Find a differential equation such that

a) y -> 2/5 as t->infinity

b) y -> -3/7 as t->infinity

c) y diverges from 2/5 as t->infinity

For each of the following functions use the quadratic formula to find the zeros of f. Then, find the maximum or minimum value of f(x).

(a)  f(x) = x² - 10x

Zeros of f (If there are no real zeros, enter NONE.)
... (smaller value)
....  (larger value)

Maximum or Minimum Value of f(x)
The minimum  value of f(x) is ....  when x =   .

(b)  f(x) = -2x² - 3x + 2
Zeros of f (If there are no real zeros, enter NONE.)
....(smaller value)
....  (larger value)

Maximum or Minimum Value of f(x)
The maximum  value of f(x) is....   when x =   .

Business Funding Question.

Solving a problem

You are supposed to negotiate 2 bank credits:

- one for intermediate trade with the USA (Import of iPhones 7) and

- second – for the construction of the iPhone plant in Rome.

Suggest your terms and conditions: (sum, currency, duration, interest rate, procedure of drawing and reimbursement, collateral – if any etc.)

Required approximately 1 page in word.

Given f(x,y) =(x³y- 2x²y)

a) find the directional derivative of f(x,y) at (1, 2) in the direction of <-3,4>

b)find the maximum value of directional derivative at (2,4) and the direction in which this occurs

Principle Of Discrete Math

In a paragraph (4-6 sentences), reflect on how recurrence relations are/can be used in your discipline.

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?