Question Number 209424 by Tawa11 last updated on 09/Jul/24 Commented by Tawa11 last updated on 09/Jul/24 $$\mathrm{In}\:\mathrm{this}\:\mathrm{kind}\:\mathrm{of}\:\mathrm{probability},\:\mathrm{is}\:\mathrm{the}\:\mathrm{formular}. \\ $$$$\mathrm{p}\left(\mathrm{x}\:=\:\mathrm{r}\right)\:\:=\:\overset{\mathrm{n}} {\:}\mathrm{C}_{\mathrm{r}} \:\mathrm{p}^{\mathrm{r}} \:\mathrm{q}^{\mathrm{n}\:−\:\mathrm{r}} \\ $$$$\mathrm{or} \\…
Question Number 209393 by Shrodinger last updated on 08/Jul/24 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{{ln}\left({tanx}\right)}{\mathrm{1}+{tanx}}{dx} \\ $$ Commented by Frix last updated on 09/Jul/24 $$\mathrm{I}\:\mathrm{think}\:\mathrm{it}'\mathrm{s}\:−\frac{\pi^{\mathrm{2}} }{\mathrm{16}} \\ $$…
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Question Number 209356 by mnjuly1970 last updated on 08/Jul/24 $$ \\ $$$$\:\:\:\:\:{Evaluate}\:: \\ $$$$ \\ $$$$ \\ $$$$\:\:\:\:\mathrm{lim}_{\:{n}\rightarrow\infty} \:\underset{{k}=\mathrm{0}} {\overset{{n}−\mathrm{1}} {\prod}}\:{cos}\:\left(\frac{\mathrm{2}^{\:{k}} .\pi}{\mathrm{2}^{\:{n}} \:−\mathrm{1}}\:\right)\:\:=\:?\:\:\:\:\:\:\:\:\:\: \\ $$$$…
Question Number 209389 by a.lgnaoui last updated on 08/Jul/24 $$\mathrm{Cercle}\:\mathrm{C}\:\:\:\mathrm{de}\:\mathrm{rayon}\:\boldsymbol{\mathrm{R}}=\mathrm{5} \\ $$$$\mathrm{petits}\:\mathrm{cercles}\:\mathrm{de}\:\mathrm{meme}\:\mathrm{rayon}\:\boldsymbol{\mathrm{r}} \\ $$$$\mathrm{Determiner}\:\mathrm{Surface}\:\left(\boldsymbol{\mathrm{ABCDEF}}\right)? \\ $$ Commented by a.lgnaoui last updated on 08/Jul/24 Terms of…
Question Number 209357 by mnjuly1970 last updated on 08/Jul/24 $$ \\ $$$$\:\:\:\:\:\:{Evaluate}\:: \\ $$$$ \\ $$$$\:\:\:\:\:\mathrm{B}_{{n}} =\:\underset{{k}=\mathrm{3}} {\overset{{n}} {\prod}}\:\frac{\:{k}^{\:\mathrm{2}} −\mathrm{1}}{{k}^{\mathrm{2}} \:+\:{k}\:−\mathrm{6}}=\:? \\ $$ Answered by…
Question Number 209358 by peter frank last updated on 08/Jul/24 Commented by mr W last updated on 08/Jul/24 $${if}\:{the}\:{bowl}\:{is}\:{smooth},\:{why}\:{should}\:{the}\: \\ $$$${small}\:{block}\:{rotate}\:{with}\:{the}\:{bowl}\:{and} \\ $$$${not}\:{fall}\:{to}\:{the}\:{middle}\:{of}\:{the}\:{bowl}? \\ $$…
Question Number 209359 by peter frank last updated on 08/Jul/24 Commented by mr W last updated on 08/Jul/24 $$“{with}\:{a}\:{vertical}\:{velocity}\:{v}''\:{should}\:{be} \\ $$$$“{with}\:{a}\:{velocity}\:{v}''. \\ $$$${answer}\:\frac{{v}^{\mathrm{2}} −{g}^{\mathrm{2}} {x}^{\mathrm{2}}…
Question Number 209385 by efronzo1 last updated on 08/Jul/24 Answered by Rasheed.Sindhi last updated on 08/Jul/24 $${p}\left({x}\right)={ax}^{\mathrm{2}} +{bx}+\mathrm{1}\Rightarrow{p}\left(\mathrm{1}\right)={a}+{b}+\mathrm{1} \\ $$$${q}\left({x}\right)={bx}^{\mathrm{2}} +{ax}+\mathrm{1}\Rightarrow{q}\left(\mathrm{1}\right)={b}+{a}+\mathrm{1} \\ $$$${p}\left(\:{q}\left(\mathrm{1}\right)\:\right)={q}\left(\:{p}\left(\mathrm{1}\right)\:\right) \\ $$$${p}\left({a}+{b}+\mathrm{1}\right)={q}\left({a}+{b}+\mathrm{1}\right)…
Question Number 209353 by alcohol last updated on 08/Jul/24 Answered by Berbere last updated on 08/Jul/24 $${f}\left({x}+{y}\right)={f}\left({x}\right).{f}\left({y}\right) \\ $$$${f}\left({x}\right)={f}\left(\frac{{x}}{\mathrm{2}}+\frac{{x}}{\mathrm{2}}\right)=\left({f}\left(\frac{{x}}{\mathrm{2}}\right)\right)^{\mathrm{2}} \geqslant\mathrm{0} \\ $$$$\forall{x}\in\mathbb{R}\:{f}\left({x}\right)\geqslant\mathrm{0} \\ $$$${f}\left({x}+{y}\right)={f}\left({x}\right){f}\left({y}\right)\:\forall{y}\in\mathbb{R}\:{fixe}\:{x}\rightarrow{f}\left({x}+{y}\right)\:{est}\:{derivable} \\…