Problem 2. If all the capacities in a network are integer-valued, show that the maxi- mum flow returned by the Max-Flow Min-Cut Algorithm is integer-valued.
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A: Use this code:import matplotlib.pyplot as plt # Setting up a diagram for the tensor product of R^2…
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Q: Solve the following Gourset problem Utt - Uxx = 0 U|x-t=0 4x2 = U|x+t=0 = 4x.
A: The wave equation provided is:Utt−Uxx=0and the initial conditions are:1. U∣x−t=0=4x2,2.…
Q: 4.
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A: Here is the explanation and handwritten calculations.
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Q: Compute for 21+ dt. (Hint: Express the integral 2+eit as a path integral.)
A: Steps and explanations are as follows:In case of any doubt, please let me know. Thank you.
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Q: Don't use chat gpt It Chatgpt means downvote
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Q: Can you please solve with as much detail as possible as these are midterm prep questions. Thank you
A: Step 1: Step 2: Step 3: Step 4:
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A: GIVEN : Ans ( a ) : Ans ( b ) : Ans ( c ) :
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A: Step 1: Step 2: Step 3: Step 4:
Q: Please solve all proofs fast without AI
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Q: Already got wrong Chatgpt answer Plz don't use chat gpt
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Q: Use proof by induction to prove this. Don't use any other method. Thank you.
A: SOLUTION:
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A: Solution: here:Uxx=U_xx8Uxy=8U_xy4Uy=4U_y 1. Principal PartThe principal part of a second-order PDE…
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- 1. Given an array of strings, return another array containing all of its longest strings. NOTF: use "len" function to return the number of characters in a given text string. For inputArray = ["aba", "aa", "ad", "vcd", "aba"], the output should be solution (inputArray) = ["aba", "vcd", "aba"].3. A spreadsheet consists of cells indexed by a row and a column. Each cell contains either a value or a formula that depends on the values of other cells. (a) Describe a graph, digraph, or network that models an arbitrary spreadsheet and allows you to answer the remaining parts of this question. (b) Explain, by referring to the graph, digraph, or network, when it is possible to change the value of cell x without changing the value of cell y. (c) Explain, by referring to the graph, digraph, or network, when it is possible to calculate the values of all cells in the spreadsheet. Consider the following spreadsheet with 5 rows, 7 columns, and 35 cells. For exam- ple, cell el contains a value, whereas cell al contains a formula that depends on the values cells el and 95. a b с d e f g 1 el+g5 al-c5 110 al+cl 180 f5-el c1+c2 2 al+bl a2+c4 240 a2+c2 120 f5-e2 e3+e5 3 a2+b2 a3-c3 100 a3+c1 200 f5-e3 f1+f2 4 a3+b3 a4+c2 220 a4+c2 100 f5-e4 f3+f4 5 a4+b4 a5-c1 130 a5+c5 120 g3+g4 gl+g2 (d) Can…3. A spreadsheet consists of cells indexed by a row and a column. Each cell contains either a value or a formula that depends on the values of other cells. (a) Describe a graph, digraph, or network that models an arbitrary spreadsheet and allows you to answer the remaining parts of this question. (b) Explain, by referring to the graph, digraph, or network, when it is possible to change the value of cell x without changing the value of cell y. (c) Explain, by referring to the graph, digraph, or network, when it is possible to calculate the values of all cells in the spreadsheet. Consider the following spreadsheet with 5 rows, 7 columns, and 35 cells. For exam- ple, cell el contains a value, whereas cell al contains a formula that depends on the values cells el and 95. a b с 1 el+g5 al-c5 110 d al+cl 180 e f g f5-el c1+c2 2 al+b1 a2+c4 240 a2+c2 120 f5-e2 e3+e5 3 a2+b2 a3-c3 100 a3+c1 200 f5-e3 f1+f2 4 a3+b3 a4+c2 220 a4+c2 100 f5-e4 f3+f4 5 a4+b4 a5-c1 130 a5+c5 120 g3+g4 g1+g2 (d) Can…
