Question Number 213999 by issac last updated on 24/Nov/24 $$\int\int…\int_{\:\mathcal{D}} \:\:{e}^{−\left({z}_{\mathrm{1}} ^{\mathrm{2}} +{z}_{\mathrm{2}} ^{\mathrm{2}} …+{z}_{{n}} ^{\mathrm{2}} \right)} \mathrm{da} \\ $$$$\mathcal{D}=\underset{\boldsymbol{\mathrm{n}}\:\boldsymbol{\mathrm{times}}} {\left[\mathrm{0},\infty\right)×\left[\mathrm{0},\infty\right)……\left[\mathrm{0},\infty\right)} \\ $$$$\int_{\mathrm{0}} ^{\:\pi} \:{e}^{−\mathrm{sin}^{\mathrm{2}}…
Question Number 214020 by ajfour last updated on 24/Nov/24 Commented by ajfour last updated on 24/Nov/24 $${Red}\:{area}\:=\:{Blue}\:{area}.\:{Find}\:{r}\:{in} \\ $$$${terms}\:{of}\:{k},\:\phi. \\ $$ Answered by dionigi last…
Question Number 214005 by RoseAli last updated on 24/Nov/24 $${find}\:{all}\:{zero}\:{divisors}\:{of}\:{Z}_{\mathrm{24}} \\ $$ Answered by TonyCWX08 last updated on 24/Nov/24 $$\mathrm{1}×\mathrm{24} \\ $$$$\mathrm{2}×\mathrm{12} \\ $$$$\mathrm{3}×\mathrm{8} \\…
Question Number 214000 by golsendro last updated on 24/Nov/24 $$\:\:\mathrm{Let}\:\mathrm{y}\left(\mathrm{x}\right)\:\mathrm{be}\:\mathrm{the}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{diff}\:\mathrm{eq}. \\ $$$$\:\:\mathrm{y}\:'=\:\frac{\mathrm{cos}\:\mathrm{x}+\mathrm{y}}{\mathrm{cos}\:\mathrm{x}}\:,\:\mathrm{y}\left(\mathrm{0}\right)=\mathrm{0} \\ $$$$\:\:\mathrm{Find}\:\mathrm{y}\left(\frac{\pi}{\mathrm{6}}\right). \\ $$ Commented by mr W last updated on 24/Nov/24 $${do}\:{you}\:{mean}\:\mathrm{cos}\:\left({x}+{y}\right)\:{instead}\:{of}…
Question Number 214001 by RoseAli last updated on 24/Nov/24 $$\mathrm{find}\:\mathrm{all}\:\mathrm{solutions}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation}\:{x}^{\mathrm{2}} ={x}\:\mathrm{in}\:\mathrm{each}\:\mathrm{of}\:\mathrm{the}\:\mathrm{rings}\: \\ $$$${Z}_{\mathrm{2}} \: \\ $$$${Z}_{\mathrm{3}} \\ $$$$\mathrm{and}\:\mathrm{Z}_{\mathrm{6}} \\ $$ Answered by TonyCWX08 last updated…
Question Number 214002 by RoseAli last updated on 24/Nov/24 $${find}\:{the}\:{integers}\:{x}\:{that}\:{satisfies}\:{a}\:{congruence}\:\mathrm{3}{x}=\mathrm{4}\:\left({mod}\:\mathrm{11}\right)\:. \\ $$ Answered by Rasheed.Sindhi last updated on 24/Nov/24 $$\mathrm{3}{x}\equiv\mathrm{4}\left({mod}\:\mathrm{11}\right) \\ $$$$\mathrm{3}{x}\equiv\mathrm{4}+\mathrm{11}\left({mod}\:\mathrm{11}\right) \\ $$$$\mathrm{3}{x}\equiv\mathrm{15}\left({mod}\:\mathrm{11}\right) \\…
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Question Number 213991 by Spillover last updated on 23/Nov/24 Answered by MathematicalUser2357 last updated on 28/Nov/24 $$\mathrm{Then}\:\mathrm{K}\:\mathrm{is}\:\underset{{r}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\left(−\mathrm{1}\right)^{{r}} \centerdot\underset{{i}=\mathrm{1}} {\overset{{r}−\mathrm{1}} {\prod}}\left(\mathrm{1}−\mathrm{2}{i}\right)}{\mathrm{2}^{\mathrm{3}{r}+\mathrm{1}} \centerdot\left(\mathrm{2}{r}+\mathrm{1}\right)\centerdot{r}!} \\ $$…
Question Number 213948 by issac last updated on 22/Nov/24 $$\mathrm{evaluate}. \\ $$$$\mathrm{1}.\:\frac{\mathrm{1}}{\pi}\int_{\mathrm{0}} ^{\:\pi} \:\:{e}^{−\boldsymbol{{i}}\left({t}−\mathrm{sin}\left({t}\right)\right)} \mathrm{d}{t} \\ $$$$\mathrm{2}.\:\int_{\mathrm{0}} ^{\:\mathrm{a}} \int_{\mathrm{0}} ^{\:\mathrm{a}} \:\:\sqrt{{u}^{\mathrm{2}} +{v}^{\mathrm{2}} −\mathrm{6}{u}+\mathrm{9}}\:\mathrm{d}{u}\mathrm{d}{v} \\ $$$$\mathrm{3}.\:\int_{\mathrm{0}}…
Question Number 213960 by Tawa11 last updated on 22/Nov/24 Commented by Tawa11 last updated on 22/Nov/24 $$\mathrm{Prove}\:\mathrm{by}\:\mathrm{Mathematical}\:\mathrm{Induction} \\ $$ Answered by A5T last updated on…