For instance, it is commonly accepted now that the famous Gutenberg – Richter law decays more rapidly than a pure power-law tail because of a finite exponential cutoff in the upper tail.

For optical fibers, a power-law index profile is an index of refraction profile characterized by

For power-law profiles, single-mode operation occurs for a normalized frequency, V, less than approximately

For the power-law relationship V < sub > out </ sub > = V < sub > in </ sub >< sup > γ </ sup >, the curve on a log – log plot is a straight line, with slope everywhere equal to gamma ( slope is represented here by the derivative operator ):

For any such square the middle corner of these will be called the vertex of the square and the corner not on the curve will be called the diagonal point of the square.

For the lines of any plane, **yp, meeting Q in a conic C, are transformed into the congruence of secants of the curve C' into which C is transformed in the point involution on Q.

For output, the machine would have a printer, a curve plotter and a bell.

For some choices of P < sub > 1 </ sub > and P < sub > 2 </ sub > the curve may intersect itself, or contain a cusp.

For Dunedin, George Smith Duncan further developed the Hallidie model, introducing the pull curve and the slot brake ; the former was a way to pull cars through a curve, since Dunedin's curves were too sharp to allow coasting, while the latter forced a wedge down into the cable slot to stop the car.

For a curve of constant width such as the Reuleaux triangle, the width and diameter are the same because all such pairs of parallel tangent lines have the same distance.

For example, if u < sub > 1 </ sub > is an eigenvector of A, with a real eigenvalue smaller than one, then the straight lines given by the points along α u < sub > 1 </ sub >, with α ∈ R, is an invariant curve of the map.

For a given quantity of a consumer good, the point on the demand curve indicates the value, or marginal utility, to consumers for that unit.

For elliptic-curve-based protocols, it is assumed that finding the discrete logarithm of a random elliptic curve element with respect to a publicly known base point is infeasible.

For current cryptographic purposes, an elliptic curve is a plane curve which consists of the points satisfying the equation

For each of the prime fields, one elliptic curve is recommended.

For each of the binary fields, one elliptic curve and one Koblitz curve was selected.

( For example, dark matter is invoked to explain the galactic rotation curve.

For a population of size n, with a sequence of values y < sub > i </ sub >, i = 1 to n, that are indexed in non-decreasing order ( y < sub > i </ sub > ≤ y < sub > i + 1 </ sub >), the Lorenz curve is the continuous piecewise linear function connecting the points ( F < sub > i </ sub >, L < sub > i </ sub > ), i

For a probability density function f ( x ) with the cumulative distribution function F ( x ), the Lorenz curve L ( F ( x )) is given by:

For a cumulative distribution function F ( x ) with inverse x ( F ), the Lorenz curve L ( F ) is given by:

For a specific demand curve the supply " curve " would be the price / quantity combination at the point where marginal revenue equals marginal cost.

For whatever reasons, after translations and publications of the Instituzioni analitiche ... the curve has become known as the " Witch of Agnesi ".

For example, profit maximization lies behind the neoclassical theory of the firm, while the derivation of demand curves leads to an understanding of consumer goods, and the supply curve allows an analysis of the factors of production.

: For prices above the prevailing price the curve is relatively elastic

: For prices below the point the curve is relatively inelastic

For a real-valued function of a single real variable, the derivative at a point equals the slope of the tangent line to the graph of the function at that point.

For example, the following arguments fit the slippery slope scheme with the inductive interpretation:

For most substances, the slope is positive as exemplified by the dark green line.

For example, a 100 % or 1000 ‰ slope is 45 °.

For example, the slope of the secant intersecting y = x < sup > 2 </ sup > at ( 0, 0 ) and ( 3, 9 ) is 3.

For example, it is not hard to conceive of a person, who is familiar with the concept of skiing or sledding, standing sideways on a plank of wood and riding down a snow-covered slope.

For nonlinear systems, the responsivity is the local slope ( derivative ).

For sufficiently small signals, the dynamic resistance allows the Ohm's law small signal resistance to be calculated as approximately one over the slope of a line drawn tangentially to the V-I curve at the DC operating point.

For real-valued functions of several real variables, this holds if and only if the absolute value of the slopes of all secant lines are bounded by K. The set of lines of slope K passing through a point on the graph of the function forms a circular cone, and a function is Lipschitz if and only if the graph of the function everywhere lies completely outside of this cone ( see figure ).

For instance, a line of irrational slope on a torus never returns to its origin.

For example, Huayin is on the north slope of Mount Hua.

For instance, when a massive sphere is caused to roll down a slope starting from a point of unstable equilibrium, then its velocity is assumed to be caused by the force of gravity accelerating it ; the small push that was needed to set it into motion is not explicitly dealt with as a cause.

For example, in linear interpolation, a line that increases one ordinate ( y-value ) for every two abscissa ( x-value ) has a ratio ( also known as slope or rise-over-run ) of 1 / 2.

For this the slope of the yawing moment curve must be positive.

For example, if a corporation builds a ski slope, and gives rights of use ( usufruct ) as gifts to corporate partners, these cannot last in perpetuity, but must terminate after a period that must be specified, e. g. 10 years.

For instance, if the mercury in a thermometer moves 1 cm when the temperature changes by 1 ° C, the sensitivity is 1 cm /° C ( it is basically the slope Dy / Dx assuming a linear characteristic ).

For example, a slope that has a rise of 5 feet for every 100 feet of run would have a slope ratio of 1 in 20.

For example, in a rack railway, the rotation of a pinion mounted on a locomotive or a railcar engages a rack between the rails and pulls a train along a steep slope.

For oblique fonts, the slope is increased from 12 ° to 16 °, and the character widths were adjusted optically.

For climbing a fixed rope attached to snow anchors on a steep slope, only one Jumar is used as the other hand is used for holding the ice axe.