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svet-max [94.6K]
2 years ago
6

What is 4N? I am very confused

Mathematics
1 answer:
alexdok [17]2 years ago
8 0

Answer:

Step-by-step explanation:

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The nine squares of a 3-by-3 chessboard are to be colored red and blue. The chessboard is free to rotate but cannot be flipped o
nignag [31]

Answer:

a_n = 2^{\frac{n^2-1}{4} + 1} + \frac{2^{n^2} - \, 2^{\frac{n^2-1}{4} + 1}}{4}

For n = 3, there are 134 possibilities

Step-by-step explanation:

First, lets calculate the generating function.

For each square we have 2 possibilities: red and blue. The Possibilities between n² squares multiply one with each other, giving you a total of 2^n² possibilities to fill the chessboard with the colors blue or red.

However, rotations are to be considered, then we should divide the result by 4, because there are 4 ways to flip the chessboard (including not moving it), that means that each configuration is equivalent to three other ones, so we are counting each configuration 4 times, with the exception of configurations that doesnt change with rotations.

A chessboard that doesnt change with rotations should have, in each position different from the center, the same colors than the other three positions it could be rotated into. As a result, we can define a <em>symmetric by rotations chessboard</em> with only (n²-1)/4 + 1 squares (the quarter part of the total of squares excluding the center plus the center).

We cocnlude that the total of configurations of symmetrical boards is 2^{\frac{n^2-1}{4} + 1}

Since we have to divide by 4 the rest of configurations (because we are counted 4 times each one considering rotations), then the total number of configutations is

a_n = 2^{\frac{n^2-1}{4} + 1} + \frac{2^{n^2} - \, 2^{\frac{n^2-1}{4} + 1}}{4}

If n = 3, then the total amount of possibilities are

a_3 = 2^{\frac{3^2-1}{4} + 1} + \frac{2^{3^2} - \, 2^{\frac{3^2-1}{4} + 1}}{4} =  134

3 0
3 years ago
Which statement provides a set of arguments that supports the relationship
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Answer:sdasda

Step-by-step explanation:

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2 years ago
Find the coordinates of the image of point R(3, –5) rotated 180° about the origin.
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The answer is (-3,5)
Hope that helped.

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Write the following ratio as a reduced fraction. Simplify your answer when possible: 50 to 45
professor190 [17]

Answer:

10 to 9 or 10/9

Step-by-step explanation:

50 divided by 5 equals ten and 45 divided by 5 equals 9. So the simplified answer of 50 to 45 is 10 to 9 in a fraction, it would be 10/9.

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2 years ago
How do you factor-200
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Could you be more specific please ?
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