The eigenvalues of the coefficient matrix can be found by inspection or factoring. Apply the eigenvalue method to find a general solution of the system.

x'₁ = 6x₁ + 6x₂ + 2x₃

x'₂ = -8x₁ - 8x₂ - 6x₃

x'₃ = 8x₁ + 8x₂ + 6x₃

What is the general solution in matrix form?
x(t) =

Feature selection is the process of reducing the dimensionality of the feature space to increase performance and decrease running time (since there are fewer features). Outline a feature selection method for the unigram words feature representation using word relations Please explain the methods, not just theory. This question is from the book:Text Data Management and Analysis: A Practical Introduction to Information Retrieval and Text Mining

1. You are in charge of optimizing cell phone service for T-mobile at school because it drops calls all the time. You need to add the capacity for 10,000 more calls and 100,000 more text messages per day. You can buy Megacells that can handle 800 calls and 2000 texts a day for $1000 each, and super cells that can handle 200 calls and 30,000 texts for $ 650 each, and basic cells that can handle 100 calls and 100 texts for $125. how many of each should you buy to minimize the cost of this upgrade?

You're putting together gift baskets for a silent auction. The total value of the items in each basket must be $150 or less. The values of the available items are $90, $70, $110, $50, $30, $80, $120, $20, $100, $100, $60, $40, $70, $40, $90, $120, $60, $40, $80, and $110. (a) If you pack the items in the order listed above using the first fit algorithm, how many baskets will you make? ____ baskets (b) If you pack the items in the order listed above using the next fit algorithm, how many baskets will you make? ____ baskets (c) If you rearrange the items according to their value so that the most expensive item is first and then pack the items using the first fit algorithm, how many baskets will you make? ____ baskets

Discrete Math

answer question 2 only

1) You have 10 identical snails you want to feed to your 4 starfish (named SFA, SFB, SFC, and SFD).

a. One way to distribute the snails is to give 3 snails to SF-A, 2 snails to SF-B, 0 snails to SF-C, and 5 snails to SF-D. How would you represent this outcome as a stars-and-bars diagram?

b. How many ways are there to distribute the snails all together? Briefly explain.

c. How many ways could you distribute the snails provided that SF-A or SF-B (or both) get more than 2 snails? Briefly explain. (Hint: Starfish love snails as much as pie.)

2) What if the snails in the previous question were NOT identical? How many ways can you distribute the snails to the starfish (giving each starfish all of their snails at the same time, not in any particular order)? Explain your answer and why it makes sense that it is larger than the answer to part (b) above.

Find the Fourier series for the function on the interval (-π,π)

1. f(x) = 1 -sin(x)+3cos(2x)
2. f(x )= cos²(x)
3. f(x) = sin²(x)

• recognise the value of working systematically and keeping a record of the work we do.
• see how algebra can be used to prove why certain structures arise within a problem.
• ecognise how a problem can be developed.
• practise the use of algebra to prove why structures arise in other problems.

Could someone please explain these points in simple but in detailed

Question: How does prey density affect search time and handling time? Hypothesis: Greater prey density  lower search time, handling time You will need 2 timekeepers – one for search time (t.t.d. = time to discovery) One for handling time (h.t.) 1 data scribe 1 predator Experimental design: make a field of background objects, place your prey items randomly in this field. For example: Your setup could be a field of less desirable wrapped candies, and the prey can be more desirable Hershey’s kisses; or perhaps a background of peanuts in the shell, and the prey some other more delectable object (in these cases the predator can really eat the prey); or you might use all non-edible objects for background and prey, but something to manipulate on the prey items like folding them up, unwrapping, something to represent “handling time”. The blindfolded predator must search until one prey is encountered and picked up (t.t.d. recorded); then the predator unwraps and eats the prey (h.t. recorded when finally swallowed and finger signals ‘done’) The predator keeps searching and eating until all prey are discovered. REPEAT for each density with same predator. Repeat overall experiment at least once, changing roles, with a different person as predator. With your data: For each predator, calculate the mean search time and handling time for each density. Plot your results on a graph with prey density on the x-axis and the response variable(s) on the y-axis. What can you conclude? Interpret your results. Compare among predators and discuss possible reasons for any differences. Each student will write a short report describing their set-up, their data summary, and interpretation, and submit it for one essay credit.

