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Track transition curve

The change of superelevation from zero in a tangent segment to the value selected for the body of a following curve occurs over the length of a transition curve that connects the tangent and the curve proper. Over the length of the transition the curvature of the track will also vary from zero at the end abutting the tangent segment to the value of curvature of the curve body, which is .


Cut-away view of an air foil bearing-supported turbocharger. A turbocharger, colloquially known as a turbo, is a turbine-driven, forced induction device that increases an internal combustion engine& 39;s efficiency and power output by forcing extra compressed air into the combustion chamber.


The derivative f′ x of a curve at a point is the slope of the line tangent to that curve at that point. This slope is determined by considering the limiting value of the slopes of secant lines. Here the function involved dn in red is f x = x 3 − x. The tangent line in green which passes through the point −3/2, −15/8 has a .


CORDIC for COordinate Rotation DIgital Computer , also known as Volder& 39;s algorithm, including Circular CORDIC Jack E. Volder , Linear CORDIC, Hyperbolic CORDIC John Stephen Walther , and Generalized Hyperbolic CORDIC GH CORDIC Yuanyong Luo et al. , is a simple and efficient algorithm to calculate trigonometric functions, hyperbolic functions, square roots, multiplications, divisions, and .

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The HP-65 is the first magnetic card-programmable handheld calculator. Introduced by Hewlett-Packard in 1974 at an MSRP of $795 equivalent to $4,121 in 2019 , it featured nine storage registers and room for 100 keystroke instructions.


Yet the benefits outweigh the costs; for the 150 hp 110 kW to drive the supercharger the engine generates an additional 400 hp 300 kW , a net gain of 250 hp 190 kW . This is where the principal disadvantage of a supercharger becomes apparent; the engine must withstand the net power output of the engine plus the power to drive the supercharger.

Wang Laboratories

Wang Laboratories was a computer company founded in 1951, by An Wang and G. Y. Chu. The company was successively headquartered in Cambridge, Massachusetts 1954–1963 , Tewksbury, Massachusetts 1963–1976 , and finally in Lowell, Massachusetts 1976–1997 .

Logistic function

A typical application of the logistic equation is a common model of population growth see also population dynamics , originally due to Pierre-François Verhulst in 1838, where the rate of reproduction is proportional to both the existing population and the amount of available resources, all else being equal.

Quaternions and spatial rotation

A visualization of a rotation represented by an Euler axis and angle. In 3-dimensional space, according to Euler& 39;s rotation theorem, any rotation or sequence of rotations of a rigid body or coordinate system about a fixed point is equivalent to a single rotation by a given angle θ about a fixed axis called the Euler axis that runs through the fixed point.


The tension at c is tangent to the curve at c and is therefore horizontal without any vertical component and it pulls the section to the left so it may be written −T 0, 0 where T 0 is the magnitude of the force. The tension at r is parallel to the curve at r and pulls the section to the right.

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Taylor series

The Taylor series can be used to calculate the value of an entire function at every point, if the value of the function, and of all of its derivatives, are known at a single point. Uses of the Taylor series for analytic functions include: The partial sums the Taylor polynomials of the series can be used as approximations of the function .

Trigonometric functions

Proportionality constants are written within the image: sin θ, cos θ, tan θ, where θ is the common measure of five acute angles. In mathematics , the trigonometric functions also called circular functions , angle functions or goniometric functions 1 2 are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.