y'' − 3y' + 2y =− x sin x

STEP BY STEP CAREFULL INSTRUCTION.

ONLY USE PARTICULAR SOLUTION METHOD.

NOT PARTIAL FRACTION DECOMPOSITION

This is the whole problem, Just having trouble finding the -xsinx part of it

2. Find a general solution to the differential equation y'' − 3y' + 2y = x^2 + 1 − x sin x + xe^2x .

Suppose an elevator is controlled by two commands: ↑ to move the elevator up one floor and ↓ to move the elevator down one floor. Assume that the building is arbitrarily tall and that the elevator starts at floor x.

A)Write an LL(1) grammar that generates arbitrary command sequences that (1) never cause the elevator to go below floor x and (2) always return the elevator to floor x at the end of the sequence. For example, ↑↑↓↓ and ↑↓↑↓ are valid command sequences, but ↑↓↓↑ and ↑↓↓ are not. For convenience, you may consider a null sequence as valid.

B)Prove that your grammar is LL(1) (you need to provide the first, follow, and predict sets, as well as the complete parse table).

Find the point on the line 2x − y + 2 = 0 that is closest to the point (1, 5).

Suppose you’ve down-selected to two versions of your system (called “System A” and “System B”). Estimated profit for System A is $0.65 per unit and for System B is $0.75 per unit. You seek to maximize total profit.3 However, to manufacture these systems at your company, you’ll need to compete for internal resources. To manufacture a single unit of System A requires 3.0 minutes of machining, 2.0 minutes at a soldering station, and 4.0 minutes for final software testing. System B requires 2.5 minutes of machining and 6 minutes of software testing. Capacity of the machining department is 1,100 minutes per week, capacity of the soldering station is 500 minutes per week, and capacity of final software testing is 1,500 minutes per week.

(a) Write this problem in the form of a constrained linear optimization program.

(b) How many units of System A and B should you produce, and what is the total profit?

discrete math
4.
(4 pts) Be sure to explain all your answers.
(a) For which values of n does the graph Kn contain an Euler circuit?
(b) For which values of n does the graph Kn contain a Hamilton circuit?

thank you so much in advance!

For a rectangle

-describe the type of groups of a rectangle

-describe the orders of the groups

-describe the structure of the groups

-describe the elements of the groups (make sure to name all the elements and describe them as a group of permutations on the vertices)

- describe each group as subgroups of permutation groups

-describe all possible orders, types and generators for each subgroup of the group

-are any of these groups cyclic and or abelian?

-are any of these subgroups cyclic and or abelian?

-are there subgroups of every possible order?

-which subgroups are isomorphic and how do you know?

Expand f(x) = 10 + 2x + x^4 in terms of the Legendre polynomials, showing the first 5 coefficients.

Given the series of numbers:
{1.,0.612547,0.466856,0.375214,0.311459,0.264691,0.229088,0.201197,0.17884,0.160573,0.145406,0.132639,0.121764,0.112404,0.104273,0.0971538,0.0908741,0.0852989,0.08032,0.0758497,0.0718166,0.0681615,0.0648355,0.0617975,0.0590128,0.056452,0.05409,0.0519052,0.0498791,0.0479955,0.0462403,0.0446012,0.0430675,0.0416295,0.0402789,0.0390081,0.0378105,0.0366801,0.0356115,0.0346001,0.0336414,0.0327315}

What is the 100th term to 12-decimal places? How is this sequence made?

state and prove Theorem Holomorphy of Rλ

                                    A         B          C          D         E

Fixed Startup Cost        $3400 $2200 $2750 $1800 $1200
Cost per MW-hr          $6        $5        $7        $7        $8
Maximum Capacity      2200    1900    2600    1600    3200

Part A: Formulate a Binary-Integer Problem that minimizes the total cost. Write the complete algebraic form, and clearly state the decision variables, objective function, and the constraints.

