Question Number 46430 by MrW3 last updated on 26/Oct/18 Commented by MrW3 last updated on 27/Oct/18 $${maybe}\:{we}\:{should}\:{at}\:{first}\:{forget}\:{the} \\ $$$${length}\:{of}\:{the}\:{rope}\:{ring}.\:{the}\:{question} \\ $$$${is}\:{just}\:{if}\:{the}\:{rope}\:{can}\:{rest}\:{in}\:{a}\:{inclined} \\ $$$${position}\:{on}\:{the}\:{surface}\:{of}\:{cone}. \\ $$…
Question Number 46427 by hassentimol last updated on 26/Oct/18 $$\mathrm{Give}\:\mathrm{a}\:\mathrm{proof}\:\mathrm{for}\:\mathrm{the}\:\mathrm{following}. \\ $$$$ \\ $$$$ \\ $$$$\forall\:{a}\:\in\:\mathbb{R}^{\ast} \:,\:\left({b},{c}\right)\:\in\:\mathbb{R}\:,\:{x}\:\in\:\mathbb{C}\:: \\ $$$$ \\ $$$$ \\ $$$${ax}^{\mathrm{2}} \:+\:{bx}\:+\:{c} \\…
Question Number 177493 by ali009 last updated on 06/Oct/22 $${find}\:{the}\:{laplace}\:{transform}\:{of} \\ $$$${f}\left({t}\right)={ln}\left({t}\right) \\ $$ Commented by JDamian last updated on 06/Oct/22 Is it suitable for Laplace Transform? Commented by ali009…
Question Number 111954 by Hassen_Timol last updated on 05/Sep/20 $${P}\mathrm{roof}\:\mathrm{for}\:\mathrm{the}\:\mathrm{following}\:: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:{n}!\:\geqslant\:\mathrm{2}×\mathrm{3}^{{n}−\mathrm{2}} \\ $$$$ \\ $$ Answered by mathmax by abdo last updated…
Question Number 177476 by Skabetix last updated on 05/Oct/22 Commented by Slomenist1 last updated on 05/Oct/22 $${bonjour}\:{stp}\:{donne}\:{la}\:{serie}\:{complete}\:{elle}\:{semble}\:{belle} \\ $$$$ \\ $$ Commented by Skabetix last…
Question Number 111934 by mohammad17 last updated on 05/Sep/20 Answered by Aina Samuel Temidayo last updated on 05/Sep/20 $$\sqrt{\mathrm{x}+\mathrm{5}}+\sqrt{\mathrm{2x}+\mathrm{1}}=\mathrm{4x}−\mathrm{10} \\ $$$$\mathrm{Squaring}\:\mathrm{both}\:\mathrm{sides},\mathrm{we}\:\mathrm{have} \\ $$$$\mathrm{x}+\mathrm{5}+\mathrm{2x}+\mathrm{1}+\mathrm{2}\sqrt{\left(\mathrm{x}+\mathrm{5}\right)\left(\mathrm{2x}+\mathrm{1}\right)}=\mathrm{16x}^{\mathrm{2}} +\mathrm{100}−\mathrm{80x} \\…
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Question Number 111879 by mathdave last updated on 05/Sep/20 $${prove}\:{that}\: \\ $$$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}{n}\underset{{k}=\mathrm{1}} {\overset{{n}−\mathrm{1}} {\sum}}\frac{\mathrm{ln}\left({k}+{n}\right)−\mathrm{ln}\left({n}\right)}{{k}^{\mathrm{2}} +{n}^{\mathrm{2}} }=\frac{\pi}{\mathrm{8}}\mathrm{ln2} \\ $$ Answered by Dwaipayan Shikari last updated…