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This last form of the Hill equation is advantageous because a plot of versus [] yields a linear plot, which is called a Hill plot. [ 7 ] [ 8 ] Because the slope of a Hill plot is equal to the Hill coefficient for the biochemical interaction, the slope is denoted by n H {\displaystyle n_{H}} .
A slope which falls down to a deep valley on its western side and a shallower one on its eastern side has a westerly aspect or is a west-facing slope. The direction a slope faces can affect the physical and biotic features of the slope, known as a slope effect .
Vegetation and slope stability are interrelated by the ability of the plant life growing on slopes to both promote and hinder the stability of the slope. The relationship is a complex combination of the type of soil , the rainfall regime , the plant species present, the slope aspect , and the steepness of the slope.
Fig. 1: Isoclines (blue), slope field (black), and some solution curves (red) of y' = xy. The solution curves are y = C e x 2 / 2 {\displaystyle y=Ce^{x^{2}/2}} . Given a family of curves , assumed to be differentiable , an isocline for that family is formed by the set of points at which some member of the family attains a given slope .
The line with equation ax + by + c = 0 has slope -a/b, so any line perpendicular to it will have slope b/a (the negative reciprocal). Let (m, n) be the point of intersection of the line ax + by + c = 0 and the line perpendicular to it which passes through the point (x 0, y 0). The line through these two points is perpendicular to the original ...
Specifically, a straight line on a log–log plot containing points (x 0, F 0) and (x 1, F 1) will have the function: = (/) (/), Of course, the inverse is true too: any function of the form = will have a straight line as its log–log graph representation, where the slope of the line is m.
A non-vertical line can be defined by its slope m, and its y-intercept y 0 (the y coordinate of its intersection with the y-axis). In this case, its linear equation can be written = +. If, moreover, the line is not horizontal, it can be defined by its slope and its x-intercept x 0. In this case, its equation can be written
Biological exponential growth is the unrestricted growth of a population of organisms, occurring when resources in its habitat are unlimited. [1] Most commonly apparent in species that reproduce quickly and asexually , like bacteria , exponential growth is intuitive from the fact that each organism can divide and produce two copies of itself.