The time period of a pendulum is `T = 2*pi*sqrt(L/9.8)` . Write in function notation. What is the range and domain. For what value of L is T = 10 s.
The time period of a pendulum with length L is given by `T(L) = 2*pi*sqrt(L/9.8)`
The length of a pendulum cannot be negative, and neither can the time period. The domain of the function is `[0, oo}` and the range is also `[0, oo}` .
If T = 10, the corresponding value of L is determined by solving:
`10 = 2*pi*sqrt(L/9.8)`
=> `sqrt (L/9.8) = 5/pi`
=> `L = (25*9.8)/pi^2`
=> `L ~~ 24.82` m