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In mathematics, a rate is the quotient of two quantities, often represented as a fraction. [1] If the divisor (or fraction denominator) in the rate is equal to one expressed as a single unit, and if it is assumed that this quantity can be changed systematically (i.e., is an independent variable), then the dividend (the fraction numerator) of the rate expresses the corresponding rate of change ...
For example, a slope that has a rise of 5 feet for every 1000 feet of run would have a slope ratio of 1 in 200. (The word "in" is normally used rather than the mathematical ratio notation of "1:200".) This is generally the method used to describe railway grades in Australia and the UK.
Slope illustrated for y = (3/2)x − 1.Click on to enlarge Slope of a line in coordinates system, from f(x) = −12x + 2 to f(x) = 12x + 2. The slope of a line in the plane containing the x and y axes is generally represented by the letter m, [5] and is defined as the change in the y coordinate divided by the corresponding change in the x coordinate, between two distinct points on the line.
Stream gradient (or stream slope) is the grade (or slope) of a stream. It is measured by the ratio of drop in elevation and horizontal distance. [ 1 ] It is a dimensionless quantity , usually expressed in units of meters per kilometer (m/km) or feet per mile (ft/mi); it may also be expressed in percent (%).
The slope a measures the rate of change of the output y per unit change in the input x. In the graph, moving one unit to the right (increasing x by 1) moves the y-value up by a: that is, (+) = +. Negative slope a indicates a decrease in y for each increase in x.
The slope of a graph of ... The unit of k is mol dm −3 s −1. [14] ... For example, a rate law of the form = [] + [] ...
For example, if the MRS xy = 2, the consumer will give up 2 units of Y to obtain 1 additional unit of X. As one moves down a (standardly convex) indifference curve, the marginal rate of substitution decreases (as measured by the absolute value of the slope of the indifference curve, which decreases).
A road going directly uphill has slope 40%, but a road going around the hill at an angle will have a shallower slope. For example, if the road is at a 60° angle from the uphill direction (when both directions are projected onto the horizontal plane), then the slope along the road will be the dot product between the gradient vector and a unit ...