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Category: Algebra

125-12-10-or-11-

Question Number 153780 by liberty last updated on 10/Sep/21 $$\:\lfloor\:\frac{\mathrm{125}}{\mathrm{12}}\:\rfloor\:=\mathrm{10}\:{or}\:\mathrm{11}\:? \\ $$ Answered by puissant last updated on 10/Sep/21 $$\lfloor\frac{\mathrm{125}}{\mathrm{12}}\rfloor=\lfloor\mathrm{10},\mathrm{41}\rfloor=\mathrm{10}.. \\ $$ Commented by liberty…

Question-22701

Question Number 22701 by selestian last updated on 22/Oct/17 Answered by ajfour last updated on 22/Oct/17 $${e}^{\left(\frac{\mathrm{sin}\:^{\mathrm{2}} {x}}{\mathrm{1}−\mathrm{sin}\:^{\mathrm{2}} {x}}\right)\mathrm{ln}\:\mathrm{2}} \:={e}^{\mathrm{ln}\:\mathrm{2}^{\mathrm{tan}\:^{\mathrm{2}} {x}} } \:=\mathrm{2}^{\mathrm{tan}\:^{\mathrm{2}} {x}} \\…

Prove-without-any-software-0-1-0-1-1-x-y-2-2-dxdy-gt-pi-4-

Question Number 153764 by mathdanisur last updated on 10/Sep/21 $$\mathrm{Prove}\:\mathrm{without}\:\mathrm{any}\:\mathrm{software}: \\ $$$$\underset{\:\mathrm{0}} {\overset{\:\mathrm{1}} {\int}}\:\underset{\:\mathrm{0}} {\overset{\:\mathrm{1}} {\int}}\:\sqrt{\mathrm{1}\:-\:\left(\frac{\mathrm{x}\:+\:\mathrm{y}}{\mathrm{2}}\right)^{\mathrm{2}} }\:\mathrm{dxdy}\:>\:\frac{\pi}{\mathrm{4}} \\ $$ Commented by alisiao last updated on…

Determine-all-pairs-x-y-of-integers-which-satisfy-x-2-y-2-16y-1-0-

Question Number 153763 by mathdanisur last updated on 10/Sep/21 $$\mathrm{Determine}\:\mathrm{all}\:\mathrm{pairs}\:\left(\mathrm{x};\mathrm{y}\right)\:\mathrm{of}\:\mathrm{integers} \\ $$$$\mathrm{which}\:\mathrm{satisfy} \\ $$$$\mid\mathrm{x}^{\mathrm{2}} \:-\:\mathrm{y}^{\mathrm{2}} \mid\:-\:\sqrt{\mathrm{16y}\:+\:\mathrm{1}}\:=\:\mathrm{0} \\ $$ Answered by liberty last updated on 10/Sep/21…