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Problem Set:Q1 How much will you have in 8 years by investing $350 at the end of every month into an investment that earns 4.8% compounded monthly? Q2 An ordinary annuity consists of 50 semi-annual deposits of $700. What is the future value of the annuity if it earns interest at the rate of 6% compounded semi-annually for the first 15 years and 8% compounded semi-annually for the last 10 years? Q3 An ordinary annuity with an opening bala...
DescriptionWrite three separate MATLAB programs to approximate the sine curve between 0 and 2π using curve fitting by(a) a polynomial curve of power 4;(b) a cubic spline;(c) Lagrange’s interpolating polynomial or Newton’s interpolating polynomial.You may refer to the textbook (Numerical Methods for Engineers by Chapra and Canale) for the algorithms, but I expect that you can work that out yourself given the lecture materials. ...
InstructionsFormulas to use: Combinations, Permutations, Partial Permutations, Factorial, Factorial Permutations, Counting: subsets, distinct subsets, sequences, cardinality of powerset To do: Please justify why you are using a certain rule (i.e. multiplication rule), by correctly using its definition, Break all problems into cases (Proofs with cases: choose between proofs by-cases or If-then statement proofs) Skills: Logica...
Questions: 1) [10 marks] Consider the “mortgage equation” from lecture 1(the slide is copied below) 2) [10 marks] Read the following texts “How Populations Grow: The Exponential and Logistic Equations” 3) [10 marks] Read the following texts Logistic function as a forecasting model: It’s application to business and economics Describe briefly the problems the author had solved ...
Question 1Devise appropriate tests of convergence, and thus explore the merits from a computational efficiency viewpoint the Jacobi, Gauss-Seidel and Successive Over-relaxation (SOR) techniques to solve the PDE for τ = 0.05. You will need to be able to prescribe appropriate criteria of where you place your far-field domains in x = ±∞ and y∞, and prescription of number of unknowns (i.e (L, N) grid points) as well as wor...
Method of Steepest Descent or AscentQuestion 1Write a program, in MATLAB or Python to perform optimization of a 2D polynomial function f(x, y) using the method of steepest descent or ascent.The algorithm is given in the textbook but write it down in pseudo-code first. Use the method of Golden Section for the optimization problem in 1D that is produced as a step in the solution. You will also need to have a function that takes partial different...
Task Short Answer. Answer the indicated question. Given a group of students: G = {Allen, Brenda, Chad, Dorothy, Eric} or G = {A, B, C, D, E}, list and count the different ways of choosing the following officers or representatives for student congress. Assume that no one can hold more than one office. 1) Three representatives, if two must be male and one must be female. Use a tree diagram showing all possible results when...
Task(Fill in the blanks) The symbol called the ________ is used in derivations to explicitly indicate that a ________ has been derived. 1. (Pick one) How many lines should be cited for an application of⊥I? a. one b. two c. three 2. How many lines should be cited for an application of¬I? a. one b. two c. three 3. Can negation introduction (¬I) be used to derive any type of formula other than a n...
Assessment InformationYou will find information about TMAs in the ‘Assessment’ area of the website. Please read that information before beginning work on this TMA. The marks allocated to each part of each question are indicated in brackets in the margin. You may use Maxima to check answers, but it should not be used otherwise to answer TMA questions except where explicitly indicated. TMA answers must show...
Problem 1 - Types of Exams and First Question Difficulty Probability1. A professor gives only two types of exams, “easy†and “challengingâ€. The probability of a challenging exam is 0.80. The probability that the first question on the exam will be difficult is 0.90 if the exam is challenging and is 0.15 if it is easy.a. What is the probability that the first question on you...
InstructionsThere are 30 questions in total, make sure you attempt all and number them correctly on this document and in your working notes. Total = 100 Marks 1. Suppose p is true, q is true, s is false. Find the truth value of (~s?p) ? (q?~s) (4 MARKS) 2. Suppose p is false, s is false, r is true. Find the truth value of ~[(s?p) ? ~r] (4 MARKS) 3. Suppose p is false, q is true, s is true. Find the truth value of...
Part 1 - Tossing Fair and Unfair Dice1. (25 pts) Tossing a fair and unfair die. Suppose you have a 5-sided die, with sides numbered 1, 2, 3, 4, and 5. (a) Write a MATLAB program to simulate the tossing of a 5-sided fair die (i.e., all sides are equally likely), for t =10, 50, 100, 500 and 1000 tosses. Based on the simulation, what is the estimated probability of obtaining an odd number? (b) Suppose X is a random variable denoting the outcome o...
A review of relevant background literature on assessment in mathematics. As a minimum you must include: (i) a brief description of the three recognised main types of assessment (Diagnostic, formative, summative). (ii) What teachers need to take into consideration when implementing different types of assessment (e.g. time spent in terms of knowledge gained about the student's mathematics understanding). (iii) What are some of the advantages/disadv...
(1) The governing equation for the temperature distribution with time on a 2D square plate measuring 1 unit by1 unit is ∂T/∂t = ∂2T/∂x2 + ∂2T/∂y2 , subjected to the Dirichlet boundary conditions for T provided in Fig.1. You are to obtain the following:(a) The temperature contour plot on the square plate with time, say at t=0.01, 0.1 and at steady state. (You can provide contours at other times t...
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