of the data. Also, the creation of a trend line allows a correlation between the two subjects to be viewed easier. Trend lines help people accurately determine future outcomes that can come in handy if there is a problem. This is possible because trend lines make it easier to find the slope intercept equation. This equation could be used to find future points in the graph. In this essay I will try to determine who is the best basketball player between Lebron James and Michael Jordan by using a trend line. Before finding the better player, we first have…
In observing other students trying out along with me (similar to the teachers who observed Maria in chapter 8), it has been valuable to see how they handle these misconceptions and the whole process has been eye-opening with regards to the number of things to consider in my own planning for these “mock” teaching scenarios.Turning to the article on functions by NCTM, I was reminded of my own mathematics learning experiences in middle and high school. I feel as if my understanding of functions…
Inverse Functions of Trigonometric Functions As high schoolers go their their teenage years of high school they learn from a variety of subjects. From math to science to history, there is a depth of knowledge to be learned. For math 3 and math 4, we are introduced to the world of trigonometry. So far, we have learned that there are currently three main trigonometric functions, cosine, sine, and tangent. But today I want to explore the other side of the trigonometric world, the inverse…
In 1540, a man by the name of Lodovico Ferrari, please be aware that I don’t think his name has anything to do with the sports car, was an Italian mathematician known for discovering the solutions to quartic functions. A quartic function is a function of the form ax^4 + bx^3 +cx^2 +dx+e, where a is a nonzero, which is defined by a polynomial raised to the fourth degree, called quartic polynomial. We will probably go more in depth about these quartic polynomials soon in class. My quartic…
THE SINE FUNCTION (SIN) Sine function is an odd function. Trigonometric Ratios in a Triangle Definition of sinα in a Triangle is the following statement: For any acute angle α, we draw a right triangle that includes α. The sine of α, abbreviated sin α, is the ratio of the length of the opposite this angle to the length of the hypotenuse of the triangle. If we simplify we get a formula which says: It is shown in a diagram below. We can see immediately that this definition has a weak point. It…
number, it would be said to be a linear function. Common examples of linear function would be distance traveled over time for objects traveling at constant speed; cost of gas in relation to gallons used. Certain situations are linear or not based on whether or not the rate of change is constant or varies. Linear systems are represented by f(x) = mx + b; the slope (m) and the y-intercept (b). In a table that represents a linear function, the input and out puts will be a set of solutions that will…
taking seriously. In this unit 5 learning journal, my concentration would be on Exponential and Logarithmic Functions. In section 1, we are told that among all the functions we have examine so far in this course, the exponential and logarithmic functions are the very ones that mostly impact our daily lives the most (Yakir, 2011). In previous learning, we dealt with various functions which includes terms like x2 or x2=3, that is, terms of the form xp where the base of the term, x, varies but the…
Equipment used in this experiment in addition to the materials used for the bungee jump apparatus included Vernier LabPro, connected to the Dual Range Force sensor and the Ultrasonic Motion Detector, and Logger Pro. The Dual Range Force sensor was used for measuring the force, given in Newtons, of the bungee jump either pulling or pushing on the attached hook. The Ultrasonic Motion Detector provided information on the change in the bungee jump’s position by measuring its distance from the…
identification may result in unreliable prediction for complex systems where our understanding of the physics of the system is insufficient. Here we used a non-parametric approach as control of walking in humans is a complex task involving many degrees of freedom. We chose to perturb the system using visual perturbations as the input since the optic flow has a profound effect on the perception of speed. We measured muscle activations and kinematics as the output of the system. In linear time…
It uses the same x and y values as the graph. I chose to use a positive cosine equation to represent a scenario where Mars is at its aphelion at day 0. This is because a positive cosine function starts at the highest value, where Mars is farthest away from the Sun (aka the aphelion). This equation is a form of the parent function y = a cos(b(x-c)) + d. The “a” value in my equation represents half the distance from the aphelion to the perihelion, or the distance from the aphelion to the…