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Category: Algebra

Find-the-number-of-4-digit-numbers-so-that-when-decomposed-into-prime-factors-have-the-sum-of-prime-factors-equal-to-the-sum-of-the-exponents-

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-211251

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) \\…

x-1-1-3-x-2-1-3-2x-3-1-3-0-x-

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-211157

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…