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Question-227024

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Question Number 227024 by mr W last updated on 26/Dec/25 Commented by mr W last updated on 26/Dec/25 $${the}\:{floor}\:{is}\:{smooth}.\:{the}\:{small}\:{ball} \\ $$$${is}\:{released}\:{from}\:{rest}\:{at}\:{the}\:{position} \\ $$$${as}\:{shown}.\:{find}\:{the}\:{locus}\:{of}\:{the}\: \\ $$$${small}\:{ball}\:{in}\:{given}\:{coordinate}…

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If-and-are-root-of-the-equation-x-2-2x-4-0-and-for-n-N-Show-that-n-n-2-n-1-cos-npi-3-

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Question Number 227016 by Spillover last updated on 25/Dec/25 $${If}\:\alpha\:{and}\:.\beta\:\:{are}\:{root}\:{of}\:{the}\:{equation} \\ $$$${x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{4}=\mathrm{0}\:{and}\:{for}\:{n}\in\mathbb{N} \\ $$$${Show}\:{that}\: \\ $$$$\alpha^{{n}} +\beta^{{n}} =\mathrm{2}^{{n}+\mathrm{1}} \mathrm{cos}\:\left(\frac{{n}\pi}{\mathrm{3}}\right) \\ $$ Answered by Frix…

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in-a-cup-filled-with-a-liquid-of-density-a-bubble-rests-in-the-liquid-in-h-deepness-radius-initial-of-the-bubble-r-i-initial-density-of-the-bubble-i-mass-amp-temparature-is-constant-a-small

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Question Number 227011 by fantastic2 last updated on 25/Dec/25 $${in}\:{a}\:{cup}\:{filled}\:{with}\:{a}\:{liquid}\:{of}\:{density}\:\rho,{a} \\ $$$${bubble}\:{rests}\:{in}\:{the}\:{liquid}\:{in}\:{h}\:{deepness}. \\ $$$${radius}\:{initial}\:{of}\:{the}\:{bubble}={r}_{{i}} \\ $$$$\:{initial}\:{density}\:{of}\:{the}\:{bubble}=\sigma_{{i}} \\ $$$$\left(\:{mass\&temparature}\:{is}\:{constant}\right) \\ $$$${a}\:{small}\:{jerk}\:{is}\:{given}\:{to}\:{the}\:{cup}\:{and}\:{the} \\ $$$${bubble}\:{starts}\:{to}\:{go}\:{upwards}. \\ $$$${find}: \\…

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