Problem 5)
A long shunt 600 V, 1200-rpm DC motor has a series field winding resistance of 0.05 Ω, a shunt field winding resistance of 200 Ω, and an armature resistance of 0.1 Ω. The machine is connected to 600 V DC source. The rotational loss is 3.2 kW. If the machine draws a 100 A from the supply, calculate
a. Back EMF
b. Determine the machine’s converted power (or developed power) and its efficiency.
c. Determine the speed regulation if the machine draws 165 A at full load.
  

The PARTITION INTO PATHS OF
LENGTH 2 problem is as follows:
INSTANCE: A graph, G = (V, E) with IV| = 3q for a positive integer q.
QUESTION: Is there a partition of V into q disjoint subsets VI, V2, ...,
Vq of 3 vertices such that, for each V1 = {Vi[1], Vi[2], Vi[3), at least two of the
three edges {Vi[1], Vi[2], {Vi[1], Vi[3], and {Vi[2], Vi[3]} belong to E?
Prove the PARTITION INTO PATHS OF LENGTH 2 problem is NP-
complete.

Use pigeonhole principle to solve please: will upvote!

Let V = {v1,…,vk} be any set of vectors in R^2 (Real Numbers to the power of 2). Suppose n agents each start at (0,0) and each takes a mV-walk where a mV-walk consists of a sequence of exactly m steps and each step moves the agent along a vector in V. Prove that, if n > (m + k − 1 , k − 1) (these are two separate terms in one parenthesis), then some pair of agents finishes their walk at the same location.

Two capacitors C₁ = 5.9 ?F, C₂ = 16.2 ?F are charged individually to V₁ = 15.7 V, V₂ = 4.9 V. The two capacitors are then connected together in parallel with the positive plates together and the negative plates together.
Calculate the final potential difference across the plates of the capacitors once they are connected.

Calculate the amount of charge (absolute value) that flows from one capacitor to the other when the capacitors are connected together.

By how much (absolute value) is the total stored energy reduced when the two capacitors are connected?

1. Treacherous Triangle Trickery. Consider a charge distribution consisting of an equilateral triangle with a point charge q fixed at each of its vertices. Let d be the distance between the center of the triangle and each vertex, let the triangle’s center be at the origin, and let one of its vertices lie on the x-axis at the point x = −d.

1.1. Compute the electric field at the center of the triangle by explicitly computing the sum of the electric fields due the charges at each vertex.

1.2. Let V (x,y) be the electric potential as a function of position. Compute an expression for V (x,y), and try to simplify it if possible.

1.3. If a point charge Q is placed at rest at the origin, will it remain at rest? Justify using electric potential and symbolic computation.

1.4. Sketch the graph of V (x, 0) versus x.

1.5. Compute the Taylor expansion of V (x, 0) about x = 0 up to the term of order x 2 .

1.6. If a point charge Q is placed at the origin and then given a suffciently small kick in the x-direction, will it remain in the vicinity for the origin forever? Does it depend on the sign of Q? Does it matter if the kick is to the left or right? Justify all answers carefully.

1.7. If there is a case where the charge Q will oscillates under a small push in the x-direction, determine the period of small oscillations if the charge in the center has mass m. If there is not such a case of oscillatory motion, explain how you know this.

Home Entertainment Online (HEO) operates an online streaming service. The company offers both a movie and a music subscription service. HEO reports revenues for the movie service separately from the music service.

Required:

Classify each of the following cost items (A–G) as:

1. Direct or indirect (D or I) costs with respect to the total number of movie subscriptions sold
2. Variable or fixed (V or F) costs with respect to how the total costs of the movie service change as the total number of subscriptions sold changes. (If in doubt, select on the basis of whether the total costs will change substantially if there is a large change in the total number of subscriptions sold.).
3. Provide comments as to why you classified the cost as D or I or V or F

You will have two answers (D or I; V or F) for each of the following items:

Create a C++ project in visual studio.

You can use the C++ project that I uploaded to complete this project.

1. Write a function that will accept two integer matrices A and B by reference parameters, and two integers i and j as a value parameter. The function will return an integer m, which is the (i,j)-th coefficient of matrix denoted by A*B (multiplication of A and B). For example, if M = A*B, the function will return m, which is equal to M[i][j].

Explain the time complexity of this function inside of the code as a comment.

2. Write a function that will accept two integer matrices C and D by reference parameters. The function will compute the transpose of C and store it in D. For your information, the transpose of matrix C is D, where D[j][i] = C[i][j].

Explain the time complexity of this function inside of the function code as a comment.

3. Write a function that will accept one integer matrix E and one column vector F by reference parameters, and one integer I as a value parameter. The function will return an integer v, which is the i-th coefficient of row vector denoted by E*F (multiplication of E and F). For example, if V = E*F, the function will return v, which is equal to V[i].

Explain the time complexity of this function inside of the function code as a comment.

Assume that the following relationship holds:

Maintenance Costs = (v * Machine Hours) + f

REQUIRED

Estimate the values of v and f and the cost equation, using,

1. the High-Low Method, and

2. the Linear Regression method.

Note, to use the linear regression method, you MUST use the Microsoft Excel program.

Make sure to report

1. The values of v and f;

2. A scatter plot of the data points, and

3. The adjusted R-square; explain what the adjusted R-square means.

4. The cost equation in the form of Y = vx + f, substituting the values for v and f from the regression output.

YOUR SUBMISSION MUST BE IN EXCEL. PLEASE INCLUDE AN EXCEL ATTACHMENT OR HYPERLINK! ONE WORKBOOK, WITH A WORKSHEET FOR EACH ANALYSIS (i.e., High-Low Method and Regression Analysis respectively).  

Write a C++ program that inputs a sequence of integers into a vector, computes the average, and then outputs the # of input values, the average, and the values themselves. There are 0 or more inputs values, followed by a negative value as the sentinel; the negative value is not stored and not counted. The following sample input:

10
20
0
99
-1

would produce the following output:

N: 4
Avg: 32.25
10
20
0
99

The main program has been written for you, your job is to implement the two functions InputData andGetAverage. See the comments in the "student.cpp" file for specific implementation details.

main.cpp

#include <iostream>
#include <vector>

using namespace std;

// functions from student.cpp:
int InputData(vector<int>& V);
double GetAverage(vector<int> V, int N);

int main()
{
// assume at most 100 inputs:
vector<int> inputs(100);
int N;
double avg;

N = InputData(inputs);
avg = GetAverage(inputs, N);

cout << "N: " << N << endl;
cout << "Avg: " << avg << endl;

for (int i = 0; i < N; ++i)
{
cout << inputs.at(i) << endl;
}

return 0;
}

student.cpp

int InputData(vector<int>& V)
{

// TODO
  
return 0;
}

//
// GetAverage
//
// Returns the average of the first N values in the vector; if N is 0 then
// 0.0 is returned.
//
double GetAverage(vector<int> V, int N)
{

// TODO

return 0.0;
}