Solve −4x3 (2x2 −9x2 ) =
2 answers:
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The value of d is -2
Step-by-step explanation:
The nth term of the arithmetic sequence is , where
is the first term
- d is the common difference between each 2 consecutive terms
The nth term of the geometric sequence is , where
- r is the common ratio between each two consecutive terms
∵ of an arithmetic sequence is 1
∵ The common difference is d, where d ≠ 0
∵ ,
,
are the first 3 terms of a geometric sequence
∵ = 1 + (2 - 1)d
∴ = 1 + d
∵ = 1 + (3 - 1)d
∴ = 1 + 2d
∵ = 1 + (6 - 1)d
∴ = 1 + 5d
∴ The first 3 terms of the geometric sequence are (1 + d) , (1 + 2d) ,
(1 + 5d)
∵ The common ratio in the geometric sequence is
∴
- Use cross multiplication with the equal fractions
∵
∴ (1 + 2d)(1 + 2d) = (1 + d)(1 + 5d)
∴ 1 + 2d + 2d + 4d² = 1 + 5d + d + 5d²
- Add like terms in each side
∴ 1 + 4d + 4d² = 1 + 6d + 5d²
- Subtract 1 from both sides
∴ 4d + 4d² = 6d + 5d²
- Subtract 4d from both sides
∴ 4d² = 2d + 5d²
- Subtract 4d² from each side
∴ 0 = 2d + d²
- Take d as a common factor
∴ 0 = d(2 + d)
- Equate each factor by 0
∴ d = 0 but we will reject it because d ≠ 0
∴ 2 + d = 0
- Subtract 2 from both sides
∴ d = -2
The value of d is -2
Learn more:
You can learn more about the sequence in brainly.com/question/1522572
#LearnwithBrainly
Note: You missed to add the dot plots chart. As I found the chart after a little research. Thus, I am attaching it and based on that dot plot chart I am solving the question which anyways would clear you concept.
Answer:
'There are about 2 more students in each class at Oak Middle School than at Poplar Middle School' is the correct statement.
Step-by-step explanation:
From the diagram, it is clear that
The data set containing Poplar Middle School:
20 20 20 21 21 21 21 21 22 22 22 22 22 22 22 23 23 23 23 24
The mean of a data set is the sum of the terms divided by the total number of terms. Using math notation we have:
The data set containing Oak Middle School:
20 21 21 22 22 23 23 23 23 24 24 24 25 25 26 26 27 27 28 29
The mean of a data set is the sum of the terms divided by the total number of terms. Using math notation we have:
So, the difference in mean will be:
Therefore, 'there are about 2 more students in each class at Oak Middle School than at Poplar Middle School' is the correct statement.