yards, bouncing back from a disappointing year. Strangely, Smith ended his last season with the same rushing total as his rookie season. I plotted these points in a graph in an excel document and created a line of best fit. This line was a cubic equation (f(x) = 1.4228x3 - 8533.3x2 + 2E+07x - 1E+10). To calculate the first derivative, I found the average rate of change of Emmitt Smith’s annual rushing yards from the two years surrounding the year I was deriving. Smith’s yards per year had an increasing
Solution of the Cubic Equation The history of any discipline is full of interesting stories and sidelines; however, the development of the formulas to solve cubic equations must be one of the most exciting within the math world. Whereas the method for quadratic equations has existed since the time of the Babylonians, a general solution for all cubic equations eluded mathematicians until the 1500s. Several individuals contributed different parts of the picture (formulas for various types of cubics)
independently, the method is now known as Newton-Raphson method. Problem Statement Newton-Raphson method is of use when it comes to approximating the root or roots of an equation. For a normal quadratic equation there is a well known formula to find the roots. There is a formula to find the roots of a 3rd and fourth degree equation but it can be troubling to find those roots, but if the function f is a polynomial of the 5th degree there is no formula that can enable us to find the root...
Cubic equations were known since ancient times, even from the Babylonians. However they did not know how to solve all cubic equations. There are many mathematicians that attempted to solve this “impossible equation”. Scipione del Ferro in the 16th century, made progress on the cubic by figuring out how to solve a 3rd degree equation that lacks a 2nd degree. He passes the solution onto his student, Fiore, right on his deathbed. In 1535 Niccolò Tartaglia figures out how to solve x3+px2=q and later
Portfolio Project Alex Abel Table of Contents Title 1 Table of Contents 2 Matrices 3 Solving Systems of Equations 4 Solving Systems of Equations Cont. 5 Matrices Examples 6 Matrices Examples Cont. 7 Set Theory 8 Set Theory Examples 9 Equations 10 Equations 11 Equation Examples 12 Functions 13 Functions Cont. 14 Function Examples 15 Function Examples
tables, cubes, and cube roots. Furthermore they were able to figure out the area of a right triangle, a rectangle and divide a circle into 360 degrees. Later on they would put together some of the ideas that make up the Pythagorean Theorem and quadratic equations.” ¹ “Sumerian mathematics were based on a system of sexagesimal or 60 numeric system which could be counted physically using the five fingers and 12 knuckles on one hand. In addition, the system used place values where digits were written in
Why Do We Teach Algebra? Until recent history, mathematics had not been taught to the general population. Only those who were rich, powerful, and/or politically connected were given the opportunity to study math beyond basic counting operations. Many of my junior high students are excited about the prospects of returning to this situation. I have the opportunity to teach remedial math and math study skills courses for a local university. Many of the college students with whom I am involved are going
A civilization is recognized as such by its form of written language. For this reason, the earliest civilization is recognized in the region of Mesopotamia with their language of Cuneiform. This ancient form of written language was inscribed on clay tablets that still remain in tact and are being salvaged hundreds of thousands of years later. Even more impressive than just writing the language, however, is the ancient Babylonians’ early mathematical discoveries. These were also recorded with cuneiform
Forgetfulness can be seen in many different lights; it can be seen a bad thing, or a good thing. In the poem “Forgetfulness” by Hart Crane, the speaker utilizes similes and metaphors to convey ideas about forgetfulness in order to develop the theme; in the poem by Billy Collins with the same name, the speaker utilizes personification and irony to convey ideas about forgetfulness to develop the theme. In the poem “Forgetfulness” by Hart Crane, the speaker uses similes and metaphors to convey ideas
Abstract—This paper is a report on the mathematics and the mathematicians of The Renaissance. During this time period, many significant advancements in mathematics occurred in many areas of mathematics, including algebra, trigonometry, and calculus. Similarly, it was during this time, due to the impending need to learn the mathematics of intricately complex and rather precise calculation, in which the abacist came into existence. Noteworthy as well are the many mathematicians who apported the mathematical
