\( 17 Q \) is directly proportional to the square root of \( d \) \( Q=4.5 \) when \( d=324 \) Find a formula for \( Q \) in terms of \( d \)

To find a formula for \( Q \) in terms of \( d \), we start with the relationship \( 17Q = k\sqrt{d} \), where \( k \) is a constant of proportionality. We know that when \( Q = 4.5 \), \( d = 324 \). Plugging in these values: \[ 17 \times 4.5 = k\sqrt{324} \] Calculating \( \sqrt{324} \): \[ \sqrt{324} = 18 \] Thus, we have: \[ 76.5 = k \times 18 \] Now, solving for \( k \): \[ k = \frac{76.5}{18} = 4.25 \] Now substituting \( k \) back into the original proportional relationship gives us: \[ 17Q = 4.25\sqrt{d} \] Finally, we can express \( Q \) in terms of \( d \): \[ Q = \frac{4.25}{17} \sqrt{d} \approx 0.25\sqrt{d} \] So the formula for \( Q \) in terms of \( d \) is: \[ Q \approx 0.25\sqrt{d} \]