Find the parametric representation for the part of the ellipsoid {eq}9x^2 + 4y^2 + z^2 =1 {/eq} that lies above xy-plane. Spherical Coordinates: Spherical coordinates are one of the three most important coordinates that exist in this space. ...
Ellipsoids are usually used as a shape of the DoA [93, 145]. Researches on the DoA have been given for uncertain polynomial continuous-time systems in [19]. Analytical approximation of a maximal invariant ellipsoid has been discussed for discrete-time systems with bounded controls [199]. The ...
The parametric equations for the normal line are represented by x(t)=x0+fx(P)t, y(t)=y0+fy(P)t, z(t)=z0+fz(P)t. The line passing through the point with the normal vector of the gradient of the surface at the point is the parametric equation of the ...
Given any curve in space, a parametric representation is a set of equations where x=x(t), y=y(t) and z=z(t) in terms of a real variable t, which is called parameter of the representation. Usually we express this in one single...
Find a vector function that represents the curve that is the intersection of the cylinder x^2 + y^2 = 1 and the hyperboloid z = x^2 + y^2. Find the parametric equation of the curve that is formed by the intersection ...
The parametric optimization approach proposed in this work can be widely applied for the parametric optimization of surface textures in other applications. Keywords: oil-lubricated long-life aircraft valve; surface texture; Reynolds equation with JFO boundary condition; Analytic Hierarchy Process; ...
While the Bloch equation can be used for simulating the signal evolution for a given flip angle, TR, TE, and the set of relaxation times for one single compartment, a model based on multiple compartments [29,51,52], including the magnetization exchange between the compartments within a voxel...