a symmetric group S5 acts on the set X5 = {(i, j) : i, j ∈ {1, 2, 3, 4, 5}}.

S5 will also act on this set. Consider the subgroup H = <(1, 2)(3, 4), (1, 3)(2, 4)>≤ S5. (a) Find the orbits of H in this action. Justify your answers. (b)

For each orbit find the stabiliser one of its members. Justify your answers.

action is this t.(i,j)=(t(i),t(j))

Mass Springs Systems problem (Differential Equations)

A mass weighing 6 pounds, attached to the end of a spring, stretches it 6 inches.

If the weight is released from rest at a point 4 inches below the equilibrium position, the system is immersed in a liquid that imparts a damping force numerically equal to 3 times the instantaneous velocity, solve:

a. Deduce the differential equation which models the mass-spring system.
b. Calculate the displacements of the mass ? (?) at all times “?”
c. Make a graph that shows the motion

Thanks for the help

Trevor, imprisoned in a cell, wishes to get a message to his friend, Franklin who is loitering outside a wall surrounding his prison. Trevor has wrapped his message round a stone, and intends to throw it from his prison cell window, over the wall, to land where Franklin can retrieve it. Trevor can throw the stone at 16 m/s. The cell window from which he can throw the stone is 6 m above the level ground outside the prison. The wall rises 10 m above the ground outside the prison, and is at a horizontal distance of 20 m from Trevor’s cell window. The stone has mass 0.2 kg.

a) Suppose that Trevor throws the stone at an angle of 2π / 9 radians (40 degrees) above the horizontal. Describe whether the stone will clear the wall, neglecting air resistance.

b) Analyze what range of launch angles will enable Trevor to get the stone over the wall, if air resistance can be neglected?

c) Trevor wants to throw the stone so that it lands as far as possible from the wall, to reduce the chances of Franklin being detected as he searches for it. Describe what launch angle should he choose (still neglecting air resistance and stone must clear the wall)? For this launch angle, analyze how far beyond the wall will the stone land?

Demand for rug-cleaning machines at Clyde’s U-Rent-It is shown in the following table. Machines are rented by the day only. Profit on the rug cleaners is $19 per day. Clyde has 3 rug-cleaning machines.

  
a. Assuming that Clyde’s stocking decision is optimal, what is the implied range of excess cost per machine? (Enter smaller value in first box and larger value in second box. Do not round intermediate calculations. Round your answers to 2 decimal places. Omit the "$" sign in your response.)

Implied range of excess cost per machine from $  to $

b. Your answer from part a has been presented to Clyde, who protests that the amount is too low. Does this suggest an increase or a decrease in the number of rug machines he stocks?

• Increase

• Decrease

c. Suppose now that the $19 mentioned as profit is instead the excess cost per day for each machine and that the shortage cost is unknown. Assuming that the optimal number of machines is 3, what is the implied range of shortage cost per machine? (Enter smaller value in first box and larger value in second box. Do not round intermediate calculations. Round your answers to 2 decimal places. Omit the "$" sign in your response.)

Implied range of shortage cost per machine from $  to $   

An object with mass 40.5 kg is given an initial downward velocity -3ms in a medium that exerts a resistive force with magnitude proportional to the square of the speed. The resistance is 80 N when the velocity is -4m/s. Use g=10m/s^2

a. Write out a differential equation in terms of the velocity v, and acceleration a



b. Find the velocity v(t) for the object

v(t)=

c. Upload a document with the work for parts a and b and a computer generated solution curve with a window appropriate for this situation.




d. State and interpret the end behavior for the solution found in part b.

Find the first four nonzero terms in a power series expansion about x₀ for a general solution to the given differential equation with the given value for x₀  

y'-2xy=0 , x₀=-4

the physicians in problem 3-36 have been ap-proached by a market research firm that offers to perform a study of the market at a fee of $5,000. the market researchers claim their experience enables them to use bayes' theorem to make the following statements of probability: probability of a favorable market given a favorable study = 0.82 probability of an unfavorable market given a favorable study = 0.18 probability of a favorable market given an unfavorable study = 0.11 probability of an unfavorable market given an unfavorable study = 0.89 probability of a favorable research study = 0.55 probability of an unfavorable research study = 0.45 (a) develop a new decision tree for the medical pro-fessionals to reflect the options now open with the market study. (b) use the emv approach to recommend a strategy. (c) what is the expected value of sample informa-tion? how much might the physicians be willing to pay for a market study? (d) calculate the efficiency of this sample

A furniture store manufactures 2 products; tables (X) and chairs (Y): the production process for each require a certain number of labor hours in the carpentry department and a certain number of labor hours in the painting department.
Each table takes 3 hours of carpentry work and 2 hours of painting work.
Each chair requires 4 hours of carpentry and 1 hour of painting.
During the current month, 2,400 hours of carpentry time and 1,000 hours of painting time are available.
The marketing department wants no more than 450 new chairs this month because of existing large inventory of chairs. However, the marketing department wants to make at least 100 tables this month because of low inventory of tables.
Each table brings in $7 profit and each chair yields $5 profit.
The manger wants to determine the best possible combinations of tables (X) and chairs (Y) to manufacture this month in order to earn maximum profit.
Formulate this situation as a LP problem and find an optimum solution (i.e., the best combination of X and Y)
i) by trial and error method, and
ii) graphically.
Do not forget to identify the feasible region when you draw these constraints on a graph.

A new drug has been developed to treat a particular condition, and it is alleged to be more effective than traditional treatment. An experiment will be conducted to test whether the statement is true. To perform the hypothesis test, a confidence level of 99% is selected for the hypothesis test. The new drug will be administered to a sample of 200 individuals with the condition, selected at random. An additional 300 individuals will be randomly selected and will be administer traditional treatment. Of ins 200 individuals treated with the new drug. 120 were completely cured. Of those treated with the traditional method, 220 were completely cured.

a. Is there statistical evidence to support the claim that the new drug is more effective? Carry out the appropriate test and conclude (10 nts)

b. If you were a patient of this condition, what treatment would you select? Justify your answer (7 pts)

How many numbers between 9 and 3009 are divisible by 2, 5, or 11? Please answer correctly. Thanks