Question Number 6135 by sanusihammed last updated on 15/Jun/16 $${Of}\:{all}\:{rectangular}\:{boxes}\:{without}\:{a}\:{lid}\:{and}\:{having}\:{a}\:{given}\: \\ $$$${surface}\:{area}\:.\:{Find}\:{the}\:{one}\:{with}\:{maximum}\:{volume}. \\ $$ Commented by FilupSmith last updated on 15/Jun/16 $$\mathrm{Edge}\:\mathrm{lengths}\:{a},\:{b},\:{c} \\ $$$$\mathrm{Max}\:\mathrm{volume}\:\mathrm{when}\:{a}={b}={c} \\…
Question Number 6136 by sanusihammed last updated on 15/Jun/16 $${Show}\:{that}\:{of}\:{all}\:{rectangles}\:{inscribed}\:{in}\:{a}\:{given}\:{circle}\: \\ $$$${the}\:{square}\:{has}\:{a}\:{maximum}\:{area}. \\ $$ Answered by Rasheed Soomro last updated on 15/Jun/16 $${All}\:{the}\:{rectangles}\:{inscribed}\:{in}\:{same}\:{circle} \\ $$$${have}\:{equal}\:{diagonals}\:{and}\:{vice}\:{versa}.…
Question Number 5940 by sanusihammed last updated on 05/Jun/16 Answered by FilupSmith last updated on 06/Jun/16 $${Are}\:{of}\:{non}\:{shaded}: \\ $$$${A}_{\mathrm{1}} =\frac{\mathrm{1}}{\mathrm{2}}{r}\left(\theta−\mathrm{sin}\:\theta\right) \\ $$$$\therefore\mathrm{Total}\:\mathrm{A}{rea}: \\ $$$${A}=\pi{r}^{\mathrm{2}} −\frac{\mathrm{1}}{\mathrm{2}}{r}\left(\theta−\mathrm{sin}\:\theta\right)…
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Question Number 71348 by ajfour last updated on 13/Oct/19 Commented by ajfour last updated on 13/Oct/19 $${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} \\ $$$${in}\:{radius},\:{how}\:{much}\:{earth}\:{is}\:{dug} \\ $$$${out}\:{from}\:{it}?\:{If}\:{the}\:{inner}\:{wall}\:{of} \\ $$$${well}\:{is}\:{plastered}\:{at}\:\:{Rupees}\:\mathrm{20}\: \\ $$$${per}\:{m}^{\mathrm{2}} .\:{WHAT}\:\:\mathbb{WILL}\:\:{BE}\:\:{ITS} \\ $$$$\mathcal{COST}\:? \\ $$$$ \\ $$$$…