Use inductive reasoning to predict the next number in the pattern: 832, 208, 52...
2 answers:
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Answer:
D'(-2, 2); C''(3, -1); A'''(4, -2); and B''(4, 2)
Step-by-step explanation:
See attachment for the figure.
<u>For D'</u>, rotating the point (2, 2) 90° counterclockwise. This maps each point (x, y)→(-y, x); it takes (2, 2)→(-2, 2).
For C'', rotating the point (1, 3) 90° clockwise. This maps each point (x, y)→(y, -x); it takes (1, 3)→(3, -1).
For A''', rotating the point (-4, 2) 180° clockwise. This maps every point (x, y)→(-x, -y); it takes (-4, 2)→(4, -2).
For B'', rotating the point (-2, 4) 270° counterclockwise. This is the similar as rotating the point 90° clockwise. This maps every point (x, y)→(y, -x); it takes (-2, 4)→(4, 2).
Step-by-step explanation:
Cubes have square faces, so the area of the base is b².
The volume of the cube is b³.
The height of each pyramid is half the height of the cube, so h = b/2. Which means b = 2h.
The cube is made of 6 square pyramids with the same base and height. Therefore, each pyramid has 1/6 the volume of the cube. So the volume of each pyramid is b³/6.
