Question Solved1 Answer 1. Find the general solution of: a. D(D – 4)y = e2x b. y" + 16y = 48 sin 4x

(b) Calculate the following line integrals in a counterclockwise direction around the triangular path as shown in Figure \( \mathbf{Q} 3 \) (b). \[ \int_{C} x^{2} y d x+x d y \] \( (10 \) marks) (c) Calculate the following line integrals by using Green's Theorem, where \( C \) is the path from \( (0,0) \) to \( (1,1) \) along the graph of \( y=x^{3} \) and (b) Calculate the following line integrals in a counterclockwise direction around the triangular path as shown in Figure Q3 (b). ∫C​x2ydx+xdy (10 marks) (c) Calculate the following line integrals by using Green's Theorem, where C is the path from (0,0) to (1,1) along the graph of y=x3 and from (1,1) to (0,0) along the graph of y=x. ∮C​y3dx+(x3+3xy2)dy (5 marks)

A point charge q = +39.0 μC moves from A to B separated by a distance d = 0.171 m in the presence of an external electric field E with arrow of magnitude 300 N/C directed toward the right as in the following figure. 4. +-22 points SerCP11 16 P.006 My Notes Ask Your Teacher a distance d -0.171 m in the presence of an external electric field E of magnitude 300 N/C directed toward the right as in A point charge q = +39.0 μC moves from A to B separated by the following figure. (a) Find the electric force exerted on the charge magnitude direction --Select b)Find the work done by the electric force (c) Find the change in the electric potential energy of the charge (d) Find the potential difference between A and B Need Help? Read It [A point charge g = +39.0 1iC moves from A to B separated by a distance d = 0.171 min the presence of an external electric feld E of magnitude 300 N/C directed toward the right as in the following figure. E ——>}- A B (2) Find the electric force exerted on the charge. magnitude " direction Select (0) Find the work done by the electric force. a (©) Find the change in the electric poter 2 ‘energy of the charge. (¢) Find the potential difference between A ang 8. Va- Vz v Necd Help? a 

2) Create a maths problem and model solution corresponding to the following question: "Find the directional derivative of the following two-variable function for the supplied point and unit vector" Evaluate the directional derivative at the point (2, 5). Ensure that your supplied function uses both x and y, has 3 terms, and that at least one of those terms 2) Create a maths problem and model solution corresponding to the following question: "Find the directional derivative of the following two-variable function for the supplied point and unit vector" Evaluate the directional derivative at the point (2, 5). Ensure that your supplied function uses both x and y, has 3 terms, and that at least one of those terms contains √x. You may choose the vector representing the direction you will evaluate the directional derivative in, and the derivative must be a multiple of √2.

Find a realization for the proper rational matrix 2 2s - 3 (s + 1)(s + 2) S-2 s +1 S +2 Ĝ(s) S +1 = S

3) Create a maths problem and model solution corresponding to the following question: “Determine the derivative with respect to x for the following function" Your problem should provide a function that requires use of the chain rule and the product rule to differentiate, contains tanh(2x), and produces a derivative that includes In(3)

55. In the single-phase diode bridge rectifier shown in figure, the load resistor is R= 7512. The source voltage is V=230sinot, Where o = 211 x 50 radians per second. The power dissipated in the load resistor R is 안 WW R ☆ ☆