Adam dropped a rubber ball from a window 40 ft above the sidewalk the ball always bounces half of the height that it drops how far will the ball have travled by the time it hits the sidewalk the 4th time

The ball will reach a height of 5 ft by the 4th time.

Step-by-step explanation:

The initial height of the ball is 40 ft, when it bounces from the floor once the height will be 20 ft, the second time it'll be 10 ft, and so on. The sequence that can represent the maximum height of the ball after each bounce is:

{40, 20, 10,...}

This kind of sequence is called a geometric progression, in this kind of progression the next number is related to the one before it by the product of a constant called ratio, in this case 1/2. To calculate a specific position in this sequence we only need the ratio and the first number, using the formula below:

a_n = a*r^(n-1)

Where n is the position we want to know, a is the first number and r is the ratio. In this case we have:

a_4 = 40*(1/2)^(4-1) = 40*(1/2)^3 = 40/8 = 5

The ball will reach a height of 5 ft by the 4th time.

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.

x= 149. 24+7=31. 180-31=149

your welcome