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Leya [2.2K]
3 years ago
5

Estimate the perimeter of the figure The perimeter is about ____ units.

Mathematics
1 answer:
storchak [24]3 years ago
8 0

Answer:

18

Step-by-step explanation:

Do it by count how many side are there by the squares

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A geometric sequence has first term 1/9 and common ratio 3. Which is the first term of the sequence which exceeds 1000?
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a_{n}= \frac{1}{9}  (3)^{n-1}
(We know this from a=1/9 and r=3)
Simplifying this, we get:
\frac{1}{9} (3)^{-1} (3)^n

Since we're finding the first term that exceeds 1000, let's set it equal to 1000.

\frac{1}{27}(3)^n=1000
Multiplying both sides by 27
3^n=27000

log_{3}27000=n

n≈9.2

We have to round n up, since if n=9, the value would be <1000.
Therefore n=10. Substituting n=10,
\frac{1}{27}3^{10}
=2187

Therefore the first term that exceeds 1000 is 2187, and it is the 10th term
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