Question Number 124666 by benjo_mathlover last updated on 05/Dec/20 $$\:{Find}\:{the}\:{volume}\:{that}\:{remains} \\ $$$${after}\:{the}\:{hole}\:{of}\:{radius}\:\mathrm{1}\:{bored}\: \\ $$$${through}\:{the}\:{center}\:{of}\:{a}\:{solid} \\ $$$${sphere}\:{of}\:{radius}\:\mathrm{3}. \\ $$$$\left({a}\right)\:\mathrm{18}\pi\:\:\:\:\left({b}\right)\:\frac{\mathrm{28}}{\mathrm{3}}\pi\:\:\:\:\left({c}\right)\:\mathrm{36}\pi\:\:\:\:\left({d}\right)\:\frac{\mathrm{56}\pi}{\mathrm{3}} \\ $$$$ \\ $$$$ \\ $$ Commented…
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Question Number 124651 by benjo_mathlover last updated on 05/Dec/20 Answered by liberty last updated on 05/Dec/20 $${for}\:−\mathrm{3}\leqslant{x}\leqslant\mathrm{3}\:\rightarrow\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} \:=\:\mathrm{9}\:;\:{g}\left({x}\right)=\sqrt{\mathrm{9}−{x}^{\mathrm{2}} } \\ $$$${for}\:\mathrm{3}\leqslant{x}\leqslant\mathrm{6}\rightarrow\left({x}−\frac{\mathrm{9}}{\mathrm{2}}\right)^{\mathrm{2}} +{y}^{\mathrm{2}} =\:\frac{\mathrm{9}}{\mathrm{4}} \\…
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Question Number 190079 by uchihayahia last updated on 26/Mar/23 $$ \\ $$$$ \\ $$$$\:{F}\left({t}\right)=\left(\mathrm{4}{t}^{\mathrm{3}} ,\mathrm{2}{cos}\left(\mathrm{2}{t}\right),\mathrm{3}{e}^{\mathrm{3}{t}} \right) \\ $$$$\:{find}\:{F}\:'\left({t}\right) \\ $$$$\:{F}\:'\left({t}\right)=\left(\mathrm{12}{t}^{\mathrm{2}} ,-\mathrm{4}{sin}\left(\mathrm{2}{t}\right),\mathrm{9}{e}^{\mathrm{3}{t}} \right) \\ $$$$\:{is}\:{my}\:{answer}\:{correct}? \\…
Question Number 58971 by hovea cw last updated on 02/May/19 Commented by hovea cw last updated on 02/May/19 $$\mathrm{hd}\:\mathrm{plz} \\ $$ Answered by tanmay last…
Question Number 124485 by snipers237 last updated on 03/Dec/20 $${Let}\:{S}^{{n}} =\left\{\left({x}_{\mathrm{0}} ,….,{x}_{{n}} \right)\in\mathbb{R}^{{n}+\mathrm{1}} \:/\:\:\:\underset{{i}=\mathrm{0}} {\overset{{n}} {\sum}}{x}_{{i}} ^{\mathrm{2}} \:\leqslant\mathrm{1}\right\} \\ $$$${Find}\:\:{Vol}\left({S}^{{n}} \right)\:{for}\:{all}\:{n}\geqslant\mathrm{3} \\ $$ Terms of…
Question Number 124483 by snipers237 last updated on 03/Dec/20 $$\:{Develop}\:{the}\:{function}\:{f}\left({x}\right)={e}^{{x}} {sinx} \\ $$$${Then}\:{Deduce}\:{that}\: \\ $$$$\underset{{k}=\mathrm{0}} {\overset{\left[\frac{{n}−\mathrm{1}}{\mathrm{2}}\right]} {\sum}}\left(−\mathrm{1}\right)^{{k}} {C}_{{n}} ^{\mathrm{2}{k}+\mathrm{1}} \:=\:\mathrm{2}^{\frac{{n}}{\mathrm{2}}} {sin}\left(\frac{{n}\pi}{\mathrm{4}}\right) \\ $$ Answered by…
Question Number 124415 by snipers237 last updated on 03/Dec/20 $${Let}\:{a}>\mathrm{0},\:\:\:{A}=\left\{{f}\in{C}^{\mathrm{2}} \left(\left[\mathrm{0},{a}\right],\mathbb{R}\right)\:,\:{f}\left(\mathrm{0}\right)={f}'\left(\mathrm{0}\right)=\mathrm{0}\right\} \\ $$$${N}_{\mathrm{1}} \left({f}\right)=\:{sup}\left\{\mid{f}\left({x}\right)\mid+\mid{f}''\left({y}\right)\mid\:\:\:,{x},{y}\in\left[\mathrm{0},{a}\right]\right\} \\ $$$${N}_{\mathrm{2}} \left({f}\right)={sup}\left\{\mid{f}\left({x}\right)+{f}''\left({x}\right)\mid\:\:\:,{x}\in\left[\mathrm{0},{a}\right]\right\} \\ $$$${Prove}\:{that}\:{N}_{\mathrm{1}} {and}\:{N}_{\mathrm{2}} \:{are}\:{equivalents}\:{norms} \\ $$ Commented by…
Question Number 58720 by Forkum Michael Choungong last updated on 28/Apr/19 $${find}\:\frac{{dy}}{{dx}}\:{given}\:{that}\:\:{y}\:=\:{cos}\left({x}°\right) \\ $$ Answered by tanmay last updated on 28/Apr/19 $$\mathrm{180}^{{o}} =\pi\:{radian} \\ $$$${x}^{{o}}…