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The grade (US) or gradient (UK) (also called stepth, slope, incline, mainfall, pitch or rise) of a physical feature, landform or constructed line refers to the tangent of the angle of that surface to the horizontal. It is a special case of the slope, where zero indicates horizontality. A larger number indicates higher or steeper degree of "tilt".
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.
[1] [2] This property should not be confused with the definition of an ellipse using a directrix line below. Using Dandelin spheres , one can prove that any section of a cone with a plane is an ellipse, assuming the plane does not contain the apex and has slope less than that of the lines on the cone.
The change in slope of a deflection curve between two points of a beam is equal to the area of the M/EI diagram between those two points.(Figure 02) Figure 02-Mohr's First Theorem Mohr's second theorem
A Lissajous curve / ˈlɪsəʒuː /, also known as Lissajous figure or Bowditch curve / ˈbaʊdɪtʃ /, is the graph of a system of parametric equations. which describe the superposition of two perpendicular oscillations in x and y directions of different angular frequency ( a and b). The resulting family of curves was investigated by Nathaniel ...
The phrase "linear equation" takes its origin in this correspondence between lines and equations: a linear equation in two variables is an equation whose solutions form a line. If b ≠ 0, the line is the graph of the function of x that has been defined in the preceding section. If b = 0, the line is a vertical line (that is a line parallel to ...
We can see that the slope (tangent of angle) of the regression line is the weighted average of (¯) (¯) that is the slope (tangent of angle) of the line that connects the i-th point to the average of all points, weighted by (¯) because the further the point is the more "important" it is, since small errors in its position will affect the ...
The Van 't Hoff equation relates the change in the equilibrium constant, Keq, of a chemical reaction to the change in temperature, T, given the standard enthalpy change, ΔrH⊖, for the process. The subscript means "reaction" and the superscript means "standard". It was proposed by Dutch chemist Jacobus Henricus van 't Hoff in 1884 in his book ...