Answer:
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Step-by-step explanation:
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The height the ball rebounds to after its third bounce with the initial height by 10 feet is 6.141 feet.
<h3>What is Algebra?</h3>
Algebra is the study of mathematical symbols and the rule involves manipulating these mathematical symbols.
Suppose you drop a ball from a height of 10 feet. After the ball hits the floor, it rebounds to a height defined by the recursive formula
![\rm a_n = 0. 85\ a_{n - 1}](https://tex.z-dn.net/?f=%5Crm%20a_n%20%3D%200.%2085%5C%20a_%7Bn%20-%201%7D)
a₀ = 10 feet
For n = 1, the height will be
![\rm a_1 = 0. 85\ a_{0}\\\\a_1 = 0.85*10\\\\a_1 = 8.5](https://tex.z-dn.net/?f=%5Crm%20a_1%20%3D%200.%2085%5C%20a_%7B0%7D%5C%5C%5C%5Ca_1%20%3D%200.85%2A10%5C%5C%5C%5Ca_1%20%3D%208.5)
For n = 2, the height will be
![\rm a_2 = 0. 85\ a_{1}\\\\a_2 = 0.85*8.5\\\\a_2 = 7.225](https://tex.z-dn.net/?f=%5Crm%20a_2%20%3D%200.%2085%5C%20a_%7B1%7D%5C%5C%5C%5Ca_2%20%3D%200.85%2A8.5%5C%5C%5C%5Ca_2%20%3D%207.225)
For n = 3, the height will be
![\rm a_3 = 0. 85\ a_{0}\\\\a_3 = 0.85*7.225\\\\a_3 = 6.14125 \approx 6.141](https://tex.z-dn.net/?f=%5Crm%20a_3%20%3D%200.%2085%5C%20a_%7B0%7D%5C%5C%5C%5Ca_3%20%3D%200.85%2A7.225%5C%5C%5C%5Ca_3%20%3D%206.14125%20%5Capprox%206.141)
More about the Algebra link is given below.
brainly.com/question/953809