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The midpoint method computes + so that the red chord is approximately parallel to the tangent line at the midpoint (the green line). In numerical analysis , a branch of applied mathematics , the midpoint method is a one-step method for numerically solving the differential equation ,
The seven-year itch is a popular belief, sometimes asserted to have statistical validity, that happiness in a marriage or long-term romantic relationship declines after around seven years. [ 1 ] The phrase was used in the title of the 1952 play The Seven Year Itch by George Axelrod , and gained popularity following the 1955 film adaptation ...
Given two points of interest, finding the midpoint of the line segment they determine can be accomplished by a compass and straightedge construction.The midpoint of a line segment, embedded in a plane, can be located by first constructing a lens using circular arcs of equal (and large enough) radii centered at the two endpoints, then connecting the cusps of the lens (the two points where the ...
The standard logistic function is the logistic function with parameters =, =, =, which yields = + = + = / / + /.In practice, due to the nature of the exponential function, it is often sufficient to compute the standard logistic function for over a small range of real numbers, such as a range contained in [−6, +6], as it quickly converges very close to its saturation values of 0 and 1.
The midpoint theorem generalizes to the intercept theorem, where rather than using midpoints, both sides are partitioned in the same ratio. [1] [2] The converse of the theorem is true as well. That is if a line is drawn through the midpoint of triangle side parallel to another triangle side then the line will bisect the third side of the triangle.
This equation is a rearrangement of the definition of velocity: :=. As such, without the introduction of any assumptions, it is a tautology . The quantity theory of money adds assumptions about the money supply, the price level, and the effect of interest rates on velocity to create a theory about the causes of inflation and the effects of ...
The aggregation problem is the difficult problem of finding a valid way to treat an empirical or theoretical aggregate as if it reacted like a less-aggregated measure, say, about behavior of an individual agent as described in general microeconomic theory [1] (see representative agent and heterogeneity in economics). The second meaning of ...
The conjecture is that there is a simple way to tell whether such equations have a finite or infinite number of rational solutions. More specifically, the Millennium Prize version of the conjecture is that, if the elliptic curve E has rank r , then the L -function L ( E , s ) associated with it vanishes to order r at s = 1 .