Question Number 143666 by ajfour last updated on 16/Jun/21 Commented by ajfour last updated on 19/Jun/21 $${If}\:{the}\:{upper}\:{disc}\:{is}\:{released} \\ $$$${at}\:{angle}\:\alpha,\:{find}\:\alpha\:{such}\:{that} \\ $$$${disc}\:{loses}\:{contact}\:{with} \\ $$$${the}\:{fixed}\:{hemisphere}\:{just} \\ $$$${when}\:{it}\:{hits}\:{the}\:{ground}.…
Question Number 12591 by @ANTARES_VY last updated on 26/Apr/17 $$\boldsymbol{\mathrm{This}} \\ $$$$\oint\left(\boldsymbol{\mathrm{x}}\right)=\mathrm{3}−\frac{\boldsymbol{\mathrm{x}}^{\mathrm{2}} }{\boldsymbol{\mathrm{x}}^{\mathrm{4}} +\mathrm{3}\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\mathrm{1}}\:\:\boldsymbol{\mathrm{find}}\:\:\boldsymbol{\mathrm{the}} \\ $$$$\boldsymbol{\mathrm{sphere}}\:\:\boldsymbol{\mathrm{of}}\:\:\boldsymbol{\mathrm{function}}\:\:\boldsymbol{\mathrm{values}} \\ $$ Commented by ajfour last updated on…
Question Number 12590 by tawa last updated on 26/Apr/17 $$\mathrm{In}\:\mathrm{a}\:\mathrm{basic}\:\mathrm{version}\:\mathrm{of}\:\mathrm{pocker}\:,\:\mathrm{each}\:\mathrm{players}\:\mathrm{is}\:\mathrm{dealth}\:\mathrm{5}\:\mathrm{cards}\:\mathrm{from}\:\mathrm{a}\:\mathrm{standard} \\ $$$$\mathrm{52}\:\mathrm{cards}\:\left(\mathrm{no}\:\mathrm{pocker}\right).\:\mathrm{How}\:\mathrm{many}\:\mathrm{diferent}\:\mathrm{5}\:\mathrm{cards}\:\mathrm{pocker}\:\mathrm{hand}\:\mathrm{are}\:\mathrm{there}\:??? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 78122 by Tony Lin last updated on 14/Jan/20 $$\underset{{x}\rightarrow\mathrm{1}^{−} } {\mathrm{lim}}{lnx}\centerdot{ln}\left(\mathrm{1}−{x}\right)=? \\ $$ Commented by msup trace by abdo last updated on 14/Jan/20…
Question Number 143653 by mim24 last updated on 16/Jun/21 Answered by ajfour last updated on 16/Jun/21 $${x}^{\mathrm{2}} −\mathrm{6}{x}−\mathrm{2}\sqrt{\mathrm{3}}=\mathrm{0} \\ $$$${x}_{\mathrm{1}} {x}_{\mathrm{2}} =−\mathrm{2}\sqrt{\mathrm{3}} \\ $$$${x}_{\mathrm{1}} +{x}_{\mathrm{2}}…
Question Number 78119 by jagoll last updated on 14/Jan/20 $${find}\:{the}\:{center}\:{point}\:{ellips} \\ $$$$\mathrm{5}{x}^{\mathrm{2}} +\mathrm{8}{y}^{\mathrm{2}} −\mathrm{24}{x}−\mathrm{24}{y}+\mathrm{4}{xy}=\mathrm{0} \\ $$ Commented by jagoll last updated on 14/Jan/20 $${this}\:{problem}\:{is}\:{right}\:{or}\:{not}? \\…
Question Number 12580 by @ANTARES_VY last updated on 26/Apr/17 $$\boldsymbol{\mathrm{Find}}\:\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{smaillest}}\:\:\boldsymbol{\mathrm{value}}\:\:\boldsymbol{\mathrm{of}}\:\:\boldsymbol{\mathrm{the}} \\ $$$$\boldsymbol{\mathrm{sum}} \\ $$$$\boldsymbol{\mathrm{x}}\left(\boldsymbol{\mathrm{x}}+\mathrm{1}\right)\left(\boldsymbol{\mathrm{x}}+\mathrm{2}\right)\left(\boldsymbol{\mathrm{x}}+\mathrm{3}\right). \\ $$ Answered by ajfour last updated on 26/Apr/17 $$\left({x}^{\mathrm{2}} +\mathrm{3}{x}\right)\left({x}^{\mathrm{2}}…
