Answer:
1/336
Step-by-step explanation:
Answer:
We've learned that the circumference is the distance around the circle and the diameter is the distance across the circle going through the center. ... To find the circumference given the diameter, you multiply the diameter by pi. To find the diameter given the circumference, you divide the circumference by pi.
Step-by-step explanation:
The ratio is the same each time (2/3), so this can be modeled as a geometric sequence.
an = a₁ (r)^(n-1)
where an is the nth term, a₁ is the first term, and r is the common ratio.
On the first rebound, the ball rises to 2/3 × 2 = 4/3, so a₁ = 4/3.
an = 4/3 (2/3)^(n-1)
On the sixth rebound, the ball rises to:
a₆ = 4/3 (2/3)^(6-1)
a₆ = 4/3 (32/243)
a₆ = 128/729
a₆ ≈ 0.176
Hey!
First change all the fractions so that they have a common denominator: 40
![3 \frac{39}{40} = 3 \frac{39}{40}](https://tex.z-dn.net/?f=%203%20%5Cfrac%7B39%7D%7B40%7D%20%3D%203%20%5Cfrac%7B39%7D%7B40%7D%20%20%20)
![3 \frac{19 \times 2}{20 \times 2} = 3 \frac{38}{40}](https://tex.z-dn.net/?f=%203%20%5Cfrac%7B19%20%5Ctimes%202%7D%7B20%20%5Ctimes%202%7D%20%3D%203%20%5Cfrac%7B38%7D%7B40%7D%20%20%20%20)
![3 \frac{1 \times 20}{2 \times 20} = 3 \frac{20}{40}](https://tex.z-dn.net/?f=%203%20%5Cfrac%7B1%20%5Ctimes%2020%7D%7B2%20%5Ctimes%2020%7D%20%3D%203%20%5Cfrac%7B20%7D%7B40%7D%20%20%20%20)
Now order them:
![3 \frac{39}{40} , 3 \frac{19}{20} , 3 \frac{1}{2}](https://tex.z-dn.net/?f=%203%20%5Cfrac%7B39%7D%7B40%7D%20%2C%203%20%5Cfrac%7B19%7D%7B20%7D%20%2C%203%20%5Cfrac%7B1%7D%7B2%7D%20%20)
Good luck and hope this helps! :)
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