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In the 2016 NCAA Final Four Semifinal game between Villanova and Oklahoma, at a critical moment in the game, a ball was dropped by a Villanova player out of bounds, but of course, the refs chose to give it back to Villanova, instead of doing the fair, honest, honorable thing and give it to Oklahoma (the replay doesn't lie!). It was dropped from a height of
10ft, and each subsequent bounce is
65% of the previous. How far had it traveled when it hit the ground for the
4^("th ") time? (You can round your answer to the nearest tenth)

$13$ . In the $2016$ NCAA Final Four Semifinal game between Villanova and Oklahoma, at a critical moment in the game, a ball was dropped by a Villanova player out of bounds, but of course, the refs chose to give it back to Villanova, instead of doing the fair, honest, honorable thing and give it to Oklahoma (the replay doesn't lie!). It was dropped from a height of $10 \mathrm{ft}$ , and each subsequent bounce is $65 \%$ of the previous. How far had it traveled when it hit the ground for the $4^{\text {th }}$ time? (You can round your answer to the nearest tenth)

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Circles: word problems

Full solution

Q.

13

. In the

2016

NCAA Final Four Semifinal game between Villanova and Oklahoma, at a critical moment in the game, a ball was dropped by a Villanova player out of bounds, but of course, the refs chose to give it back to Villanova, instead of doing the fair, honest, honorable thing and give it to Oklahoma (the replay doesn't lie!). It was dropped from a height of

10 \mathrm{ft}

, and each subsequent bounce is

65 \%

of the previous. How far had it traveled when it hit the ground for the

4^{\text {th }}

time? (You can round your answer to the nearest tenth)

Calculate First Bounce Height: First bounce height: $10\text{ft} \times 65\% = 6.5\text{ft}$ .
Calculate Second Bounce Height: Second bounce height: $6.5\text{ft} \times 65\% = 4.225\text{ft}$ .
Calculate Third Bounce Height: Third bounce height: $4.225\,\text{ft} \times 65\% = 2.74625\,\text{ft}$ .
Calculate Fourth Bounce Height: Fourth bounce height: $2.74625\text{ft} \times 65\% = 1.7850625\text{ft}$ .
Calculate Total Distance Traveled: Total distance traveled after four bounces: $(10\,\text{ft} + 6.5\,\text{ft} + 4.225\,\text{ft} + 2.74625\,\text{ft} + 1.7850625\,\text{ft}) \times 2 - 10\,\text{ft}$ (since the last bounce doesn't include a return trip to the ground).

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