Question Number 25745 by rita1608 last updated on 13/Dec/17 $${find}\:{the}\:{volume}\:{of}\:{the}\:{solid}\: \\ $$$${generated}\:{by}\:{thr}\:{revolution}\:{of}\:{the} \\ $$$${curve}\:{y}\left({x}^{\mathrm{2}} +{a}^{\mathrm{2}} \right)={a}^{\mathrm{3}} \:{about}\:{itd}\: \\ $$$${asymptote}. \\ $$ Answered by jota@ last…
Question Number 25744 by rita1608 last updated on 13/Dec/17 $${find}\:{the}\:{surface}\:{area}\:{of}\:{the}\:{solid}\: \\ $$$${formed}\:{by}\:{the}\:{rotation}\:{of}\:{the}\:{arc}\:{of}\: \\ $$$${the}\:{cycloid}\:{x}={a}\left({t}+{sin}\:{t}\right),\: \\ $$$${y}={a}\left(\mathrm{1}+{cost}\right)\:{about}\:{x}\:{axis} \\ $$ Answered by ajfour last updated on 14/Dec/17…
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Question Number 25655 by rita1608 last updated on 12/Dec/17 $${use}\:{lagranges}\:{mean}\:{value}\:{theorem}\:{to} \\ $$$${prove}\:{that}\: \\ $$$${x}<{sin}^{−\mathrm{1}} {x}<\frac{{x}}{\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }},\mathrm{0}<{x}<\mathrm{1}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 25656 by rita1608 last updated on 12/Dec/17 $${trace}\:{the}\:{curve}\: \\ $$$${y}^{\mathrm{2}} \left({x}+\mathrm{1}\right)={x}^{\mathrm{2}} \left(\mathrm{3}−{x}\right) \\ $$$${clearly}\:{stating}\:{all}\:{the}\:{properties}\:{used} \\ $$$${for}\:{tracing}. \\ $$ Commented by ajfour last updated…
Question Number 25634 by rita1608 last updated on 12/Dec/17 $${find}\:{the}\:{equation}\:{of}\:{the}\:{tangent}\:{to}\: \\ $$$${the}\:{curve}\:\sqrt{{x}}+\sqrt{{y}}=\sqrt{{a}}\:{at}\:{any}\:{point} \\ $$$$\left({x},{y}\right){on}\:{it}. \\ $$ Answered by mrW1 last updated on 13/Dec/17 $$\frac{{dx}}{\mathrm{2}\sqrt{{x}}}+\frac{{dy}}{\mathrm{2}\sqrt{{y}}}=\mathrm{0} \\…
Question Number 25635 by rita1608 last updated on 12/Dec/17 $${let}\:{f}\:{be}\:{the}\:{function}\:{defined}\:{on} \\ $$$$\left[−\mathrm{1},\mathrm{1}\right]\:{by} \\ $$$${f}\left({x}\right)=\left\{\begin{cases}{−\mathrm{1},{if}\:{x}\:{is}\:{rational}}\\{\mathrm{1},{if}\:{x}\:{is}\:{irrational}.}\end{cases}\right. \\ $$$${find}\:{U}\left({P},{f}\right)\:{and}\:{L}\left({P},{f}\right).{f}\:{is}\:{integrable} \\ $$$${or}\:{not}\:? \\ $$ Commented by rita1608 last updated…
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Question Number 25630 by tawa tawa last updated on 12/Dec/17 Answered by jota@ last updated on 13/Dec/17 $${m}_{{B}} {g}−{T}={m}_{{B}} {a} \\ $$$${T}={m}_{{A}} {a}.\:{Then} \\ $$$${m}_{{B}}…
Question Number 91149 by Rio Michael last updated on 28/Apr/20 $$\mathrm{A}\:\mathrm{particle}\:\mathrm{starts}\:\mathrm{from}\:\mathrm{rest}\:\mathrm{and}\:\mathrm{moves}\:\mathrm{in}\:\mathrm{a}\:\mathrm{straight}\:\mathrm{line}\:\mathrm{on}\:\mathrm{a}\:\mathrm{smooth}\: \\ $$$$\mathrm{horizontal}\:\mathrm{surface}.\:\mathrm{Its}\:\mathrm{acceleration}\:\mathrm{at}\:\mathrm{time}\:{t}\:\mathrm{seconds}\:\mathrm{is}\:\mathrm{given}\:\mathrm{by} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{k}\left(\mathrm{4}{v}\:+\:\mathrm{1}\right)\:\mathrm{ms}^{−\mathrm{2}} \\ $$$$\mathrm{where}\:{k}\:\mathrm{is}\:\mathrm{a}\:\mathrm{positve}\:\mathrm{constant}\:\mathrm{and}\:{v}\:\mathrm{ms}^{−\mathrm{1}} \:\mathrm{is}\:\mathrm{the}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{the}\:\mathrm{particle}. \\ $$$$\mathrm{Given}\:\mathrm{that}\:{v}\:=\:\frac{{e}^{\mathrm{2}} −\mathrm{1}}{\mathrm{4}}\:\mathrm{when}\:{t}\:=\:\mathrm{1}.\:\:\mathrm{show}\:\mathrm{that}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{v}\:=\:\frac{\mathrm{1}}{\mathrm{4}}\left({e}^{\mathrm{2}{t}} −\mathrm{1}\right) \\…