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#### 56Question: An air quality researcher models pollutant concentrations in a grid where three vertices of a regular octahedron are located at $(1, 0, 0)$, $(-1, 0, 0)$, and $(0, 1, 0)$. Find the coordinates of the fourth vertex, given all coordinates are integers.
#### 30,600The learning technologies researcher designed an adaptive learning module that adjusts difficulty based on student performance. If the initial difficulty level is 50 units and it increases by 120% after a student masters content, then decreases by 30% after a mistake, what is the final difficulty level?
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#### 13 quarters, 26 dimes, 78 nickels
#### 20 metros de ancho, 40 metros de largo
+ 3 + 9 + 27 + 7 + 21 + 63 + 189 = (1 + 3 + 9 + 27) + (7 + 21 + 63 + 189) = 40 + 280 = 320
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#### 68.571. A cylindrical water tank with a radius of 3 meters and a height of 5 meters is currently half full. How much more water (in cubic meters) does the tank need to fill completely?
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#### 6Question: An ancient Andean ceremonial platform is shaped like a regular hexagon with side length $ 5 $ meters. If each side is extended outward by $ 2 $ meters to form a larger regular hexagon, by how many square meters does the area increase?
