[tex]\boxed{\bf \bigg(a\, ; b \bigg) \cdot \bigg[a\, ; b\bigg] = a \cdot b}[/tex]
[tex]\bf \bigg(a\, ; b \bigg) = 15[/tex]
[tex]\bf \bigg[ \: a\, ; b \bigg]=360[/tex]
[tex]\bf \implies a \cdot b = 15 \cdot 360 =5400[/tex]
[tex]\bf \bigg(a\, ; b \bigg) = 15 \implies \Bigg\{ a=15k \\\bf \bigg(a\, ; b \bigg) = 15 \implies \Bigg \{ b = 15 p[/tex]
[tex]\mathbf{(k\, ; p )=1 } \mathsf{\; -prime \; intre\; ele}[/tex]
[tex]\bf a \cdot b = 5400 \iff 15k \cdot 15p = 5400[/tex]
[tex]\bf 15^2 \cdot k \cdot p = 5400\; \bigg| :15^2 \iff k \cdot p = 24[/tex]
[tex]\bf D_{24}= \{1;2;3;4;6;8;12;24\} \implies (k\, ; p) \in D_{24}[/tex]
[tex]\bf dar \; \bigg(k\, ;p\bigg)=1 \implies \bigg(k\, ; p \bigg) \in \bigg\{ \bigg(1\, ;24\bigg); \bigg(3\, ;8\bigg);\bigg(8\, ;3\bigg);\bigg(24\, ;1\bigg)\bigg\}[/tex]
[tex]\bf \iff \Bigg\{ a=15k=15 \rightarrow b = 15p =15 \cdot 24=360[/tex]
[tex]\bf \iff \Bigg\{ a=15k=15 \cdot 3=45 \rightarrow b=15p=15 \cdot 8 = 120[/tex]
[tex]\bf \iff \Bigg\{ a=15k=15 \cdot 8 = 120 \rightarrow b = 15p = 15 \cdot 3 = 45[/tex]
[tex]\bf \iff \Bigg\{ a=15k = 15 \cdot 24=360 \rightarrow b=15p=15[/tex]
[tex]\bf Dar : \; a < b \implies \boxed{\bf \bigg(a\, ;b\bigg)\in \Bigg\{ \bigg(360\, ; 15\bigg);\bigg(120\, ;45\bigg) \Bigg\} }[/tex]
[tex]\mathsf{Avem \; doua \; solutii\; \implies \boxed{ \bf Raspunsul \; este \; B }}[/tex]
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[tex]\mathsf{Privind \; desenul \; atasat \; observam\; ca \; acul\; de \; la\; minutul\; 30\; cade \; pe \; ora \; 6\; (18) : }[/tex]
- [tex]\bf 12 \rightarrow 13 \; = 1\, h[/tex]
- [tex]\bf 13 \rightarrow 14 = 1\, h[/tex]
- [tex]\bf 14 \rightarrow 15 = 1\, h[/tex]
- [tex]\bf 15 \rightarrow 16 = 1\, h[/tex]
- [tex]\bf 16 \rightarrow 17 = 1\, h[/tex]
- [tex]\bf 17 \rightarrow 18 = 1\, h[/tex]
[tex]\bf \iff 12 \rightarrow 18 = 6h[/tex]
[tex]\bf ceasul=cerc \implies ceasul = 360^{\circ}[/tex]
[tex]\mathbf{ceasul = 12\, h \implies 360^{\circ} : 12\, h =30^{\circ} }[/tex]
[tex]\bf \implies 6\, h = 6 \cdot 30^{\circ} \implies \boxed{\bf \angle= 180^{\circ} (A)}[/tex]
#copaceibrainly
