Question Number 84680 by M±th+et£s last updated on 15/Mar/20 $${show}\:{that} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \int_{\mathrm{0}} ^{\mathrm{1}} \int_{\mathrm{0}} ^{\mathrm{1}} \frac{{log}\left({xyz}\right)}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\left(\mathrm{1}+{y}^{\mathrm{2}} \right)\left(\mathrm{1}+{z}^{\mathrm{2}} \right)}\:{dx}\:{dy}\:{dz}=\frac{−\mathrm{3}\pi^{\mathrm{2}} {G}}{\mathrm{16}} \\ $$ Answered…
Question Number 84681 by Power last updated on 15/Mar/20 Commented by mathmax by abdo last updated on 15/Mar/20 $${I}\:=\int\:\:\frac{\mathrm{15}{sinx}\:+\mathrm{2}{cosx}}{\mathrm{98}{sinx}\:−\mathrm{7}{cosx}}{dx}\:\Rightarrow{I}\:=\frac{\mathrm{15}}{\mathrm{98}}\int\:\:\frac{{sinx}+\frac{\mathrm{2}}{\mathrm{15}}{cosx}}{{sinx}−\frac{\mathrm{7}}{\mathrm{98}}{cosx}}{dx} \\ $$$${let}\:{determine}\:{A}\:=\int\:\:\frac{{sinx}+{acosx}}{{sinx}\:+{bcosx}}{dx}\:\:{we}\:{di}\:{the}\:{changement} \\ $$$${tan}\left(\frac{{x}}{\mathrm{2}}\right)={t}\:\Rightarrow\:{A}\:=\int\frac{\frac{\mathrm{2}{t}}{\mathrm{1}+{t}^{\mathrm{2}} }+{a}\frac{\mathrm{1}−{t}^{\mathrm{2}} }{\mathrm{1}+{t}^{\mathrm{2}}…
Question Number 84677 by jagoll last updated on 15/Mar/20 $$\underset{\mathrm{k}\:=\:\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{k}^{\mathrm{2}} }{\mathrm{2}^{\mathrm{k}} }\:?\: \\ $$ Commented by Tony Lin last updated on 15/Mar/20 $$\frac{\mathrm{1}}{\mathrm{1}−{x}}=\mathrm{1}+{x}+{x}^{\mathrm{2}}…
Question Number 19140 by Tinkutara last updated on 05/Aug/17 $$\mathrm{A}\:\mathrm{racing}\:\mathrm{car}\:\mathrm{travels}\:\mathrm{on}\:\mathrm{a}\:\mathrm{track}\:\left(\mathrm{without}\right. \\ $$$$\left.\mathrm{banking}\right)\:{ABCDEFA}.\:{ABC}\:\mathrm{is}\:\mathrm{a}\:\mathrm{circular} \\ $$$$\mathrm{arc}\:\mathrm{of}\:\mathrm{radius}\:\mathrm{2}{R}.\:{CD}\:\mathrm{and}\:{FA}\:\mathrm{are} \\ $$$$\mathrm{straight}\:\mathrm{paths}\:\mathrm{of}\:\mathrm{length}\:{R}\:\mathrm{and}\:{DEF}\:\mathrm{is} \\ $$$$\mathrm{a}\:\mathrm{circular}\:\mathrm{arc}\:\mathrm{of}\:\mathrm{radius}\:{R}\:=\:\mathrm{100}\:\mathrm{m}.\:\mathrm{The} \\ $$$$\mathrm{co}-\mathrm{efficient}\:\mathrm{of}\:\mathrm{friction}\:\mathrm{on}\:\mathrm{the}\:\mathrm{road}\:\mathrm{is}\:\mu\:= \\ $$$$\mathrm{0}.\mathrm{1}.\:\mathrm{The}\:\mathrm{maximum}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{the}\:\mathrm{car}\:\mathrm{is} \\ $$$$\mathrm{50}\:\mathrm{ms}^{−\mathrm{1}} .\:\mathrm{Find}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{time}\:\mathrm{for}…
Question Number 84674 by jagoll last updated on 15/Mar/20 $$\frac{\mathrm{6}−\mathrm{log}_{\mathrm{16}} \:\left(\mathrm{x}^{\mathrm{4}} \right)}{\mathrm{3}+\mathrm{2log}_{\mathrm{16}} \left(\mathrm{x}^{\mathrm{2}} \right)}\:<\:\mathrm{2} \\ $$ Commented by jagoll last updated on 15/Mar/20 $$\left(\mathrm{i}\right)\:\mathrm{x}\:\neq\:\mathrm{0}\: \\…
Question Number 19137 by Tinkutara last updated on 05/Aug/17 $$\mathrm{Figure}\:\mathrm{shows}\:\left({x},\:{t}\right),\:\left({y},\:{t}\right)\:\mathrm{diagram}\:\mathrm{of}\:\mathrm{a} \\ $$$$\mathrm{particle}\:\mathrm{moving}\:\mathrm{in}\:\mathrm{2}-\mathrm{dimensions}.\:\mathrm{If}\:\mathrm{the} \\ $$$$\mathrm{particle}\:\mathrm{has}\:\mathrm{a}\:\mathrm{mass}\:\mathrm{of}\:\mathrm{500}\:\mathrm{g},\:\mathrm{find}\:\mathrm{the} \\ $$$$\mathrm{force}\:\left(\mathrm{direction}\:\mathrm{and}\:\mathrm{magnitude}\right)\:\mathrm{acting} \\ $$$$\mathrm{on}\:\mathrm{the}\:\mathrm{particle}. \\ $$ Commented by Tinkutara last updated…
Question Number 19135 by gourav~ last updated on 05/Aug/17 $${solve}\:{for}\:{x}: \\ $$$$\mathrm{2}^{\mid{x}+\mathrm{2}\mid} −\mid\mathrm{2}^{{x}+\mathrm{1}} −\mathrm{1}\mid=\mathrm{2}^{{x}+\mathrm{1}} +\mathrm{1} \\ $$ Answered by ajfour last updated on 05/Aug/17 $$\mathrm{x}+\mathrm{2}\geqslant\mathrm{0}\:\:\Rightarrow\:\:\mathrm{x}\geqslant−\mathrm{2}…
Question Number 84666 by jagoll last updated on 14/Mar/20 $$\int\:{x}\:\mathrm{sin}^{−\mathrm{1}} \left({x}\right)\:{dx}\: \\ $$ Commented by mathmax by abdo last updated on 15/Mar/20 $${A}\:=\int\:{xarcsinx}\:{dx}\:\:{by}\:{parts}\:\:{u}^{'} ={x}\:{and}\:{v}={arcsinx}\:\Rightarrow \\…
Question Number 84667 by Power last updated on 14/Mar/20 Commented by Power last updated on 15/Mar/20 $$\boldsymbol{\mathrm{please}}\:\boldsymbol{\mathrm{see}} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 150202 by tabata last updated on 10/Aug/21 $${lim}_{{x}\rightarrow\mathrm{2}} \left(\frac{\mathrm{16}−\mathrm{4}^{{x}} }{\mathrm{9}−\mathrm{3}^{{x}} }\right)\:{with}\:{out}\:{lophital} \\ $$ Commented by tabata last updated on 10/Aug/21 $$?????? \\ $$…