Question Number 91715 by 174 last updated on 02/May/20 Commented by mathmax by abdo last updated on 02/May/20 $${let}\:{A}_{{n}} =\int_{\mathrm{0}} ^{\frac{\mathrm{1}}{\:\sqrt{{n}}}} \:\:\:\:\frac{{n}\sqrt{\mathrm{1}+{x}^{\mathrm{4}} }}{\mathrm{1}+{n}^{\mathrm{2}} {x}^{\mathrm{2}} }{dx}\:{changement}\:{nx}\:={t}\:{give}\:…
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Question Number 26156 by bbbbbb last updated on 21/Dec/17 $${a}\:{two}\:{digit}\:{number}\:{is}\:\mathrm{3}\:{more}\:{than} \\ $$$$\mathrm{4}\:{times}\:{the}\:{sum}\:{of}\:{its}\:{digits}.\:{if} \\ $$$$\mathrm{18}\:{is}\:{added}\:{to}\:{this}\:{number}\:.{the}\: \\ $$$${sum}\:{is}\:{equal}\:{to}\:{number}\:{obtained} \\ $$$${by}\:{interchanging}\:{the}\:{digits}.{find}\:{the}\:{number} \\ $$ Answered by mrW1 last updated…
Question Number 91654 by Rio Michael last updated on 02/May/20 $$\mathrm{th}\:\mathrm{position}\:\mathrm{vector}\:\mathrm{of}\:\mathrm{a}\:\mathrm{particle}\:{p}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{3}\:\mathrm{kg}\:\mathrm{is}\:\mathrm{given}\:\mathrm{by}\: \\ $$$$\:{r}\:=\:\left[\left(\mathrm{cos}\:\mathrm{2}{t}\right)\:{i}\:+\:\left(\mathrm{sin}\:\mathrm{2}{t}\right){j}\right]\:\mathrm{m} \\ $$$$\mathrm{given}\:\mathrm{that}\:{p}\:\:\mathrm{was}\:\mathrm{intitialy}\:\mathrm{at}\:\mathrm{rest}. \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{cartesian}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{its}\:\mathrm{path}\:\mathrm{and}\:\mathrm{describe}\:\mathrm{it}. \\ $$ Answered by Kunal12588 last updated on…
Question Number 91655 by Rio Michael last updated on 02/May/20 $$\mathrm{A}\:\mathrm{particle}\:\mathrm{is}\:\mathrm{projected}\:\mathrm{with}\:\mathrm{an}\:\mathrm{intial}\:\mathrm{velocity}\:\mathrm{of}\:{u}\:\mathrm{ms}^{−\mathrm{1}} \:\mathrm{at}\:\mathrm{an}\:\mathrm{angle}\:\alpha\:\mathrm{to}\: \\ $$$$\mathrm{the}\:\mathrm{ground}\:\mathrm{from}\:\mathrm{a}\:\mathrm{point}\:\mathrm{O}\:\mathrm{on}\:\mathrm{the}\:\mathrm{ground}.\:\mathrm{Given}\:\mathrm{that}\:\mathrm{it}\:\mathrm{clears} \\ $$$$\mathrm{two}\:\mathrm{walls}\:\mathrm{of}\:\mathrm{hieght}\:{h}\:\mathrm{and}\:\mathrm{distances}\:\mathrm{2h}\:\mathrm{and}\:\mathrm{4h}\:\mathrm{respectively}\:\mathrm{from}\:\mathrm{O}. \\ $$$$\left(\mathrm{a}\right)\:\mathrm{find}\:\mathrm{the}\:\mathrm{tangent}\:\mathrm{of}\:\alpha \\ $$$$\left(\mathrm{b}\right)\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{hieght} \\ $$$$\left(\mathrm{c}\right)\:\mathrm{the}\:\mathrm{range}\:\mathrm{and}\:\mathrm{period}\:\mathrm{of}\:\mathrm{the}\:\mathrm{particle} \\ $$$$\left(\mathrm{d}\right)\:\mathrm{show}\:\mathrm{that}\:{u}^{\mathrm{2}} \:=\:\frac{\mathrm{4}}{\mathrm{26}}\:\mathrm{g}{h}\:…
Question Number 26113 by tawa tawa last updated on 19/Dec/17 Answered by ajfour last updated on 20/Dec/17 $$\mu_{{upper}} {mg}={kx} \\ $$$$\mu_{{upper}} {mg}+\mu_{{lower}} \left({M}+{m}\right){g}={F} \\ $$$${so}\:\:\:\boldsymbol{{x}}=\frac{\mathrm{0}.\mathrm{9}×\mathrm{15}×\mathrm{10}}{\mathrm{325}}\:=\frac{\mathrm{135}}{\mathrm{325}}\:…
Question Number 91638 by Maclaurin Stickker last updated on 02/May/20 $${Find}\:{the}\:{general}\:{term}: \\ $$$$\underset{{n}=\mathrm{1}} {\overset{{k}} {\sum}}{n}^{{n}} \\ $$ Answered by frc2crc last updated on 03/May/20 $${search}\:{for}\:{Faulhaber}\:{formular}…
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