A first order AR process is given by th =-0-8X+-1 tet) Find the ACF for lag Xt Ime 2 and describe it. 0,1,2... 7. Plot the correlogram
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- 40 identical balls are rolling along a straight line. They all have speed equal to v, but some of them might move in opposite directions. When two of them collide they immediately switch their direction and keep the speed v. What is the maximal number of collision's that can happen?Solve for y2 by using reduction of order And for nonhomogeneous using undetermined coefficients linear mathematicsFind genral and particular solution
- In a large tank there are 1000 gallons (gal) of water with a concentration of 1 pound (lb)per gallon of a pollutant. Water with a concentration of 2.5 lb/gal flows in at a rate of 8gal/min (gallons per minute). At the same time, water flows out at the same rate throughan outlet at the bottom. (Assume that the incoming solution is perfectly mixed in the tankat all times.) When will the concentration of pollutant reach 2 lb/gal?Find the general solution of the Higher Order LDE with cc. Show your full solution.2.solve using any methods (variable separable DE, exact DE or homogenous/non homogenous DE)
- Determine the longest interval in which the given initial value problem is certain to have a unique twice-differentiable solution. Do not attempt to find the slotuion. (Enter your answer using interval notation.) (x-2)y''+y'+(x-2)(tanx)y=0 y(3)=1 y'(3)=6Suppose U solves the heat equation on the real lineUt = 4Uxx, x ∈ Rwith initial valueU(x, 0) = (4, x ≤ 02, x > 0.(i) Use the Fourier-Poisson formula to give an explicit expression for the solutionU.(ii) Describe the qualitative behaviour of U in this case as t → ∞ and plot outthe solution at several instants of time to explain your answer. What is the limitof U as t → ∞?find a general solution show the work
- In a factory there is a 10,000 liter water tank that contains 0.01% colorant. From the beginning (t = 0) water with a dye content of 0.001% is pumped into the tank at a rate of 4 l/min. The water leaves the tank at the same speed. Calculate the percentage of chlorine in the tank after 60 minutes (iterations) taking time intervals of one minute: - using the approximate method of Euler and Runge Kutta of 4 order.solve for y(2) using Improved Euler's methodverify that the given function is a particular solu-tion to the specified nonhomogeneous equation. Find the general solu-tion and evaluate its arbitrary constants to find the unique solution satisfying the equation and the given initial conditions. y′′ - 2y′ + y = 2ex, yp = x2ex, y(0) = 1, y′(0) =0