You drop a ball from a height of 0.5 meters. each curved path has 52% of the height of the previous path. a. write a rule for the sequence using centimeters. the initial height is given by the term n = 1. b. what height will the ball be at the top of the sixth path?

a)

b)

Step-by-step explanation:

If each curved path has 52% of the previous height this means that

Then the radius of convergence is 0.52 and this is a geometric series.

The geometric series have the form:

Where

is the first term of the series and r is the radius of convergence.

In this problem

meters = 50 cm

a) Then the rule for the sequence is:

b) we must calculate

d 25 pi/6

step-by-step explanation:

the diameter is 10 inches

the radius is 1/2 of the diameter or 5 inches

the area of the circle is

a = pi r^2

  = pi 5^2

  = 25 pi

the slice is 60 degrees of the entire circle.

60 degrees out of 360   60/360 = 1/6

the area of the slice is 1/6 of the circle

a slice = 1/6 a circle

a slice = 1/6 * 25 pi