Question Number 24042 by Tinkutara last updated on 11/Nov/17 $${f}\left({x}\right)\:=\:\mathrm{sin}\left(\mathrm{sin}^{\mathrm{2}} {x}\right)\:+\:\mathrm{cos}\left(\mathrm{sin}^{\mathrm{2}} {x}\right)\:\mathrm{then}\:\mathrm{the} \\ $$$$\mathrm{range}\:\mathrm{of}\:{f}\left({x}\right)\:\mathrm{is} \\ $$ Commented by mrW1 last updated on 11/Nov/17 $$\left[\mathrm{1},\sqrt{\mathrm{2}}\right] \\…
Question Number 89576 by M±th+et£s last updated on 18/Apr/20 $${is}\:\:\underset{{x}\rightarrow{a}} {{lim}}\lfloor{f}\left({x}\right)\rfloor=\lfloor\underset{{x}\rightarrow{a}\:} {{lim}}\:{f}\left({x}\right)\rfloor\: \\ $$ Commented by mr W last updated on 18/Apr/20 $${i}\:{think}\:{no}. \\ $$$${example}\:{f}\left({x}\right)=\frac{\mathrm{sin}\:{x}}{{x}}…
Question Number 155109 by qaz last updated on 25/Sep/21 $$\mathrm{how}\:\mathrm{many}\:\mathrm{terms}\:\mathrm{contain}\:“\:\mathrm{ab}^{\mathrm{2}} \mathrm{c}^{\mathrm{3}} \:''\:\mathrm{in}\:\left(\mathrm{a}+\mathrm{2b}+\mathrm{3c}+\mathrm{4d}^{\mathrm{2}} +\mathrm{5e}^{\mathrm{3}} \right)^{\mathrm{10}} \:? \\ $$ Answered by mr W last updated on 26/Sep/21…
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Question Number 155106 by mathdanisur last updated on 25/Sep/21 $$\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\begin{cases}{\sqrt{\mathrm{x}+\mathrm{y}}\:-\:\sqrt{\mathrm{x}-\mathrm{y}}\:+\:\sqrt{\mathrm{x}^{\mathrm{2}} -\mathrm{y}^{\mathrm{2}} }\:=\:\mathrm{5}}\\{\mathrm{2x}\:+\:\mathrm{3}\sqrt{\mathrm{x}^{\mathrm{2}} -\mathrm{y}^{\mathrm{2}} }\:=\:\mathrm{19}}\end{cases} \\ $$ Commented by benhamimed last updated on 25/Sep/21…
Question Number 24032 by Tinkutara last updated on 11/Nov/17 $$\mathrm{A}\:\mathrm{hemispherical}\:\mathrm{bowl}\:\mathrm{of}\:\mathrm{radius}\:{R}\:=\:\mathrm{0}.\mathrm{1} \\ $$$$\mathrm{m}\:\mathrm{is}\:\mathrm{rotating}\:\mathrm{about}\:\mathrm{its}\:\mathrm{own}\:\mathrm{axis}\:\left(\mathrm{which}\right. \\ $$$$\left.\mathrm{is}\:\mathrm{vertical}\right)\:\mathrm{with}\:\mathrm{an}\:\mathrm{angular}\:\mathrm{velocity}\:\omega. \\ $$$$\mathrm{A}\:\mathrm{particle}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{10}^{−\mathrm{2}} \:\mathrm{kg}\:\mathrm{on}\:\mathrm{the} \\ $$$$\mathrm{frictionless}\:\mathrm{inner}\:\mathrm{surface}\:\mathrm{of}\:\mathrm{the}\:\mathrm{bowl}\:\mathrm{is} \\ $$$$\mathrm{also}\:\mathrm{rotating}\:\mathrm{with}\:\mathrm{the}\:\mathrm{same}\:\omega.\:\mathrm{The} \\ $$$$\mathrm{particle}\:\mathrm{is}\:\mathrm{at}\:\mathrm{a}\:\mathrm{height}\:{h}\:\mathrm{from}\:\mathrm{the}\:\mathrm{bottom} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{bowl}.…
Question Number 155101 by SANOGO last updated on 25/Sep/21 $${soit}:\:{y}\:{y}'+{xy}^{\mathrm{2}} +{x}=\mathrm{0}\:,{avec}\:{f}\left(\mathrm{0}\right)=\mathrm{1} \\ $$$${f}''\left(\mathrm{0}\right)=? \\ $$ Commented by tabata last updated on 25/Sep/21 $$\boldsymbol{{yy}}^{'} \:=\:−\boldsymbol{{x}}\:\left(\boldsymbol{{y}}^{\mathrm{2}} \:+\:\mathrm{1}\right)\:\Rightarrow\:\frac{\boldsymbol{{y}}\:}{\boldsymbol{{y}}^{\mathrm{2}}…
Question Number 155100 by mathdanisur last updated on 25/Sep/21 $$\mathrm{Determine}\:\mathrm{all}\:\mathrm{triangle}\:\mathrm{with}: \\ $$$$\mathrm{1}.\mathrm{The}\:\mathrm{lengths}\:\mathrm{of}\:\mathrm{sides}\:\mathrm{positive}\:\mathrm{integers} \\ $$$$\:\:\:\:\:\mathrm{and}\:\mathrm{at}\:\mathrm{least}\:\mathrm{one}\:\mathrm{is}\:\mathrm{prime}\:\mathrm{number}. \\ $$$$\mathrm{2}.\mathrm{The}\:\mathrm{semiperimetr}\:\mathrm{is}\:\mathrm{positive}\:\mathrm{integer} \\ $$$$\:\:\:\:\:\mathrm{and}\:\mathrm{area}\:\mathrm{is}\:\mathrm{equal}\:\mathrm{with}\:\mathrm{perimetr}. \\ $$ Commented by MJS_new last updated…
Question Number 89560 by peter frank last updated on 18/Apr/20 $${without}\:{use}\:{intergration} \\ $$$${by}\:{party} \\ $$$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} {e}^{\theta} \mathrm{cos}\:\mathrm{2}\theta\:{d}\theta \\ $$ Commented by mathmax by abdo…
Question Number 24025 by ajfour last updated on 11/Nov/17 Commented by ajfour last updated on 11/Nov/17 $${Find}\:{the}\:{closest}\:{distance}\:{of} \\ $$$${approach}\:{of}\:{B}\:{and}\:{R}\:\:\left({if}\:{it}\:{is}\right. \\ $$$$\left.{yet}\:{to}\:{come}\right)\:{and}\:{time}\:{after} \\ $$$${which}\:{they}\:{are}\:{closest}. \\ $$$${Situation}\:{has}\:{been}\:{shown}\:{for}…