d this is the problem i m doing in math and i m having trouble figuring it out

irs during primary recovery. This problem explores some aspects of this behavior. Consider the expansion of methane from 300 bars to 50 bars at a constant temperature of 40 C (313 K). Methane obeys the following equation of state V =(RT/P)+C+(D/T) where C = 31 cm3/mol, D = -693cm3K/mole, and R = 83.14bar cm3/mole K. Note that the units of energy are bar-cm3/mole in this problem. Report your answer in bar-cm3/mole (a) What is the change in enthalpy during the expansion (b) What is the change in internal energy? (c) What is the heat removed? (d) How much work does the system do during the expansion?

and in the decimal system. How many digits are there in these two numbers all together? C.1379. Alex and Burt took their rabbits to a whole salesman to sell them to him at once. Each of them got as many dollars for each of their rabbits as many as the rabbits they each took to him. But, because their rabbits were so beautiful, they each got as many extra dollars for their rabbits from the salesman as many as the rabbits they each sold him. This way Alex received $202 more than Burt. How many rabbits did they each sell to the salesman? C.1380. How many {a, b, c} sets are there containing three positive whole elements, where the product of a, b, and c is 2310? C.1381. Let a, b, c, and d be different digits. Find their values so that the following sum has the least possible number of divisors, but the sum itself is the greatest possible. C.1382. Fill in a 25×25 grid by using the numbers +1 and -1. Create the products of the 25 numbers in each column and in each row. Could the sum of these 50 numbers be: a) 0 b) 10 c) 17? C.1383. Is there such a triangle in which the heights are 1, 2, and 3 units long? C.1384. You put a plain on each side of a regular, square-based pyramid. How many sections do these 5 planes divide the space?

tasks that will be merged together as one essay with subheadings etc. Detail is needed for all of them. Citations will need to be made too. The assignment brief is attached. P task is the easier bit, M is slightly harder, D is to achieve top grade.

subgame perfect Nash equilibrium? Question 3: In which situations should we need the mixed extension of a game? Question 4: Find, if any, all Nash equilibria of the following famous matrix game: L R U (2,0) (3,3) D (3,4) (1,2) Question 5: What is the difference between a separating equilibrium and a pooling equilibrium in Bayesian games? Question 6: Give another name for, if it exists, the intersection of the players’ best-response « functions » in a game? Question 7: assuming we only deal with pure strategies, the Prisoner’s Dilemma is a situation with: No Nash equilibrium One sub-optimal Nash equilibrium One sub-optimal dominant profile No dominant profile Question 8: If it exists, a pure Nash equilibrium is always a profile of dominant strategies: True False Question 9: All games have at least one pure strategy Nash equilibrium: True False Question 10: If a tree game has a backward induction equilibrium then it must also be a Nash equilibrium of all of its subgames: Tr 2/2 Question 11: The mixed Nash equilibrium payoffs are always strictly smaller than the pure Nash equilibrium payoffs: True False Question 12: Which of the following statements about dominant/dominated strategies is/are true? I. A dominant strategy dominates a dominated strategy in 2x2 games. II. A dominated strategy must be dominated by a dominant strategy in all games. III. A profile of dominant strategies must be a pure strategy Nash equilibrium. IV. A dominated strategy must be dominated by a dominant strategy in 2x2 games. I, II and IV only I, II and III only II and III only I and IV only I, III and IV only I and II only Question 13: A pure strategy Nash equilibrium is a special case of a mixed strategy Nash equilibrium: True False Question 14: Consider the following 2x2 matrix game: L R U (3,2) (2,4) D (-1,4) (4,3) The number of pure and mixed Nash equilibria in the above game is: 0 1 2 3 Exercise (corresponding to questions 15 to 20 below): assume a medical doctor (M) prescribes either drug A or drug B to a patient (P), who complies (C) or not (NC) with each of this treatment. In case of compliance, controlled by an authority in charge of health services quality, the physician is rewarded at a level of 1 for drug A and 2 for drug B. In case of noncompliance, the physician is « punished » at -1 level for non-compliance of the patient with drug A and at -2 level for non-compliance with drug B. As for the compliant patient, drug A should give him back 2 years of life saved and drug B, only 1 year of life saved. When noncompliant with drug A, the same patient wins 3 years of life (due to avoiding unexpected allergic shock for instance), and when non-compliant with drug B, the patient loses 3 years of life. Question 15: You will draw the corresponding matrix of the simultaneous doctor-patient game. Question 16: Find, if any, the profile(s) of dominant strategies of this game. Question 17: Find, if any, the pure strategy Nash equilibrium/equilibria of this game. Question 18: Find, if any, the mixed strategy Nash equilibrium/equilibria of this game. Questions 19 and 20: Now the doctor prescribes first, then the patient complies or not: draw the corresponding extensive-form game (= question 19) AND find the subgame perfect Nash equilibrium/equilibria (=