Question Number 12577 by tawa last updated on 26/Apr/17 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{generated}\:\mathrm{when}\:\mathrm{the}\:\mathrm{curve}\:\:\mathrm{x}\:=\:\mathrm{a}\left(\theta\:−\:\mathrm{sin}\theta\right),\:\left(\mathrm{1}\:−\:\mathrm{cos}\theta\right) \\ $$$$\theta\:=\:\mathrm{0},\:\theta\:=\:\pi\:\:\mathrm{rotates}\:\mathrm{about}\:\mathrm{x}−\mathrm{axis}\:\mathrm{through}\:\mathrm{2}\pi\:\mathrm{radian}. \\ $$$$\mathrm{Note}:\:\mathrm{1}\:−\:\mathrm{cos}\theta\:=\:\mathrm{2}\:\mathrm{sin}^{\mathrm{2}} \left(\frac{\theta}{\mathrm{2}}\right) \\ $$ Answered by mrW1 last updated on 26/Apr/17 $${x}={a}\left(\theta−\mathrm{sin}\:\theta\right)…
Question Number 143650 by Rankut last updated on 16/Jun/21 $${If}\:\:{the}\:{function}\:{f}\:{and}\:{g}\:{are}\:{defined} \\ $$$${on}\:{the}\:{set}\:{of}\:{real}\:{numbers},{are}\:{such} \\ $$$${that}\:\boldsymbol{{gof}}\left(\boldsymbol{{x}}\right)=\frac{\mathrm{2}\boldsymbol{{x}}−\mathrm{5}}{\mathrm{3}\boldsymbol{{x}}+\mathrm{7}}\:\:\:{and}\: \\ $$$$\boldsymbol{{g}}\left(\boldsymbol{{x}}\right)=\frac{\mathrm{3}\boldsymbol{{x}}+\mathrm{2}}{\boldsymbol{{x}}−\mathrm{5}}. \\ $$$$\boldsymbol{\mathrm{find}}\:\:\boldsymbol{\mathrm{an}}\:\boldsymbol{\mathrm{expression}}\:\boldsymbol{\mathrm{for}}\:\:\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}\right) \\ $$ Answered by ajfour last updated…
Question Number 12576 by tawa last updated on 26/Apr/17 $$\mathrm{Given}\:\mathrm{two}\:\mathrm{functions}\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{and}\:\mathrm{g}\left(\mathrm{x}\right)\:\mathrm{with}\:\mathrm{f}\left(\mathrm{1}\right)\:=\:\mathrm{7},\:\mathrm{g}\left(\mathrm{2}\right)\:=\:\mathrm{1}\:,\:\mathrm{f}'\left(\mathrm{1}\right)\:=\:\mathrm{204} \\ $$$$\mathrm{and}\:\mathrm{g}'\left(\mathrm{x}\right)\:=\:\mathrm{22}.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{derivative}\:\mathrm{of}\:\:\mathrm{f}\left(\mathrm{g}\left(\mathrm{x}\right)\right)\:\mathrm{at}\:\mathrm{x}\:=\:\mathrm{2} \\ $$ Answered by mrW1 last updated on 26/Apr/17 $$\frac{{df}}{{dx}}=\frac{{df}\left({g}\right)}{{dg}}×\frac{{dg}\left({x}\right)}{{dx}}={f}'\left({g}\left({x}\right)\right)×{g}'\left({x}\right) \\ $$$$={f}'\left({g}\left(\mathrm{2}\right)\right)×{g}'\left(\mathrm{2}\right)={f}'\left(\mathrm{1}\right)×{g}'\left(\mathrm{2}\right)=\mathrm{204}×\mathrm{22} \\…