Question Number 90018 by Rio Michael last updated on 20/Apr/20 $$\mathrm{expand}\:,\:\mathrm{ln}\left(\mathrm{1}\:+\:\mathrm{sin}\:{x}\right)\:\mathrm{right}\:\mathrm{up}\:\mathrm{to}\:\mathrm{the}\:\mathrm{term}\:\mathrm{in}\:{x}^{\mathrm{3}} \\ $$ Commented by mathmax by abdo last updated on 21/Apr/20 $${sinx}\:={x}−\frac{{x}^{\mathrm{3}} }{\mathrm{6}}\:+{o}\left({x}^{\mathrm{3}} \right)\:\Rightarrow{ln}\left(\mathrm{1}+{sinx}\right)={ln}\left(\mathrm{1}+{x}−\frac{{x}^{\mathrm{3}}…
Question Number 24482 by Tinkutara last updated on 18/Nov/17 $$\mathrm{Neglecting}\:\mathrm{friction}\:\mathrm{and}\:\mathrm{mass}\:\mathrm{of}\:\mathrm{pulleys}, \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{acceleration}\:\mathrm{of}\:\mathrm{mass}\:{B}? \\ $$ Commented by ajfour last updated on 18/Nov/17 $${Let}\:{tension}\:{in}\:{string}\:{on}\:{which} \\ $$$${B}\:{hangs}\:{be}\:{T}. \\…
Question Number 90019 by Rio Michael last updated on 20/Apr/20 $$\mathrm{find}\:\mathrm{the}\:\mathrm{gcd}\left(\mathrm{2467},\:\mathrm{1367}\right) \\ $$ Answered by MJS last updated on 21/Apr/20 $$\mathrm{2467}\:\mathrm{is}\:\mathrm{prime}\:\mathrm{and}\:\mathrm{1367}\:\mathrm{is}\:\mathrm{prime}\:\Rightarrow \\ $$$$\mathrm{gcd}\:\left(\mathrm{2467},\:\mathrm{1367}\right)\:=\mathrm{1} \\ $$…
Question Number 24477 by sushmitak last updated on 18/Nov/17 $$\mathrm{A}\:\mathrm{particle}\:\mathrm{moving}\:\mathrm{horizonatally} \\ $$$$\mathrm{collides}\:\mathrm{perpendiculrly}\:\mathrm{at}\:\mathrm{one}\:\mathrm{end} \\ $$$$\mathrm{of}\:\:\mathrm{a}\:\mathrm{rod}\:\mathrm{having}\:\mathrm{equal}\:\mathrm{mass}\:\mathrm{and} \\ $$$$\mathrm{placed}\:\mathrm{on}\:\mathrm{a}\:\mathrm{horizontal}\:\mathrm{surface}. \\ $$$$\mathrm{The}\:\mathrm{book}\:\mathrm{says}\:\mathrm{that}\:\mathrm{particle}\:\mathrm{will} \\ $$$$\mathrm{continue}\:\mathrm{to}\:\mathrm{move}\:\mathrm{along}\:\mathrm{the}\:\mathrm{same} \\ $$$$\mathrm{direction}\:\mathrm{regardless}\:\mathrm{of}\:\mathrm{value}\:\mathrm{of} \\ $$$${e}\:\left(\mathrm{coefficient}\:\mathrm{of}\:\mathrm{restitution}\right). \\…
Question Number 24479 by Tinkutara last updated on 18/Nov/17 $$\mathrm{Describe}\:\mathrm{the}\:\mathrm{energy}\:\mathrm{transformations} \\ $$$$\mathrm{that}\:\mathrm{take}\:\mathrm{place}\:\mathrm{when}\:\mathrm{a}\:\mathrm{skier}\:\mathrm{starts} \\ $$$$\mathrm{sking}\:\mathrm{down}\:\mathrm{a}\:\mathrm{hill},\:\mathrm{but}\:\mathrm{after}\:\mathrm{a}\:\mathrm{time}\:\mathrm{is} \\ $$$$\mathrm{brought}\:\mathrm{to}\:\mathrm{rest}\:\mathrm{by}\:\mathrm{striking}\:\mathrm{a}\:\mathrm{snowdrift}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 24465 by Tinkutara last updated on 18/Nov/17 $$\mathrm{Two}\:\mathrm{blocks}\:\mathrm{of}\:\mathrm{masses}\:{m}_{\mathrm{1}} \:\mathrm{and}\:{m}_{\mathrm{2}} \:\mathrm{are} \\ $$$$\mathrm{placed}\:\mathrm{in}\:\mathrm{contact}\:\mathrm{with}\:\mathrm{each}\:\mathrm{other}\:\mathrm{on}\:\mathrm{a} \\ $$$$\mathrm{horizontal}\:\mathrm{platform}.