What are the applications of hyperbolic functions?

For example, the hyperbolic cosine function may be used to describe the shape of the curve formed by a high-voltage line suspended between two towers (see catenary). Hyperbolic functions may also be used to define a measure of distance in certain kinds of non-Euclidean geometry.

What does hyperbolic scaling mean?

Hyperbolic growth and decline are characterized by a sudden and complete breakout or breakdown that instantly reaches infinity.

What is hyperbolic function in mathematics?

a function of an angle expressed as a relationship between the distances from a point on a hyperbola to the origin and to the coordinate axes, as hyperbolic sine or hyperbolic cosine: often expressed as combinations of exponential functions.

What is hyperbolic dependence?

For an enzyme-catalysed reaction, there is usually a hyperbolic relationship between the rate of reaction and the concentration of substrate, as shown below: (A) At low concentration of substrate, there is a steep increase in the rate of reaction with increasing substrate concentration.

What are the applications of functions in mathematics?

In mathematics, function application is the act of applying a function to an argument from its domain so as to obtain the corresponding value from its range.

What other applications of hyperbola do you see in your daily life?

Hyperbolas in Real Life

• A guitar is an example of hyperbola as its sides form hyperbola.
• Dulles Airport has a design of hyperbolic parabolic.
• Gear Transmission having pair of hyperbolic gears.
• The Kobe Port Tower has hourglass shape, that means it has two hyperbolas.

What is hyperbolic example?

hyperbolic Add to list Share. If someone is hyperbolic, they tend to exaggerate things as being way bigger deals than they really are. Hyperbolic statements are tiny dogs with big barks: don’t take them too seriously.

Is hyperbolic the same as logarithmic?

The inverse hyperbolic sine function is asymptotic to a pair of logarithmic functions. The graph of the inverse hyperbolic cosine function is identical to half of a rotated catenary curve, and is asymptotic to a logarithmic function.

What is hyperbolic sine used for?

Just as cosine and sine are used to define points on the circle defined by x2+y2=1, the functions hyperbolic cosine and hyperbolic sine are used to define points on the hyperbola x2−y2=1.

What is a hyperbolic reaction?

The definition of hyperbolic is something that has been exaggerated or enlarged beyond what is reasonable. An example of something that would be described as hyperbolic is a reaction by a person that is completely out-of-proportion to the events occurring.

What’s the difference between hyperbolic and hyperbole?

If someone is hyperbolic, they tend to exaggerate things as being way bigger deals than they really are. Hyperbolic statements are tiny dogs with big barks: don’t take them too seriously. Hyperbolic is an adjective that comes from the word hyperbole, which means an exaggerated claim.

What is hyperbolic growth?

The reciprocal function, exhibiting hyperbolic growth. When a quantity grows towards a singularity under a finite variation (a “finite-time singularity”) it is said to undergo hyperbolic growth.

What is the quadratic-hyperbolic growth function?

This means that with hyperbolic growth the absolute growth rate of the variable x in the moment t is proportional to the square of the value of x in the moment t . Respectively, the quadratic-hyperbolic function looks as follows:

When did the world population undergo hyperbolic growth?

Certain mathematical models suggest that until the early 1970s the world population underwent hyperbolic growth (see, e.g., Introduction to Social Macrodynamics by Andrey Korotayev et al. ).

What is hyperhyperbolic media?

Hyperbolic media have become an important class of artificial photonic materials for research and is expected to be the first optical metamaterial to find widespread applicability in device applications. Here, we will look at deriving the effective medium permittivities for an anisotropic multilayer composite with a uniaxial symmetry.