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  2. Differential of a function - Wikipedia

    en.wikipedia.org/wiki/Differential_of_a_function

    Linearity: For constants a and b and differentiable functions f and g, (+) = +. Product rule: For two differentiable functions f and g, () = +. An operation d with these two properties is known in abstract algebra as a derivation.

  3. Distance between two parallel lines - Wikipedia

    en.wikipedia.org/wiki/Distance_between_two...

    Because the lines are parallel, the perpendicular distance between them is a constant, so it does not matter which point is chosen to measure the distance.

  4. Distance from a point to a line - Wikipedia

    en.wikipedia.org/wiki/Distance_from_a_point_to_a...

    If a = 0 and b ≠ 0, the line is horizontal and has equation y = -c/b. The distance from (x 0, y 0) to this line is measured along a vertical line segment of length |y 0 - (-c/b)| = |by 0 + c| / |b| in accordance with the formula. Similarly, for vertical lines (b = 0) the distance between the same point and the line is |ax 0 + c| / |a|, as ...

  5. Darcy friction factor formulae - Wikipedia

    en.wikipedia.org/wiki/Darcy_friction_factor_formulae

    The Reynolds number Re is taken to be Re = V D / ν, where V is the mean velocity of fluid flow, D is the pipe diameter, and where ν is the kinematic viscosity μ / ρ, with μ the fluid's Dynamic viscosity, and ρ the fluid's density. The pipe's relative roughness ε / D, where ε is the pipe's effective roughness height and D the pipe ...

  6. Area of a triangle - Wikipedia

    en.wikipedia.org/wiki/Area_of_a_triangle

    Taking L to be the x-axis, the line integral between consecutive vertices (x i,y i) and (x i+1,y i+1) is given by the base times the mean height, namely (x i+1 − x i)(y i + y i+1)/2. The sign of the area is an overall indicator of the direction of traversal, with negative area indicating counterclockwise traversal.

  7. Probability density function - Wikipedia

    en.wikipedia.org/wiki/Probability_density_function

    To compute the quotient Y = U/V of two independent random variables U and V, define the following transformation: = / = Then, the joint density p(y,z) can be computed by a change of variables from U,V to Y,Z, and Y can be derived by marginalizing out Z from the joint density.

  8. Marginal distribution - Wikipedia

    en.wikipedia.org/wiki/Marginal_distribution

    Suppose there is data from a classroom of 200 students on the amount of time studied (X) and the percentage of correct answers (Y). [4] Assuming that X and Y are discrete random variables, the joint distribution of X and Y can be described by listing all the possible values of p(x i,y j), as shown in Table.3.

  9. Joint probability distribution - Wikipedia

    en.wikipedia.org/wiki/Joint_probability_distribution

    If the points in the joint probability distribution of X and Y that receive positive probability tend to fall along a line of positive (or negative) slope, ρ XY is near +1 (or −1). If ρ XY equals +1 or −1, it can be shown that the points in the joint probability distribution that receive positive probability fall exactly along a straight ...