Solve Homogeneous differential equation. Please show work

(4x - 2y)dx + (2x - 9y)dy = 0

Assisted Instruction:

Has to be in PERL SCRIPTING LANGUAGE with NO SUBROUTINES

Programming Exercise:

Write a program in PERL with NO SUBROUTINES to allow the user to pick a type of arithmetic problem to study. An option of 1 means addition problems only, 2 means subtraction problems only, 3 means multiplication problems only, 4 means division problems only and 5 means random mixture of all these types.
(Computer- Assisted Instruction) The use of computers in education is referred to as computer- assisted instruction (CAI). Write a program that will help an elementary school student learn arithmetic operations. Use a Random object to produce two positive one- digit integers. The program should then prompt the user with a question, such as
How much is 6 times 7?
The student then inputs the answer. Next, the program checks the student’s answer. If it’s correct, display the message "Very good!" and ask another multiplication question. If the answer is wrong, display the message "No. Please try again." and let the student try the same question repeatedly until the student finally gets it right.
Modifying Exercise: (Computer- Assisted Instruction: Reducing Student Fatigue) One problem in CAI environments is student fatigue. This can be reduced by varying the computer’s responses to hold the student’s attention, so that various comments are displayed for each answer as follows: Possible responses to a correct answer: Very good! Excellent! Nice work! Keep up the good work!
Possible responses to an incorrect answer: No. Please try again. Wrong. Try once more. Don't give up! No. Keep trying. Use random- number generation to choose a number from 1 to 4 that will be used to select one of the four appropriate responses to each correct or incorrect answer. Use a switch or if statement to issue the responses.
Modifying Exercise (Computer- Assisted Instruction: Monitoring Student Performance) More sophisticated computer- assisted instruction systems monitor the student’s performance over a period of time. Count the number of correct and incorrect responses typed by the student. After the student types 10 answers, your program should calculate the percentages that are correct. If the percentage is lower than 75%, display "Please ask your teacher for extra help.", then reset the program so another student can try it. If the percentage is 75% or higher, display "Congratulations, you are ready to go to the next level!", then reset the program so another student can try it.

1. Amazon Appliance Company has three installers. Larry earns $355 per week, Curly earns $460 per week, and Moe earns $585 per week. The company's SUTA rate is 5.4%, and the FUTA rate is 6.0% minus the SUTA. As usual, these taxes are paid on the first $7,000 of each employee's earnings.

a. How much SUTA and FUTA tax does Amazon owe for the first quarter of the year?

SUTA: $

FUTA: $

b. How much SUTA and FUTA tax does Amazon owe for the second quarter of the year?

SUTA: $

FUTA: $

2.

As the payroll manager for Stargate Industries, your task is to complete the following weekly payroll record. The company pays overtime for all hours worked over 40 at the rate of time-and-a-half. Round to the nearest cent when necessary.

1. Find all eigenvalues of each of the following matrices. (a) |10 −18 b) |2 −1 (c) |5 4 2

6 −11 | 5 -2| 4 5 2

2 2 2|

N players are bidding on an object in a first price auction. The object has a value of v_i for each player i, where v₁ > v₂> ... >v_n> 0. Each player bids secretly choosing nonnegative real number. The winner is the player who bids the largest number, and that player must pay the amount they bid. If it tie, then the player with the lowest index wins. Formulate this situation as a strategic game( describe the players, actions, and payoff functions) and show that in all the Nash equilibrium, player 1 wins the auction.

Suppose that the array X consists of real numbers X[1], X[2], …, X[N]. Write a pseudocode program to compute the minimum of these numbers.

if S is non empty and it has a lower bound, then it has an infimum, inf S

Start of proof:

b<=s for all s in S

LB: {y in R:y<=S, for all s in S}

LB is bounded above by X and LB is non empty since b is in LB

Find supLB=infS, thats what needs to be completed

1. Southwest Clothing Company, produces denim jeans, is planning to introduce a new line of lime green jeans. Each pair of jeans costs $5.50 for fabric and $3.00 for labor. Each pair will be sold for $24.99 each. Fixed costs are estimated as $10,000 per month. Southwest intends to build an EXCEL model to explore the options for production.

a. Set up a spreadsheet model to calculate total profit with production quantity as the decision variable - assuming that Southwest will sell all of the jeans that are produced.

b. Use the Excel tool Data/What-If Analysis/Goal Seek to determine the break-even quantity for the jeans.

c. Use the Excel tool Data/What-If Analysis/Data Table to create a one-way table to demonstrate the sensitivity of profit to changes in selling price per pair of jeans

            Use prices of 21.99 23.99 25.99, 27.99 and 31.99 in your table.

d. Create a graph of the one-way table results.

A radioactive material disintegrates at a rate proportional to the amount currently present. If Q(t) is the amount present at time t, then

dQ/dt=−rQ

where r>0 is the decay rate.

If 300 mg of a mystery substance decays to 80.84 mg in 3 weeks, find the time required for the substance to decay to one-half its original amount. Round the answer to 3 decimal places.

