PPT-2.5 – Applications of Linear Equations and Modeling

PointSlope Form   The pointslope form allows you to use ANY point together with the slope to form the equation of the line Find the equation of a line that passes through the point and has a slope of 3. N is the process noise or disturbance at time are IID with 0 is independent of with 0 Linear Quadratic Stochastic Control 52 brPage 3br Control policies statefeedback control 0 N called the control policy at time roughly speaking we choo e Ax where is vector is a linear function of ie By where is then is a linear function of and By BA so matrix multiplication corresponds to composition of linear functions ie linear functions of linear functions of some variables Linear Equations Slope-Intercept Form | Point-Slope Form | Horizontal & Vertical Lines . Learning Objectives. Determine the equation of a line given the slope and . y. -intercept. Determine the equation of a line given the slope and any point. Another Look at Linear Graphs. Zero Slope & Lines with Undefined Slope. Horizontal & Vertical Lines. Graphing Using Both . Intercepts . (Cover-Up Method). (0,?). and . (?,0). Solving Equations Graphically. 3.1 – . Systems of Linear Equations in Two Variables. 1. Suppose we have two linear equations. :. . . Together, they make a ________________________________ (also called a . ___________________).. By:. Emily Zhou. What is a Linear Equation?. A linear equation is an equation whose graph forms a straight line.. Linear equations are usually shown on a coordinate plane. Real life situations of linear equations include the stock market as well as the payments of a car.. Reals. Dana . Moshkovitz. , MIT. Joint work with . Subhash. . Khot. , NYU. We propose an approach for proving the . unique games conjecture . by studying the hardness of approximately solving . real. Andrew Pendergast. Dynamical Systems modeling. Dynamical Systems: Mathematical object to describe behavior that changes over time. Modeling a functional relationship such that time is a primary variable wherein a value or vector function is produced . Bei Xiao . American University. April 13. Final project. Due May 4. th. .. The final websites will be shared among students!! . Presentations will be recorded as a 5 . mins. you-tube video! We will learn how to do this. . Equations Using Algebra Tiles . Objectives. Solving Equations Involving the Distributive Property. Solving Multi-Step Equations. Solving Equations. The development of the equation solving model is based on two ideas.. 2. 8.1: First Order Systems. We now look at systems of linear differential equations.. One of the main reasons is that any nth order differential equation with n > 1 can be written as a first order system of n equations in n unknown functions..  .  . Solutions are found at the intersection of the equations in the system.. Types of Solutions. Section 8.1 – Systems of Linear Equations. Consistent System. One solution. Consistent System. Infinite solutions. What we will learn. Solve linear equations using addition and subtraction. Solve linear equations using multiplication and division. Use linear equations to solve real-life problems. Needed Vocab. Equation:. Net ionic equations are useful in that they show only those chemical species directly . participating in . a chemical . reaction. The keys to being . able to . write net ionic equations are the ability to recognize monatomic and polyatomic ions, .