Hint: Some binary variables and big number constraints are needed in this problem

Part B: Set up and solve a linear spreadsheet model to determine the operating plan that will minimize their overall costs. For full credit, the model must be linear (no multiplication of changing cells, no IF statements, no MAX statements, etc.)

The Ponchatrain Bridge is a​ 16-mile toll bridge that crosses Lake Ponchatrain in New Orleans.​ Currently, there are 7 toll​ booths, each staffed by an employee. Since Hurricane​ Katrina, the Port Authority has been considering replacing the employees with machines. Many factors must be considered because the employees are unionized. ​ However, one of the Port​ Authority's concerns is the effect that replacing the employees with machines will have on the times that drivers spend in the system. Customers arrive to any one toll booth at a rate of 12 per minute. In the exact change lanes with​ employees, the service time is essentially constant at 4 seconds for each driver. With​ machines, the average service time would still be 4 ​seconds, but it would be negative exponential rather than​ constant, because it takes time for the coins to rattle around in the machine.

For the​ "Exact Change​ Lane" with employee

The average time driver spends waiting to pay the toll ​= __ seconds​ (round your response to two decimal​ places).

The average time spent by a driver in the toll system​ (waiting and​ paying) ​= __ seconds​ (round your response to two decimal​ places)

The average number of drivers waiting in the line to pay the toll at a toll

booth​=__ drivers​ (round your response to two decimal​ places).

The average number of drivers at any toll​ booth, namely, in the system ​= __ drivers​ (round your response to two decimal​ places).

For the lane with the proposed machine

The average time driver spends waiting to pay the toll ​= __ seconds​ (round your response to two decimal​ places).

The average time spent by a driver in the toll system​ (waiting and​ paying) ​= __ seconds​ (round your response to two decimal​ places).

The average number of drivers waiting in the line to pay the toll at a toll booth​= __ drivers​ (round your response to two decimal​ places).

The average number of drivers at any toll​ booth, namely, in the system drivers​ __ (round your response to two decimal​ places).

As a result of proposed​ change, the average time spent per driver waiting in the line to pay the toll increases by __ (round your response to the nearest whole​ number).

As a result of proposed​ change, the average time spent per driver in the toll system increases by __ (round your response to the nearest whole​ number).

As a result of proposed​ change, the average number of drivers waiting in the line to pay the toll increases by (round your response to the nearest whole​ number).

As a result of proposed​ change, the average number of drivers at any toll booth increases by​ (round your response to the nearest whole​ number).

t^2 y'' − 4ty' + 6y = t^4*e^t , t > 0. Use variation of parameters to find a particular solution given that y1 = t^2 and y2 = t^3 are a fundamental set of solutions to the corresponding homogeneous equation

On a separate sheet of paper, practice the clustering technique to develop a topic for the writing assignment. Follow the instructions: 1. Choose one of the suggested topics. Write the topic in a large circle in the center. 2. Think about the topic for one or two minutes. Then write each new idea that comes into your mind in smaller circles around the large circle. 3. Think about the idea in each smaller circle for one or two minutes. Write any new ideas in even smaller circles. 4. Look over your groups of circles. Which groups have the largest number of ideas? These are probably the most productive ideas for your paragraph. TOPICS • a word that describes your home culture • an important term from your major field of study • a definition of what a good teacher is • a definition of culture shock • what the word success means to you • a definition of a what a leader is

STEP 3: Write the first draft. • Write FIRST DRAFT at the top of your paper. • Begin your paragraph with a topic sentence. Use the definition from your cluster diagram. As needed, modify the definition so that it is like the ones you wrote in Practice 4 on page 126. . For unity, present your supporting information in a logical order. • Use transition signals to make your paragraph coherent. . Try to include a word origin and/or idiom that goes well with your topic. Pay attention to sentence structure. Include a variety of sentence patterns: simple, compound, and complex sentences. Use adjective clauses and appositives. Punctuate them correctly. • Write a conclusion that tells why the topic is important, interesting, or unique. • Write a title. It should clearly identify your topic. For examples, look at the titles of the models in this chapter

write a definition paragraph on one of the topics: