Sam has 100 feet of fencing. Does he have enough fencing to enclose a circular region whose area is 630 square feet? Show work!
1 answer:
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Answer:
see explanation
Step-by-step explanation:
(1)
Note the ratio of consecutive terms is common, that is
2000 ÷ 2500 = 0.8
1600 ÷ 2000 = 0.8
1280 ÷ 1600 = 0.8
This indicates that the series is geometric with common ratio r = 0.8
The sum to n terms of a geometric series is
=
← a is the first term
Here a = 2500 and r = 0.8, thus
=
=
= 8404
(2)
Note the difference in consecutive terms is common, that is
3 - 11 = - 8
- 5 - 3 = - 8
- 13 - (- 5) = - 8
This indicates that the series is arithmetic with common difference d = - 8
The sum to n terms of an arithmetic series is
= a₁ + (n - 1)d ← a₁ is the first term
Here a₁ = 11 and d = - 8, thus
= 11 + (13 × - 8) = 11 - 104 = - 93
Answer:
Query (A)
Query (B)
Query (C)