Quadratic function

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II INTRODUCTION The purpose of this lab was to demonstrate and observe the effect a large focal spot and a small focal spot will have on the resolution of the image. Chapter 3 of Practical Radiographic Imaging states that resolution is “the ability to distinguish two adjacent details as being separate and distinct from each other” (Carrol, 2007, p. 48). This definition of resolution helps to explain what will be looking for to retrieve the data for this lab. As stated in Chapter 16 of…

Now on the other hand, using the triangle inequality and then (33) we have ∥u − uh∥ L1(Ω) ≥ ∥uI − uh∥ L1(Ω) − ∥u − uI∥ L1(Ω) ≥ ∥uI − Tpuh∥ L1(Ω) − ∥uh − Tpuh∥ L1(Ω) − ∥u − uI∥ L1(Ω) ≥ ∥uI − Tpuh∥ L1(Ω) − ∥uh − Tpuh∥ L1(Ω) − C2hp+1|u| Wp+1 1 (Ω); ≥ ∥uI − Tpuh∥ L1(Ω) − C∥u − uh∥ L1(Ω) − −C3hp+1|u| Wp+1 1 (Ω); from which we conclude that ∥u − uh∥ L1(Ω) ≥ C0∥uI − Tpuh∥ L1(Ω) − C3hp+1|u| Wp+1 1 (Ω) ≥ C0 vuut ΣN i=1 ∥uI − Tpuh∥2 L1(Ω∗ i ) − C3hp+1|u| Wp+1 1 (Ω)(36) ; where Ω∗ i is as in the proof of…

A ball, and a feather dropped at the same height will hit the ground at the same time when placed in a vacuum space. This is because acceleration of motion is the same for both object, and in this experiment, we are going to calculate accelerated motion using inclined planes. In this experiment, we will see whether “distance traveled is directly proportional to the square of the time”, and “if speed of a falling object depend only on the height from which it falls”. This experiment will give us…

This step completes the segmentation removing static objects from the grayscale images $T_i$ using Eigen-Background decomposition. First, each image $T_i \in \mathbb{R}^{n_x\times n_y} $ is reshaped into a column vector $I_i \in \mathbb{R}^{n_p\times 1}$. These $n_t$ vectors become the $i-th$ column of a video matrix $A(n_p\, , \, n_t)$, after having removed the average image: \begin{equation} A_{(n_s \times n_t)}=\begin{pmatrix} \hat{I}_1 & \hat{I}_2 & \cdots & \hat{I}_{n_t}…

Well, I’m glad to hear you’re interested in coming West. The Gold Rush is over, but there is still opportunity to mine out valuable metals and ores. I want you to take that brain of yours and help me start a business, I’ll pay you handsomely for it. I want to hire some men coming from the South to mine for me (for a fair sum), we’ll be doing some quartz mining. I’ve made enough friends to get some investors who will allow us to mine out their land too. I want you to monitor finances and the…

Duck Soup was a movie that came out on November 17, 1933. This was approximately three years into the American Great Depression, with a broken economy and unemployment rate at its highest of 25 percent. This was a time when America was at its all-time low. Duck Soup is a movie made as a direct representation of America during the Great Depression. The writers purposely made it a comedy because the audience would get the joke. In Duck Soup, Rufus T. Firefly becomes the president of the country…

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…

thinking, I have chosen to examine my video from 2:45 – 3:25. During this time, I asked students for their answers to the problem given to them and their reasoning for this answer. In essence, I was hoping to target students’ knowledge of inverse functions and how they applied it to solving a situational problem. More specifically, if they were able to find the error in a solution of an inverse algebraic problem and explain their reasoning for this error. Moreover, once a student was able to…

Introduction I’m going to start this paper with introducing the history of Pascal’s Triangle, time ranging from 2nd century BC to 18th century AD. Among all the academic works by ancient mathematicians, I’m going to focus on Jiu Zhang Suan Shu [Nine Chapters on the Mathematical Art] composed by Chinese scholars around 2nd century BC-10th century AD. I will use the binomial expansions derived from Pascal’s triangle as an example and then illustrate the coefficients expansion in general. After…