Respuesta :
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.
