Use Euler's method, with step size, h = 0.1, to approximate the solution at t = 0.3 for the initial value problem dx = x-t , x(0)=1 dt

Use the graphical method to find the optimal solution for the following LP equations: Min Z=10 X1 + 25 X2 Subject to X1220, X2 ≤40 ,XI +X2 ≥ 50 X1, X2 ≥ 0.

Using masons rule find the transfer function G(s) = C(s)/R(s)

A small mixing tank with a long discharge line is attached to an input source pump: R1 R2 C Ps I a) Develop the Transfer function for the height deviation as result of a supply pressure deviation: H(s) as a function of the linearized resistances, the tank capacitance, and line inertance. When P,(s) modeling this, assume that the resistance and inertance are both throughout the lines such that the same pressure drop is across R2 and I. (Note, this can also be modeled using an equivalent electrical circuit where I and R2 are in series)

Solve the initial value problem below using the method of Laplace transforms. y"- y' - 30y = 0, y(0) = - 1, y'(0) = 49

For each transfer function write the corresponding differential equation. For problem c simplify the answer by explicitly computing all derivatives

The steady-state distribution of temperature on a heated plate can be modeled by the Laplace equation, a²T ²T + a²x a²y If the plate is represented by a series of nodes as illustrated in Figure, centered finite-divided differences can be substituted for the second derivatives, which results in a system of linear algebraic equations. Use the Gauss-Seidel method to solve for the temperatures of the nodes in Figure. 0= Submission date: 09/01/2024 25°C T12 T₂2 250°C # T₁1 T₂1 250 CO 75°C 25°C 75°C 0°C 0°C