(1) Multivariate model: ŷ = ß0 + Â1x1 + ß2x₂ (2) Univariate model: y = 50 + 51x1 IC
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- homogenous linear de with constant coefficientsFind an explicit solution of the given initial value problem using our method in solving First Order Linear Differentia Equation31 - Find the regression model. Regresyon modelini bulunuz. Y X 2 5 5 9 7 4 4 11A) y=-3,21+2,11xB) y=2,56+5,43xC) y=5,27+0,11x
- 2. Factory A produces a solution of 40% concentration of chemical Y at a rate of 7 kg/min, while factory B produces a solution of 20% concentration of chemical Y at a rate of 4 kg/min. Both solutions are fed into a mixer containing 60 kg of a 25% concentration solution of chemical Y. The mixture leaves the mixer at a rate of 10 kg/min. Assuming uniform mixing, what will be the concentration of chemical Y in the final solution after 20 minutes?2)Find an explicit solution of the given initial value problem using separation of variables.The number of defects on the front side (X) of a wooden panel and the number of defects on the rear side (Y) of the panel are under study. Suppose that the joint pmf of X and Y is modeled as fxy (x,y)=c(x+y), x=1,2,3 and y=1,2,3. Check if the number of defects on the front side (X) of a wooden panel and the number of defects on the rear side (Y) of the panel are independent.
- A hand-held calculator will suffice for the Problem. The problem an initial value problem and its exact solution are given. Approximate the values of x(0.2) and y(0.2)in three ways: (a) by the Euler method with two steps of size h = 0.1; (b) by the improved Euler method with a single step of size h = 0.2; and (c) by the Runge–Kutta method with a single step of size h = 0.2. Compare the approximate values with the actual values x(0.2) and y(0.2). x' = 2x - 5y, x(0) = 2, y' = 4x - 2y, y(0) = 3; x(t) = 2cos 4t -11/4 sin 4t, y(t) = 3cos 4t + 1/2sin 4tA hand-held calculator will suffice for the Problem. The problem an initial value problem and its exact solution are given. Approximate the values of x(0.2) and y(0.2)in three ways: (a) by the Euler method with two steps of size h = 0.1; (b) by the improved Euler method with a single step of size h = 0.2; and (c) by the Runge–Kutta method with a single step of size h = 0.2. Compare the approximate values with the actual values x(0.2) and y(0.2). x' = x + 2y, x(0) = 0,y' = 2x + y, y(0) = 2;x(t) = e3t - e-t , y(t) = e3t + e-tA hand-held calculator will suffice for the Problem. The problem an initial value problem and its exact solution are given. Approximate the values of x(0.2) and y(0.2)in three ways: (a) by the Euler method with two steps of size h = 0.1; (b) by the improved Euler method with a single step of size h = 0.2; and (c) by the Runge–Kutta method with a single step of size h = 0.2. Compare the approximate values with the actual values x(0.2) and y(0.2). x' = 3x + 4y, x(0) = 1, y' = 3x + 2y, y(0) = 1; x(t) = 1/7 (8e6t - e-t), y(t) =1/7(6e6t + e-t)
- A hand-held calculator will suffice for the Problem. The problem an initial value problem and its exact solution are given. Approximate the values of x(0.2) and y(0.2)in three ways: (a) by the Euler method with two steps of size h = 0.1; (b) by the improved Euler method with a single step of size h = 0.2; and (c) by the Runge–Kutta method with a single step of size h = 0.2. Compare the approximate values with the actual values x(0.2) and y(0.2). x' = x -2y, x(0) = 0, y' = 2x + y, y(0) = 4; x(t) = -4et sin 2t, y(t) = 4et cos 2tA hand-held calculator will suffice for the Problem. The problem an initial value problem and its exact solution are given. Approximate the values of x(0.2) and y(0.2)in three ways: (a) by the Euler method with two steps of size h = 0.1; (b) by the improved Euler method with a single step of size h = 0.2; and (c) by the Runge–Kutta method with a single step of size h = 0.2. Compare the approximate values with the actual values x(0.2) and y(0.2). x' = 5x - 9y, x(0) = 0, y' = 2x - y, y(0) = -1; x(t) = 3e2t sin 3t, y(t) = e2t(sin 3t - cos 3t)A hand-held calculator will suffice for the Problem. The problem an initial value problem and its exact solution are given. Approximate the values of x(0.2) and y(0.2)in three ways: (a) by the Euler method with two steps of size h = 0.1; (b) by the improved Euler method with a single step of size h = 0.2; and (c) by the Runge–Kutta method with a single step of size h = 0.2. Compare the approximate values with the actual values x(0.2) and y(0.2). x' = 9x + 5y, x(0) = 1, y' = -6x - 2y, y(0) = 0; x(t) = -5e3t + 6e4t, y(t) = 6e3t + 6e4t
