Question Number 211277 by mr W last updated on 04/Sep/24 Commented by mr W last updated on 04/Sep/24 $${find}\:{the}\:{volume}\:{of}\:{the}\:{tetrahedron} \\ $$$${in}\:{terms}\:{of}\:{a},{b},{c},\:\theta\:{with}\:\mathrm{0}<\theta\leqslant\mathrm{120}°. \\ $$ Commented by…
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Question Number 211235 by behi834171 last updated on 01/Sep/24 Commented by behi834171 last updated on 01/Sep/24 $$\angle\boldsymbol{{ABC}};\:{is}\:{given}. \\ $$$$\boldsymbol{{D}};{is}\:{a}\:{point}\:{as}\:{it}\:{showen},{and} \\ $$$$\boldsymbol{{DG}}\:\:\&\:\boldsymbol{{DF}};\:{are}\:{distance}\:{of}:\boldsymbol{{D}},\:{from}: \\ $$$$\boldsymbol{{AB}}\:\&\:\boldsymbol{{BC}},{such}\:{that}:\frac{\boldsymbol{{DG}}}{\boldsymbol{{DF}}}=\boldsymbol{{k}}\left(\boldsymbol{{constant}}\right) \\ $$$$\boldsymbol{{find}}\:\:\boldsymbol{{the}}\:\:\boldsymbol{{locus}}\:\boldsymbol{{of}}:\:\boldsymbol{{D}}\:.…
Question Number 211188 by Ari last updated on 30/Aug/24 Answered by mr W last updated on 30/Aug/24 $${AB}={x} \\ $$$${BC}={y} \\ $$$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} =\mathrm{12}^{\mathrm{2}} \\…
Question Number 211167 by cherokeesay last updated on 30/Aug/24 Commented by Frix last updated on 30/Aug/24 $$\mathrm{12} \\ $$ Answered by som(math1967) last updated on…
Question Number 211190 by mr W last updated on 30/Aug/24 Answered by A5T last updated on 31/Aug/24 $${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}.…