confused. hellp math?

Question

show and explain:i need help

The diagram shown below represents the path of a ball that is dropped from a height of 18 feet. On its first bounce, the ball rebounds to a height of 12 feet; on its second bounce, it rebounds to a height of 8 feet.

A.Show that the ratio of the height of Bounce 1 to the starting height is equal to the ratio of the height of Bounce 2 to the height of Bounce 1. Show your work or explain

B.Create a table like the one shown below in your Student Answer Booklet.
Bounce, b Height, h
(in feet)
0 (Starting height) 18
1 12
2 8
3
4
5

If the pattern in the table continues, complete your table to show the height of bounces 3, 4, and 5.

C.Based on the pattern shown in the table, if h is the height of a certain bounce, write an expression that represents the height of the next bounce in terms of h.

D.Based on the pattern shown in the table, write an equation that represents the relationship between height, h, and bounce,

Answer 1

The ratio means the relationship of one number divided by another. The first part is asking you, are two ratios equal?
The first ratio is 18 : 12, so divide 18 by 12.
The second ratio is 12 : 8, so divide 12 by 8.

Answer 2

Well, just looking at the pattern I can see that the ball rebounds 2/3 each bounce...

18 * 2/3 = 12
12 * 2/3 = 8

So the next bounce will be:

8 * 2/3 = 16/3 = 5 1/3 feet

h(i) = 2/3 h(o)

A) 12:18 = 8:12
12/18 = 8/12
2/3 = 2/3

B)

0 : 18
1 : 12
2 : 8
3 : 5 1/3
4 : 3 5/9
5 : 2 10/27

C) b = bounce, b = h * 2/3

D) same as above


Hope this helps!