Menu Close

Author: Tinku Tara

Question-211143

Question Number 211143 by boblosh last updated on 29/Aug/24 Answered by A5T last updated on 29/Aug/24 $${Let}\:{width}\:{be}\:{w}\Rightarrow{w}={y}+\mathrm{12} \\ $$$${perimeter}=\mathrm{2}\left({w}+{y}\right) \\ $$$$\mathrm{2}\left({w}+\mathrm{30}+{y}+\mathrm{30}\right)=\mathrm{3}×\mathrm{2}\left({w}+{y}\right) \\ $$$$\Rightarrow{w}+{y}=\mathrm{30}\Rightarrow{y}+\mathrm{12}+{y}=\mathrm{30}\Rightarrow{y}=\mathrm{9} \\ $$$$\Rightarrow{length}=\mathrm{9}\:{and}\:{width}=\mathrm{21}…

Question-211115

Question Number 211115 by Durganand last updated on 28/Aug/24 Answered by som(math1967) last updated on 28/Aug/24 $${tanA}+\mathrm{2}{tan}\mathrm{2}{A}+\frac{\mathrm{4}}{{tan}\mathrm{2}.\mathrm{2}{A}} \\ $$$$={tanA}+\mathrm{2}{tan}\mathrm{2}{A}+\frac{\mathrm{4}\left(\mathrm{1}−{tan}^{\mathrm{2}} \mathrm{2}{A}\right)}{\mathrm{2}{tan}\mathrm{2}{A}} \\ $$$$={tanA}+\frac{\mathrm{2}{tan}^{\mathrm{2}} \mathrm{2}{A}+\mathrm{2}−\mathrm{2}{tan}^{\mathrm{2}} \mathrm{2}{A}}{{tan}\mathrm{2}{A}}\: \\…

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}.…