Answer:
[tex]y = \frac{384}{9}[/tex]
Step-by-step explanation:
Given
[tex]y\ \alpha\ x^2[/tex] --- direct variation
[tex](x,y) = (3,24)[/tex]
Required
y when x = 4
[tex]y\ \alpha\ x^2[/tex]
Express as an equation
[tex]y = kx^2[/tex]
Substitute: [tex](x,y) = (3,24)[/tex]
[tex]24 = k*3^2[/tex]
[tex]24 = k*9[/tex]
Solve for k
[tex]k = \frac{24}{9}[/tex]
To solve for y when x = 4, we have:
[tex]y = kx^2[/tex]
[tex]y = \frac{24}{9} * 4^2[/tex]
[tex]y = \frac{24}{9} * 16[/tex]
[tex]y = \frac{24 * 16}{9}[/tex]
[tex]y = \frac{384}{9}[/tex]
