Question Number 203919 by Samuel12 last updated on 02/Feb/24 $$\:\: \\ $$ Answered by Mathspace last updated on 02/Feb/24 $$\mathrm{1}={e}^{\mathrm{2}{ik}\pi} \:\:{let}\:{z}={re}^{{i}\theta} \\ $$$${z}^{\mathrm{5}} =\mathrm{1}\:\Leftrightarrow{r}^{\mathrm{5}} {e}^{{i}\mathrm{5}\theta}…
Question Number 203941 by Panav last updated on 02/Feb/24 $$\boldsymbol{{If}}\:\boldsymbol{{a}}^{\mathrm{2}\:} −\boldsymbol{{a}}+\mathrm{2}=\mathrm{0}\:\boldsymbol{{and}}\:\boldsymbol{{x}}^{\mathrm{2}} =\boldsymbol{{a}}^{\mathrm{6}} +\mathrm{2}\boldsymbol{{a}}^{\mathrm{4}} +\boldsymbol{{a}}^{\mathrm{2}} \:\boldsymbol{{then}}\:\boldsymbol{{find}}\:\boldsymbol{{x}}? \\ $$$$\boldsymbol{{IIT}}−\boldsymbol{{JEE}}\:\boldsymbol{{based}}\:\boldsymbol{{question}}.\:\boldsymbol{{Find}}\:\boldsymbol{{sol}}^{\boldsymbol{{n}}} . \\ $$ Answered by Rasheed.Sindhi last updated…
Question Number 203900 by necx122 last updated on 01/Feb/24 $${Let}\:{A}\:\in\:{R}^{{N}×{N}} \:{be}\:{a}\:{symmetric}\:{positive} \\ $$$${definite}\:{matrix}\:{and}\:{b}\:\in\:{R}^{{N}} \:{a}\:{vector}. \\ $$$${If}\:{x}\:\in\:{R}^{{N}} ,\:{evaluate}\:{the}\:{integral} \\ $$$${Z}\left({A},{b}\right)\:=\:\int{e}^{−\frac{\mathrm{1}}{\mathrm{2}}{x}^{{T}} {Ax}\:+\:{b}^{{T}} {x}} {dx}\:{as}\:{a}\:{function} \\ $$$${of}\:{A}\:{and}\:{b}. \\…
Question Number 203901 by explorerapollo last updated on 01/Feb/24 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 203897 by NasaSara last updated on 01/Feb/24 Answered by AST last updated on 01/Feb/24 $${cos}^{\mathrm{2}} \left({x}\right)−{cos}\left({x}\right)=\sqrt{\mathrm{1}−{cos}^{\mathrm{2}} {x}} \\ $$$$\Rightarrow{cos}^{\mathrm{4}} \left({x}\right)+\mathrm{2}{cos}^{\mathrm{2}} \left({x}\right)−\mathrm{2}{cos}^{\mathrm{3}} \left({x}\right)−\mathrm{1}=\mathrm{0} \\…
Question Number 203898 by necx122 last updated on 02/Feb/24 $${Let}\:{f}\left({W}\right)\:{be}\:{a}\:{function}\:{of}\:{vector}\:{W}\:\in\: {R}^{{N}} , \\ $$$${i}.{e}.\:{f}\left({W}\right)\:=\:\frac{\mathrm{1}}{\mathrm{1}\:+\:{e}^{−{W}^{{T}} {x}} } \\ $$$${Determine}\:{the}\:{first}\:{derivative}\:{and} \\ $$$${matrix}\:{of}\:{second}\:{derivatives}\:{of}\:{f}\:{with} \\ $$$${respect}\:{to}\:{W} \\ $$$$ \\…
Question Number 203891 by York12 last updated on 02/Feb/24 $$ \\ $$ Answered by sniper237 last updated on 01/Feb/24 $${The}\:{last}\:{factor}\:{should}\:{be}\:\left(\frac{{c}}{{a}+{b}}+\frac{{a}}{{b}+{c}}\right) \\ $$$${If}\:\:{so}\:,\:{Let}\:{named}\:{P}\:{that}\:{product} \\ $$$${Divide}\:{each}\:{factor}\:{by}\:{c},{a},{b}\:{resp} \\…
Question Number 203909 by Davidtim last updated on 01/Feb/24 $${prove}\:{that}\:\:\:\mathrm{0}^{{n}} =\mathrm{0}\:\:\:,\:\:\:\:{n}>\mathrm{0} \\ $$ Answered by Mathspace last updated on 01/Feb/24 $$\mathrm{0}^{{n}} ={lim}_{{x}\rightarrow\mathrm{0}^{+} } \:\:{x}^{{n}} \\…
Question Number 203910 by Davidtim last updated on 01/Feb/24 $${if}\:\:\:{y}=\left(\mathrm{1}−{x}\right)\left(\mathrm{2}−{x}\right)\left(\mathrm{3}−{x}\right)\centerdot\centerdot\centerdot\left({n}−{x}\right) \\ $$$${y}^{'} =? \\ $$ Answered by mr W last updated on 01/Feb/24 $${y}=\underset{{k}=\mathrm{1}} {\overset{{n}}…
Question Number 203911 by Davidtim last updated on 01/Feb/24 $${if}\:\mathrm{11}^{\mathrm{800}} \:{divide}\:{by}\:\mathrm{9}\:{what}\:{will}\:{be}\:{the}\: \\ $$$${remainder}? \\ $$ Answered by AST last updated on 01/Feb/24 $$\mathrm{11}^{\mathrm{800}} \equiv\mathrm{2}^{\mathrm{800}} =\left(\mathrm{2}^{\mathrm{6}}…