On Friday, March 16, Mr. Post’s beginning checking balance is $80, and his account is credited for a deposit for $50. The same d
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Answer:
424 cm²
Step-by-step explanation:
The figure is composed of a square and a trapezium on top
A of square = 18² = 324 cm²
A of trapezium = h (b₁ + b₂ )
where h is the perpendicular height and b₁, b₂ the parallel bases
Here h = 8, b₁ = 18 and b₂ = 7 , then
A = 0.5 × 8 × (18 + 7) = 4 × 25 = 100 cm²
Area of hexagonal park = 324 + 100 = 424 cm²
First part of question:
Find the general term that represents the situation in terms of k.
The general term for geometric series is:
= the first term of the series
= the geometric ratio
would represent the height at which the ball is first dropped. Therefore:
We also know that the ball has a rebound ratio of 75%, meaning that the ball only bounces 75% of its original height every time it bounces. This appears to be our geometric ratio. Therefore:
Our general term would be:
Second part of question:
If the ball dropped from a height of 235ft, determine the highest height achieved by the ball after six bounces.
represents the initial height:
represents the number of times the ball bounces:
Plugging this back into our general term of the geometric series:
represents the highest height of the ball after 6 bounces.
Third part of question:
If the ball dropped from a height of 235ft, find the total distance traveled by the ball when it strikes the ground for the 12th time.
This would be easier to solve if we have a general term for the <em>sum </em>of a geometric series, which is:
We already know these variables:
Therefore: