Given that if a ball is dropped from x feet, it bounces up to 2/3 x feet.
And the ball is dropped from 10 feet, that is x=10 feet,
So,before the first bounce it travels 10 feet distance.
Between first and second bounce it travels 
Between second and third bounce, it travels 
Between third and fourth bounce, it travels 
Like that between 29th and 30th bounce, it travels 
Hence total distance traveled is
=![10+20[(\frac{2}{3}) +(\frac{2}{3}) ^{2} +(\frac{2}{3}) ^{3} +.....+(\frac{2}{3} )^{29} ]](https://tex.z-dn.net/?f=10%2B20%5B%28%5Cfrac%7B2%7D%7B3%7D%29%20%2B%28%5Cfrac%7B2%7D%7B3%7D%29%20%5E%7B2%7D%20%2B%28%5Cfrac%7B2%7D%7B3%7D%29%20%5E%7B3%7D%20%2B.....%2B%28%5Cfrac%7B2%7D%7B3%7D%20%29%5E%7B29%7D%20%5D)
= ![10+20[\frac{\frac{2}{3}*(1-(\frac{2}{3})^{29}) }{1-\frac{2}{3} }]](https://tex.z-dn.net/?f=10%2B20%5B%5Cfrac%7B%5Cfrac%7B2%7D%7B3%7D%2A%281-%28%5Cfrac%7B2%7D%7B3%7D%29%5E%7B29%7D%29%20%20%7D%7B1-%5Cfrac%7B2%7D%7B3%7D%20%7D%5D)
= 10+20*2*(1-
)
= 49.9997 feet ≈ 50 feet approximately.
2t + 8 ≥ -4(t+1)
PEMDAS
2t + 8 ≥ -4t - 4
2t + 12 ≥ -4t
12 ≥ -6t
-2 ≤ t
Answer:
For #3 the answer is 113.04 (6 + g) / 32
Step-by-step explanation:
A = Pi * r * (r + g)
12/2 = 6 ft
A = 3.14 * (6) * (6 + g) = 113.04 (6 + g) square feet
113.04 (6 + g) / 32
The 15th term will be 71. Why? Well, see below for an explanation!
By subtracting all of these numbers by the term that comes prior to them, we will find that all of them result in 5. Because of this, we know that each time the term increases, 5 is being added to the numbers. Additionally, I noticed that all of the numbers in this arithmetic sequence only end in a 1 or a 6. Because of this, we can apply the same principle when adding 5 each time:
First term: 1
Second term: 6
Third term: 11
Fourth term: 16
Fifth term: 21
Sixth term: 26
Seventh term: 31
Eighth term: 36
Ninth term: 41
Tenth term: 46
Eleventh term: 51
Twelfth term: 56
Thirteenth term: 61
Fourteenth term: 66
Fifteenth term: 71
By adding 5 each time and keeping in mind that the digits all end in only 1 or 6, we will find that the fifteenth term results in 71. Therefore, the 15th term is 71.
Your final answer: The 15th term of this arithmetic sequence comes down to be 71. If you need extra help, let me know and I will gladly assist you.
Answer:
< 1 = 88
< 2 = 92
Step-by-step explanation:
First add 4x - 4 + 4x = 180
X = 23
4(23) - 4 = 88
4(23) = 92
