The length of time ( T ) in seconds it takes the pendulum of a clock to swing through one complete cycle is given by the formula T = 2 π √ L 32 Where L is the length, in feet, of the pendulum, and π π is approximately 22/7 . How long must the pendulum be if one complete cycle takes 9 seconds? in feet

Answer:3.24 feet.Step-by-step explanation:We have been given that length of time ( T ) in seconds it takes the pendulum of a clock to swing through one complete cycle is given by the formula [tex]T=2\pi \sqrt{\frac{L}{32}}[/tex], where, L is the length, in feet, of the pendulum.To find the length of pendulum, we will substitute [tex]T=2[/tex] in the given formula as:[tex]2=2\pi \sqrt{\frac{L}{32}}[/tex]Divide both sides by 2:[tex]\frac{2}{2}=\frac{2\pi \sqrt{\frac{L}{32}}}{2}[/tex][tex]1=\pi \sqrt{\frac{L}{32}}[/tex]Substitute [tex]\pi=\frac{22}{7}[/tex]:[tex]1=\frac{22}{7}\sqrt{\frac{L}{32}}[/tex]Multiply both sides by [tex]\frac{7}{22}[/tex]:[tex]1\times \frac{7}{22}=\frac{7}{22}\times \frac{22}{7}\sqrt{\frac{L}{32}}[/tex][tex]\frac{7}{22}=\sqrt{\frac{L}{32}}[/tex]Square both sides:[tex](\frac{7}{22})^2=(\sqrt{\frac{L}{32}})^2[/tex] [tex]\frac{7^2}{22^2}=\frac{L}{32}[/tex] [tex]\frac{49}{484}=\frac{L}{32}[/tex] [tex]\frac{49}{484}\times 32=\frac{L}{32}\times 32[/tex] [tex]\frac{1568}{484}=L[/tex] Switch sides:[tex]L=\frac{1568}{484}[/tex][tex]L=3.23966942[/tex][tex]L\approx 3.24[/tex]Therefore, the length of the pendulum is approximately 3.24 feet.