Question

On the first swing, a pendulum swings through an arc of length 65 cm. On the successive swing, the length of the arc is 85% of the length of the previous swing.

Find the length of the arc on the fourth swing. Round your answer to the nearest centimeter.


A.221 cmB.39.918 cmC.33.93 cmD.165.75 cm

Answer 1

The Correct Answer Is B

Answer 2

Answer:

B. 39.918 cm

Step-by-step explanation:

We know that the length of the first swing, the arc is 65 cm, and the successive swing the arc is 85% of the length of the previous swing.

The problem is asking for the length of the arc on the fourth swing:

We know that the arc of every consecutive swing will be 85% of the swing before, and we know that 85% = 0.85

So the length of the arc of the second swing will be:

85% * length of the arc on the first swing, or

0.85 * 65 cm = 55.25 cm

Now, to know the length of the arc on the third swing we multiply the length of the arc on the second swing times 0.85:

0.85 * 55.25 cm = 46.962 cm

And finally, the length of the arc on the fourth swing will be the length of the arc in the third swing times 0.85:

0.85 * 46.962 cm = 39.918 cm