If \( y \) varies directly as the square of \( x \), and \( y=98 \) when \( x=7 \), calculate \( y \) when \( x=5 \). [WAEC]

Since \( y \) varies directly as the square of \( x \), we can express this relationship with the equation: \[ y = kx^2 \] where \( k \) is the constant of proportionality. We can find \( k \) using the given values \( y = 98 \) and \( x = 7 \). Substituting these values into the equation gives us: \[ 98 = k(7^2) \] \[ 98 = k(49) \] \[ k = \frac{98}{49} = 2 \] Now, we can write the equation for \( y \): \[ y = 2x^2 \] Next, to find \( y \) when \( x = 5 \), we substitute \( 5 \) into the equation: \[ y = 2(5^2) \] \[ y = 2(25) \] \[ y = 50 \] Therefore, when \( x = 5 \), \( y = 50 \).