9514 1404 393
Answer:
L = 882/121 feet
Step-by-step explanation:
Set the appropriate variables in the equation to the given values and solve for the unknown.
[tex]T=2\pi\sqrt{\dfrac{L}{32}}\\\\3=2\left(\dfrac{22}{7}\right)\sqrt{\dfrac{L}{32}} \qquad\text{fill in given values}\\\\ \dfrac{3\cdot7}{44}=\sqrt{\dfrac{L}{32}} \qquad\text{multiply by $\dfrac{7}{44}$}\\\\ \left(\dfrac{21}{44}\right)^2=\dfrac{L}{32}\qquad\text{square both sides}\\\\ \dfrac{32\cdot441}{1936}=L \qquad\text{multiply by 32}\\\\ \boxed{L=\dfrac{882}{121}}\qquad\text{reduce the fraction}[/tex]
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Additional comment
That's about 7.3 feet. (You can compare this to what you know about the time it takes for a cycle when swinging on a swing set.)
