1. Determine if the two expressions are equivalent and explain your reasoning.
1 answer:
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Answer:
about 10,652 balls
Step-by-step explanation:
The length of the court is 94 ft × 12 in/ft = 1128 in. That is 1128/8.5 ≈ 132.7 times the diameter of a ball.
The width of the court is 50 ft × 12 in/ft = 600 in. That is 600/8.5 ≈ 70.6 times the diameter of a ball.
When the balls are hexagonally packed, their row spacing is only (√3)/2 ≈ 0.866 times the ball diameter, so by cutting out one ball per row on alternate rows, about 15% more rows can be put in place. That is, there can be 81 rows of balls, alternating between 132 and 131 balls per row.
The number of balls that fit in that arrangement is ...
132×81 - 40 = 10,652
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Since there is some extra space beyond the last row, the balls can be "randomized" and a few more balls added, probably at least 2 or 3.
