Question Number 18142 by Tinkutara last updated on 15/Jul/17 $$\mathrm{An}\:\mathrm{object}\:{A}\:\mathrm{is}\:\mathrm{kept}\:\mathrm{fixed}\:\mathrm{at}\:\mathrm{the}\:\mathrm{point} \\ $$$${x}\:=\:\mathrm{3}\:\mathrm{m}\:\mathrm{and}\:{y}\:=\:\mathrm{1}.\mathrm{25}\:\mathrm{m}\:\mathrm{on}\:\mathrm{a}\:\mathrm{plank}\:{P} \\ $$$$\mathrm{raised}\:\mathrm{above}\:\mathrm{the}\:\mathrm{ground}.\:\mathrm{At}\:\mathrm{time}\:{t}\:=\:\mathrm{0}, \\ $$$$\mathrm{the}\:\mathrm{plank}\:\mathrm{starts}\:\mathrm{moving}\:\mathrm{along}\:\mathrm{the}\:{x}- \\ $$$$\mathrm{direction}\:\mathrm{with}\:\mathrm{an}\:\mathrm{acceleration}\:\mathrm{1}.\mathrm{5}\:\mathrm{ms}^{−\mathrm{2}} . \\ $$$$\mathrm{At}\:\mathrm{the}\:\mathrm{same}\:\mathrm{instant}\:\mathrm{a}\:\mathrm{stone}\:\mathrm{is}\:\mathrm{projected} \\ $$$$\mathrm{from}\:\mathrm{the}\:\mathrm{origin}\:\mathrm{with}\:\mathrm{a}\:\mathrm{velocity}\:\overset{\rightarrow} {{u}}\:\mathrm{as} \\…
Question Number 18140 by Tinkutara last updated on 15/Jul/17 $$\mathrm{From}\:\mathrm{a}\:\mathrm{tower}\:\mathrm{of}\:\mathrm{height}\:{H},\:\mathrm{a}\:\mathrm{particle}\:\mathrm{is} \\ $$$$\mathrm{thrown}\:\mathrm{vertically}\:\mathrm{upward}\:\mathrm{with}\:\mathrm{speed} \\ $$$${u}.\:\mathrm{The}\:\mathrm{time}\:\mathrm{taken}\:\mathrm{by}\:\mathrm{the}\:\mathrm{particle},\:\mathrm{to} \\ $$$$\mathrm{hit}\:\mathrm{the}\:\mathrm{ground},\:\mathrm{is}\:{n}\:\mathrm{times}\:\mathrm{that}\:\mathrm{taken}\:\mathrm{by} \\ $$$$\mathrm{it}\:\mathrm{to}\:\mathrm{reach}\:\mathrm{the}\:\mathrm{highest}\:\mathrm{point}\:\mathrm{of}\:\mathrm{its}\:\mathrm{path}. \\ $$$$\mathrm{The}\:\mathrm{relation}\:\mathrm{between}\:{H},\:{u}\:\mathrm{and}\:{n}\:\mathrm{is} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{2}{gH}\:=\:{n}^{\mathrm{2}} {u}^{\mathrm{2}} \\ $$$$\left(\mathrm{2}\right)\:{gH}\:=\:\left({n}\:−\:\mathrm{2}\right)^{\mathrm{2}}…
Question Number 83674 by Power last updated on 05/Mar/20 Commented by Power last updated on 05/Mar/20 $$\mathrm{sir}\:\:\mathrm{MJS} \\ $$ Answered by mahdi last updated on…
Question Number 149208 by pete last updated on 03/Aug/21 $$\mathrm{If}\:\mathrm{loga}\:\mathrm{and}\:\mathrm{logb}\:\mathrm{are}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{mx}^{\mathrm{2}} +\mathrm{nx}+\mathrm{s}=\mathrm{0},\:\mathrm{fimd}\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{m},\:\mathrm{n}\:\mathrm{and} \\ $$$$\mathrm{s}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{logab}. \\ $$ Answered by gsk2684 last updated on 03/Aug/21 $$\mathrm{log}\:{a}\:+\mathrm{log}\:{b}\:=−\frac{{n}}{{m}}…
Question Number 83675 by niroj last updated on 05/Mar/20 $$ \\ $$$$\: \\ $$$$\:\:\mathrm{evaluate}: \\ $$$$\:\mathrm{2}\:\int_{\mathrm{0}} ^{\:\mathrm{2}} \:\frac{\sqrt{\mathrm{x}+\mathrm{1}}}{\mathrm{x}^{\mathrm{2}} +\mathrm{4}}\mathrm{dx} \\ $$$$\:\:\:\:\: \\ $$$$\:\: \\ $$…
Question Number 83672 by jagoll last updated on 05/Mar/20 $${x}^{\mathrm{2}} \:+\:\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\:=\:\mathrm{51}\: \\ $$$${find}\:{x}\: \\ $$ Answered by john santu last updated on 05/Mar/20 $${x}^{\mathrm{2}}…
Question Number 149205 by ArielVyny last updated on 03/Aug/21 $$\int_{−\infty} ^{\mathrm{0}} \frac{{t}}{\left(\mathrm{1}−{t}\right)^{\mathrm{2}} }{dt} \\ $$ Answered by MJS_new last updated on 03/Aug/21 $$\int\frac{{t}}{\left(\mathrm{1}−{t}\right)^{\mathrm{2}} }{dt}=\int\frac{{dt}}{{t}−\mathrm{1}}+\int\frac{{dt}}{\left({t}−\mathrm{1}\right)^{\mathrm{2}} }=…
Question Number 18135 by Tinkutara last updated on 15/Jul/17 $$\mathrm{Let}\:{x}\:\mathrm{be}\:\mathrm{the}\:\mathrm{LCM}\:\mathrm{of}\:\mathrm{3}^{\mathrm{2002}} \:−\:\mathrm{1}\:\mathrm{and} \\ $$$$\mathrm{3}^{\mathrm{2002}} \:+\:\mathrm{1}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{last}\:\mathrm{digit}\:\mathrm{of}\:{x}. \\ $$ Commented by mrW1 last updated on 15/Jul/17 $$\mathrm{0} \\…
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Question Number 83668 by jagoll last updated on 05/Mar/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:{x}\:\mathrm{cos}\:{x}−{x}}{{x}^{\mathrm{2}} \:\mathrm{sin}\:\left(\mathrm{2}{x}\right)}\:=\: \\ $$ Answered by john santu last updated on 05/Mar/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\frac{\mathrm{1}}{\mathrm{2}}\:\mathrm{sin}\:\left(\mathrm{2}{x}\right)−{x}}{{x}^{\mathrm{2}} \:\mathrm{sin}\:\left(\mathrm{2}{x}\right)}\:=\:…