Cost of Production Report

The Cutting Department of Karachi Carpet Company provides the following data for January. Assume that all materials are added at the beginning of the process.

a. Prepare a cost of production report for the Cutting Department. If an amount is zero or a blank, enter in "0". For the The rate used to allocate costs between completed and partially completed production.cost per equivalent unit computations, round your answers to two decimal places.

Find the equilibrium vector for the transition matrix below.

0.75...0.10...0.15

0.10...0.70...0.20

0.10...0.40...0.50

The equilibrium vector is...

Find the equilibrium vector for the transition matrix below.

0.58...0.12...0.30

0........0.59...0.41

0..........0..........1

The equilibrium vector is...

0.65...0.10...0.25

0.10...0.65...0.25

0.10...0.30...0.60

The equilibrium vector is...

Find the equilibrium vector for the transition matrix below.

0.4......0.6

0.3......0.7

The equilibrium vector is....

Find the equilibrium vector for the transition matrix below.

0.2...0.2...0.6

0.2...0.4...0.4

0.2...0.3...0.5

The equilibrium vector is...

Find the equilibrium vector for the transition matrix below.

0.2...0.2...0.6

0.8...0.1...0.1

0.2...0.4...0.4

The equilibrium vector is ...

Suppose we define the relation R on the set of all people by the rule "a R b if and only if a is Facebook friends with b."

Is this relation reflexive? Is is symmetric? Is it transitive? Is it an equivalence relation?

Briefly but clearly justify your answers.

DISCRETE MATH

1.Prove that the set of all integers that are not multiples of three is countable.

I actually did question 1-7, but I do have some problems in 8 and 9.

part I: Project Rescue (25 points) The Park Rangers protecting our national forests typically carry communication and sighting equipment that is used to help locate lost hikers, forest fires, airplanes crashes and other such like. In one instance, a light plane P crashed in a dense part of the forest, with the crash occurring to the northeast of a ranger R who witnessed the event. The witness was located 12 miles due east of the ranger station S. The bearing from the witness to the crash site was 20º, while the bearing from the Ranger Station, based on the smoke plume from the wreckage, was 52º. Answer the questions that follow, showing work to support your answers and rounding answers to nearest tenth, unless otherwise indicated. Answer the “Why?” questions in complete sentences.   

1) Use the information given to draw RSP. Draw the triangle large enough to fit the box below, labeling all given information and measurements appropriately.

2) What is the measure of ∠ PSR? Why?


3) What is the measure of ∠ PRS?



4) What is the measure of ∠ RPS? Why

5) Can we use the Law of Sines to find the distances SP and RP? Why/why not?

6) What is the distance SP from the ranger station to the crash site?

7) What is the distance RP from the ranger who witnessed the crash to the crash site?

part II: Project Rescue (15 points) Redraw the figure in Part I in the box below. A search and rescue team T is assembling at a point that is 7 miles due east of the ranger station S, directly between the ranger station and the witness. Draw a line connecting point T and point P.

8) How far is the rescue team T from the crash site?
9) What direction should they head to reach the crash site? Answer in terms of a bearing.

1. What is the gradient of the least squares loss with regularization? This classifier is actually called ridge regression. Hint: Recall the least squares loss for a given point xi is (yi-(wTxi+w0))^2 .The regularized loss would be (yi-(wTxi+w0))2+||w||^2. Now write this out for three coordinate data where w=(w1,w2,w3) and xi=(xi1,xi2,xi3)and solve df/dw1 without and with regularization.