Question Number 198839 by Guillaume last updated on 24/Oct/23 $${lim}\:{sin}\left({x}\right)\:=\:? \\ $$$${x}\rightarrow+\infty \\ $$ Commented by Frix last updated on 25/Oct/23 $$\mathrm{Does}\:\mathrm{not}\:\mathrm{exist}. \\ $$ Terms…
Question Number 198832 by ajfour last updated on 24/Oct/23 Commented by ajfour last updated on 24/Oct/23 $${The}\:{radii}\:{are}\:{a}\left({green}\right),\:{b}\left({brown}\right), \\ $$$$\:{c}\left({blue}\right). \\ $$$${Find}\:{v}\:{and}\:{V}\:\:{when}\:{green}\:{ball}\:{comes} \\ $$$${sliding}\:{at}\:{speed}\:{u}\:{its}\:{centre}\:{is}\:{at} \\ $$$$\left({a},{a},{z}\right)\:\:\:\:{z}>{a}.\:{This}\:{pushes}\:{other}…
Question Number 198802 by MathedUp last updated on 24/Oct/23 $$\mathrm{radius}\:{r}\:\mathrm{circle}\:;\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} ={r}^{\mathrm{2}} \\ $$$$\hat {\boldsymbol{\mathrm{F}}}\left({x},{y},{z}\right)={yz}\hat {\boldsymbol{\mathrm{e}}}_{\mathrm{1}} +{x}\hat {\boldsymbol{\mathrm{e}}}_{\mathrm{2}} −{xy}\hat {\boldsymbol{\mathrm{e}}}_{\mathrm{3}} \\ $$$$\mathrm{Find}\:\mathrm{flux}\:\boldsymbol{\rho}=\int\int_{\:\boldsymbol{\Sigma}} \:\hat {\boldsymbol{\mathrm{F}}}\centerdot\hat…
Question Number 198828 by a.lgnaoui last updated on 24/Oct/23 $$\:\:\boldsymbol{\mathrm{Show}}\:\boldsymbol{\mathrm{th}{at}}: \\ $$$$\:\boldsymbol{{Area}}\left(\boldsymbol{{blue}}\:\boldsymbol{{circle}}\right)=\boldsymbol{{Area}}\left(\boldsymbol{{Green}}\:\:\boldsymbol{{circle}}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$ Commented by a.lgnaoui last updated on 24/Oct/23 Answered by…
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Question Number 198763 by mr W last updated on 24/Oct/23 Commented by mr W last updated on 24/Oct/23 $$\mathrm{8}\:{small}\:{balls}\:{and}\:{a}\:{big}\:{ball}\:{on}\:{a} \\ $$$${table}\:{touch}\:{each}\:{other}. \\ $$$${if}\:{the}\:{radius}\:{of}\:{the}\:{small}\:{balls}\:{is}\:{r}, \\ $$$${find}\:{the}\:{radius}\:{of}\:{the}\:{big}\:{ball}.…
Question Number 198785 by sonukgindia last updated on 24/Oct/23 Answered by AST last updated on 24/Oct/23 $$\frac{\mathrm{1}}{\mathrm{197}}\equiv{x}\left({mod}\:\mathrm{3000}\right)\Rightarrow\mathrm{197}{x}\equiv\mathrm{1}\left({mod}\:\mathrm{3000}\right) \\ $$$$\mathrm{197}{x}\equiv\mathrm{1}\left({mod}\:\mathrm{3}\right)\Rightarrow−{x}\overset{\mathrm{3}} {\equiv}\mathrm{1}\Rightarrow{x}\overset{\mathrm{3}} {\equiv}\mathrm{2} \\ $$$$\mathrm{197}{x}\equiv\mathrm{1}\left({mod}\:\mathrm{8}\right)\Rightarrow\mathrm{5}{x}\equiv\mathrm{1}\left({mod}\:\mathrm{8}\right)\Rightarrow{x}\overset{\mathrm{8}} {\equiv}\mathrm{5} \\…
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Question Number 198786 by sonukgindia last updated on 24/Oct/23 Commented by Frix last updated on 24/Oct/23 $$\mathrm{If}\:{a},\:{b},\:{c},\:{d},\:{e}\:\in\mathbb{N}: \\ $$$$\mathrm{1}.\:{abc}=\mathrm{2}^{\mathrm{3}} ×\mathrm{3} \\ $$$$\mathrm{2}.\:{bcd}=\mathrm{2}^{\mathrm{2}} ×\mathrm{3}×\mathrm{5} \\ $$$$\mathrm{3}.\:{cde}=\mathrm{2}^{\mathrm{3}}…
Question Number 198754 by essaad last updated on 24/Oct/23 Answered by Frix last updated on 24/Oct/23 $${x}^{\frac{\mathrm{1}}{\mathrm{2}}} +{x}^{\frac{\mathrm{2}}{\mathrm{3}}} =\mathrm{12} \\ $$$$\mathrm{We}\:\mathrm{can}\:\mathrm{only}\:\mathrm{approximate} \\ $$$${x}\approx\mathrm{20}.\mathrm{4490371248} \\ $$…