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Author: Tinku Tara

Question-211105

Question Number 211105 by peter frank last updated on 28/Aug/24 Answered by mm1342 last updated on 28/Aug/24 $${z}={z}_{\mathrm{1}} {z}_{\mathrm{2}} ={cos}\frac{\mathrm{12}\pi}{\mathrm{5}}+{isin}\frac{\mathrm{12}\pi}{\mathrm{5}} \\ $$$$={cos}\frac{\mathrm{2}\pi}{\mathrm{5}}+{isin}\frac{\mathrm{2}\pi}{\mathrm{5}}={e}^{\frac{\mathrm{2}\pi}{\mathrm{5}}{i}\:} \Rightarrow{z}^{\mathrm{5}} ={e}^{\mathrm{2}\pi{i}} =\mathrm{1}…

Question-211099

Question Number 211099 by peter frank last updated on 27/Aug/24 Answered by A5T last updated on 27/Aug/24 $$\mathrm{2}^{{logx}} =\mathrm{2}^{\frac{{log}_{\mathrm{2}} {x}}{{log}_{\mathrm{2}} \mathrm{10}}} ={x}^{\frac{\mathrm{1}}{{log}_{\mathrm{2}} \mathrm{10}}} ={x}^{{log}_{\mathrm{10}} \mathrm{2}}…

Question-211058

Question Number 211058 by mr W last updated on 27/Aug/24 Commented by mr W last updated on 27/Aug/24 $${find}\:{the}\:{radius}\:{R}\:{of}\:{the}\:{largest}\:{sphere} \\ $$$${which}\:{can}\:{be}\:{placed}\:{between}\:{the}\:{red} \\ $$$${and}\:{blue}\:{planes}\:{in}\:{the}\:{first}\:{octant}. \\ $$$${assume}\:\mathrm{0}<{p}\leqslant{a},\:\mathrm{0}<{q}\leqslant{b},\:\mathrm{0}<{r}\leqslant{c}.…

Question-211079

Question Number 211079 by Ari last updated on 27/Aug/24 Answered by A5T last updated on 27/Aug/24 $${Suppose}\:{DB}\bot{AC} \\ $$$${A}_{\mathrm{2}} =\frac{{DB}×{AB}}{\mathrm{2}}=\mathrm{63};{A}_{\mathrm{1}} =\frac{{EA}×{AB}}{\mathrm{2}}=\mathrm{144} \\ $$$$\frac{{A}_{\mathrm{2}} }{{A}_{\mathrm{1}} }=\frac{\mathrm{63}}{\mathrm{144}}=\frac{{DB}}{{EA}}=\frac{\mathrm{7}}{\mathrm{16}}\Rightarrow\frac{{A}_{\mathrm{3}}…

Question-211001

Question Number 211001 by lmcp1203 last updated on 26/Aug/24 Commented by mr W last updated on 26/Aug/24 $${is}\:{the}\:“{inclined}\:{plane}''\:{just}\:{a}\:{wedge} \\ $$$${which}\:{can}\:{slide}\:{frictionlessly}\:{on}\:{the} \\ $$$${ground}?\:{or}\:{the}\:{wedge}\:{is}\:{fixed}\:{with} \\ $$$${the}\:{ground}? \\…