Math t Solution

IntroductionParametric equations express a set of related quantities as explicit functions of an independent variable, known as a parameter. An equation, relating variables x and y in Cartesian coordinates, can be expressed by parametric equations which describe a position on the curve.Find information about parametric equations yourself.Sample QuestionParametric equations express a set of related quantities as explicit functions of an independent variable, known as a parameter. An equation, relating variables and in Cartesian coordinates, can be expressed by parametric equations which describe a position on the curve.1 The parametric equations of a plane curve are defined by .Tabulate the values , and , and plot the curve.2 (a) Find three sets of parametric equations for the curve whose equation is .(b) Is it possible to choose as the parametric equation for ? Can you start with any choice for the parametric equation for ?(c) Can you start with any choice for the parametric equation for ?3 Suppose that the position of a particle at time is given by,and the position of another particle is given by,(a) Sketch the paths of the particles on the same coordinate axes.(b) How many points of intersection are there?(c) Determine whether there is any point where the particles collide.Sample SolutionScroll down for solution Question 1 Question 2(a) Three sets of parametric equations.

Let me know if you know more.(b) is impossible to be chosen as the parametric equation for because must be always positive as for every values of . We can start with any choice for the parametric equation for as long as is not negative.(c) Basically, we can start with any choice for the parametric equation for because .Question 3(a) The curve in pink is . And the curve in black is . (b) Based on the graph above, there are two points of intersection.(c) To determine whether the particles collide, we need to solve the simultaneous equations from the parametric equations. Please remember the particles does not collide even you are able to solve the equations. You must verify the values. Collision happens only when positions are the same with same . Verification Hence, the particles collide at . Hence, the particles do not collide.Please do yourself for and .The particles collide at only 1 point.