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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...
LocationYou are going on a dream vacation with five of your closest friends for a week. Since you are taking a math course, your friends asked you to come up with a budget to see how much it will cost each of you. Please identify your location in the US (input in Cell D2) and then determine the total costs (for everyone going) - remember to be thorough so the group does not run out of money. Your expense list must include the...
Newton Raphson MethodQ1. Use the Newton Raphson Method to determine √7 3 correct to 7 decimal places by considering the function ff(xx)= xx3 − 7. Q2 The Colebrook equation is used for turbulent flows through rough pipes. The Colebrook equation is where f is the Darcy friction factor; ε is the roughness height; Rh is the hydraulic radius and Re is the Reynolds number. Use the following values: Re = 4900, &...
Conversion of Portions1. What is the conversion needed to convert from the following amounts to the target portions? a. From 25 portions to 20 portions? b. From 45 portions to 65 portions? c. From 50 portions to 350 portions? d. From 350 portions to 30 portions? 2. In a container of frozen RTS Cream of Celery Soup product, the manufacturer guarantees that the soup contains 1/5 real celery. If the frozen soup yields 2.45 L of soup, what ...
QuestionsSubmission Guidelines - Each problem must be written in a separate page. - Solutions written in LaTeX or other similar word processor are preferred, but neatly hand written solutions are acceptable. If your exam is not clearly written, you may receive no credit or lose points. - Make sure to indicate when you are using a particular result or property that it is not standard or implicitly assumed (such as citing a proposition or the...
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 ...
Word Graphs with Exactly Six Vertices and Nine Edges1. A word graph is a graph where the vertices are three-letter English words and two words are adjacent if and only if they have a different first, second or third letter but the same letter in the other two positions. Draw a word graph with exactly six vertices and exactly nine edges. Label the vertices with the corresponding words but no further justification is needed. 2. A busy univers...
Task Bearing design a. A uni-directional thrust bearing is required to support a load of 500 kN. The start-up load is zero. The shaft diameter is 500 mm and the inside diameter of the pads is 10% greater than this. The bearing will operate at a speed of 3000 rpm. The lubricant available is a mineral oil ISO grade 46 with a viscosity index of 95. A directed lubricant supply will be used with a bearing inlet temperature of 60 ...
Questions: i) A rectangular water tank (see in the figure below) is being filled with water at a constant rate of 20 litres per second. If the base of the tank is 1 metre wide and 2 metres long, determine the rate of change in the height of the water in the tank. Express your answer in cm / sec). ii) The total surface area S of a cone of base radius (r) and perpendicular height (h) is given by the following equation: If (r) and (h) are...
Estimating the Mean Cholesterol Levels of Heart Patients You wish to estimate the mean cholesterol levels of patients two days after they had a heart attack. To estimate the mean, you collect data from 28 heart patients. Justify for full credit.(a) Which of the followings is the sample?(i) Mean cholesterol levels of 28 patients recovering from a heart attack suffered two days ago(ii) Cholesterol level of the person recovering from heart attack s...
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...
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