There are basically SEVERAL continuity equations, one for each conserved quantity. The equations themselves are simply statements that matter (in the example of conservation of mass) will not appear out of nothing, or suddenly teleport to a far-away place.
derivation of pedal equation
http://en.wikipedia.org/wiki/Navier-Stokes_equations Please go to this page.
They could be the coordinates of a straight line equation
Yes if it is a straight line equation
You can either measure or estimate the coordinates visually from the graph, or solve the equation underlying the graph.
derivation of pedal equation
The graph (on Cartesian coordinates) of a quadratic equation is a parabola.
-4x + 9y = 0 is the equation of a line in the Cartesian plane and the coordinates of any of the infinite number of points on that line will satisfy the equation.
the equation that convert from cartesian to polar coordinates and vice versa r = sqrt (x*x+y*y); phi = atan2 (y, x); x = r*cos (phi); y = r*sin (phi);
it is easy you can see any textbook........
The equation in Cartesian coordinates is x2 + y2 = 6 But much simpler are the polar coordinates: r = 6 and 0 ≤ q < 360 degrees.
To derive the Navier-Stokes equations in spherical coordinates, we start with the general form of the Navier-Stokes equations in Cartesian coordinates and apply the transformation rules for spherical coordinates ((r, \theta, \phi)). This involves expressing the velocity field, pressure, and viscous terms in terms of the spherical coordinate components. The continuity equation is also transformed accordingly to account for the divergence in spherical coordinates. Finally, we reorganize the resulting equations to isolate terms and ensure they reflect the physical properties of fluid motion in a spherical geometry.
http://en.wikipedia.org/wiki/Navier-Stokes_equations Please go to this page.
The equation that is not used in the derivation of the keyword is the quadratic formula.
Gibbs-duhem-margules equation and its derivation
If you put an 'equals' sign ( = ) between the 'By' and the 'Cz', you have the generic equation for any straight line in 3-dimensional Cartesian coordinates.
It is the straight line equation that can be used to locate coordinates of x and y on the Cartesian plane