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Symbolab is an answer engine [1] that provides step-by-step solutions to mathematical problems in a range of subjects. [2] It was originally developed by Israeli start-up company EqsQuest Ltd., under whom it was released for public use in 2011. In 2020, the company was acquired by American educational technology website Course Hero. [3] [4]
It is a special case of the slope, where zero indicates horizontality. A larger number indicates higher or steeper degree of "tilt". Often slope is calculated as a ratio of "rise" to "run", or as a fraction ("rise over run") in which run is the horizontal distance (not the distance along the slope) and rise is the vertical distance.
the slope field is an array of slope marks in the phase space (in any number of dimensions depending on the number of relevant variables; for example, two in the case of a first-order linear ODE, as seen to the right). Each slope mark is centered at a point (,,, …,) and is parallel to the vector
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.
For example, if the feed is a saturated liquid, q = 1 and the slope of the q-line is infinite (drawn as a vertical line). As another example, if the feed is saturated vapor, q = 0 and the slope of the q-line is 0 (a horizontal line). [2] The typical McCabe–Thiele diagram in Figure 1 uses a q-line representing a partially vaporized feed.
Equivalently, the slope could be estimated by employing positions x − h and x. Another two-point formula is to compute the slope of a nearby secant line through the points (x − h, f(x − h)) and (x + h, f(x + h)). The slope of this line is (+) ().
Similar calculations are carried out to determine pixel positions along a line with negative slope. Thus, if the absolute value of the slope is less than 1, we set dx=1 if x s t a r t < x e n d {\displaystyle x_{\rm {start}}<x_{\rm {end}}} i.e. the starting extreme point is at the left.
In algebra, the partial fraction decomposition or partial fraction expansion of a rational fraction (that is, a fraction such that the numerator and the denominator are both polynomials) is an operation that consists of expressing the fraction as a sum of a polynomial (possibly zero) and one or several fractions with a simpler denominator. [1]