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Find y when x=14 if y varies directly with x2 and y=72 when x=6

Sagot :

Luanaidn
[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.

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