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Question-5357

Question Number 5357 by Junaid Mirza last updated on 11/May/16 Commented by Yozzii last updated on 11/May/16 $${Let}\:{the}\:{lowest}\:{position}\:{of}\:{the}\:{bob}\:{be} \\ $$$${that}\:{where}\:{its}\:{gravitational}\:{potential} \\ $$$${energy}\:{is}\:{zero}.\:{Then},\:{by}\:{the}\:{law}\:{of} \\ $$$${conservation}\:{of}\:{energy}\:{for}\:{the}\:{bob}, \\…

2-1-3-a-1-b-1-c-1-d-a-b-c-d-Z-What-s-b-

Question Number 70885 by naka3546 last updated on 09/Oct/19 $$\sqrt[{\mathrm{3}}]{\mathrm{2}}\:\:=\:{a}\:+\:\frac{\mathrm{1}}{{b}\:+\:\frac{\mathrm{1}}{{c}\:+\:\frac{\mathrm{1}}{{d}\:+\:\ldots}}} \\ $$$${a},\:{b},\:{c},\:{d}\:\:\in\:\mathbb{Z}^{+} \\ $$$${What}'{s}\:\:{b}\:\:? \\ $$ Answered by MJS last updated on 09/Oct/19 $$\mathrm{the}\:\mathrm{continued}\:\mathrm{fraction}\:\mathrm{of}\:\sqrt[{\mathrm{3}}]{\mathrm{2}}\:\mathrm{is}\:\mathrm{non}+\mathrm{periodic} \\…

If-4-2-5-and-4-2-5-are-solutions-of-x-2-5a-b-x-3b-a-0-whete-a-and-b-are-real-numbers-determine-the-product-of-ab-

Question Number 70874 by Mr. K last updated on 09/Oct/19 $${If}\:\mathrm{4}−\mathrm{2}\sqrt{\mathrm{5}}\:{and}\:\mathrm{4}+\mathrm{2}\sqrt{\mathrm{5}\:}\:{are}\:{solutions} \\ $$$${of}\:{x}^{\mathrm{2}} +\left(\mathrm{5}{a}−{b}\right){x}+\left(\mathrm{3}{b}−{a}\right)=\mathrm{0} \\ $$$${whete}\:{a}\:{and}\:{b}\:{are}\:{real}\:{numbers},\: \\ $$$${determine}\:{the}\:{product}\:{of}\:\boldsymbol{{ab}}. \\ $$ Answered by tw000001 last updated…

Question-5337

Question Number 5337 by Junaid Mirza last updated on 09/May/16 Commented by prakash jain last updated on 09/May/16 $$\mathrm{4}\:\mathrm{is}\:\mathrm{correct}. \\ $$$$\mathrm{Relative}\:\mathrm{refractive}\:\mathrm{index}\:\:_{\mathrm{1}} \mu_{\mathrm{2}} =\frac{\mu_{\mathrm{2}} }{\mu_{\mathrm{1}} }…

Question-70847

Question Number 70847 by A8;15: last updated on 08/Oct/19 Answered by mind is power last updated on 08/Oct/19 $$\begin{cases}{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} =\mathrm{2}}\\{\mathrm{2}{x}^{\mathrm{4}} +{xy}^{\mathrm{3}} +{x}^{\mathrm{2}} {y}^{\mathrm{2}} −{x}^{\mathrm{3}}…

Question-70838

Question Number 70838 by A8;15: last updated on 08/Oct/19 Answered by mind is power last updated on 08/Oct/19 $${X}^{\mathrm{3}} −\mathrm{1}=\left({X}−\mathrm{1}\right)\left({X}^{\mathrm{2}} +{X}+\mathrm{1}\right) \\ $$$${X}^{\mathrm{3}} +\mathrm{1}=\left({X}+\mathrm{1}\right)\left({X}^{\mathrm{2}} −{X}+\mathrm{1}\right)…

Question-70834

Question Number 70834 by Maclaurin Stickker last updated on 08/Oct/19 Answered by mind is power last updated on 08/Oct/19 $$\sum_{{k}=\mathrm{1}} ^{{n}−\mathrm{1}} \frac{\mathrm{1}}{{log}_{{x}} \left(\mathrm{2}^{{k}} \right){log}_{{x}} \left(\mathrm{2}^{\left.{k}+\mathrm{1}\right)}…