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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.
A slope field (also called a direction field[ 1]) is a graphical representation of the solutions to a first-order differential equation [ 2] of a scalar function. Solutions to a slope field are functions drawn as solid curves. A slope field shows the slope of a differential equation at certain vertical and horizontal intervals on the x-y plane ...
The Clausius–Clapeyron relation describes a Phase transition in a closed system composed of two contiguous phases, condensed matter and ideal gas, of a single substance, in mutual thermodynamic equilibrium, at constant temperature and pressure. Therefore, [ 7]: 508. Using the appropriate Maxwell relation gives [ 7]: 508 where is the pressure.
The standard mild slope equation, without extra terms for bed slope and bed curvature, provides accurate results for the wave field over bed slopes ranging from 0 to about 1/3. [11] However, some subtle aspects, like the amplitude of reflected waves, can be completely wrong, even for slopes going to zero.
The Hall effect is the production of a potential difference (the Hall voltage) across an electrical conductor that is transverse to an electric current in the conductor and to an applied magnetic field perpendicular to the current. It was discovered by Edwin Hall in 1879. [ 1][ 2]
Definition. The Bode plot for a linear, time-invariant system with transfer function ( being the complex frequency in the Laplace domain) consists of a magnitude plot and a phase plot. The Bode magnitude plot is the graph of the function of frequency (with being the imaginary unit ). The -axis of the magnitude plot is logarithmic and the ...
If y 1 ≠ b, then the slope of this line is =. This can also be found using implicit differentiation . When the centre of the circle is at the origin, then the equation of the tangent line becomes x 1 x + y 1 y = r 2 , {\displaystyle x_{1}x+y_{1}y=r^{2},} and its slope is d y d x = − x 1 y 1 . {\displaystyle {\frac {dy}{dx}}=-{\frac {x_{1 ...
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