Question Number 211190 by mr W last updated on 30/Aug/24 Answered by A5T last updated on 31/Aug/24 $${Let}\:\angle{BCD}=\angle{CBD}=\theta\Rightarrow\angle{DBA}=\mathrm{90}°−\theta \\ $$$$\Rightarrow\angle{ADB}=\mathrm{90}°−\theta\Rightarrow\angle{DAB}=\mathrm{2}\theta \\ $$$$\angle{BCA}=\angle{CAB}=\mathrm{45}°\Rightarrow\angle{ACD}=\mathrm{45}°−\theta\Rightarrow?=\mathrm{45}°−\mathrm{2}\theta \\ $$$${Let}\:{CD}={BD}={x}\:{and}\:{AD}={AB}={BC}={y} \\…
Question Number 211145 by mr W last updated on 29/Aug/24 Commented by mr W last updated on 30/Aug/24 $${thanks}!\:{but}\:{i}\:{think}\:{people}\:{know}\: \\ $$$${what}\:{i}\:{exactly}\:{mean}. \\ $$ Commented by…
Question Number 211118 by behi834171 last updated on 28/Aug/24 Commented by mr W last updated on 28/Aug/24 Commented by mr W last updated on 28/Aug/24…
Question Number 211127 by behi834171 last updated on 28/Aug/24 $$ \\ $$Two circles are assumed that have the same center. How many circles are there…
Question Number 211058 by mr W last updated on 27/Aug/24 Commented by mr W last updated on 27/Aug/24 $${find}\:{the}\:{radius}\:{R}\:{of}\:{the}\:{largest}\:{sphere} \\ $$$${which}\:{can}\:{be}\:{placed}\:{between}\:{the}\:{red} \\ $$$${and}\:{blue}\:{planes}\:{in}\:{the}\:{first}\:{octant}. \\ $$$${assume}\:\mathrm{0}<{p}\leqslant{a},\:\mathrm{0}<{q}\leqslant{b},\:\mathrm{0}<{r}\leqslant{c}.…
Question Number 211079 by Ari last updated on 27/Aug/24 Answered by A5T last updated on 27/Aug/24 $${Suppose}\:{DB}\bot{AC} \\ $$$${A}_{\mathrm{2}} =\frac{{DB}×{AB}}{\mathrm{2}}=\mathrm{63};{A}_{\mathrm{1}} =\frac{{EA}×{AB}}{\mathrm{2}}=\mathrm{144} \\ $$$$\frac{{A}_{\mathrm{2}} }{{A}_{\mathrm{1}} }=\frac{\mathrm{63}}{\mathrm{144}}=\frac{{DB}}{{EA}}=\frac{\mathrm{7}}{\mathrm{16}}\Rightarrow\frac{{A}_{\mathrm{3}}…
Question Number 211016 by mr W last updated on 26/Aug/24 Commented by mr W last updated on 26/Aug/24 $${find}\:{x}=? \\ $$$$ \\ $$$${the}\:{original}\:{question}\:{was}\:{deleted}\:{by} \\ $$$${the}\:{questioner}\:{for}\:{some}\:{reasons}.…
Question Number 210948 by cherokeesay last updated on 23/Aug/24 Commented by cherokeesay last updated on 23/Aug/24 $$\mathrm{If}\:\mathrm{only}\:\mathrm{the}\:\mathrm{result}\:\mathrm{is}\:\mathrm{accompanied}\:\mathrm{by}\:\mathrm{a} \\ $$$$\mathrm{diagam}\:\mathrm{it}\:\mathrm{will}\:\mathrm{be}\:\mathrm{perfect}. \\ $$$${thanks}. \\ $$ Answered by…
Question Number 210935 by mr W last updated on 22/Aug/24 $${at}\:{what}\:{times},\:{if}\:{exist},\:{are}\:{the}\: \\ $$$${angles}\:{betwen}\:{the}\:{hour}\:{hand},\:{the} \\ $$$${minute}\:{hand}\:{and}\:{the}\:{second}\:{hand} \\ $$$${of}\:{a}\:{clock}\:{exactly}\:\mathrm{120}°? \\ $$$${assume}\:{that}\:{the}\:{hands}\:{of}\:{the}\:{clock} \\ $$$${move}\:{uniformly}. \\ $$ Answered by…
Question Number 210761 by mr W last updated on 18/Aug/24 Commented by mr W last updated on 18/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}.…