Question Number 84461 by Tony Lin last updated on 13/Mar/20 $${p}^{\mathrm{2}} +\mathrm{3}{q}^{\mathrm{2}} =\mathrm{11907},\:{p},{q}\in\mathbb{Z},{find}\:{p\&q} \\ $$ Commented by mr W last updated on 13/Mar/20 $${i}\:{got}\:{only}\:{two}\:{solutions}: \\…
Question Number 18924 by Tinkutara last updated on 01/Aug/17 $$\mathrm{A}\:\mathrm{spring}\:\mathrm{of}\:\mathrm{force}\:\mathrm{constant}\:{k}\:\mathrm{is}\:\mathrm{cut}\:\mathrm{into} \\ $$$$\mathrm{two}\:\mathrm{pieces}\:\mathrm{such}\:\mathrm{that}\:\mathrm{one}\:\mathrm{piece}\:\mathrm{is}\:\mathrm{twice} \\ $$$$\mathrm{as}\:\mathrm{long}\:\mathrm{as}\:\mathrm{the}\:\mathrm{other}.\:\mathrm{Then}\:\mathrm{the}\:\mathrm{longer} \\ $$$$\mathrm{piece}\:\mathrm{will}\:\mathrm{have}\:\mathrm{a}\:\mathrm{force}\:\mathrm{constant}\:\mathrm{of} \\ $$ Answered by ajfour last updated on 01/Aug/17…
Question Number 84459 by jagoll last updated on 13/Mar/20 $$\begin{cases}{\mathrm{log}_{\mathrm{10}} \left(\mathrm{x}\right)+\frac{\mathrm{log}_{\mathrm{10}} \left(\mathrm{x}\right)+\mathrm{8log}_{\mathrm{10}} \left(\mathrm{y}\right)}{\mathrm{log}_{\mathrm{10}} ^{\mathrm{2}} \left(\mathrm{x}\right)+\mathrm{log}_{\mathrm{10}} ^{\mathrm{2}} \left(\mathrm{y}\right)}=\mathrm{3}}\\{\mathrm{log}_{\mathrm{10}} \left(\mathrm{y}\right)+\frac{\mathrm{8log}_{\mathrm{10}} \left(\mathrm{x}\right)−\mathrm{log}_{\mathrm{10}} \left(\mathrm{y}\right)}{\mathrm{log}_{\mathrm{10}} ^{\mathrm{2}} \left(\mathrm{x}\right)+\mathrm{log}_{\mathrm{10}} ^{\mathrm{2}} \left(\mathrm{y}\right)}=\mathrm{0}}\end{cases} \\…
Question Number 18922 by Tinkutara last updated on 01/Aug/17 $$\mathrm{Consider}\:\mathrm{a}\:\mathrm{block}\:\mathrm{sliding}\:\mathrm{over}\:\mathrm{a}\:\mathrm{smooth} \\ $$$$\mathrm{inclined}\:\mathrm{surface}\:\mathrm{of}\:\mathrm{inclination}\:\theta.\:\mathrm{Relating} \\ $$$$\mathrm{to}\:\mathrm{Newton}'\mathrm{s}\:\mathrm{second}\:\mathrm{law}\:\mathrm{applied}\:\mathrm{on}\:\mathrm{the} \\ $$$$\mathrm{block},\:\mathrm{select}\:\mathrm{the}\:\mathrm{incorrect}\:\mathrm{alternative}. \\ $$$$\left(\mathrm{1}\right)\:\Sigma{F}_{{y}'} \:\neq\:\mathrm{0} \\ $$$$\left(\mathrm{2}\right)\:\Sigma{F}_{{y}} \:=\:\mathrm{0} \\ $$$$\left(\mathrm{3}\right)\:\Sigma{F}_{{x}} \:=\:−{mg}\:\mathrm{sin}\:\theta…
Question Number 84456 by M±th+et£s last updated on 13/Mar/20 $${y}={ln}\sqrt{\frac{{a}+{sin}\left({x}\right)}{{b}−{sin}\left({x}\right)}} \\ $$$${if}\:\left(\frac{{dy}}{{dx}}\right)^{\mathrm{2}} −{tan}^{\mathrm{2}} \left({x}\right)=\mathrm{1} \\ $$$${show}\:{that}\:{a}={b} \\ $$ Commented by jagoll last updated on 13/Mar/20…
Question Number 149989 by ZiYangLee last updated on 08/Aug/21 $$\mathrm{By}\:\mathrm{subs}\:{u}^{\mathrm{2}} =\mathrm{4}+{x},\:\mathrm{evaluate}\:\int\:\frac{\sqrt{\mathrm{4}+{x}}}{{x}}\:{dx} \\ $$ Answered by puissant last updated on 08/Aug/21 $$\int\frac{\sqrt{\mathrm{4}+{x}}}{{x}}{dx}={Q} \\ $$$${u}=\sqrt{\mathrm{4}+{x}}\:\rightarrow\:{u}^{\mathrm{2}} =\mathrm{4}+{x}\:\rightarrow\:{x}={u}^{\mathrm{2}} −\mathrm{4}…
Question Number 18918 by Tinkutara last updated on 01/Aug/17 $$\mathrm{A}\:\mathrm{bird}\:\mathrm{sits}\:\mathrm{on}\:\mathrm{a}\:\mathrm{stretched}\:\mathrm{telegraph} \\ $$$$\mathrm{wire}.\:\mathrm{The}\:\mathrm{additional}\:\mathrm{tension}\:\mathrm{produced} \\ $$$$\mathrm{in}\:\mathrm{the}\:\mathrm{wire}\:\mathrm{is} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{Zero} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{Greater}\:\mathrm{than}\:\mathrm{weight}\:\mathrm{of}\:\mathrm{the}\:\mathrm{bird} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{Less}\:\mathrm{than}\:\mathrm{the}\:\mathrm{weight}\:\mathrm{of}\:\mathrm{the}\:\mathrm{bird} \\ $$$$\left(\mathrm{4}\right)\:\mathrm{Equal}\:\mathrm{to}\:\mathrm{the}\:\mathrm{weight}\:\mathrm{of}\:\mathrm{the}\:\mathrm{bird} \\ $$ Commented…
Question Number 18916 by uttam1987 last updated on 01/Aug/17 $${x}^{\mathrm{2}} −\mathrm{7}{x}+\mathrm{12}<{mod}\left({x}−\mathrm{4}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 84448 by jagoll last updated on 13/Mar/20 $$\mathrm{5}^{\frac{\mathrm{x}^{\mathrm{2}} −\mathrm{7}\mid\mathrm{x}\mid+\mathrm{10}}{\mathrm{x}^{\mathrm{2}} −\mathrm{6x}+\mathrm{9}}} \:<\:\mathrm{1} \\ $$ Answered by john santu last updated on 13/Mar/20 $$\frac{\mathrm{x}^{\mathrm{2}} −\mathrm{7}\mid\mathrm{x}\mid+\mathrm{10}}{\mathrm{x}^{\mathrm{2}}…
Question Number 149986 by mnjuly1970 last updated on 08/Aug/21 Answered by mindispower last updated on 08/Aug/21 $${ln}\left(\mathrm{1}+{e}^{{x}} \right)={x}+{ln}\left({e}^{−{x}} +\mathrm{1}\right) \\ $$$${I}=\int_{\mathrm{0}} ^{\infty} \frac{{x}}{\mathrm{1}+{e}^{\mathrm{2}{x}} }{dx}+\int_{\mathrm{0}} ^{\infty}…