You find yourself in a maze walking and you reach a 3-way intersection. The roads have signs as follows: -on the left: “bad idea street” -in front of you: “don’t even try it road” -on the right: “you’re lost avenue” On each one of the roads there is a street vendor (hey, it’s Miami, they are everywhere!). You talk to the street vendors and this is what they tell you (after you buy some of their goods of course): -Street vendor on “bad idea street”: “This road will take you straight to Cold Stone Creamery. Also, if “you’re lost avenue” leads you to Cold Stone Creamery, then “don’t even try it road” will also take you to Cold Stone Creamery.” -Street vendor on “don’t even try it road”: “Neither “bad idea street” nor “you’re lost avenue” takes you to Cold Stone Creamery.” -Street vendor on “you’re lost avenue”: “Follow “bad idea street” and you’ll reach Cold Stone Creamery. Furthermore, follow “don’t even try it road” and you will never leave this maze (Muahaha).” It is common knowledge that street vendors never tell the truth. Furthermore, you are dying for some ice-cream, after a whole day of being lost in the maze. Can a road be chosen (with 100% certainty) such that it will take you to your neighborhood Cold Stone Creamery? If it can be done, which road would you choose? Provide formal language and propositional logic facts (propositions) that formalize the problem and prove(show steps) whether a road can be chose so that you can be sure it will lead you to Cold Stone Creamery(for some yummy ice-cream).

   Assignment ID is p1

NOTE: Algebraic expressions follow FORTRAN conventions.
Use full calculator precision for intermediate values.


Use the bisection method with the function defined by:

A=(X + 1.62) / 5.39
B=(X - 3.77) / 5.39
P1=((A-1)**2)*(1+2*A)
P2=((B+1)**2)*(1-2*B)
F(X) = (P1 * (-1.24) ) + (P2 * 4.13)

Start with interval (Xleft,Xright) = (-1.62, 3.77)
The function values at these end points are
F(Xleft) = -1.24
F(Xright) = 4.13

The new approximation interval bracketing the root
after ONE bisection is (______1______,______2______).
Function values at these end points are: ______3______, and 1.445

The new approximation interval bracketing the root
after ONE MORE bisection is (______4______,______5______).
Function values at these end points are: -0.400937 and ______6______.

The new approximation interval bracketing the root
after ONE MORE bisection is (______7______,______8______).

If Xmid satisfies the convergence criterior |f(Xmid)|<=0.00001,
then the root Xmid is ______9______.

ANSWER SECTION:
SELECTIONS FOR BLANK NUMBER 1
(a) 0.73
(b) 1.075
(c) -1.62
(d) -0.21
(e) -0.68
SELECTIONS FOR BLANK NUMBER 2
(a) 1.075
(b) 3.77
(c) -0.235
(d) -0.895
(e) -1.62
SELECTIONS FOR BLANK NUMBER 3
(a) 1.445
(b) -3.23
(c) -1.24
(d) -3.89
(e) 2.07
SELECTIONS FOR BLANK NUMBER 4
(a) 1.075
(b) -0.2725
(c) -2.3525
(d) 1.3875
(e) -1.1025
SELECTIONS FOR BLANK NUMBER 5
(a) 3.525
(b) 2.4225
(c) -0.2725
(d) -0.145
(e) 1.075
SELECTIONS FOR BLANK NUMBER 6
(a) 1.445
(b) 3.29094
(c) 0.575
(d) -0.745
(e) -0.400937
SELECTIONS FOR BLANK NUMBER 7
(a) 1.075
(b) 0.40125
(c) 1.2775
(d) 0.6575
(e) -0.2725
SELECTIONS FOR BLANK NUMBER 8
(a) -1.41875
(b) 1.74875
(c) 0.40125
(d) 2.68125
(e) -0.2725
SELECTIONS FOR BLANK NUMBER 9
(a) 1.8501
(b) 1.4001
(c) 1.74875
(d) -0.829902
(e) 0.0600983

Show that any open subset of R (w. standard topology) is a countable union of open intervals. Please explain how to do, I only understand why it is true.
What is required to fully prove this. What definitions should I be using.

Let p be an odd prime (i.e., any prime other than 2). Form two vector spaces V₁, V₂ over F_p (prime field of order p) with bases corresponding to the edges and faces of an icosahedron (so that V₁ has dimension 30 and V2 has dimension 20). Let T : V₁ → V₂ be the linear transformation defined as follows: given a vector v ∈ V₁, T(v) is the vector in V₂ whose component corresponding to a given face is the sum of the components of v corresponding to the edges around that face. Prove that T is surjective. (Hint: one option is to look closely at the five edges emanating from a single vertex.)

Let S be the set of all integers x ∈ {1,2,...,100} such that the decimal representation of x does not contain the digit 4. (The decimal representation does not have leading zeros.) • Determine the size of the set S without using the Complement Rule. • Use the Complement Rule to determine the size of the set S. (You do not get marks if you write out all numbers from 1 to 100 and mark those that belong to the set S.)

Let S be the set of all integers x > 6543 such that the decimal representation of x has distinct digits, none of which is equal to 7, 8, or 9. (The decimal representation does not have leading zeros.) Determine the size of the set S.

(do not just write out all elements of S.)