Given the function below find f(-2).
1 answer:
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Answer:
65,280
Step-by-step explanation:
Consider the 4×4 grid ...
where each of a, b, c, d is a 2×2 array of tiles. Let's use the notation a' to represent the 2×2 array "a" rotated right 1/4 turn. For 90° rotational symmetry, we must have b=a', c=b'=a'', d=c'=b''=a'''. That is, once "a" is determined, the rest of the grid is determined. Since "a" consists of 4 tiles, each of which can be black or white, there are 2^4 = 16 patterns that have 90° rotational symmetry.
The same will be true of 270° rotational symmetry, for the same reason.
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For 180° rotational symmetry, we must have c=a'' and d=b''. Then the combination of "a" and "b" together fully determines the grid. Together, "a" and "b" consist of 8 tiles, so there are 2^8 = 256 ways to pattern the grid so it will have 180° rotational symmetry. (Of those, 16 have 90° symmetry, and 16 have 270° symmetry. The sets are overlapping.)
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The 16 tiles of the grid can be colored 2^16 = 65,536 different ways. As we have seen, 256 of those colorings result in 180° rotational symmetry. Then the number of colorings that have no rotational symmetry is ...
65,536 -256 = 65,280 . . . . colorings not rotationally symmetric
Answer:
y = -0.2x - 5.8
Step-by-step explanation:
If a line is given in the form y = mx + b, the "m" is the slope.
For the line given y = 5x, the slope is 5
The line that is perpendicular to this will have slope that is "negative reciprocal of that".
So, the perpendicular line will have slope of
So, the Perpendicular Line will have equation:
y = -1/5x + b
Let's find b by replacing x with 6 and y with -7 [the point given]. So we have:
So the equation of perpendicular line = y = -0.2x - 5.8