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Patterns Withing Systems of Linear Equations...? School School Crest Mathematics HL Portfolio Type I PATTERNS WITHIN SYSTEMS OF **LINEAR** **EQUATIONS** Candi Candi Number Examination Session Contents Introduction 2 Part A. System of **linear** **equations** formed with arithmetic progressions. 5 Arithmetic progressions 5 Constants in a system of **linear** **equations** 5 Searching for a pattern 6 Pattern repeated in other systems 8 Graphing **equations** with arithmetic progress coefficients 10 Generalize result for systems 11 Extension to systems of **linear** **equations** 13 Part B. System of **linear** **equations** formed with geometric...

16 Pages(4000 words)Math Problem

Linear and Non Linear Programming..., the manager will be in trouble. Regression, for example, may help the manager to forecast his sales based on past record, but he must make sure that the user of his product has not undergone any changes in taste and preference. Therefore, an econometric model may prove a better aid than pure mathematics and statistics.
**Linear** and Non **linear** programming:
In **linear** programming, the statement of the optimisation (maximisation or minimisation, as the case may be) problem runs in a **linear** form where these variables are restricted to values satisfying a system of **linear** constraints, i.e., a system of **linear** **equations**, and...

7 Pages(1750 words)Essay

SYSTEM OF LINEAR EQUATIONS slp 3...System of **Linear** **Equations** A system of **linear** **equations** allows us to solve for variable by the addition of more information (additional **equations**). Foe example, if we eat in a fast food restaurant and we order 4 cheeseburgers and 3 orders of French fries, and the bill comes to $18, the **linear** **equation** would be 4X + 3Y = 18 where X = cost of a cheeseburger
Y = cost of French fries
$18 = total cost
However, there is not enough information to determine the cost of each cheeseburger, or an order of fries. In fact, theoretically there are an infinite number of solutions. However, if we return to the...

2 Pages(500 words)Speech or Presentation

Linear Correlation...This study tests the correlation between chief executive officers (CEO) salaries and the degree of success of a company. The data of CEO Salaries andtotal Revenue in 2006 was collected for different organization from various respective companies. The data comprised 25 different companies of different size and market capitalization. It was expected to find strong positive correlation between CEO salaries and organization total revenue. Statistical analysis was conducted to conclude evidence in this relationship.
Null Hypothesis: (Ho)
There is no correlation between chief executive officer salaries and their respective company net revenues.
Alternative Hypothesis: (HA)
Chief executive officer salaries are positively correlated... study tests...

2 Pages(500 words)Essay

Solving Equations...In this project, Bluman (2004, p. 331) challenged students to examine an **equation**, x2 – x + 41, which purportedly yields prime numbers. Students choose numbers to substitute to x in the formula and observe if prime numbers occur. An added challenge was to venture into finding a number, which when substituted in the given **equation**, will result in a composite number.
It is presupposed that a prime number is one whose factors are itself and 1, is common knowledge. On the other hand, a composite number may not be that much of a common knowledge. A definition is thus, provided: a composite number is “any whole number greater than one that is not a prime number … [it] always has at least one divisor other...

4 Pages(1000 words)Assignment

Linear Programming...Summary Brass Ltd. is in need of an optimal solution to its product manufacturing problem. The problem involves manufacturing of two products amid a number of constraints such as availability of capacity, regulations on maximum output and controlled selling prices. The purpose of the report is to find an optimal solution to this problem using a **linear** programming model. The model has been solved using excel solver and the optimal solution is obtained. Further, a sensitivity analysis has been used to consider the impact of capacity increase on profitability. The report concludes with a few recommendations.
1. Problem Statement
Brass Ltd. manufactures two products named Masso and Russo. These products require machining and...

5 Pages(1250 words)Assignment

Graph key features of functions, linear equations and linear inequalities...Difference Between a **Linear** **Equation** and a Function. A **linear** **equation**, y = mx + b, refers to an **equation** which exhibits a **linear** relationship between the domain or set of x-values and the corresponding range or set of y-values. **Linear** **equations** are normally first degree with respect to both ‘x’ and ‘y’ except in case where x = constant in which the degree of ‘y’ is zero and ‘x’ remains the same at any value of ‘y’ and in case where y = constant in which the slope is zero as well as the degree of ‘x’. All **linear** **equations** are function.
Examples of a...

2 Pages(500 words)Essay

Equations.... Explain why your example does not model a function.
A function is not modelled in this example because of the repeating value of ‘x’ in ordered pairs (8, -7) and (8, -1) which fail to show the correspondence that must be one-to-one for the relation to be considered a function.
Part 2
f. Select any two integers between -12 and +12 which will become solutions to a system of two **equations**.
The two integers are: 3 and 8
g. Write two **equations** that have your two integers as solutions. Show how you built the **equations** using your integers. Your solution and **equations** should not be the same as those of other students or the textbook. There are...

1 Pages(250 words)Assignment

Quadratic equations...Can you think of examples of processes that could be modeled with quadratic **equations**? In the real world, ‘Quadratic **Equations**’ can prove useful in a number of ways as –
(1) Modeling costs for a general store –
In C(x) = -0.03x2 + 57x + 310, for instance, the independent variable ‘x’ may refer to the number of materials bought which a store needs in order to produce sellable items. These materials are worth the variable cost C(x) with fixed cost of $310. Since the parabolic curve opens downward, as characterized by the negative leading coefficient, one manages to determine that a maximum cost is reached when x = -57/[ 2(-0.03) ]. The cost may be predicted to decline once the store decides to...

1 Pages(250 words)Assignment

Molecular and ionic equations...s Post-Laboratory Assignment Molecular and ionic **equations** Step1 Molecular **equation** Cu(s)+4NHO3 (aq) Cu(NO3)2 (aq)+2NO2 (g)+2H2O (g)
Ironic **equation**
Cu(s)+4H+(aq)+4NO3-(aq) Cu2+(aq)+2NO3-(aq)+ 2N3+(aq)+4O2-(aq)+ 2H2O (g)
Step 2
Molecular **equation**
Cu(NO3)2 (aq)+2NaOH(aq) Cu(OH)2 (s)+2NaNO3 (aq)
Ionic **equation**
Cu2+(aq)+ 2NO3-(aq)+2Na+(aq)+2OH-(aq) Cu2+(aq)+ 2OH-(aq)+2 Na+(aq)+ 2NO3-(aq)
Step 3
Molecular **equation**
Cu(OH)2 (s) CuO(s) +H2O(g)
Ionic **equation**
Cu2+(aq)+ 2OH-(aq) Cu2+(aq)+O2-+ H2O(g)
Step...

1 Pages(250 words)Assignment