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

find two power series solutions of 2x^2 y''-xy'+(x+1)y=0 about the center at the point x=0

1. Consider the problem of two polluting sources in the region, each of which generated 10 units of pollution for a total of 20 units released into the environment. The government determined that emissions must be reduced by 12 units across the region to achieve the ”socially desirable level of pollution”. Each firm faces different abatement cost conditions modelled as follows: for Polluter 1, marginal abatement cost is MAC₁ = 2.6Q₁, while the total abatement cost is TAC1 = 1.3(Q1)². For Polluter 2, marginal abatement cost is MAC2 = 0.52Q₂, while the total abatement cost is TAC2 = 0.26(Q2)², where Q₁ is the amount of pollution controlled (abated) by Polluter 1, and Q₂ is the amount of pollution controlled (abated) by Polluter 2.

(a) What is the cost effective abatement allocation across polluting sources? What is the total cost to achieve this goal?

(b) Assume that the government implements the 12-units standard uniformly, requiring each polluter to abate by 6 units. What is the total cost to achieve this goal? Is it more / less than the total cost from part a)? Comment on your findings.

Consider now other possible policies like a tradable emission permits (TEP’s) system and an emission tax as ways to achieve the cap of 8 units of emissions.

(c) Assume that the government imposes emission charge set at $4 for each polluter. Show how each firm responses to tax. Does $4 unit tax achieve the 12-unit abatement standard? If not, is $4 unit tax too high or too low? Discuss.

(d) Assume that the government decides to issue permits rather than impose tax. It issues 8 permits, each of which allows the bearer to emit 1 unit of pollution. The government allocates 4 permits to each polluter.

i. If the permits system does not allow for trading, what would be each firm’s response - cost, abatement required to this allocation?

ii. Assume now that trading is allowed and that two firms agree on the purchase and sale of permit at a price of $8.00. What would be each firm’s response - cost, abatement required, revenue to this price?

iii. Does the outcome from part (ii) represent the cost effective solution? If yes - why? If not, describe what happens next.

find the solution of the given initial value problem

1.   y''+4y=t²+3e^t, y(0) =0, y'(0) =2

2. y''−2y'+y=te^t +4, y(0) =1, y'(0) =1

find the general solution of the given differential equation

1. y''+2y'=3+4sin2t

2. 2y''+3y'+y=t² +3sint