0
Add your answer:
Earn +20 pts
How can you tell if an equation is a parabola?
Any and all conics, parabolas included, take the form Ax2 + Bxy + Cy2 + Dx + Ey + F = 0, with A, B, and C not all zero. The parabolas themselves have B2 - 4AC = 0.
What is a quadratic graph?
In general, the graph of a quadratic equationy = ax2 + bx + c is a parabola.If a > 0, then the parabola has a minimum point and it opens upwards (U-shaped) eg.y = x2 + 2x − 3If a < 0, then the parabola has a maximum point and it opens downwards (n-shaped) eg.General equation of Quadratic Function:Ax2 + Bxy + Cy2 + Dx + Ey + F = 0 with A, B, C not all zero.the graphs of quadratic equations are all conic sectionsBased on the values of the constants A,B,C the following cases emerge:1. Parabola2. Circle3. Ellipse4. Hyperbola5. Rectangular HyperbolaThe wiki reference tells you the rules for determining which graph you are working with based on the constants, A, B, and C.
2000 Toyota tacoma me got a miss fire on cy2 you put new plugs and wires what could be the reason it is still on?
If its a trd and you didnt use ngk that's your problem
VC-dimension for spheres?
If we are considering spheres of dimension d then the following argument shows that the VC dimension of these spheres cannot be more than O(d2). Notice that the equation of a sphere is a quadratic equation and has (d+1)2 coefficients. Lets work in R2 for clarity - any sphere looks like s(x,y) = ax2+bxy+cy2+dx+ey+f = 0 and a point (x,y) is in the sphere if s(x,y) < 0 and outside if s(x,y) > 0.Now simply interpret this situation in a 5 dimensional space with a new set of coordinates X,Y,Z,V,W. Simply make a change of coordinates X = x2, Y = xy, Z = y2, V = x, W = y. In this new space the old quadratic equation simply looks like a hyperplane ! Since the VD dimension of d-dimensional hyperplanes is d+1, we realize that the spheres in d-dimensions are no more powerful than hyperplanes in O(d2) dimensions and hence have a VC dimension of O(d2).I do not know if this argument can be tightened.
What is a symbolic method?
In mathematics, the symbolic method in invariant theory is a highly formal algorithm developed in the 19th century for computing form invariants — invariants of algebraic forms. It is based on repeated applications of the Omega process (which involves symbolic partial differentiation -- hence the name) to increase the number of variables of a homogeneous form while decreasing the degree. By clever mathematics, the invariant of the form is then reduced to a vector invariant of many dependent variables, most of which then cancel out. In the classical 19th century definition, a form invariant is a function of the coefficients of a (usually binary) form. It is invariant if it remains the same under any transformation in the transformation group in question. The simplest classic examples of form invariants are the trace and discriminant of conic sections. These are functions of the coefficients of the general conic, ax2 + bxy + cy2 + dx + ey = 0. The transformation group is the group of translations, reflections and rotations.
