Begin by graphing the function. To do that make a table of values.
16.44 feet and 29.16 feet
Practice makes perfect
We can begin by graphing the function t=1.11sqrt(l) where t will be represented by the vertical axis and l will be represented by the horizontal axis. To do that let's make a table of values.
l
1.11sqrt(l)
t
0
1.11sqrt(0)
0
1
1.11sqrt(1)
1.11
4
1.11sqrt(4)
2.22
9
1.11sqrt(9)
3.33
16
1.11sqrt(16)
4.44
25
1.11sqrt(25)
5.55
Next, we will plot the points and connect them with a smooth curve.
To approximate the length of the pendulums that take 4.5 seconds and 6 seconds to complete one full cycle, we will draw horizontal lines from the vertical axis where t=4.5 and t=6 to the graph. Then, we will graph vertical lines from the intersection points to the horizontal axis.
As we can see from the graph, the length of a pendulum that takes 4.5 seconds to complete one full cycle is about 16.5 feet. The length of the other pendulum is about 29.2 feet. Let's verify our answers algebraically. To do so, we will substitute use the equation. We will begin with the first pendulum.
Our operations verify that our answer for the length of first pendulum. Proceeding in the same way, we can verify our answer for the length of second pendulum.
