The period T (in seconds) of a pendulum is given by T=2pi sqrt ((L)/(32)) where L. stands for the length (in feet)of the pendulum. If pi =3.14 and the period is 1.57 seconds, what is the length? 8 feet 2 feet 20 feet 16 feet

## Step 1: Set up the equation<br />### Use the given formula for the period of a pendulum, \( T = 2 \pi \sqrt{\frac{L}{32}} \), and substitute \( T = 1.57 \) and \( \pi = 3.14 \).<br />\[ 1.57 = 2 \times 3.14 \times \sqrt{\frac{L}{32}} \]<br /><br />## Step 2: Simplify the equation<br />### Divide both sides by \( 2 \times 3.14 \) to isolate the square root term.<br />\[ \frac{1.57}{6.28} = \sqrt{\frac{L}{32}} \]<br /><br />## Step 3: Solve for the square root<br />### Calculate the left side of the equation.<br />\[ 0.25 = \sqrt{\frac{L}{32}} \]<br /><br />## Step 4: Square both sides<br />### Eliminate the square root by squaring both sides of the equation.<br />\[ 0.25^2 = \frac{L}{32} \]<br />\[ 0.0625 = \frac{L}{32} \]<br /><br />## Step 5: Solve for \( L \)<br />### Multiply both sides by 32 to find \( L \).<br />\[ L = 0.0625 \times 32 \]<br />\[ L = 2 \]