\:\mathrm{The}\:\mathrm{coefficient}\:\mathrm{of} \\ $$$$\mathrm{friction}\:\mathrm{between}\:\mathrm{the}\:\mathrm{platform}\:\mathrm{and}\:\mathrm{the} \\ $$$$\mathrm{two}\:\mathrm{blocks}\:\mathrm{is}\:\mathrm{the}\:\mathrm{same}.\:\mathrm{The}\:\mathrm{platform} \\ $$$$\mathrm{moves}\:\mathrm{with}\:\mathrm{an}\:\mathrm{acceleration}.\:\mathrm{The}\:\mathrm{force} \\ $$$$\mathrm{of}\:\mathrm{interaction}\:\mathrm{between}\:\mathrm{the}\:\mathrm{blocks}\:\mathrm{is} \\…
Question Number 24460 by sushmitak last updated on 18/Nov/17 $$\mathrm{A}\:\mathrm{uniform}\:\mathrm{rod}\:\mathrm{of}\:\mathrm{AB}\:\mathrm{of}\:\mathrm{mass} \\ $$$$\mathrm{m}=\mathrm{1}.\mathrm{12}\:\mathrm{kg}\:\mathrm{and}\:\mathrm{lengtj}\:\mathrm{l}=\mathrm{100cm}\:\mathrm{is} \\ $$$$\mathrm{placed}\:\mathrm{on}\:\mathrm{a}\:\mathrm{sharp}\:\mathrm{support}\:\mathrm{O}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{AO}={a}=\mathrm{40}{cm}.\:\mathrm{To}\:\mathrm{keep}\:\mathrm{the}\:\mathrm{rod} \\ $$$$\mathrm{horizontal},\:\mathrm{its}\:\mathrm{end}\:\mathrm{A}\:\mathrm{is}\:\mathrm{ties}\:\mathrm{with}\:\mathrm{a} \\ $$$$\mathrm{thread}.\:\mathrm{Calculate}\:\mathrm{reaction}\:\mathrm{of}\:\mathrm{support} \\ $$$$\mathrm{O}\:\mathrm{on}\:\mathrm{the}\:\mathrm{rod}\:\mathrm{when}\:\mathrm{the}\:\mathrm{thread}\:\mathrm{is}\:\mathrm{burnt}. \\ $$$$\left({g}=\mathrm{10}\:\mathrm{m}\centerdot\mathrm{s}^{−\mathrm{2}} \right)…
Question Number 89986 by M±th+et£s last updated on 20/Apr/20 $$\int_{\mathrm{0}} ^{\mathrm{1}} \left(−\mathrm{1}\right)^{\lfloor\frac{\mathrm{1}}{{x}}\rfloor} \:{dx} \\ $$ Commented by M±th+et£s last updated on 20/Apr/20 $${nice}\:{and}\:{correct}\:{solution}\:{thank}\:{you} \\ $$$${sir}…
Question Number 89980 by swizanjere@gmail.com last updated on 20/Apr/20 Commented by john santu last updated on 20/Apr/20 $${x}^{\mathrm{2}} −\mathrm{3}{x}−\mathrm{5}=\mathrm{0}\:\begin{cases}{\alpha}\\{\beta}\end{cases} \\ $$$${the}\:{eq}\:{with}\:{roots}\:\begin{cases}{\alpha−\mathrm{3}}\\{\beta−\mathrm{3}}\end{cases} \\ $$$${equal}\:{to}\::\:\left({x}+\mathrm{3}\right)^{\mathrm{2}} −\mathrm{3}\left({x}+\mathrm{3}\right)−\mathrm{5}\:=\mathrm{0} \\…
Question Number 24447 by Tinkutara last updated on 18/Nov/17 $${Figure}\:{shows}\:{two}\:{discs}\:{of}\:{same}\:{mass} \\ $$$${m}.\:{They}\:{are}\:{rigidly}\:{attached}\:{to}\:{a}\:{spring} \\ $$$${of}\:{stiffness}\:{k}.\:{The}\:{system}\:{is}\:{in} \\ $$$${equilibrium}.\:{From}\:{this}\:{equilibrium} \\ $$$${position},\:{the}\:{upper}\:{disc}\:{is}\:{pressed} \\ $$$${down}\:{slowly}\:{by}\:{a}\:{distance}\:{x}\:{and} \\ $$$${released}.\:{Find}\:{the}\:{minimum}\:{value}\:{of} \\ $$$${x},\:{if}\:{the}\:{lower}\:{disc}\:{is}\:{just}\:{lifted}\:{off} \\…