PYTHON A perpetuity pays a coupon value of C each and every period forever. Given a discount rate of r, the value of a perpetuity is given by V=∑t=1∞C(1+r)t Thus, the value of a perpetuity is described by an infinite series. Mathematically, this summand can be reduced to V=C/r We'll refer to the first equation above as the "summation formula" and the second equation as the "shortcut formula". That is, the summation formula uses an infinite series, whereas the shortcut formula expresses the value of a perpetuity as simply the ratio of the coupon value to the discount rate. Create a function that returns the value of a perpetuity using the shortcut formula. def shortcut_formula(C, r):

PYTHON A perpetuity pays a coupon value of C each and every period forever. Given a discount rate of r, the value of a perpetuity is given by V=∑t=1∞C(1+r)t Thus, the value of a perpetuity is described by an infinite series. Mathematically, this summand can be reduced to V=C/r We'll refer to the first equation above as the "summation formula" and the second equation as the "shortcut formula". That is, the summation formula uses an infinite series, whereas the shortcut formula expresses the value of a perpetuity as simply the ratio of the coupon value to the discount rate. Create a function that returns the value of a perpetuity using the shortcut formula. def shortcut_formula(C, r):

C++ Programming: From Problem Analysis to Program Design

8th Edition

ISBN:9781337102087

Author:D. S. Malik

Publisher:D. S. Malik

Chapter10: Classes And Data Abstraction

Section: Chapter Questions

Problem 19PE

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Note that for this question, you can in addition use ``land'' for the symbol ∧ ``lor'' for the symbol ∨ ``lnot'' for the symbol ¬. Given the following three sentences:A) Every mathematician is married to an engineer.B) A bachelor is not married to anyone.C) If George is a mathematician, then he is not a bachelor. a) Convert A,B,C into three FOL sentences, whereMn(x): x is a mathematician.Er(x): x is an engineer.Md(x,y): x is married to y.Br(x): x is a bachelor.george: George is a constant. b) Show that A does-not-entail C. (Hint: Consider defining an interpretation I such that I models A, but does-not-model C.)c) Show that {A,B} entails C. (Hint: For a given interpretation I, consider two difference cases, the case where Mn(george) is true, and the case Mn(george) is false. For both cases, argue that it is always that I models C).d) Convert A,B, lnot C into a set of clausal forms, number your clauses. (Note that C is negated here!) e) Derive the empty clause from the set of clauses…
Consider the problem of making change for n cents using the fewest number of coins. Assume that we live in a country where coins come in k dierent denominations c1, c2, . . . , ck, such that the coin values are positive integers, k ≥ 1, and c1 = 1, i.e., there are pennies, so there is a solution for every value of n. For example, in case of the US coins, k = 4, c1 = 1, c2 = 5, c3 = 10, c4 = 25, i.e., there are pennies, nickels, dimes, and quarters. To give optimal change in the US for n cents, it is sufficient to pick as many quarters as possible, then as many dimes as possible, then as many nickels as possible, and nally give the rest in pennies. Design a bottom-up (non-recursive) O(nk)-time algorithm that makes change for any set of k different coin denominations. Write down the pseudocode and analyze its running time. Argue why your choice of the array and the order in which you fill in the values is the correct one. Notice how it is a lot easier to analyze the running time of…
Consider the problem of making change for n cents using the fewest number of coins. Assume that we live in a country where coins come in k dierent denominations c1, c2, . . . , ck, such that the coin values are positive integers, k ≥ 1, and c1 = 1, i.e., there are pennies, so there is a solution for every value of n. For example, in case of the US coins, k = 4, c1 = 1, c2 = 5, c3 = 10, c4 = 25, i.e., there are pennies, nickels, dimes, and quarters. To give optimal change in the US for n cents, it is sufficient to pick as many quarters as possible, then as many dimes as possible, then as many nickels as possible, and nally give the rest in pennies. Design a bottom-up (non-recursive) O(nk)-time algorithm that makes change for any set of k different coin denominations. Write down the pseudocode and analyze its running time. Argue why your choice of the array and the order in which you ll in the values is the correct one.
Consider the problem of making change for n cents using the fewest number of coins. Assume that we live in a country where coins come in k dierent denominations c1, c2, . . . , ck, such that the coin values are positive integers, k ≥ 1, and c1 = 1, i.e., there are pennies, so there is a solution for every value of n. For example, in case of the US coins, k = 4, c1 = 1, c2 = 5, c3 = 10, c4 = 25, i.e., there are pennies, nickels, dimes, and quarters. To give optimal change in the US for n cents, it is sufficient to pick as many quarters as possible, then as many dimes as possible, then as many nickels as possible, and nally give the rest in pennies. Prove that the coin changing problem exhibits optimal substructure. Design a recursive backtracking (brute-force) algorithm that returns the minimum number of coins needed to make change for n cents for any set of k different coin denominations. Write down the pseudocode and prove that your algorithm is correct.
More and more seafood is being farm-raised these days. A model (differentialequation) used for the rate of change for a fish population, P(t) in farmingponds is given by P'(t) = b(1-(P(t)/Pm)) - hP(t) where b is the birth rate, PM is the maximum number of fish the pond cansupport, and h is the rate the fish are harvested. Write a python code that implements the Forward Euler method to solve thedifferential equation Suppose that the carrying capacity PM = 20, 000 fish with a birth rateof 6% and a harvesting rate of h = 0%, use your Python code to findand plot the numerical solution for the first 400 days for different valuesof y0. Pick y0 < 20, 000, y0 > 20, 000. Don’t forget to label all your plotswith x and y axes label, titles and legends. Use a time step ∆t = 0.1
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Let l be a line in the x-yplane. If l is a vertical line, its equation is x = a for some real number a. Suppose l is not a vertical line and its slope is m. Then the equation of l is y = mx + b, where b is the y-intercept. If l passes through the point (x₀, y₀), the equation of l can be written as y - y₀ = m(x - x₀). If (x₁, y₁) and (x₂, y₂) are two points in the x-y plane and x₁ ≠ x₂, the slope of line passing through these points is m = (y₂ - y₁)/(x₂ - x₁). Instructions Write a program that prompts the user for two points in the x-y plane. Input should be entered in the following order: Input x₁ Input y₁ Input x₂
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Suppose we have a nice young couple who borrow $700000 from the bank, at an annual interest rate of3.124%. The mortgage is a 30 year loan, so they need to pay it off within 360 months total. Our happycouple decide to set their monthly mortgage payment at $2000 per month. Will they pay off the loan intime or not?Note that the monthly balance will be calculated asbalance = (im × previous balance) - monthly paymentwhere the convert annual interest to a monthly multiplier im is calculated as im = (1 +i)1/12 and i = annualinterest rate.Write a loop for track the total payment in 360 months so that we can evaluate if the couple can pay off theloan. Write in R Please and thank you.
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