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where x is a variable we are interested in solving for, we can use cross-multiplication to determine that x = b c d . {\displaystyle x={\frac {bc}{d}}.} For example, suppose we want to know how far a car will travel in 7 hours, if we know that its speed is constant and that it already travelled 90 miles in the last 3 hours.
The criss-cross algorithm visits all 8 corners of the Klee–Minty cube in the worst case. It visits 3 additional corners on average. The Klee–Minty cube is a perturbation of the cube shown here. In mathematical optimization, the criss-cross algorithm is any of a family of algorithms for linear programming.
In this example, the rule says: multiply 3 by 2, getting 6. The sets {A, B, C} and {X, Y} in this example are disjoint sets, but that is not necessary.The number of ways to choose a member of {A, B, C}, and then to do so again, in effect choosing an ordered pair each of whose components are in {A, B, C}, is 3 × 3 = 9.
Another method of multiplication is called Toom–Cook or Toom-3. The Toom–Cook method splits each number to be multiplied into multiple parts. The Toom–Cook method is one of the generalizations of the Karatsuba method. A three-way Toom–Cook can do a size-3N multiplication for the cost of five size-N multiplications. This accelerates the ...
The complexity of an elementary function is equivalent to that of its inverse, since all elementary functions are analytic and hence invertible by means of Newton's method. In particular, if either exp {\displaystyle \exp } or log {\displaystyle \log } in the complex domain can be computed with some complexity, then that complexity is ...
Create a cozy bedroom even Mrs. Claus would envy with Christmas quilts, flannel sheets, plaid throw blankets and festive throw pillows.
Some of the algorithms Trachtenberg developed are ones for general multiplication, division and addition. Also, the Trachtenberg system includes some specialised methods for multiplying small numbers between 5 and 13. The section on addition demonstrates an effective method of checking calculations that can also be applied to multiplication.
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