2) Another way to think about this situation is as a "pursuit curve". Suppose that instead of being a dragged object we have a heat seeking missile pursuing the initial object. If one knew in advance the path the object was taking one could choose the shortest straight line path to intercept. But if that is not known the heat seeking capability is needed. At any given point in time the missile is headed straight towards the target. The target moving means that the missile is constantly adjusting its path. The differential equation can be much more difficult to solve but there are numerical methods. Using units of kilometers suppose that the target is traveling according to the equation y = v1 - x2. It starts at the point (0,1) and takes 10 seconds moving at a constant speed to reach the point (1,0). YOU DO: What geometric shape is being traced? Thus, what is the target's speed in kilometers per hour? YOU DO: Give this situation instead using parametric equations YOU DO: Give this situation instead using a polar equation.
Family of Curves
A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.
XZ Plane
In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.
Euclidean Geometry
Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.
Lines and Angles
In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 1 images
