Asuper bounce ball is dropped from a height of 64 ft. with each bounce, the ball reaches a height that is three-fourths the height of the previous bounce. after how many bounces will the ball bounce up to a height less than 9 in.?

After 17 bounces the height of ball is less than 9 in.

Step-by-step explanation:

It is given that a super bounce ball is dropped from a height of 64 ft. With each bounce, the ball reaches a height that is three-fourths the height of the previous bounce.

If initial height of ball is 64, then the height of ball after first bounce is

The height of ball after second bounce is

It is a geometric progression,

Where, 64 is first term and is common ratio.

Convert inches to ft.

The nth term of a geometric progression,

Using scientific calculator we get

Therefore the height of ball is more than 9 after 16 bounces but the height of ball is less than 9 after 17 bounces.

x= -3

step-by-step explanation:

step 1: simplify brackets

4 - x - 1 = 6

step 2: simpilfy

3 - x = 6

step 3: subtract 3 from both sides

-x = 6 - 3

step 4: simpilfy 6 - 3

-x = 3

step 5: multiply both sides by -1

x = -3

answer: the common difference is -0.10