For certain values of the parameters a and b, the fixed point iteration Pn = a p-1+ Pn-1 8. converges quadratically to the fixed point p = 1. The value of a is which of the followings? %3D Select one: О а. 0 O b. 4 O c. 3 O d. -2 O e. 5
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- determine whether or not the solution converges: an=5+2n3/4n+6n3For arbitray values of K and b, when does the maximum growth rate occur (in terms of K and b)? P(t)=(Kt2)/(t2+b) the maximum growth rate occurs at t=____How did you apply the concept of maxima/minima in answering the problem? Angelo, who is in a rowboat 2 kilometers from a straight shoreline wishes to go back to his house, which is on the shoreline and 6 kilometers from the point on the shoreline nearest Angelo. If he can row at 6 kph and run at 10 kph, how should he proceed to get to his house in the least amount of time?
- Suppose M(0) is any value between 0 and k = 100. Can we say anything about long term behavior of the corresponding solutions?In the given question ,, two models R1 and R2 are given for revenue (in millions of dollars) for a corporation. Both models are estimates of revenues from 2020 through 2025, with t= 0 corresponding to 2020. Which model projects the greater revenue? How much more total revenue does thatmodel project over the six-year period? R1 = 7.21 + 0.26t + 0.02t2 R2 = 7.21 + 0.1t + 0.01t2If two resistors with respective resistance R1 and R2 are hooked up in parallel, the net resistance R is related to R1 and R2 by 1/R = 1/R1 + 1/R2. If the resistances are measured in ohms as R1 = 150Ω, R2 = 400Ω, both with a possible error of 10%, what is the net resistance and the maximum possible error in the calculated value of R?
- In 1960, the population of a town was 1414 thousand people. Over the course of the next 50 years, the town grew at a rate of 30 people per year. Hint: let t=0 be 1960, and t=1 be 1961, etc. A) Assuming this continues, what is the population predicted to be in 2020? B) Set up and solve the equation to find in which year the population will reach 16 thousand. Give your answer in a form like 1980 or 1994.A loan L is repaid using increasing payments. The first payment, made at t = 1, is of amount 200,and each subsequent payment increases by a factor of (1.05), with the last payment at t = 20. However, att = 10, the borrower decides to make an additional payment of X, which allow him to halve the size of theremaining payments (t = 11, ..., 20). Determine L and X if the effective interest is 8%.The number of parts produced per hour by a worker is given byN = 4 + 3t2 - t3 Where t is the number of hours on the job without a break. a) If the worker arrives at 8 a.m., at what time will she be at her maximum productivity? b) How many parts would she have produced in the day till she reaches her maximum productivity?
- . Find the general solution, and if an initial value is given, solve the IVP: y" + y = 3r²A car with a constant speed of 21 m/s leaves the finish line 5 seconds after a car with a constant speed of 18 m/s. Answer the following questions: 1.- How long does it take for the second car to catch up with the first? 2.- How many seconds will it take for each of the cars to travel 100 meters? 3.- If both cars left the finish line at the same time, at what time will they meet at the same point? Is it possible?. A woman saved GH¢ 30,000 in a bank A, whose rate was x % per annum and GH¢ 20,000 in another bank B whose interest rate was y % per annum. Her total interest in two years was GH¢ 6,400. If she had saved GH¢ 20,000 in bank A and GH¢ 30,000 in bank B for the same period, he would have gained GH¢ 200 as additional interest. Find the values of X and Y