Question Number 10776 by j.masanja06@gmail.com last updated on 24/Feb/17 $$\mathrm{if}\:\:\:\mathrm{D}\:=\begin{vmatrix}{\mathrm{1}}&{\mathrm{3sin}\theta}&{\mathrm{1}}\\{\mathrm{sin}\theta}&{\mathrm{1}}&{\mathrm{3cos}\theta}\\{\mathrm{1}}&{\mathrm{sin}\theta}&{\mathrm{1}}\end{vmatrix}\:\mathrm{the}\:\mathrm{maxi} \\ $$$$\mathrm{mum}\:\mathrm{value}\:\mathrm{of}\:\mathrm{D}\:\mathrm{is}? \\ $$ Answered by sandy_suhendra last updated on 24/Feb/17 $$\mathrm{D}=\mathrm{1}+\mathrm{9}\:\mathrm{sin}\theta\:\mathrm{cos}\theta+\mathrm{sin}\theta\:\mathrm{cos}\theta−\left(\mathrm{1}+\mathrm{3}\:\mathrm{sin}\theta\:\mathrm{cos}\theta+\mathrm{3}\:\mathrm{sin}\theta\:\mathrm{cos}\theta\right)\:\:\:\:\: \\ $$$$\:\:\:\:=\mathrm{4}\:\mathrm{sin}\theta\:\mathrm{cos}\theta=\mathrm{2}\:\mathrm{sin}\:\mathrm{2}\theta \\…
Question Number 10774 by j.masanja06@gmail.com last updated on 24/Feb/17 Answered by sandy_suhendra last updated on 24/Feb/17 $$=\begin{vmatrix}{\mathrm{log}_{\mathrm{3}} \mathrm{1024}\:\:\:\:\mathrm{1}}\\{\mathrm{log}_{\mathrm{3}} \mathrm{8}\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{2}}\end{vmatrix}×\begin{vmatrix}{\mathrm{log}_{\mathrm{2}} \mathrm{3}\:\:\:\:\mathrm{log}_{\mathrm{4}} \mathrm{3}}\\{\mathrm{log}_{\mathrm{3}} \mathrm{4}\:\:\:\:\mathrm{log}_{\mathrm{3}} \mathrm{4}}\end{vmatrix} \\ $$$$=\left(\mathrm{2log}_{\mathrm{3}}…
Question Number 141847 by iloveisrael last updated on 24/May/21 $$\:\mathcal{I}\:=\:\int\:\frac{\mathrm{sec}\:{x}}{\mathrm{1}+\mathrm{csc}\:{x}}\:{dx}\: \\ $$ Answered by MJS_new last updated on 24/May/21 $$\int\frac{\mathrm{sec}\:{x}}{\mathrm{1}+\mathrm{csc}\:{x}}= \\ $$$$\:\:\:\:\:\left[{t}=\mathrm{tan}\:\frac{{x}}{\mathrm{2}}\:\rightarrow\:{dx}=\mathrm{2cos}^{\mathrm{2}} \:\frac{{x}}{\mathrm{2}}\:{dt}\right] \\ $$$$=−\mathrm{4}\int\frac{{t}}{\left({t}−\mathrm{1}\right)\left({t}+\mathrm{1}\right)^{\mathrm{3}}…
Question Number 10773 by ketto last updated on 24/Feb/17 Answered by mrW1 last updated on 24/Feb/17 $$\mathrm{3}!=\mathrm{6}\:{ways} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 141846 by ArielVyny last updated on 24/May/21 $$\sum_{{k}\geqslant\mathrm{0}} \left({C}_{{n}} ^{{k}} \right)^{\mathrm{2}} \\ $$ Answered by mindispower last updated on 24/May/21 $$\underset{{k}\geqslant\mathrm{0}} {\sum}{C}_{{n}} ^{{k}}…
Question Number 76306 by Hassen_Timol last updated on 26/Dec/19 $${z}\:=\:{a}\:+\:{bi} \\ $$$${Z}\:=\:\frac{−\mathrm{7}\:+\:{z}}{−\mathrm{3}\:+\:{iz}} \\ $$$$ \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{all}\:\mathrm{the}\:\mathrm{points}\:\mathrm{M} \\ $$$$\mathrm{of}\:\mathrm{coordonates}\:\left({a},{b}\right)\:\mathrm{such}\:\mathrm{as}\:{Z}\:\mathrm{is}\:\mathrm{real}\:? \\ $$ Answered by mr W last…
Question Number 141840 by Study last updated on 23/May/21 $${sin}^{\mathrm{2}} \left(\mathrm{360}−{x}\right)−\frac{{cos}\left({x}−\mathrm{180}\right)\centerdot{tan}\left(−{x}\right)\centerdot{sin}\left(\mathrm{90}−{x}\right)\centerdot{cos}\left(\mathrm{360}−{x}\right)}{{sin}\left(\mathrm{180}−{x}\right)}=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 76307 by Master last updated on 26/Dec/19 Answered by mr W last updated on 26/Dec/19 $${x}\neq\mathrm{1} \\ $$$$\mathrm{125}\left(\mathrm{1}+{x}^{\mathrm{5}} \right)=\mathrm{11}\left(\mathrm{1}+{x}\right)^{\mathrm{5}} \\ $$$$\mathrm{125}\left(\mathrm{1}−{x}+{x}^{\mathrm{2}} −{x}^{\mathrm{3}} +{x}^{\mathrm{4}}…
Question Number 10768 by 2525 last updated on 24/Feb/17 $$\mathrm{Solve}\:\mathrm{the}\:\mathrm{following}\:\mathrm{differential}\:\mathrm{equations}\: \\ $$$$\mathrm{by}\:\mathrm{power}\:\mathrm{series}. \\ $$$${y}^{//} −\mathrm{2}{y}\:=\:\mathrm{4}{x}^{\mathrm{2}} {e}^{{x}^{\mathrm{2}} } \\ $$ Commented by 2525 last updated on…
Question Number 76302 by john santuy last updated on 26/Dec/19 $${given}\:{vektor}\:{a}=\left(\mathrm{3},{x},−\mathrm{2}\right) \\ $$$${b}=\left(−\mathrm{6},−\mathrm{2},{y}\right)\:.\:{what}\:{the}\:{value}\:{x}\: \\ $$$${and}\:{y}\:{if}\:{a}\:{and}\:{b}\:{are}\:{parallel}? \\ $$ Answered by benjo last updated on 26/Dec/19 $$\mathrm{a}×\mathrm{b}\:=\mathrm{0}…