Investigating the Relationship of the Dots Inside a Shape of Different Sizes AIM: I have been set a task for my coursework to find out the relationship of the dots inside a shape of different sizes. PLAN:I have planned to use a specific quadrilateral shape for my investigation in which lines will be 45o (diagonal), one dot to the other; touching each others ends and being closed from all sides. I will be using the following technique for my investigation. First of all I will commence with
Vedic Mathematics And Sutras Related To Mathematics Among four Vedas Rig Veda is the root for Vedic mathematics which is an ancient method. It consists of 16 basic formulas also called sutras or aphorisms and 14 sub formulas. During the early part of the 20th century a Hindu scholar and mathematician, Jagadguru Swami Sri Bharati Krishna Tirthaji Maharaja presented this [10]. The meaning word "veda" is "knowledge" in sanskrit. Famous Indian Mathematicians like Aryabhatta, Brahmagupta, and Bhaskara
complex, such as with cubic and quadratic functions, mathematicians call upon more convoluted methods of finding roots. For many functions, there exist formulas which allow us to find roots. The most common such formula is, perhaps, the quadratic formula. When functions reach a degree of five and higher, a convenient, root-finding formula ceases to exist. Newton’s method is a tool used to find the roots of nearly any equation. Unlike the cubic and quadratic equations, Newton’s method – more accurately
develop foundation to graph and solve quadratic equations (Larson, Boswell, Kanold & Stiff, 2007). Applicable California Common Core Content Standards for Mathematics are moderately vigor and requires students to: 1. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. (Common Core Standard A-SSE-3b) 2. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and
graphically and solving quadratic equations in the complex number system. With these skills and concepts, I was able to apply them to real-world situations. This portfolio shows the various methods to determine the zeros of a quadratic functions. I had learned the four different methods: solve by factoring, square rooting, completing the square, and using the quadratic formula. If an equation is factorable, all four methods can be used to determine the zeros. If an equation is not factorable, the
I have used the TI-84 graphic display calculator, the software Geoegebra and Microsoft Excel to do my calculations. I have even investigated the values of D, for polynomials of higher powers and tried to come up with a general solution for all equations. I have been able to do this portfolio from the knowledge learnt from classroom discussions and through various other resources. Question 1 “Consider the parabola y = (x−3)2 + 2 = x2−6x+11 and the lines
results I know. Pattern Number Number of Squares 1st Difference 2nd Difference 1 1 4 4 2 5 8 3 13 4 12 4 25 The 2nd difference is constant; therefore the equations will be quadratic. The general formula for a quadratic equation is an2 + bn +c. The coefficient of n2 is half that of the second difference Therefore so far my formula is: 2n2 + [extra bit] I will now attempt to find the extra bit for this formula. Pattern Number
graphs in the program. After data collection, a linear fit and a quadratic curve was tested upon the graph of distance vs. time. It was found out that a quadratic curve would fit better for the distance vs. time graph rather than a linear fit. This shows that the distance follows a parabolic curve as time progress during a free fall. This is shown by the equation X = X0 + V0t – 1/2gt2, or D= V0t – 1/2gt2 .A quadratic equation has a form ax2 + bx + c = 0, where ax2 is –1/2gt2 , bx is V0t, and
given equation is given below (Fig 1.1) 1. ‘Find the four Intersections made my the parabola x2-6x+11 and the lines y=x and y=2x’ The co-ordinates for the intersections of the parabola and the two given lines are Ans 1. To find the co-ordinates using technology graph the parabola and the two lines required, and note the points of intersection. Alternatively solve the quadratic equation but substituting the value of y = x and y = 2x Giving the two equations To find
farther from 0 the parabola becomes thinner. The result was a little too thin. My final function was: Y= -0.033(X-8.5)2+2.33 I changed -0.035 to 0.033. As a gets closer to 0 the parabola becomes wider. Below the final quadratic function, Y= -0.033(X-8.5)2+2.33 is superimposed onto my original data points. [IMAGE] In the tables below, the results when the different lengths are substituted into the function, can be compared with our initial