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Bivariate (two variable) quadratic function(y minimum/maximum)

A bivariate (two variable) quadratic function is a second-degree polynomial which describes a quadratic surface and has the form: f(x,y)=Ax^2 + By^2 + Cx + ... more

Minimum or maximum value of the quadratic function

A quadratic function, a quadratic polynomial, a polynomial of degree 2, or simply a quadratic, is a polynomial function in one or more variables in which ... more

Critical point of a cubic function ( local maximum )

A cubic function is a function of the form f(x): ax3 + bx2 + cx + d.
The critical points of a cubic equation are those values of x where the slope of ... more

Critical point of a cubic function ( local minimum )

A cubic function is a function of the form f(x): ax3 + bx2 + cx + d.
The critical points of a cubic equation are those values of x where the slope of ... more

Quartic equation

Solves a univariate polynomial equation of the fourth degree. (For possitive values of x)

... more

Cubic equation

Solves a univariate polynomial equation of the third degree.

... more

Discriminant of the Quadratic Equation

In algebra, the discriminant of a polynomial is a function of its coefficients, typically denoted by a capital 'D’ or the capital Greek letter Delta ... more

Quadratic Equation 1st Root

A quadratic equation with real or complex coefficients has two solutions, called roots. These two solutions may or may not be distinct, and they may or may ... more

Quadratic Equation 2nd Root

A quadratic equation with real or complex coefficients has two solutions, called roots. These two solutions may or may not be distinct, and they may or may ... more

Quadratic equation

Solves a univariate polynomial equation of the second degree. This formula will calculate both roots and both real and complex roots.

... more

Y-Coordinate of the focus of the parabola of a Quadratic Function

A parabola is a graph of a quadratic function, such as y=ax^2+bx+c. A parabola is the set of all points equidistant from a point that is called the focus ... more

Y-Coordinate of the vertex, of the parabola of a Quadratic Function

Parabolas with axes of symmetry parallel to the y-axis have equations of the form y=ax^2+bx+c.
The x-coordinate and y-coordinate at the vertex can be ... more

Vieta's formulas ( sum of quadratic polynomial roots)

In mathematics, Vieta’s formulas are formulas that relate the coefficients of a polynomial to sums and products of its roots.
P(x)=ax^2 + bx + c,

... more

X-Coordinate of the vertex, of the parabola of a Quadratic Function

Parabolas with axes of symmetry parallel to the y-axis have equations of the form y=ax^2+bx+c.
The x-coordinate and y-coordinate at the vertex can be ... more

Vieta's formulas ( product of quadratic polynomial roots)

In mathematics, Vieta’s formulas are formulas that relate the coefficients of a polynomial to sums and products of its roots.
P(x)=ax^2 + bx + c,

... more

Drag equation ( for fluids)

Drag (sometimes called air resistance, a type of friction, or fluid resistance, another type of friction or fluid friction) refers to forces acting ... more

Ball Screw - Frictional Resistance

A ball screw is a mechanical linear actuator that translates rotational motion to linear motion with little friction. A threaded shaft provides a helical ... more

Damping ratio ( related to damping coefficients)

Linear damping occurs when a potentially oscillatory variable is damped by an influence that opposes changes in it, in direct proportion to the ... more

Thermal Expansion - Linear

Thermal expansion is the tendency of matter to change in volume in response to a change in temperature through heat transfer. When a substance is heated, ... more

Chladni's Law

Chladni’s law, named after Ernst Chladni, relates the frequency of modes of vibration for flat circular surfaces with fixed center as a function of ... more

Critical Buckling Stress of a Column with Buckling Coefficient

Column or pillar in architecture and structural engineering is a structural element that transmits, through compression, the weight of the structure above ... more

Sears–Haack body (Drag Coefficient related to the maximum Radius)

The Sears–Haack body is the shape with the lowest theoretical wave drag in supersonic flow, for a given body length and given volume. The mathematical ... more

Elliptic curve (equation)

In mathematics, an elliptic curve (EC) is a smooth, projective algebraic curve of genus one, on which there is a specified point.Any elliptic curve can be ... more

Maximum Spring Force (Fully Compressed)

A spring is an elastic object used to store mechanical energy. Springs are usually made out of spring steel. Small springs can be wound from pre-hardened ... more

Strouhal number (In metrology)

In dimensional analysis, the Strouhal number is a dimensionless number describing oscillating flow mechanisms.
In metrrology, specifically axial-flow ... more

Möbius transformation (Möbius function)

In geometry and complex analysis, a Möbius transformation of the plane is a rational function of one complex variable. A Möbius transformation can be ... more

Sears–Haack body (Drag Coefficient related to the Volume)

The Sears–Haack body is the shape with the lowest theoretical wave drag in supersonic flow, for a given body length and given volume. The mathematical ... more

Worksheet 324

The main span of San Francisco’s Golden Gate Bridge is 1275 m long at its coldest. The bridge is exposed to temperatures ranging from –15ºC to 40ºC . (a) What is its change in length between these temperatures? Assume that the bridge is made entirely of steel.

Strategy

Use the equation for linear thermal expansion to calculate the change in length , ΔL . Use the coefficient of linear expansion, α ,for steel from Table 13.2, and note that the change in temperature, ΔT , is 55ºC

Thermal Expansion - Linear

(b) convert the change in temperature if Kelvin and Fahrenheit degrees. **
**this section is not included in the Reference material

Celsius <-> Kelvin
Celsius <-> Fahrenheit

Discussion

Although not large compared with the length of the bridge, this change in length is observable. It is generally spread over many expansion joints so that the expansion at each joint is small.

Reference : OpenStax College,College Physics. OpenStax College. 21 June 2012.
http://openstaxcollege.org/textbooks/college-physics
Creative Commons License : http://creativecommons.org/licenses/by/3.0/

Minimum Velocity in Friction Banked Turn

A banked turn (aka. banking turn) is a turn or change of direction in which the vehicle banks or inclines, usually towards the inside of the turn. For a ... more

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