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Solving Mathematical Problems

3 pages (750 words)

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... I was in a room with 4 other people and wanted to shake everyone's hand, four handshakes would happen. It gets trickier though if I wanted to know how many handshakes there would be if everyone wanted to shake everyone else's hand once. By using diagrams to find out how many handshakes would happen for different numbers of people, a pattern might be found. This pattern could make it much easier to solve the problem for even larger numbers of people. Patterns can be very helpful to find out the answers to mathematical problems.
To find out how many handshakes there would be with 5 people in the room I had to make a diagram. At the top of my diagram I had colored five colored dots represent each p...

Differential Equation problems

3 pages (750 words)

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... is easy to solve part (b) first then look at part (a). (b) Since f '(x) is a solution to (7), it must follow the sign of f(x) 2/3. Since f(x)2 is always positive and 1/3rd root of a positive number is also positive f '(x) should be > or = 0
Since f(a) =0, we have f'(a) also to be zero. Now we can have f(x) be > 0. In this case the function is monotonically increasing, but since f(b) is also zero there must be an abrupt drop down to zero, which is not possible as f(x) and f '(x) are continuously varying function. An abrupt change would mean f '(x) is discontinuous and hence f(x). Thus f (x) must be zero in the given interval.
Now coming to part (a)
If c is with in I then f(c) =0 and from (7) we h...

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Analyse and model engineering situations and solve problems using Ordinary differential equations

10 pages (2500 words)

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... Task Learning Outcome 4 Analyse engineering problems and formulate mathematical model using first order differential equations 1. A heated object is allowed to cool in a room temperature which has a constant temperature of T0: a. Analyse the cooling process. As observed in reality, when such heated object is allowed to cool in a room, the object with an initially high temperature cools to an extent when its temperature becomes relatively bearable to the sense of touch, or that is to say towards a temperature at which the room is similarly felt. This empirical observation coincides to the Newton’s Law of Cooling which states that “the rate of change of the temperature of an object is proportional to...

Mathematical Tasks

8 pages (2000 words)

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... Head: ICT MATHS Discuss your own work on three of the mathematics tasks in Chapters 2, 3 and 4, using no more than one task from any one chapter
Name:
University:
Course:
Date:
Tutor:
Date:
Working on mathematical tasks involving geometric thinking, as experienced in various tasks, falls under different levels of difficult from learner to learner. For example, there are problems those mere calculations in order to arrive at conclusions, while there are problems that need applications of mathematical concepts and problem solving techniques in order to arrive at a solution. These latter problems may be tricky and hard to conceptualize but with a clear basis and knowledge of different types of probl...

Numerical analysis

6 pages (1500 words)

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... analysis The solution of differential equations often can not be limited to simple trivial methods. A number of equations can be solved analytically including systems of equations and equations of higher degree. But nevertheless there exist a big number of real problems where differential equations which describe the state of real-time processes can not be solved using simple differentiation and integration rules. These types of problems (especially systems of differential equations) are solved numerically using a number of similar algorithms which are based on the principles of numerical integration. The definition of the task "solve differential equation" means "integrate differential equation" so ...

Create my own exam

3 pages (750 words)

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... Math Problems Theorem Two triangles, A and B are both drawn with different shapes and are drawn within the same circle with all their edges touching the sides of the circle and one of the sides for each triangle passing through the centre. If the sides of each triangle are measured and summed for each triangle then the resulting value will be equal. That is to say if triangle A sides are found to be o, p, q, and triangle B sides are x, y, z then o + p + q = x + y + z Proof: Suppose triangle A has sides o, p, q and triangle B has sides x, y, z and one of the sides for each triangle passes through the centre of the circles then that those two sides for each triangle will be equal. A line passing...

Tangled Triangles

4 pages (1000 words)

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... the biggest value of the area to perimeter ratio for triangles Scenario: Tangled Triangles. Two are discussing howto find the biggest value of the area: perimeter ratio for triangles. One of them suggests that this can be done with measurements of 40, 60 and 80- but forgets to say what units were used, and whether they were angles or sides.
Which triangle gives the biggest value for the area: perimeter ratio
Investigate further.
Brainstorming
Let us start investigating this problem by looking back in time and history of this problem. It not only makes our study more interesting, it also throws light on the path that we should follow. It is a well-known fact that for an arbitrary closed curve in ...

Algebra Math Problem

6 pages (1500 words)
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... Final Project The system of linear equations may be applied to mixture problems in which itemsof various types or grades are sold at distinct values. This is particularly useful for starting entrepreneurs who consider establishing business on a small-scale with simple calculations carried out. Application: Matthew would like to put up a small coffee-bean store selling two special varieties of coffee – Arabica(M) and Robusta(H). He estimates obtaining profit from each kg of Arabica(M) worth $10.50 and from each kg of Robusta(H) costing $9.25. If he desires to have 2500 kgs of bean-mixture sold for $9.74 per kg, how much of each kind must be present in the mixture? Solution: Let x = the quantity of...

