Question Number 8993 by tawakalitu last updated on 11/Nov/16 $$\int\mathrm{sin}\left(\mathrm{e}^{\mathrm{2x}} \right)\:\mathrm{dx} \\ $$ Commented by FilupSmith last updated on 12/Nov/16 $${u}={e}^{\mathrm{2}{x}} \:\Rightarrow\:{du}=\frac{\mathrm{1}}{\mathrm{2}}{e}^{\mathrm{2}{x}} {dx} \\ $$$$\int\mathrm{sin}\left({e}^{\mathrm{2}{x}}…
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Question Number 74526 by Kunal12588 last updated on 25/Nov/19 $${prove}\:{that} \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}{tan}^{−\mathrm{1}} {x}={cos}^{−\mathrm{1}} \left(\sqrt{\frac{\mathrm{1}+\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}{\mathrm{2}\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}}\right) \\ $$$${using}\:{substitution}\:{x}={cos}\:\mathrm{2}\theta \\ $$ Answered by mind is power…
Question Number 8991 by Chantria last updated on 11/Nov/16 $${prove} \\ $$$$\:\:\:\:{a}^{\mathrm{3}} +{b}^{\mathrm{3}} +{c}^{\mathrm{3}} \geqslant\mathrm{3}{abc}\:;\:\forall{a},{b},{c}\geqslant\mathrm{0} \\ $$ Answered by aydnmustafa1976 last updated on 14/Nov/16 $${A}.{M}\geqslant{G}.{M}\:\:\:\left(\:{a}^{\mathrm{3}}…
Question Number 74527 by Maclaurin Stickker last updated on 25/Nov/19 Commented by Maclaurin Stickker last updated on 25/Nov/19 $${In}\:{the}\:{figure}\:{determine}\:{the}\:{radius} \\ $$$${of}\:{the}\:{smallest}\:{circumference}\:{as}\:{a} \\ $$$${function}\:{of}\:{the}\:{radius}\:\boldsymbol{\mathrm{R}}\:{of}\:{the}\:{quadrant}. \\ $$…
Question Number 8988 by Daily last updated on 10/Nov/16 $${prove} \\ $$$$\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}{k}\left({k}+\mathrm{1}\right)={k}\left({k}+\mathrm{1}\right)\left({k}+\mathrm{2}\right)/\mathrm{3} \\ $$ Answered by 123456 last updated on 11/Nov/16 $${s}\left({n}\right)=\underset{{k}=\mathrm{1}} {\overset{{n}}…
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Question Number 74522 by necxxx last updated on 25/Nov/19 $${A}\:{rope}\:{inclined}\:{at}\:{angle}\:\mathrm{37}°\:{to}\:{the}\: \\ $$$${horizontal}\:{is}\:{used}\:{to}\:{drag}\:{a}\:\mathrm{50}{kg}\:{block} \\ $$$${along}\:{a}\:{level}\:{floor}\:{with}\:{an}\:{acceleration} \\ $$$${of}\:\mathrm{1}{m}/{s}^{\mathrm{2}} \:.{The}\:{coefficient}\:{of}\:{friction} \\ $$$${between}\:{the}\:{block}\:{and}\:{the}\:{floor}\:{is}\:\mathrm{0}.\mathrm{2}. \\ $$$${What}\:{is}\:{the}\:{tension}\:{in}\:{the}\:{rope}? \\ $$ Commented by…
Question Number 140056 by Ndala last updated on 03/May/21 $$\mathrm{Prove}\:\mathrm{the}\:\mathrm{folowing}\:\mathrm{result}: \\ $$$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \mathrm{cot}\:\theta\centerdot\left(\mathrm{log}\:\mathrm{sec}\:\theta\right)^{\mathrm{3}} {d}\theta=\frac{\pi^{\mathrm{4}} }{\mathrm{240}} \\ $$$$. \\ $$$$\mathrm{I}\:\mathrm{need}\:\mathrm{your}\:\mathrm{help},\:\mathrm{if}\:\mathrm{possible}\:\mathrm{please}. \\ $$ Answered by Ar…
Question Number 74520 by chess1 last updated on 25/Nov/19 Answered by MJS last updated on 26/Nov/19 $$\mathrm{0}\leqslant{x}<\mathrm{2}\pi \\ $$$$\mathrm{tan}\:{x}\:>\mathrm{sin}\:{x} \\ $$$$\frac{\mathrm{sin}\:{x}}{\mathrm{cos}\:{x}}>\mathrm{sin}\:{x} \\ $$$$\mathrm{case}\:\mathrm{1}:\:\mathrm{sin}\:{x}\:>\mathrm{0}\:\Leftrightarrow\:\mathrm{0}<{x}<\pi \\ $$$$\frac{\mathrm{1}}{\mathrm{cos}\:{x}}>\mathrm{1}\:\Leftrightarrow\:\mathrm{0}<{x}<\frac{\pi}{\mathrm{2}}\vee\frac{\mathrm{3}\pi}{\mathrm{2}}<{x}<\mathrm{2}\pi…