college algebra question! Please help

Question

The length of time it takes a pendulum to make one complete swing and return to its startingposition varies directly as the square root of the pendulum’s length. A pendulum that is 32.5cm long makes one swing in 1.25 seconds. Predict the time it would take a pendulum of length 100 to make one swing.

Answer 1

We're told that the Time it takes to do a full swing varies directly with the sqrt of the length of the pendulum:

T = k * √(pendulum_length)

And we know that we get a full swing of 1.25 seconds with a pendulum length of 32.5 cm, so that k = 1.25 / √(32.5), so that k = approximately .219.

Then the time for a full swing of a 100-cm pendulum should be

T = .219 * √(100)

= 2.19 seconds (approximately)

Answer 2

1.25 : 32.5 :: t : 100

32.5t = 125

t = 3.846

Answer 3

all one need do is multply the known time by the ratio of the square roots of the lengths given. The length in the numerator is the length for our unknown time 100 cm, the length in the numerator is the length for the known time 32.5 cm.

one can also write t1 = k sqrt(r1) and t2 = k sqrt(r2) where k is the proportionality constant same for both relations t 1, r1, r2 are known and do the algebra...yields the ration relation mentioned to solve for unknown t2.