Question

Va rog toate exercitile sau macar 3.

Answer 1

1.) Trebuie sa aplici proportionalitatea: 
a.) $\frac{2}{a}= \frac{5}{b}$

b.)$\frac{5}{2}= \frac{b}{a}$

c.) $\frac{b}{5}= \frac{a}{2}$

2.) a.) $\frac{y}{x}= \frac{2}{3}$

b.) $\frac{x}{3}= \frac{y}{2}$

c.) $\frac{2}{y}= \frac{3}{x}$

3.) $\frac{x}{y} = \frac{3}{5}=k$ ⇒ [tex]x=3k [/tex] $y=5k$
$3k+5k=16$ ⇒ $8k=16$ ⇒ $k=2$ ⇒ $\boxed {x=6}$ $\boxed {y=10}$

4.) Avem aceeasi relatie ca la 3.) ⇒ $5k-3k=8$ ⇒ $2k=8$ ⇒ $k=4$ ⇒$\boxed {x=12}$ $\boxed {y=20}$

5.) $\frac{x+y}{y-x}$. Suma (x+y) o avem in ipoteza de la 3.), iar diferenta (y-x) la 4.) . Deci, $\frac{x+y}{y-x}= \frac{16}{8}=\boxed {2}$

6.) Stim ca x=3k, y=5k ⇒ $\frac{2x}{3x+2y}= \frac{2*3k}{3*3k+2*5k}= \frac{6k}{19k}=\boxed { \frac{6}{19} }$