Question Number 208367 by Mastermind last updated on 13/Jun/24 $$\mathrm{1}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{length}\:\mathrm{of}\:\mathrm{each}\:\mathrm{of}\:\mathrm{the}\:\mathrm{following} \\ $$$$\:\:\:\:\:\left(\mathrm{a}\right)\:\left\{\mathrm{x}\::\:−\mathrm{3}\:<\:\mathrm{x}\:<\:\mathrm{7}\right\} \\ $$$$\:\:\:\:\:\left(\mathrm{b}\right)\:\left\{\mathrm{x}\::\:\mathrm{2}\:\leqslant\:\mathrm{x}\:\leqslant\:\mathrm{6}\right\}\:\cup\:\left\{−\mathrm{3}\:\leqslant\:\mathrm{x}\:\leqslant\:−\mathrm{1}\right\} \\ $$$$\:\:\:\:\:\left(\mathrm{c}\right)\:\left\{\mathrm{x}\::\:−\mathrm{2}\:\leqslant\:\mathrm{x}\:<\:\mathrm{5}\right\}\:\cup\:\left\{\mathrm{1}\:<\:\mathrm{x}\:\leqslant\:\mathrm{7}\right\} \\ $$$$ \\ $$$$\mathrm{2}.\:\mathrm{Let}\:\mathrm{I}=\left(\mathrm{a},\:\mathrm{b}\right).\:\mathrm{Prove}\:\mathrm{that}\:\mathrm{I}\:\mathrm{is}\:\mathrm{measurable} \\ $$$$\mathrm{and}\:\mathrm{m}\left(\mathrm{I}\right)\:=\:\mathrm{L}\left(\mathrm{I}\right). \\ $$ Terms…
Question Number 208344 by mr W last updated on 13/Jun/24 Commented by mr W last updated on 13/Jun/24 $${find}\:{green}\:{area}=? \\ $$ Commented by naka3546 last…
Question Number 208361 by kgmxdd last updated on 13/Jun/24 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 208362 by hardmath last updated on 13/Jun/24 $$\mathrm{P}\left(\mathrm{x}\right)\:\:\mathrm{is}\:\mathrm{polynomial} \\ $$$$\mathrm{P}\left(\mathrm{x}\right)\:=\:\frac{\mathrm{x}^{\mathrm{4}} \:+\:\mathrm{2ax}^{\mathrm{3}} \:−\:\mathrm{bx}\:−\:\mathrm{5}}{\left(\mathrm{x}\:+\:\mathrm{1}\right)^{\mathrm{2}} } \\ $$$$\mathrm{Find}:\:\:\:\boldsymbol{\mathrm{b}}\:=\:? \\ $$ Answered by mr W last updated…
Question Number 208342 by hardmath last updated on 13/Jun/24 $$\mathrm{a},\mathrm{b},\mathrm{c}\in\mathbb{N} \\ $$$$\mathrm{x}\:=\:\mathrm{4}\left(\mathrm{2a}+\mathrm{5}\right)\:=\:\mathrm{6}\left(\mathrm{b}+\mathrm{9}\right)\:=\:\mathrm{9}\left(\mathrm{c}−\mathrm{1}\right) \\ $$$$\mathrm{find}:\:\:\:\boldsymbol{\mathrm{min}}\left(\mathrm{x}+\mathrm{a}+\mathrm{b}+\mathrm{c}\right)\:=\:? \\ $$ Answered by A5T last updated on 13/Jun/24 $${c}=\frac{\mathrm{6}\left({b}+\mathrm{9}\right)}{\mathrm{9}}+\mathrm{1}=\frac{\mathrm{2}{b}}{\mathrm{3}}+\mathrm{7}\Rightarrow{b}=\mathrm{3}{k} \\…
Question Number 208359 by alcohol last updated on 13/Jun/24 Commented by alcohol last updated on 13/Jun/24 $${please}\:{help} \\ $$ Answered by Berbere last updated on…
Question Number 208354 by kgmxdd last updated on 13/Jun/24 Commented by Frix last updated on 13/Jun/24 $$=\frac{\mathrm{4}}{\pi}!!! \\ $$$$\left(\mathrm{I}\:\mathrm{found}\:\mathrm{this}\:\mathrm{online}.\right) \\ $$ Terms of Service Privacy…
Question Number 208332 by essaad last updated on 12/Jun/24 Answered by Frix last updated on 12/Jun/24 $$\underset{{k}=\mathrm{0}} {\overset{{n}} {\prod}}\:\left({k}+{a}\right)\:={a}\left({a}+\mathrm{1}\right)\left({a}+\mathrm{2}\right)…\left({a}+{n}\right)=\frac{\left({a}+{n}\right)!}{\left({a}−\mathrm{1}\right)!} \\ $$$$\Rightarrow \\ $$$$\underset{{k}=\mathrm{0}} {\overset{{n}} {\prod}}\:\frac{{k}^{\mathrm{2}}…
Question Number 208334 by Shrodinger last updated on 12/Jun/24 $$\int_{\mathrm{0}} ^{\frac{\mathrm{4}}{\pi}} {ln}\left({cosx}\right){dx} \\ $$ Commented by Frix last updated on 12/Jun/24 $$\mathrm{This}\:\mathrm{question}\:\mathrm{has}\:\mathrm{been}\:\mathrm{answered}\:\left(\mathrm{208280}\right) \\ $$ Terms…
Question Number 208335 by Shrodinger last updated on 12/Jun/24 $$\int_{−\mathrm{1}} ^{\mathrm{1}} \sqrt{\mathrm{1}−{t}^{\mathrm{4}} }{dt} \\ $$ Answered by Frix last updated on 12/Jun/24 $$\underset{−\mathrm{1}} {\overset{\mathrm{1}} {\int}}\sqrt{\mathrm{1}−{t}^{\mathrm{4}}…