{2}} }{\mathrm{1}+\mathrm{cos}\left(\mathrm{x}\right)}\:\mathrm{is}\:\:\mathrm{defined}\:\mathrm{in}\:\mathrm{sin}\left(\mathrm{1}\right) \\ $$$$…
Question Number 200788 by hardmath last updated on 23/Nov/23 $$\mathrm{sin}\boldsymbol{\mathrm{x}}\:\:\:+\:\:\:\mathrm{cos}\boldsymbol{\mathrm{x}}\:\:\:=\:\:\:\mathrm{tg}\boldsymbol{\mathrm{x}} \\ $$$$\mathrm{x}\:=\:? \\ $$ Answered by Frix last updated on 23/Nov/23 $${x}=\mathrm{2tan}^{−\mathrm{1}} \:{t}\:\mathrm{leads}\:\mathrm{to} \\ $$$${t}^{\mathrm{4}}…
Question Number 200816 by mr W last updated on 23/Nov/23 Commented by mr W last updated on 23/Nov/23 $${find}\:{the}\:{colored}\:{areas}. \\ $$ Commented by Ari last…