Question Number 24490 by FilupES last updated on 19/Nov/17 $$\mathrm{I}\:\mathrm{hold}\:\mathrm{my}\:\mathrm{hand}\:\mathrm{behind}\:\mathrm{my}\:\mathrm{back},\:\mathrm{and}\:\mathrm{secretly} \\ $$$$\mathrm{hold}\:\mathrm{up}\:{n}\:\mathrm{fingers}\:\left(\mathrm{0}\leqslant{n}\leqslant\mathrm{5}\right). \\ $$$$\: \\ $$$$\mathrm{I}\:\mathrm{then}\:\mathrm{as}\:\mathrm{you},\:\mathrm{am}\:\mathrm{I}\:\mathrm{holding}\:\mathrm{up}\:{k}\:\mathrm{fingers}? \\ $$$$\mathrm{Where}\:{k}\:\mathrm{is}\:\mathrm{also}\:\mathrm{a}\:\mathrm{random}\:\mathrm{number}\:\mathrm{0}\leqslant{k}\leqslant\mathrm{5}. \\ $$$$\: \\ $$$$\mathrm{You}\:\mathrm{randomly}\:\mathrm{guess}\:\mathrm{Yes}\:\mathrm{or}\:\mathrm{No}. \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{you}\:\mathrm{guess}\:\mathrm{correctly}? \\…
Question Number 90024 by Rio Michael last updated on 20/Apr/20 $$\mathrm{sinh}^{−\mathrm{1}} \left[\mathrm{ln}\left({x}\:+\:\sqrt{{x}^{\mathrm{2}} \:+\:\mathrm{1}}\:\right)\right]\:=\:? \\ $$ Commented by Rio Michael last updated on 21/Apr/20 $$\mathrm{really}\:\mathrm{sir}, \\…
Question Number 155562 by 0731619 last updated on 02/Oct/21 Commented by tabata last updated on 02/Oct/21 $$\boldsymbol{{Solve}}\:::\:\sqrt{\boldsymbol{{x}}}\:+\:\boldsymbol{{y}}\:=\:\mathrm{5}\:\:,\:\sqrt{\boldsymbol{{y}}}\:+\:\boldsymbol{{x}}\:=\:\mathrm{3}\: \\ $$$$ \\ $$$$\boldsymbol{{Solution}}:: \\ $$$$ \\ $$$$\boldsymbol{{let}}:\:\boldsymbol{{a}}^{\mathrm{2}}…
Question Number 90023 by Rio Michael last updated on 20/Apr/20 $$\:\int\:{e}^{\mid{x}\mid} \:{dx}\:=\:??? \\ $$ Answered by MJS last updated on 21/Apr/20 $$\mathrm{e}^{\mid{x}\mid} =\begin{cases}{\mathrm{e}^{−{x}} ;\:{x}<\mathrm{0}}\\{\mathrm{e}^{{x}} ;\:{x}\geqslant\mathrm{0}}\end{cases}\:\Rightarrow\:\int\mathrm{e}^{\mid{x}\mid}…
Question Number 155553 by talminator2856791 last updated on 02/Oct/21 $$\: \\ $$$$\int_{−\infty} ^{\:\infty} \:\frac{\mathrm{sin}\left({x}^{\mathrm{2}} \right)\mathrm{cos}\left({x}^{\mathrm{3}} \right)}{\left(\mathrm{ln}\left(\left(\mathrm{sin}\left({x}\right)\mathrm{cos}\left({x}\right)\right)^{\mathrm{2}} \right)\right)^{\mathrm{2}} +\mathrm{1}}\:\:{dx}\:\: \\ $$$$\: \\ $$ Terms of Service…
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 $${sinx}\:={x}−\frac{{x}^{\mathrm{3}} }{\mathrm{6}}\:+{o}\left({x}^{\mathrm{3}} \right)\:\Rightarrow{ln}\left(\mathrm{1}+{sinx}\right)={ln}\left(\mathrm{1}+{x}−\frac{{x}^{\mathrm{3}}…
Question Number 90019 by Rio Michael last updated on 20/Apr/20 $$\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 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 $${Let}\:{tension}\:{in}\:{string}\:{on}\:{which} \\ $$$${B}\:{hangs}\:{be}\:{T}. \\…
Question Number 24479 by Tinkutara last updated on 18/Nov/17 $$\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 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). \\…