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The drill uses a diamond encrusted drill bit (pictured on the right) to drill through the rock. The drill produces a "core" which is photographed and split longitudinally. Half of the split core is assayed, while the other half is permanently stored for future use and re-assaying if necessary. Although a larger diameter core is the most ...
Assume that we wish to cover an a×b rectangle with square tiles exactly, where a is the larger of the two numbers. We first attempt to tile the rectangle using b×b square tiles; however, this leaves an r 0 ×b residual rectangle untiled, where r 0 < b. We then attempt to tile the residual rectangle with r 0 ×r 0 square tiles.
Figure 1. Finding the shortest path in a graph using optimal substructure; a straight line indicates a single edge; a wavy line indicates a shortest path between the two vertices it connects (among other paths, not shown, sharing the same two vertices); the bold line is the overall shortest path from start to goal.
Long division is the standard algorithm used for pen-and-paper division of multi-digit numbers expressed in decimal notation. It shifts gradually from the left to the right end of the dividend, subtracting the largest possible multiple of the divisor (at the digit level) at each stage; the multiples then become the digits of the quotient, and the final difference is then the remainder.
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In mathematics, a generating function is a representation of an infinite sequence of numbers as the coefficients of a formal power series.Generating functions are often expressed in closed form (rather than as a series), by some expression involving operations on the formal series.
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