Answer :
[tex]for\ y\ \ x^2=14^2\\
for\ y=72\ \ x^2=6^2\\\\
\frac{y}{196}=\frac{72}{36}\\
36y=72*196\ \ | divide\ by\ 36\\
\boxed{y=392}[/tex]
The approach is to first find the value of constant of proportionality 'k'.
As y varies directly with x²
So we have
y = k x².
Now when x = 6 , y = 72
Substituting the values we get
72 = k (6)²
72 = 36 k
Dividing by 36 on both sides
2 = k
So (1) becomes
y = 2 x²
Now we need to find y when x = 14
Substituting the values in (2) we get
y = 2 ×(14)²
y = 2 × 196
y = 392
Hence y = 392 when x = 14.
