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Grade is usually expressed as a percentage - converted to the angle α by taking the inverse tangent of the standard mathematical slope, which is rise / run or the grade / 100. If one looks at red numbers on the chart specifying grade, one can see the quirkiness of using the grade to specify slope; the numbers go from 0 for flat, to 100% at 45 ...
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 (%).
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.
This can be expressed in the distance traveled horizontally for a rise of one unit, or in terms of an angle of inclination or a percentage difference in elevation for a given distance of the track. The allowable gradients may be based on the ruling gradient which is the maximum gradient over which a tonnage train can be hauled with one locomotive.
The "Railways" section of the article on railway list four of the steepest grades for a non-rack railroads as ranging between 1 in 40 (2.5%) and 1 in 18 (5.5%). The Czech railroad (which looks pretty flat in the photo) would be 3.5 to 8 times steeper than that if the sign really means 20%.
The simplest example given by Thimbleby of a possible problem when using an immediate-execution calculator is 4 × (−5). As a written formula the value of this is −20 because the minus sign is intended to indicate a negative number, rather than a subtraction, and this is the way that it would be interpreted by a formula calculator.
In aerodynamics, climb gradient is the ratio between distance travelled over the ground and altitude gained, and is expressed as a percentage. The angle of climb can be defined as the angle between a horizontal plane representing the Earth's surface, and the actual flight path followed by the aircraft during its ascent.
The top grade, A, is given here for performance that exceeds the mean by more than 1.5 standard deviations, a B for performance between 0.5 and 1.5 standard deviations above the mean, and so on. [17] Regardless of the absolute performance of the students, the best score in the group receives a top grade and the worst score receives a failing grade.