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 course where the axis of symmetry is the x-axis.which is the equation 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 tip p = 5/(42 ) = 0.88 units from the vertex of the parabola. Since p is positive, the parabola opens in the positive x-direction.If B2 - 4AC 0, the conic subdivision equation describes a hyperbola or couple on 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 using the rotation equations, and hence completing the squares for x and y until the equation is in one of the following formsAssignment The dot crossroad (often referred to as the inner product in a Linear Algebra text) is a useful tool in developing several important techniques of multivariable calculus. Your task is to give a detailed description of why the slope points in the direction of the maximum increase of a function. You may restrict your essay to R3. Your essay should involveGiven that a function f is differentiable at the point (x0, y0), a directional differential coefficient 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 on a lower floor points in a curve C that lies indoors 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