- A service has five tasks, performed in sequence. In the instance when there is more than one worker assigned to a task, each worker performs the entire task and they both can be working on different “items” at the same time. Task Task time per worker Number of workers 1 2 minutes 1 2 6 minutes 1 3 14 minutes 2 4 4 minutes 1 5 15 minutes 3 What is the capacity (hourly) of the process as a whole? What is the bottleneck of the process? What is the throughput time (assuming no wait time)? Where would you expect customers to wait?Five workers are available to perform four jobs. The time it takes each worker to perform each job is given in the following table. The goal is to assign workers to jobs so as to minimize the total time required to perform the five jobs: Time Worker Job 1 Job 2 Job 3 Job 4 Job 5 1 10 15 10 15 16 2 12 8 20 16 14 3 12 9 12 18 22 4 6 12 15 18 8 5 16 12 8 12 8 Which worker should be assigned to which job? What is the total time required? (Hint: Use the Assignment model). If there are only 4 jobs (assume that job 5 is not required), how would the workers be assigned to jobs? (Hint: Change the constraints in the Assignment model).A major hotel chain is constructing a new resort hotel complex in Greenbranch Springs, WestVirginia. The resort is in a heavily wooded area, and the developers want to preserve as much ofthe natural beauty as possible. To do so, the developers want to connect all the various facilitiesin the complex with a combination walking–riding path that will minimize the amount of pathwaythat will have to be cut through the woods. The following network shows possible connectingpaths and corresponding distances (in yards) between the facilities: Determine the path that will connect all the facilities with the minimum amount of constructionand indicate the total length of the pathway.
- While you are on a 4-week vacation, you will play at least one set of tennis matches each day, but you wouldn’t play more than forty sets total during this time. Prove that no matter how you distribute your games during the four weeks, there is a span of consecutive days during which you will play exactly 15 games.Q1) Four workers are to be assigned for 4 different jobs on the basis of the worker's relative skill levels on the various machines. Four Jobs are available, so assign one job to worker. In order to maximize profitability, we wish to minimize the total cost of the assignment. Use the cost matrix given in the following, and the Hungarian assignment algorithm, to determine the optimal assignment of workers to machines, and give the cost of the optimal assignment. J1 J2 J3 J4 W1 8 26 17 11 W2 13 28 26 W3 38 19 18 15 W4 19 26 24 10 4.We need to assign 4 students (Daniel, Jeremy, Xiaoying, Ashu) to 3 different teams (Team 1, Team 2, and Team 3). Each team needs to have at least 1 student. To maximize productivity, it has been determined that Ashu and Jeremy cannot be on the same team. How many different ways are there to assign the teams?
- Assume that each full team consists of 1 doctor and 5 nurses, and that each half team consists of 1 doctor and 3 nurses. Assume also that there are 220 doctors and 920 nurses available to serve on teams. Assume also that the each full team can inoculate 240 people per hour and that each half team can inoculate 140 people per hour. How many full teams and half teams should be formed in order to maximize the number of inoculations per hour?3. Use the training data of Gauss2 example (Gauss2.train). (a). Run the K-means algorithm with K = 2 clusters and make a plot identifying the clusters. Also label the points with their known classes. = 2 clusters and make (b). Multiple all the x1 by 10. Run the K-means algorithm with K a plot identifying the clusters. Also label the points with their known classes. (c). Compare the class and cluster groupings for both plots in (a) and (b). Explain any differences between them. (d). Use agglomerative hierarchical clustering (hclust in the MASS library) to cluster the data, and divide them into 2 groups. You can use the function cutree to divide the clusters into 2 groups. Report on how the predicted cluster labels compare with actual cluster labels for each of the three methods for measuring distance between clusters, i.e. single linkage, complete linkage and average linkage. (e). Plot the dendrograms for the three methods in (d). What does the shape of the the dendrograms suggest about…The data file includes the text of three books of the Bible (Joshua, Jonah and Philippians) using the ESV translation. While these are all great books, our only interest for this project is how often each letter is used. Identify those letters whose Cls do not overlap with any the CIs of any of the other letters. (For example the CI [0.042, 0.052] overlaps with [0.050, 0.060] because the upper bound of the first CI is greater than the lower bound of the second CI.) List the letters with the non-overlapping Cis and specify how many such letters there are.
