Question Number 23288 by Tinkutara last updated on 28/Oct/17 $$\mathrm{A}\:\mathrm{uniform}\:\mathrm{chain}\:\mathrm{of}\:\mathrm{mass}\:{M}\:\mathrm{and}\:\mathrm{length} \\ $$$${L}\:\mathrm{is}\:\mathrm{hanging}\:\mathrm{from}\:\mathrm{the}\:\mathrm{table}.\:\mathrm{The}\:\mathrm{chain} \\ $$$$\mathrm{is}\:\mathrm{in}\:\mathrm{limiting}\:\mathrm{equilibrium}\:\mathrm{when}\:{l}\:\mathrm{length} \\ $$$$\mathrm{of}\:\mathrm{chain}\:\mathrm{over}\:\mathrm{hangs}.\:\mathrm{It}\:\mathrm{is}\:\mathrm{slightly} \\ $$$$\mathrm{disturbed}\:\mathrm{from}\:\mathrm{this}\:\mathrm{position}.\:\mathrm{Find}\:\mathrm{the} \\ $$$$\mathrm{speed}\:\mathrm{of}\:\mathrm{the}\:\mathrm{chain}\:\mathrm{just}\:\mathrm{after}\:\mathrm{it}\:\mathrm{completely} \\ $$$$\mathrm{comes}\:\mathrm{off}\:\mathrm{the}\:\mathrm{table}. \\ $$ Commented…
Question Number 154359 by ZiYangLee last updated on 17/Sep/21 $$\mathrm{If}\:{f}\left(\mathrm{0}\right)=\mathrm{1},\:{f}\left(\mathrm{2}\right)=\mathrm{3},\:{f}\:'\left(\mathrm{2}\right)=\mathrm{5}, \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\int_{\mathrm{0}} ^{\:\mathrm{1}} {x}\:{f}''\left(\mathrm{2}{x}\right)\:{dx}. \\ $$ Answered by aleks041103 last updated on 17/Sep/21 $$\int{xf}''\left(\mathrm{2}{x}\right){dx}=\int{xd}\left(\frac{\mathrm{1}}{\mathrm{2}}{f}'\left(\mathrm{2}{x}\right)\right)= \\…
Question Number 88820 by ajfour last updated on 13/Apr/20 Commented by ajfour last updated on 13/Apr/20 $${If}\:{both}\:{coloured}\:{regions}\:{have} \\ $$$${equal}\:{area},\:{find}\:{B}\left({x}_{{B}} \:,\:{y}_{{B}} \right)\:{in} \\ $$$${terms}\:{of}\:{c}. \\ $$…
Question Number 23285 by alibhar last updated on 28/Oct/17 $${Mode}=\mathrm{17} \\ $$$${Mean}=\mathrm{10}.\mathrm{22} \\ $$$${Median}=\mathrm{10} \\ $$$$ \\ $$$${What}\:{is}\:{the}\:{shape}\:{of}\:{the}\:{distribution}? \\ $$ Terms of Service Privacy Policy…
Question Number 154353 by liberty last updated on 17/Sep/21 Commented by mr W last updated on 17/Sep/21 $${r}=\mathrm{2}\sqrt{\mathrm{3}}\:\mathrm{sin}\:\theta \\ $$$$\mathrm{2}{r}\:\mathrm{cos}\:\theta=\mathrm{3} \\ $$$$\mathrm{4}\sqrt{\mathrm{3}}\:\mathrm{sin}\:\theta\:\mathrm{cos}\:\theta=\mathrm{3} \\ $$$$\mathrm{sin}\:\mathrm{2}\theta=\frac{\sqrt{\mathrm{3}}}{\mathrm{2}} \\…
Question Number 23283 by ajfour last updated on 28/Oct/17 $${Compute}\:{the}\:{area}\:{of}\:{a}\:{loop}\:{of} \\ $$$${the}\:{curve}\:\boldsymbol{\rho}=\boldsymbol{{a}}\mathrm{sin}\:\mathrm{2}\boldsymbol{\theta}\:;\:{and}\:{even} \\ $$$${sketch}\:{the}\:{curve},\:{please}. \\ $$ Answered by mrW1 last updated on 28/Oct/17 $$\mathrm{a}\:\mathrm{small}\:\mathrm{loop}\:\mathrm{for}\:\theta\:\mathrm{from}\:\mathrm{0}\:\mathrm{to}\:\frac{\pi}{\mathrm{2}}: \\…
Question Number 154352 by amin96 last updated on 17/Sep/21 $$\:\int\frac{{x}^{{n}−\mathrm{1}} }{{x}^{\mathrm{3}{n}+\mathrm{1}} \left({x}^{{n}} −\mathrm{1}\right)}{dx}=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 154351 by ZiYangLee last updated on 17/Sep/21 $$\int_{−\mathrm{1}} ^{\:\mathrm{0}} \:\frac{{x}−\mathrm{1}}{\:\sqrt{{x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{3}}\:}\:{dx}\:=? \\ $$ Answered by ZiYangLee last updated on 17/Sep/21 $$\int_{−\mathrm{1}} ^{\:\mathrm{0}} \:\frac{{x}−\mathrm{1}}{\:\sqrt{{x}^{\mathrm{2}}…
Question Number 88811 by jagoll last updated on 13/Apr/20 $$\begin{cases}{\left({x}+\mathrm{1}\right)^{\mathrm{2}} \left({y}+\mathrm{1}\right)^{\mathrm{2}} =\mathrm{27}{xy}}\\{\left({x}^{\mathrm{2}} +\mathrm{1}\right)\left({y}^{\mathrm{2}} +\mathrm{1}\right)\:=\mathrm{10}{xy}}\end{cases} \\ $$ Answered by john santu last updated on 13/Apr/20 $${let}\:{me}\:{try}\:…
Question Number 23274 by Tinkutara last updated on 28/Oct/17 $$\boldsymbol{\mathrm{Assertion}}:\:\mathrm{Both}\:\mathrm{N}_{\mathrm{2}} \:\mathrm{and}\:\mathrm{NO}^{+} \:\mathrm{are} \\ $$$$\mathrm{diamagnetic}\:\mathrm{substances}. \\ $$$$\boldsymbol{\mathrm{Reason}}:\:\mathrm{NO}^{+} \:\mathrm{is}\:\mathrm{isoelectronic}\:\mathrm{with}\:\mathrm{N}_{\mathrm{2}} . \\ $$ Commented by math solver last…