Controller Suggestions for ABC Company

5 pages (1250 words)

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... CASH FLOW MENT Overall risk profile of the company The demand for building products depends on demand for constructions, which is risky because construction can change swiftly following the decline in economic conditions and a rise in interest rates. Furthermore, although dealers of building materials earn steady stream of expenses, receiving payments from customers is sporadic and hence putting the company at a risk of running out of cash. The company also risks uneven cash flow as a result of bad weather, which slows down construction schedules. The company will experience challenges due to increases of prices and shortage of major raw materials used in the manufacturing of building materials;...

A Linear Programming

4 pages (1000 words)

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... Boola Boola Biscuit Company" A Linear Programming (Operation Management) Case Study Linear Programming is an essential decision making tool inProduction and Operation Management. It is used to determine the most effective way of using an organization's limited resources. {Heizer, Jay and Render, Render. "Production and Operations Management" p.240}. In mathematics, linear programming (LP) problems involve the optimization of a linear objective function (i.e., maximize profit or minimize cost) subject to linear equality and inequality contraints. {"Linear Programming." Wikipedia: The Free Encyclopedia}.
The linear problem at hand is a case of finding the best strategy to minimize cost of production a...

Assignment

4 pages (1000 words)

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... Question In your opinion, which of the inferential statistical techniques that you learned would be test the idea of a quantitative model and why? Use specific examples from the field of public affairs. There are various inferential statistical techniques available to test an idea of quantitative model such as correlation, regression analysis, ANOVA, independent samples t (or z) tests and many more. The inferential statistics helps a researcher to conclude beyond the descriptive conclusions of data. There are various quantitative data analysis methods that help in testing the quantitative model. The inferential statistical techniques correlation or bivariate regression analysis are used for...

Calculus for Business Economics

4 pages (1000 words)

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... to Review Problems Chapter 2. As given, the Price of a particular model of calculator is given by (Dollars), after x months from now,so
(a) to get the price after 5 months from now, just substitute x = 5.
(b) The change in the price in the 5th month will be
Price after 5 months - Price after 4 months, or.
(c) Let the price will be $43 after x months. So P(x) = 43. Or . Solve this equation for x.
(d) To know what happens to the price when x becomes very large, we consider the. It follows that after a long period of time the price will become $40.
4.
(a) Given. If we rename x as y, we have. Now we can substitute.
(b) and (c) Similar to part (a).
6. The average daily level of smog in the air is give...

Multiple criteria decision analysis

7 pages (1750 words)
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... Bank Selection using MCDA This project is about Bernard who would does not know the best bank to take a mortgage with. Therefore, he decides to use MCDA to help him select the best bank. He therefore lists the important factor to consider when selecting the bank as: - 1) interest rate 2) Flexibility in payments 3) duration 4) Guarantees. In connection to this the main aim of this project is to use MCDA to solve the problem.
Contents
Contents 3
1.0 Introduction 4
2.0 Aim 4
3.0 Objectives 4
4.0 Background of MCDA 5
5.0 Methodology 5
6.0 Main assumption 5
7.0 Results 6
7.1 Interest rate analysis 6
8.0 Discussion and Sensitivity of results 6
8.1 Multi – Criteria Decission Analysis 6
8.1.1Legal cost. 7
8...

A Study On Cigarette Smoking Among The Teen Population

6 pages (1500 words)

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... Table of contents Introduction Page 3 Research Plan and Aim of the study Page 4 Method of Data Collection Page 5 Mathematical Process Page 6 Survey Results Page 7-9 Analysis of result Page 10-24 Validity Page 25 Conclusion Page 26 References Page 27-28 Appendices Page 29-30 Introduction: Cigarette smoking is strongly linked to heart disease and strokes. Thousands of people die each year of diseases related to their smoking. Smoking is the biggest cause in those diseases, ahead of diabetes, obesity and lack of exercise. Individuals begin their habitual behaviors early in their teenage years. There are a series of social and peer pressures which influence teens to try and become addicted to tobacco....

Cost Benefit Analysis

12 pages (3000 words)
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... Econ 361 DE – Problem Set Two Questions Question a. Use a diagram to illustrate the deadweight loss that, in the absence of government intervention results from information asymmetry. Solution: A deadweight loss refers to specific forms of benefits that consumers or producers lose due to inefficiency within market operations. In most cases such inefficiencies are caused by monopoly pricing or taxation (Brent 89). In other words, a deadweight loss can be termed as the total surplus resulting from market distortion especially from the side of government regulations on prices and in most cases the levied taxes. Asymmetric information can lead to disappearance of markets or rather inefficient allocation ...

