pros and cons of risk probability and impact assessment, in Qualitative risk analysis?

find the polar presentation of (j-square root of 3)

Problem 1: Consider the following Initial Value Problem (IVP) where ? is the dependent variable and ? is the independent variable: ?′=sin(?)∗(1−?) with ?(0)=?0 and ?≥0
Note: the analytic solution for this IVP is: ?(?)=1+(?_0−1)?^cos(?)−1

Part 1A: Approximate the solution to the IVP using Euler’s method with the following conditions: Initial condition ?_0=−1/2; time step ℎ=1/16; and time interval ?∈[0,20]
+ Derive the recursive formula for Euler’s method applied to this IVP
+ Plot the Euler’s method approximation
+ Plot the absolute error between the approximation and the exact solution using a semilog plot

Coding errors, please type out.

Problem 1: Consider the following Initial Value Problem (IVP) where ? is the dependent variable and ? is the independent variable: ?′=sin(?)∗(1−?) with ?(0)=?0 and ? ≥ 0

Note: the analytic solution for this IVP is: y(t) = 1+(y_0 - 0)e^ cos(t)-1

Part 1B: Approximate the solution to the IVP using the Improved Euler’s method with the following conditions: Initial condition ?0=−1/2; time step ℎ=1/16; and time interval ?∈[0,20]
+ Derive the recursive formula for the Improved Euler’s method applied to this IVP
+ Plot the Improved Euler’s method approximation
+ Plot the absolute error between the approximation and the exact solution using a semilog plot

I'm having problems correctly codding these steps. Please type out.

How many ways are there for any number of people to sit in a row of 7 chairs if no two people sit next to each other? Devise a recurrence relation and explain.

Matt and Lisa are driving together to a shopping mall, looking forward to buying some clothes. Matt wants to stop by Sports Authority to buy the new jersey of his favorite hockey team, whereas Lisa wants to go to Banana Republic to buy a new outfit. Both find the idea of going together to both stores a little boring, so they agreed beforehand to split and go individually to their desired store. After shopping individually, they decide to meet at Applebee’s to grab some food before leaving. The Banana republic, the Sports Authority shops and the Applebee’s are located at (2, 3), (5, 5) and (1, 4), respectively. Suppose that the parking lot is located in a straight line given by the function y = 1/3x − 1. That is, customers can park in the mall as long as they do it on top of the line. 3-1. Assuming rectilinear distances, where should they park the car in order to minimize the total distance they must walk? Explain your results. 3-2. Suppose Matt is recovering from a leg injury, so they decided that Matt’s walking distance is twice as valuable as Lisa’s walking distance. Find the new optimal parking spot.

Systolic blood pressure was measured in a group of 30 patients diagnosed with hypertension:

1. Relying on this data find:
   • the median
   • the lower and upper quartiles
   • the 90^thpercentile
   • the interquartile range
   • the mean
   • the standard deviation
2. Discuss which approach (the mean and standard deviation or the median and interquartile range) better reflects the central tendency and variation for the given data.

​(Cost of​ short-term bank loan​) On July​ 1, 2015, the Southwest Forging Corporation arranged for a line of credit with the First National Bank​ (FNB) of Dallas. The terms of the agreement call for a $140,000 maximum loan with interest set at 1 percent over prime. In​ addition, the firm has to maintain a 19 percent compensating balance in its demand deposit account throughout the year. The prime rate is currently 14 percent. Note​: Interest is not paid in advance​ (discounted).

a. If Southwest normally maintains a $26,600 to $40,600 balance in its checking account with FNB of​ Dallas, what is the effective cost of credit under the​ line-of-credit agreement when the maximum loan amount is used for a full​ year?

b. Compute the effective cost of credit if the firm borrows the compensating balance and the maximum possible amount under the loan agreement.​ Again, assume the full amount of the loan is outstanding for a whole year.

There are 16 students in a class. Each student has either a bicycle or a      tricycle. There are exactly 37 wheels altogether.

How many bicycles do the students have?

Please prove

1. Every positive integer is a product of prime numbers.

2. If a and b are relatively prime, and a|bc, then a|c.

3. The division algorithm for F[x]. Just the existence part only, not the uniqueness part

6. Air pollution problem. Consider an airshed in which there is one major contributor to air pollution--a cement-manufacturing plant whose annual production capacity is 2.500,000 barrels of cement. Figures are not available to determine whether the plant has been operating at capacity. Although the kilns are equipped with mechanical collectors for air pollution control, the plant still emits 2.0 lb of dust per barrel of cement produced. There are two types of electrostatic precipitators that can be installed to control dust emission. The four-field type would reduce emissions by 1.5 lb of dust/barrel and would cost $0.14/barrel to operate. The five-field type would reduce emissions by 1.8 lb of dust/barrel and would cost $0.18/barrel to operate. The EPA requires that particulate emissions be reduced by at least 84%. How many barrels of cement should be produced using each new control process to minimize the cost of controls and still meet the EPA requirements1?

Using two-phase method to solve this linear programming problem.