etween. * A B D 3. Which shows the following numbers in order from least to greatest? * B C D 4. Which is the best name for this group of numbers? * A B D 5. Which point on the number line best represents √3? * A B C For question 6 and 7, write each number in either scientific notation or standard notation. 6. The diameter of Mercury is 4879 kilometers. * 7. The diameter of a bacterial cell called a mycoplasma is about 2 x 10-7 meter. * 8. In which group are the numbers in order from greatest to least? * B C D 9. Greg found the length of a hypotenuse of a right triangle to be √90 feet. Between which two integers does √90 lie? * A B C 10. Which is the best name for this group of numbers? * A C D 11. The water levels of five Texas lakes were measured on the same day in 2010. The table below shows the number of feet above or below normal level for each lake. Which list shows the numbers in the table from greatest to least? * B C D 12. Which numbers from this list are less than -0.94? * B C D 13. The length of a micrometer is approximately 0.00003937 inch. How would you express this in scientific notation? * A B C 14. The National Park Service manages approximately 84,000,000 acres of federal land. How would you express this number using scientific notation? * B C D 15. Seismosaurus is the longest known dinosaur. It measured 1800 inches. How far would 3000 Seismosaurus dinosaurs span if they were placed head to tail? Write your answer in scientific notation. *

self. "Let A, B, C, D be points in this order on the line g and let P be a point in the plane that is not on g." Show, if the inequality |AP|+|DP|>|BP|+|CP| holds for all points P that do not lie on g, that |AB|=|CD|" I appreciate all ideas or solutions :)

tal number of tomatoes d days after the first day of harvest. t=48+15d What is the meaning of the slope in this problem

C D Here is their argument. Given the obtuse angle x, we make a quadrilateral ABCD with ∠DAB = x, and ∠ABC = 90◦ , and AD = BC. Say the perpendicular bisector to DC meets the perpendicular bisector to AB at P. Then P A = P B and P C = P D. So the triangles P AD and P BC have equal sides and are congruent. Thus ∠P AD = ∠P BC. But P AB is isosceles, hence ∠P AB = ∠P BA. Subtracting, gives x = ∠P AD − ∠P AB = ∠P BC − ∠P BA = 90◦ . This is a preposterous conclusion – just where is the mistake in the “proof” and why does the argument break down there?

he efficacy of this spending is therefore relatively important. When it comes to contagious diseases, there are generally two strategies that can be adopted. The first involves prevention, which includes vaccinations to lower or eliminate the risk of contracting a disease. The second involves treatment of those unfortunate enough to get sick, treatment typically requires some form of a drug. Since pharmaceutical companies can produce both vaccines and drugs, we would like to understand the incentives they have to develop each type of medicine. To explore this question, consider a population of 100 consumers, 90 of whom have a low disease risk, say 10%. The remaining ten have a high risk – to make things simple, assume they are certain to contract the disease. In addition, suppose the disease generates personal harm equal to the loss of $100 for each individual when they are infected. Suppose also that pharmaceuticals of either form (vaccines or drugs) are costless to produce (once R & D has occurred) and are perfectly effective Question 2. What price would a profit maximising monopolist charge for a vaccine? What are the monopoly profits on the vaccine? What is the efficient outcome (i.e. SMB = SMC)? What is the welfare under the monopoly and at the efficient allocation? Question 3.Now consider the demand for the drug (assume that the vaccine is not available). Construct the demand function for the drug and plot it on a diagram. What price would a profit maximising monopolist charge for the drug? What are the monopoly profits from the drug? What is the efficient outcome? What is the welfare under the monopoly and at the efficient allocation? Question 4. If the R&D costs of the vaccine and drug are the same, what will the pharmaceutical company do? Explain your answer in terms of the variation in the willingness to pay and the size of the R& D costs. What would a social planner do? Question 5. What are the R&D cost for the vaccine and the R&D cost for the vaccine drug that would make a pharmaceutical company indifferent between developing the vaccine and the drug? Is the social planner indifferent in this case? Explain any difference.

ocity of 12.0 m/s. (a) If its initial velocity is 6.00 m/s, what is its displacement during the time interval? (b) What is the distance it travels during this interval? (c) If its initial velocity is 26.00 m/s, what is its displacement duringthe time interval? (d) What is the total distance it trav- els during the interval in part (c)? Just part d please

that models profit earned is D = n(54 – n) – 10n. I need to find the vertex of this equation, and what does the vertex tell me about this situation.. For what x-values is the function increasing? Decreasing? What does this mean in terms of daily profit for Water World? Rewrite the function in vertex form. . Solve the equation 0 = n(54 – n) – 10n for n. Describe your solution method. How are the solutions from part (e) related to the graph of this function? Are the solutions real or complex? How do you know? What do the solutions from part (e) tell you about this situation?