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Question Number 71348 by ajfour last updated on 13/Oct/19 Commented by ajfour last updated on 13/Oct/19 $${If}\:{the}\:{circle}\:{has}\:{unit}\:{radius}\:{and} \\ $$$${each}\:{part}\:{have}\:{same}\:{area},\:{find} \\ $$$${radius}\:{of}\:{circular}\:{arc}. \\ $$ Commented by…
Question Number 70980 by ~ À ® @ 237 ~ last updated on 10/Oct/19 $$\:{Soit}\:\left({E},\mathcal{A},\mu\right)\:{un}\:\:{espace}\:{mesure}\:\:.\:{On}\:{suppose} \\ $$$${qu}'{il}\:{existe}\:{un}\:{X}\in\mathcal{A}\:\:{tel}\:\:\mu\left({X}\right)=+\infty \\ $$$$\left.\mathrm{1}\right){Montrer}\:{que}\:{si}\:\:\mu\:{est}\:{semi}-{finie}\:\:{alors} \\ $$$$\forall\:{r}>\mathrm{0}\:\:{il}\:{existe}\:\:{B}\subseteq{X}\:{tel}\:{que}\:\:{r}<\mu\left({B}\right)<\:+\infty \\ $$$$ \\ $$…
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Question Number 4420 by ankitbhawarkar333gmail.com last updated on 24/Jan/16 Answered by Yozzii last updated on 24/Jan/16 $${f}\left({x}\right)={sin}\mathrm{3}{x}−\mathrm{3}{sinx} \\ $$$${f}^{'} \left({x}\right)=\mathrm{3}{cos}\mathrm{3}{x}−\mathrm{3}{cosx} \\ $$$$\therefore\:{f}^{'} \left(\pi/\mathrm{2}\right)=\mathrm{3}{cos}\frac{\mathrm{3}\pi}{\mathrm{2}}−\mathrm{3}{cos}\frac{\pi}{\mathrm{2}}=\mathrm{0}. \\ $$$${Since}\:{f}^{'}…
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Question Number 69347 by Askash last updated on 22/Sep/19 $${If}\:{a}\:{well}\:{is}\:{dug}\:\mathrm{21}{m}\:{deep}\:{and}\:\mathrm{1}.\mathrm{4}{m} \\ $$$${in}\:{radius},\:{how}\:{much}\:{earth}\:{is}\:{dug} \\ $$$${out}\:{from}\:{it}?\:{If}\:{the}\:{inner}\:{wall}\:{of} \\ $$$${well}\:{is}\:{plastered}\:{at}\:\:{Rupees}\:\mathrm{20}\: \\ $$$${per}\:{m}^{\mathrm{2}} .\:{WHAT}\:\:\mathbb{WILL}\:\:{BE}\:\:{ITS} \\ $$$$\mathcal{COST}\:? \\ $$$$ \\ $$$$…
Question Number 3250 by Filup last updated on 08/Dec/15 $$\mathrm{It}\:\mathrm{is}\:\mathrm{known}\:\mathrm{that}: \\ $$$$\zeta\left({s}\right)=\underset{{i}=\mathrm{1}} {\overset{\infty} {\sum}}{i}^{−{s}} \\ $$$$ \\ $$$$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\zeta\left({s}\right)=\underset{{i}=\mathrm{1}} {\overset{\infty} {\prod}}\left(\mathrm{1}−\frac{\mathrm{1}}{\pi\left({i}\right)^{{s}} }\right) \\ $$$$\mathrm{where}\:\pi\left({n}\right)={n}\mathrm{th}\:\mathrm{prime}…
Question Number 134097 by bobhans last updated on 27/Feb/21 $$\mathrm{In}\:\mathrm{a}\:\mathrm{square}\:\mathrm{ABCD}\:,\:\mathrm{a}\:\mathrm{triangle} \\ $$$$\mathrm{APQ}\:\mathrm{inscribed}\:\mathrm{in}\:\mathrm{it}.\:\mathrm{AP}=\mathrm{4}\:\mathrm{cm}, \\ $$$$\mathrm{PQ}=\mathrm{3}\:\mathrm{cm}\:\mathrm{and}\:\mathrm{AQ}=\mathrm{5}\:\mathrm{cm}.\:\mathrm{Point} \\ $$$$\mathrm{P}\:\mathrm{is}\:\mathrm{on}\:\mathrm{the}\:\mathrm{side}\:\mathrm{BC}\:\mathrm{and}\:\mathrm{point}\:\mathrm{Q} \\ $$$$\mathrm{is}\:\mathrm{on}\:\mathrm{side}\:\mathrm{CD}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{square}\:\mathrm{ABCD}. \\ $$ Answered by mr…
Question Number 132230 by pticantor last updated on 12/Feb/21 $$ \\ $$$$ \\ $$$$\boldsymbol{{S}}=\underset{\boldsymbol{{k}}=\mathrm{1}} {\overset{+\infty} {\sum}}\left(\frac{\mathrm{1}}{\:\sqrt{\boldsymbol{{k}}^{\mathrm{2}} −\mathrm{1}}}−\frac{\mathrm{1}}{\:\sqrt{\boldsymbol{{k}}^{\mathrm{2}} +\mathrm{1}}}\right) \\ $$$$\boldsymbol{{S}}\:={l}\:{or}\:\boldsymbol{{S}}=\infty\:\:??? \\ $$ Answered by JDamian…