1. Solve the formula \( P=\pi d+2 L+W+2 \pi d \) for \( d \)

To solve the formula \( P = \pi d + 2L + W + 2\pi d \) for \( d \), first combine like terms involving \( d \). This gives us: \[ P = 3\pi d + 2L + W \] Now, isolate \( d \) by subtracting \( 2L + W \) from both sides: \[ P - 2L - W = 3\pi d \] Finally, divide both sides by \( 3\pi \): \[ d = \frac{P - 2L - W}{3\pi} \] And there you have \( d \) expressed in terms of \( P \), \( L \), and \( W \)!