Answer:
It is given that the time period of a pendulum(T) is the time(t) the pendulum take to swing back and forth.
Given the function: [tex]L = 0.81t^2[/tex] ......[1]
where L is the length in feet of a pendulum and t is the time in second.
It is given also, a convention center has a pendulum (L) = 50 ft long.
Substitute the value of L in [1] to solve for t;
[tex]50 = 0.81 t^2[/tex]
Divide both sides by 0.81 we get;
[tex]\frac{50}{0.81} = \frac{0.81}{0.81}t^2[/tex]
Simplify:
[tex]t^2 = 61.7283951[/tex]
or
[tex]t = \sqrt{61.7283951} = 7.85674202[/tex] sec
therefore, period of pendulum (T), is 7.86 sec (nearest to hundredths)