Theorem of Pythagoras in Mathematics

12 pages (3000 words)

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... Head: Theorem of Pythagoras in Mathematics The importance of the theorem of Pythagoras in the Historical development of Mathematics
By
_________________________
The importance of the theorem of Pythagoras in the historical development of Mathematics
The Theorem that changed the fortune of Mathematics and Geometry, the Pythagoras Theorem states:
"The square described upon the hypotenuse of a right-angled triangle is equal to the sum of
the squares described upon the other two sides". (1)
The philosophy of mathematics begins with Pythagoras, who later developed Pythagoras Theorem. While believing that mathematics gave us the key to understand reality he proved that mathematics is known a prio...

Statistical Reasoning in public Health

3 pages (750 words)

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... Statistical Reasoning in Public Health HW#4 A 2003 article in the Journal of the American Medical Association1 documents the results of a randomized clinical trial designed to evaluate whether the influenza vaccine is effective in reducing the occurrence of acute otitis media (AOM) in young children. Acute otitis media is an infection that causes inflammation of the middle ear canal. In the study, children were randomized to receive either the influenza vaccine or a placebo. (randomization was done in a 2 to 1 ratio, meaning that two times as many children were randomized to the vaccine treatment as were randomized to the placebo group). The children were followed for one year after randomization,...

Project Evaluation

5 pages (1250 words)
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... Head: PROJECT EVALUATION Project Evaluation School Contents INTRODUCTION 3 ANALYSING THE FEASIBILITY OF THE PROJECT 3 JUSTIFICATION ABOUT THE METHOD USED TO EVALUATE THE PROJECT 4 OTHER FACTORS THE COMPANY MIGHT CONSIDER 6 CONCLUSION 7 Reference List 9 Appendix 10 INTRODUCTION This report analyses one of the projects that Salsbury is analyzing to invest. Salsbury is a nationwide chain of supermarkets and it is evaluating whether it should start a new retail store on the outskirts of Dingwall or not and for this purpose, the report discusses the feasibility of the retail store. The management uses one of the most widely used project evaluation techniques, Net Present Value (NPV) to evaluate the...

Statistical computation of maximum likelihood estimates using R

10 pages (2500 words)

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... calculations of maximum likelihood estimations using the statistical software R. Each question answered directly not in report style R-code
Explanatory comments
Rainfall for January was collected over a period of 80 years in a coastal town.
Variables recorded were (Xi, Yi).
Xi(j): rain or no rain.
Yi(j): amount of rain in mm.
Si: Total Monthly amount of rain in January in year (i).
I year,
J day.
mean amount of rain in wet days
p probability of Rain falls independently on each day
L likelihood for p and
F density
1. Inter Annual-statistics:
Write R-Code to calculate
A. Inter-annual mean of S
B. Inter-annual variance of S
2. First Model
A. Calculate maximum likelihood estimators (p and )
B. ...

Job selection-multiple criteria decision analysis

7 pages (1750 words)
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... Multi-Criteria Decision Analysis for Strategic Decision Making The case study involves Lynn Bamford who is about to graduate from the Department of Information Technology at the University of Technology. For the past few months she has been involved in the job search process. She grew up in Brussels and has many relatives and friends there, so she intends to find a job in a city around Europe. She has excellent curriculum vitae with a high grade point average and a strong record of campus participation in clubs and activities.
As a result, she has had a number of good interviews with various companies. She now has job offers from five companies: Systems Developers, Anderssun Consulting, Computing So...

Responsibility Accounting and Transfer Pricing

4 pages (1000 words)
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... "Metal Press" Your firm uses return on assets (ROA) to evaluate investment centers and is considering changing the valuation basis of assets from historical cost to current value. When the historical cost of the asset is updated, a price index is used to approximate replacement value. For example, a metal fabrication press, which bends and shapes metal, was bought seven years ago for $522,000. The company will add l9 percent to this cost, representing the change in the wholesale price index over the seven years. This new, higher cost figure is depreciated using the straight-line method over the same l2-year assumed life (no salvage value). Required: a. Calculate depreciation expense and book value...

Structures, Fluid Mechanics, Materials, and Soil Mechanics

11 pages (2500 words)

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... Fluid Mechanics, Materials, and Soil Mechanics
QUESTION 1
First determine whether the structure is statically determinate or indeterminate using 2n= m + r, where n= joints, m= members, r=reactions
In this case, n=11, m=19, r=3 thus 2x11=22=19+3 therefore the structure is statically determinate
Let the length of each of the 5 bays be x,
Determine the reactions at the supports = (1+1+1+1+1)/2 = 2.5 units, simply because the truss is symmetrical about the apex.
1
F 1
1
1 D H 1
C J
A B E G I K ...

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