The solution of the system is the intersection point of the graphs of the given equations. II. Solution of the System A system of equations can be solved through Eliminations method, Substitution method or by a Graphical method. A. By elimination method Example 1: Solve the system of equation by elimination method x2 + y2 = 4 - eq’n (1) x2 - y2 = 4 - eq’n (2) Assigning equation (1) & (2) and eliminate y variable by adding the two equations, we have 2x2 = 8, and solving for x x2 = 4 → x = ±2 Using the value of x and solving for y using eq’n (1) (±2)2 + y2 = 4 4 + y2 = 4 y2 = 4 - 4 y2 = 0 → y =
INTERNATIONAL ACADEMY AMMAN Extending the Domain of the Gamma Function Math Exploration Laila Hanandeh 11/10/2014 Table of Contents: Aim 2 Factorials 2 The Zero Factorial 2 Deducing the Gamma Function 3 Working Out Example 6 Analytical Continuation 9 Gamma Function Graphs 10 Real Life Applications 11 Aim: The Gamma Function is defined as an extension of the factorial function in which its argument is for complex and real numbers. (1) However, through my exploration I will determine a method to extend the domain of the gamma function to include complex numbers; this will be done through exploring the gamma function and the utilization of a process called analytical continuation. However before proceeding,
Mathematicians figured out the magic sums by using a formula including variables that can be used to find every magic constant in every magic square. The magic number would equal [n(n2 + 1)] / 2. N still equals the order. If I tried to figure out the magic constant for the order 4 magic square, I would do (4(42 + 1)/2 = (4(16+1)/2 = (4(17))/2 = 68/2 = 34. The formula worked exactly as it was supposed to and the magic constant is 34.
For example, it helps you spot right triangles and solve for the third side in a triangle. This proved to be a valuable skill when dealing with comparatively primitive geometry problems in elementary school. In this exploration I will investigate two ways how a Pythagorean triple can be generated. First, the Euclid’s theorem of generating these triplets will be explored and proved that the values generated, with the help of this formula, are in fact a Pythagorean triple corresponding to sides of a right triangle. Next, the Berggren’s Parent/Child relationships will be explored.
This equation gives us the point P(A) on sphere S corresponding to point A on the complex plane Z. The general equation for finding point (a,b,c) on S corresponding to point (x,y) on Z which is given being (Proof 2) Another way of looking at line L would be by connecting point ∞ to point P(A) in figure 3. Line L can be defined as: (University of Oxford, 2012) This is the same line L as in the first proof but in a different perspective that will help in explaining the next proof. The vector v, (a¦█(b@c-1)) is the vector used to move from point ∞ to point P(A). This can be found by subtracting the coordinates of point P(A) by the coordinates of point ∞.
History of root finding The history of root finding dates back during the Islamic Golden Age. The use of the word “root” originates from an Arabic mathematician called Al-Khwarizmi who is also coined the word “algebra” during writing his first algebra book. The root findings were started when he realize the variable as the root of which an equation grows. By solving the equation, we could find the roots. It is specifically
Monty Hall Problem: a mathematical exploration of the problem Marlou Dinkla 000768-008 Math Internal Assessment American School of The Hague Word Count: 2500 If you are into brainteasers you might have come across the Monty Hall problem. Another place were you might have stumbled upon it is on science programs like Mythbusters. In talking to my brother about his university math class, we came upon enigmas that involved math. Remembering back to my days in front of the television, I was reminded of a Mythbusters episode were they tried out the Monty Hall problem. Unbeknown to me at the time, was the ability to apply statics in finding out the best course of action.
Patrick Lewis, pencils, scratch paper Grouping Students will work in pairs so as they could discuss how to solve a problem in the poem. b) Reading (the activity was retrieved from https://betterlesson.com/lesson/613848/cells-the-basic-building-blocks-of-living-things) Students will participate in close reading of “Cells that Make Us” article. Students annotate text by first marking the text and then writing and drawing in the margins using the Avid strategy (Attachment 6) After that, students answer the questions (Attachment 7). The purpose of this activity is to reinforce the concept that living things are made of cells, the concepts of unicellular and multicellular organisms, and also connect the Microscope Mania activity with theory. Materials Cells That Make Us articles for each student Attachment 7), pencils, dictionaries Grouping At this point I would like students to work individually.
The isoperimetric problem —that of finding, among all plane figures of a given perimeter, the one enclosing the greatest area —was known to Greek mathematicians of the 2nd century BC. The term has been extended in the modern era to mean any problem in variational calculus in which a function is to be made a maximum or a minimum, subject to an auxiliary condition called the isoperimetric constraint, although it may have nothing to do with perimeters. For example, the problem of finding a solid of
The puzzle described above is called a Sudoku of rank 3. A Sudoku of rank n is and n2×n2 square grid, separated into n2 blocks, each of size n×n. The numbers used to fill the grid in are 1, 2, 3, ..., n2, and the One Rule is still in effect. The following is an example of a completed Sudoku