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Shkiper50 [21]
2 years ago
7

Use differences to find a pattern in the sequence.

Mathematics
1 answer:
frez [133]2 years ago
8 0

Answer:

  220

Step-by-step explanation:

You want to use differences to find the pattern and the next term in the sequence 3, 8, 15, 28, 51, 88, 143.

<h3>First differences</h3>

Subtracting each term from the next, we find the sequence of first differences to be ...

  5, 7, 13, 23, 37, 55

<h3>Second differences</h3>

The first differences are not constant, so we know the sequence is not linear. They are not in an arithmetic progression, so we know the sequence is not quadratic. They do not have a common ratio, so we know the sequence is not exponential.

The second differences are the differences of the sequence of first differences. They are ...

  2, 6, 10, 14, 18

<h3>Third differences</h3>

The differences of the terms of the 2nd-difference sequence are constant: 4.

  4, 4, 4, 4, 4

Constant 3rd differences mean the original sequence can be described by a 3rd degree polynomial. The coefficients found by a calculator are shown in the attachment.

<h3>Next term</h3>

Since we know the third differences are constant, we can work our way back up the chain of differences to find the next term of the original sequence.

  next 2nd difference = 18 +4 = 22

  next 1st difference = 55 +22 = 77

  next sequence term = 143 +77 = 220

The eighth term should be 220.

__

<em>Additional comment</em>

The n-th term is ...

  f(n) = 2/3n^3 -3n^2 +28/3n -4

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In this figure
alina1380 [7]

Answer:

∠y = 62.5°

∠x  =  27.5°

Step-by-step explanation:

z is right angle. ∠z = 90°

∠x = ∠y - 35

∠x + ∠y + ∠z = 180      {Angle sum property of triangle}

y - 35 + y + 90 = 180

y + y - 35 + 90 = 180 {Combine like terms}

  2y  + 55 = 180

          2y = 180 -55      {Subtract 55 from both sides}

          2y = 125         {Divide both sides by 2}

            y = 125 /2

∠y = 62.5°

∠x = 62.5 - 35 = 27.5°

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2 years ago
Please find the value of x
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Answer:

x=5

Step-by-step explanation:

The sum of the angles of a triangle are 180 degrees

The box is a right angle which is 90 degrees

60+6x+90 = 180

Combine like terms

150+6x= 180

Subtract 150 from each side

150-150+6x = 180-150

6x = 30

Divide by 6

6x/6 =30/6

x = 5

5 0
3 years ago
You are designing a container in the shape of a cylinder. The radius is 6 inches. You want the container to hold at least 324π c
goldfiish [28.3K]
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Using the parameters you specified, H = 324π/[(π)(6^2)] = 324π/36π = 324/36 = 9 inches
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Answer: side = 6.8 inches

Step-by-step explanation:

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