Question

Va rog rapid!dau coroana

Answer 1

 

Lungimea unei zale

L za = 2 cm = 20 mm

Grosimea unei zale = grosimea sarmei din care este confectionat:

G = 4 mm

Daca avem doar 2 zale, lungimea este de 2 × 20 mm din care scadem pierderile la inbinare (4 mm + 4 mm).

Vezi desenul atasat.

⇒ L_lant de 2 zale = 2 × 20 - (4 + 4) = 2 × 20 - 2 × 4 = 40 - 8 = 32 mm

La 3 zale avem 2 imbinari.

La 4 zale avem 3 imbinari.

La 5 zale avem 4 imbinari.

................................................

La n zale avem (n-1) imbinari si la o imbinare se pierd 2 grosimi de za.

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$\displaystyle\bf\\Rezolvare:\\\\1~m=1000~mm\\n\times20 - (n-1)\times (4+4)\geq 1000\\\\20n-8(n-1)\geq 1000\\\\20n-8n+8\geq 1000\\\\12n+8\geq 1000\\\\12n\geq1000-8\\\\12n\geq992\\\\n\geq\frac{992}{12}\\\\n=82~rest~8,~~~~dar~n\in N\\\\\implies~n=82+1=83\\\\\boxed{\bf n=83~de~zale}\\\\Verificare:\\\\83\times20-(83-1)\times8=\\\\=83\times20-(83-1)\times8=\\\\=83\times20-82\times8=\\\\=1660-656=1004~mm\\\\\1004~mm > 1~metru\\\\\implies \boxed{\bf83~de~zale~este~cel~mai~mic~numar~de~zale.}$