problem 7 wasnt solved

How precisely does one go about using numerical techniques in order to find a solution to a collection of equations that has been organised in a system? Explain how the algorithm works for at least one of the techniques using just your own words.

InstructionsSolve for the following problems numerically using Manual solutions and using Python Code (Numpy)Question 2. Prove the equality of the following trigonometric functions using Euler identities. Furtherprove the equality in Python. Furthermore, plot the left-hand side and right-hand side of the equation andtheir Euler forms as additional proof.

PROBLEM 21 - 0533: Write a BASIC program to solve Laplace's equation (a²V/Əx?) + (a²V/ay²) = 0. Consider a rectangular 8 by 8 grid %3D with boundary conditions such that 3 sides are assumed to be at a potential of 100. The remaining side is at zero potential as shown. Solution: We use the replacement of partial derivatives by central differences

Please answer Parts D and E of this problem

Please no written by hand solution Sedna has designed a fishpond in the shape of a right triangle wi of length a and b and hypotenuse of length c. a

Develop a python code to solve general scalar and vector ordinary differential equations using the fourt-order Runge-Kutta method   The method should have classes,modules and a main program

Problem 2: For each of the following numbers, state the base in use; that is, what is p, q, r, s? (10 points) 100001, = 3310 • 25q = 1310 25, = 2310 255 = 3710

ts) The phase plot for an ODE - f(N) is shown below. (a) Which of these could be a plat of solutions y vs z comresponding to this CDE? A. B. C. D. You can cilck the graphs above to enierge them. OA. A OB. B OC. C OD. D (D) One equilibrium solution af this ODE is y which is chogse and another equilbrium solution of this CDE is y - which is choase (C) For which of the following value(s) of the initial condtion y(0) does the solution g(z) converge as z 00? Select all that apply DA. 0) - 3 OB. 0) - 3.5 OC. p(0) - 2 OD. (0) - -1

Problem 2. The two problems below can be solved using graph coloring. For each problem, represent the situation with a graph, say whether you should be coloring vertices or edges and why, and use the coloring to solve the problem. a. Your Quidditch league has 5 teams. You will play a tournament next week in which every team will play every other team once. Each team can play at most one match each day, but there is plenty of time in the day for multiple matches. What is the fewest number of days over which the tournament can take place? b. Ten members of Math Club are driving to a math conference in a neighboring state. However, some of these students have dated in the past, and things are still a little awkward. Each student lists which other students they refuse to share a car with; these conflicts are recorded in the table below. What is the fewest number of cars the club needs to make the trip? Do not worry about running out of seats, just avoid the conflicts. Student: A B C D E F…