Question Number 211250 by RojaTaniya last updated on 01/Sep/24 $${Find}\:{the}\:{number}\:{of}\:\mathrm{4}\:{digit}\:{numbers} \\ $$$$\:{so}\:{that}\:{when}\:{decomposed}\:{into}\:{prime} \\ $$$$\:{factors},\:{have}\:{the}\:{sum}\:{of}\:{prime}\:{factors} \\ $$$$\:{equal}\:{to}\:{the}\:{sum}\:{of}\:{the}\:{exponents}? \\ $$ Answered by mr W last updated on…
Question Number 211251 by hardmath last updated on 01/Sep/24 Commented by a.lgnaoui last updated on 04/Sep/24 Commented by a.lgnaoui last updated on 05/Sep/24 $$\frac{\mathrm{sin}\:\mathrm{C}}{\mathrm{MN}}=\frac{\mathrm{sin}\:\mathrm{M}}{\mathrm{BC}−\mathrm{AB}}=\frac{\mathrm{sin}\:\mathrm{N}}{\mathrm{CD}−\mathrm{AD}}\left(\mathrm{1}\right) \\…
Question Number 211235 by behi834171 last updated on 01/Sep/24 Commented by behi834171 last updated on 01/Sep/24 $$\angle\boldsymbol{{ABC}};\:{is}\:{given}. \\ $$$$\boldsymbol{{D}};{is}\:{a}\:{point}\:{as}\:{it}\:{showen},{and} \\ $$$$\boldsymbol{{DG}}\:\:\&\:\boldsymbol{{DF}};\:{are}\:{distance}\:{of}:\boldsymbol{{D}},\:{from}: \\ $$$$\boldsymbol{{AB}}\:\&\:\boldsymbol{{BC}},{such}\:{that}:\frac{\boldsymbol{{DG}}}{\boldsymbol{{DF}}}=\boldsymbol{{k}}\left(\boldsymbol{{constant}}\right) \\ $$$$\boldsymbol{{find}}\:\:\boldsymbol{{the}}\:\:\boldsymbol{{locus}}\:\boldsymbol{{of}}:\:\boldsymbol{{D}}\:.…
Question Number 211222 by RojaTaniya last updated on 31/Aug/24 $${How}\:{many}\:{integers}\:{are}\:{there} \\ $$$$\:\:\:{such}\:{that},\:\:\mathrm{0}\leqslant{n}\leqslant\mathrm{720}\:{and}\: \\ $$$$\:\:\:{n}^{\mathrm{2}} \equiv\mathrm{1}\left({mod}\right)\mathrm{720}? \\ $$ Answered by mahdipoor last updated on 31/Aug/24 $$\Rightarrow{n}^{\mathrm{2}}…
Question Number 211207 by Etimbuk last updated on 31/Aug/24 Answered by mr W last updated on 03/Sep/24 $${e}_{\mathrm{1}} ={a}+{b}+{c}+{d} \\ $$$${e}_{\mathrm{2}} ={ab}+{bc}+{cd}+{da}+{ac}+{bd} \\ $$$${e}_{\mathrm{3}} ={abc}+{bcd}+{cda}+{dab}…
Question Number 211216 by Jubr last updated on 31/Aug/24 Answered by nikif99 last updated on 31/Aug/24 Commented by Jubr last updated on 31/Aug/24 $${Thank}\:{you}\:{sir} \\…
Question Number 211201 by efronzo1 last updated on 31/Aug/24 $$\:\:\:\sqrt[{\mathrm{3}}]{\mathrm{x}−\mathrm{1}}\:+\:\sqrt[{\mathrm{3}}]{\mathrm{x}−\mathrm{2}}\:−\sqrt[{\mathrm{3}}]{\mathrm{2x}−\mathrm{3}}\:=\:\mathrm{0} \\ $$$$\:\:\:\mathrm{x}=? \\ $$ Answered by Rasheed.Sindhi last updated on 31/Aug/24 $$\:\:\:\sqrt[{\mathrm{3}}]{\mathrm{x}−\mathrm{1}}\:+\:\sqrt[{\mathrm{3}}]{\mathrm{x}−\mathrm{2}}\:−\sqrt[{\mathrm{3}}]{\mathrm{2x}−\mathrm{3}}\:=\:\mathrm{0} \\ $$$$\because−\sqrt[{\mathrm{3}}]{\mathrm{2x}−\mathrm{3}}\:=\sqrt[{\mathrm{3}}]{\mathrm{3}−\mathrm{2x}} \\…
Question Number 211167 by cherokeesay last updated on 30/Aug/24 Commented by Frix last updated on 30/Aug/24 $$\mathrm{12} \\ $$ Answered by som(math1967) last updated on…
Question Number 211188 by Ari last updated on 30/Aug/24 Answered by mr W last updated on 30/Aug/24 $${AB}={x} \\ $$$${BC}={y} \\ $$$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} =\mathrm{12}^{\mathrm{2}} \\…
Question Number 211157 by RojaTaniya last updated on 30/Aug/24 Commented by Rasheed.Sindhi last updated on 30/Aug/24 $$\left({x},{y},{z}\right)=\left(\mathrm{1},\mathrm{0},\mathrm{0}\right),\left(\mathrm{0},\mathrm{1},\mathrm{0}\right),\left(\mathrm{0},\mathrm{0},\mathrm{1}\right) \\ $$ Answered by Rasheed.Sindhi last updated on…