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Pie
4 years ago
5

Find the first four terms of a sequence using the recursive definition. Please help

Mathematics
1 answer:
Ymorist [56]4 years ago
7 0

Answer:

2, 5, 9, 19

Step-by-step explanation:

Using the recursive formula f(n) = 2f(n - 2) + f(n - 1)

with f(1) = 2 and f(2) = 5

f(3) = 2f(3 - 2) + f(3 - 1)

     = 2f(1) + f(2) = (2 × 2) + 5 = 4 + 5 = 9

f(4) = 2f(4 - 2) + f(4 - 1)

      = 2f(2) + f(3) = (2 × 5) + 9 = 10 + 9 = 19

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Henry invested $59,000 in an account paying an interest rate of 2% compounded quarterly. Assuming no deposits or withdrawals are
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What is the longest line segment that can be drawn in a right rectangular prism that is 15 cm​ long, 11 cm​ wide, and 10 cm​ tal
sammy [17]

Answer:

  √446 ≈ 21.12 cm

Step-by-step explanation:

The longest dimension of a rectangular prism is the length of the space diagonal from one corner to the opposite corner through the center of the prism. The Pythagorean theorm tells you the square of its length is the sum of the squares of the dimensions of the prism:

  d² = (15 cm)² +(11 cm)² +(10 cm)² = (225 +121 +100) cm² = 446 cm²

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The longest line segment that can be drawn in a right rectangular prism is about 21.12 cm.

_____

<em>Additional comment</em>

The square of the face diagonal is the sum of the squares of the dimensions of that face. The square of the space diagonal will be the sum of that square and the square of the remaining prism dimenaion, hence the sum of squares of all three prism dimensions.

8 0
2 years ago
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