1.6 Change the formula to make \( d \) the subject: \( w=\frac{2 m}{d^{2} v} \) \( 1.6 .1 \quad \) Calculate the value of \( d \) if \( m=3, w=4 \) and \( v=2 \)

To make \( d \) the subject of the equation \( w=\frac{2 m}{d^{2} v} \), we start by isolating \( d^{2} \). First, we multiply both sides by \( d^{2} v \): \[ w d^{2} v = 2 m \] Then, we rearrange it to isolate \( d^{2} \): \[ d^{2} = \frac{2 m}{w v} \] Taking the square root, we get: \[ d = \sqrt{\frac{2 m}{w v}} \] Now, substitute \( m=3, w=4, \) and \( v=2 \): \[ d = \sqrt{\frac{2 \times 3}{4 \times 2}} \] \[ d = \sqrt{\frac{6}{8}} \] \[ d = \sqrt{\frac{3}{4}} \] \[ d = \frac{\sqrt{3}}{2} \] So, the value of \( d \) is \( \frac{\sqrt{3}}{2} \).