Algebra Essay Example | Topics and Well Written Essays - 1000 words

Algebra - Essay ExampleFrom the graph above, it can be seen that the parabola is rotated 45 counter-clockwise from the orientation where the axis of symmetry is the x-axis.which is the compare of a parabola centered at the origin, with the x-axis as the axis of symmetry for the parabola. With 4p = 5/2, the focal point p = 5/(42 ) = 0.88 building blocks from the vertex of the parabola. Since p is cocksure, the parabola opens in the positive x-direction.If B2 - 4AC 0, the conic section equation describes a hyperbola or pair of intersecting lines. If B2 - 4AC = 0, the conic section equation describes a parabola, line, pair of parallel lines, or no graph.Rotated conic sections can also be classified by rotating the coordinate axes by an angle where cot 2 = (A - C )/ B, by employ the rotation equations, and then completing the squares for x and y until the equation is in one of the following formsAssignment The dot intersection point (often referred to as the inner product in a Line ar Algebra text) is a useful tool in developing several important techniques of multivariable calculus. Your task is to give a detailed interpretation of why the gradient points in the direction of the maximum increase of a decease. You may restrict your essay to R3. Your essay should includeGiven that a function f is differentiable at the point (x0, y0), a directional derivative Duf(x0, y0) of the function f at a point (x0, y0) in the direction of the unit vector u = is defined byThe unit vector components are given by u1 = dx/ds and u2 = dy/ds, where s is the distance along a line given by points in the x-y plane directly below points in a curve C that lies within the surface z = f(x, y). For instance, at the beginning of the line, the point (x0, y0) lies in the x-y plane directly below the point Q0 lying in the curve C within the surface z = f(x, y). At a distance s (in the direction of u) along the line in the x-y plane, the point (x, y) is