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A Cabtaxi number is the smallest positive number that can be expressed as a sum of two integer cubes in n ways, allowing the cubes to be negative or zero as well as positive. The smallest cabtaxi number after Cabtaxi(1) = 0, is Cabtaxi(2) = 91, [ 5 ] expressed as:
When sampling a function of variables, the range of each variable is divided into equally probable intervals. sample points are then placed to satisfy the Latin hypercube requirements; this forces the number of divisions, , to be equal for each variable. This sampling scheme does not require more samples for more dimensions (variables); this ...
For solving the cubic equation x 3 + m 2 x = n where n > 0, Omar Khayyám constructed the parabola y = x 2 /m, the circle that has as a diameter the line segment [0, n/m 2] on the positive x-axis, and a vertical line through the point where the circle and the parabola intersect above the x-axis.
If b 2 – 3ac = 0, then there is only one critical point, which is an inflection point. If b 2 – 3ac < 0, then there are no (real) critical points. In the two latter cases, that is, if b 2 – 3ac is nonpositive, the cubic function is strictly monotonic. See the figure for an example of the case Δ 0 > 0.
The goal of polynomial regression is to model a non-linear relationship between the independent and dependent variables (technically, between the independent variable and the conditional mean of the dependent variable). This is similar to the goal of nonparametric regression, which aims to capture non-linear regression relationships.
Love calculator: The input is two names, and there is a button to work out the compatibility, as a percentage, of two people with these names. Formula weight calculator : The input is a chemical molecular formula , using the periodic-table symbols and notation, and there is a button to work out the percentages of its constituents.
The cube of a number n is denoted n 3, using a superscript 3, [a] for example 2 3 = 8. The cube operation can also be defined for any other mathematical expression, for example (x + 1) 3. The cube is also the number multiplied by its square: n 3 = n × n 2 = n × n × n. The cube function is the function x ↦ x 3 (often denoted y = x 3) that
JAX is a machine learning framework for transforming numerical functions developed by Google with some contributions from Nvidia. [2] [3] [4] It is described as bringing together a modified version of autograd (automatic obtaining of the gradient function through differentiation of a function) and OpenXLA's XLA (Accelerated Linear Algebra).