The usual letter for the unknown number is. A real problem can be written as: This is called an equation because there is a sign. In order to find the value of the unknown number, algebra’s rules can do whatever it likes to this equation as long as it does the same to both sides of the equation. So far it has had equation with a single unknown number. What if it has two unknown numbers? In fact, an equation with two unknown has an infinite numbers of pairs of answer. To fix a single pair of number as the answer, it needs another equation. A pair of equation, each with two unknown numbers is called simultaneous equations. They can be solved together to give the values for the unknowns that satisfy both equations simultaneously. This paper contains a mathematical research about systems of linear equation when their coefficients obey arithmetic or geometric progressions. An arithmetic progression is a sequence of numbers where each number is a certain among larger than the previous one. The numbers in the sequence are said to increase by a common difference, d. For example: is an arithmetic progression where the. The term of this sequence is. On the other hand, a geometric progression is a sequence where each number is times larger than the previous one. is known as the common ratio of the progression. The term of a geometric progression, where is the first term and is the common ratio, is: . For example, in the following geometric progression, the first term is , and the common ratio is : the term is therefore. The purpose of this portfolio is to show how with the aid of technology using appropriate computer software likes Autograph and Maxima packages (see Figure 1) is quick and easy to get graphical representations of algebraic equations. Thus, how in many situations, the graphs offers much more insight into the problem than does the algebra. Part A will consider the patterns within systems of linear equations:, where and are in arithmetic progression. While, in Part B the same coefficients obey geometric progression. Part A. System of linear equations formed with arithmetic progressions. Arithmetic progressions In algebra, letters are used in place of numbers that are not known. The usual letter for the unknown numbers are or . . The numbers are constants in an equation, for example: For instance in the above equation, and are known as constants in the equation. It says that the constant and form a arithmetic progression if they have a common difference, such as: Constants in a system of linear equations Given the system of linear equations. The coefficients are detected as follow: Examining the first equation, it sees a pattern in the constants of the equation. i.e. is the constant preceding the variable , and precede and the equation equals 3. The constant have a common dif
Algebra is one of the fascinating fields of mathematics, because algebra allows the finding of unknown numbers from information given. In algebra, letters are used in place of numbers that are not known. These letters are then manipulated in accordance with certain rules until an answer appears…
Population Trends in China
China has been documented as the world’s most populous country, with a population of about 1.3 billion, which is about a fifth of the world’s population. The rapid growth in population has become a concern to the government, such that it has introduced various measures to curb the rate of growth.
This then limits the values for a function where there is only value of x for every y whereas, the linear function gives unlimited values for both x and y as one tries to solve for such values by substituting assumptions for x to get the value of y. As mentioned earlier, functions and linear equations form lines when they are plotted on graphs so that from this point of view, it is concluded that a function is a linear equation and vice versa.
The student has selected a very good example of a manufacturing concern that implements the job order costing system in order to account for the cost of every job completed. In airplane manufacturing, each job, which is supposedly the complete manufacturing of a plane, requires substantial cost which primarily include material and highly skilled technical cost.
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?
The Hotpoint Front Control Dishwasher in White is $289.00 at Home Depot. It is not classified as energy efficient. The GE 24in. Front Control Dishwasher in Black with Steam PreWash is on sale this week for $359.10 at Home Depot, from a normal price of $399.00, and is classified as energy efficient.
Analyse the cooling process. Based on real life experience, an object subjected to heat and eventually placed in a region of lower temperature naturally undergoes cooling. In its heated state, we know that such object contains energy which flows out of it once there occurs temperature difference between it and the environment within which it is exposed.
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.
The co-ordinates of A and B are (5250000, 5250000) and (6, 6) respectively. The value of the objective function at these points is 0.45 X 5250000 = 2362500 and 2.7 respectively. The value of the objective function at the points of ray AD beyond point A would be 0.2x + 0.25(10500000 - x) i.e.
Based on the graph, significant difference in red cell folate levels exists between Groups I and II. A significant difference may also exist between Groups I and III. However, there is little difference in mean folate levels between II and III.
The data satisfies the assumption of independence.