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juan manuel adams

juan manuel a.

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1. Let $U = \mathbb{C} \setminus \{(t^2 - 2t) + it \in \mathbb{C} : t \ge 0\}$ and let $\log : U \to \mathbb{C}$ be the branch of logarithm on $U$ such that $\log 1 = 2\pi i$. Find the values of $\log i$, $\log(3i)$ and $3i$.

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Question 21 (8 points) Using prop-1-ene as your only organic starting point, devise a set of reactions that can convert it into two esters which are structural isomers of each other. The reactions must be drawn using line structures. Be sure to name each reaction and all reagents. Note: Once you react a molecule you get to use the new products as well as the reactants you started with again. It is like you have a large bottomless jar of the compound. Note: You may only use reactions covered in class

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Find the absolute maximum and absolute minimum values of f on the given interval. $f(x) = 6x^3 - 9x^2 - 216x + 6$, $[-4, 5]$ Step 1 The absolute maximum and minimum values of $f$ occur either at a critical point inside the interval or at an endpoint of the interval. Recall that a critical point is a point where $f'(x) = 0$ or is undefined. We begin by finding the derivative of $f$. $f'(x) = 18x^2 - 18x - 216$ $18x^2 - 18x - 216$

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2. Consider the probability distribution: $\theta$ f(x|$\theta$) = $\frac{\theta}{x^{\theta+1}}$, (1 ? x < ?) with $\theta$ > 0. a) Derive an expression for the maximum likelihood estimator of $\theta$. [9 pts] b) You have two sets of experimental data provided in the spread sheet, both of which come from this distribution. Derive an expression for the p-value based on the null hypothesis that both sets of data come from the same values of $\theta$ versus the alternative that they are different. In other words, for data sets 1 and 2. [8 pts] $H_0$: $\theta_1 = \theta_2$ $H_1$: $\theta_1 \neq \theta_2$, c) Provide 95% CIs for $\theta_1$ and $\theta_2$. [8 pts]

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The following secondary creep rates were obtained when samples of lead were subjected to a constant stress of 1.3 MN/m². Temperature Min. Creep rate (°C) (s?¹) 33 8.71 × 10?? 29 4.98 × 10?? 27 3.42 × 10?? Assuming the material complies with Arrhenius equation calculate the activation energy for creep of lead. R = 8.314 J/mol K. Hint: • $\mathcal{E} = Ae^{-Q/RT}$ :: $\ln \mathcal{E} = \ln A - \frac{Q}{RT}$ Plot $\ln(\mathcal{E})$ vs $\ln(1/T)$: Q = Slope × R

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3.a Given r.y = 3r + 3y + 2y in this document. [2 marks] Find the gradient vector Vo. [2 marks] Compute the gradient vector at the point 0.1.1. [2 marks] Calculate the directional derivative of o in the direction of vector e = 1,1.2 at the point 0,1.1. b [4 marks] Given that xy = Note = x + y + aan e. [2 marks] Given that the vector field F = ar + ln + y^2sinx - 2y.5r - y + 6 has zero divergence, that is VF = 0. Determine the value of a.

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C++ Programming: Hierarchy of classes: The hierarchy of references has one base class called Reference. All the References have a unique identifier, a title, an author, and a year of publication. The implementation of the classes must follow the object-oriented principles. Class Reference: Implement a class called Reference to represent the characteristics that are common to all the References. Namely, 1. All references must have a unique identifier (of type int). 2. All references have a title and author (both of type string or char*), as well as a year of publication (of type int). 3. The class Reference has a default constructor that initializes data members to default values. 4. The class Reference has one regular constructor: Reference(int id, char* author, char* title, int year). Note that you can use string instead of char*. The constructor must initialize the id, author, title, and year of publication of this reference using the given parameters. 5. int getId(): returns the unique identifier of this Reference. 6. char* getAuthor(): returns the author of this Reference. 7. char* getTitle(): returns the title of this Reference. 8. int getYear(): returns the year of publication of this Reference. 9. void print(): prints a string representation of this Reference consisting of the id number, reference title, author, and year of publication. Class Article: Article is a specialized Reference that also has information about the journal where the article is published, start page, and end page. More precisely, 1. An Article is a derived class of Reference. 2. It also stores information about the journal (type string or char*) and the startPage and endPage (both of type int). 3. It has a default constructor that initializes data members, including the data members of the base class, to default values. 4. It has one regular constructor: Article(int id, char* author, char* title, int year, char* journal, int startPage, int endPage). You can assume that the parameters are valid. 5. char* getJournal(): returns the name of the journal. 6. int getStartPage(): returns the start page. 7. int getEndPage(): returns the end page. 8. It implements the member function int getNumberOfPages(), which returns the total number of pages (computed using startPage and endPage). 9. void print(): returns a string representation of objects of Article. This member function overrides the one defined in the class Reference. *Create a test driver for class Reference and class Article

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A $1,000 face value bond currently has a yield to maturity of 11.62% the bond matures in 16 years and pays interest semi - annually the coupon rate is 9.75 percent what is the current price of this bond ?

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1. Which of the following is an example of a polynomial function? a. $f(x) = 2x^{-3} - 3x^2$ c. $y = \frac{4}{x^2} + 3x - 1$ b. $f(x) = \sqrt{9x^2} - 2x^6$ d. $f(x) = x^3 + 4x^2 - 1$

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Show that the medians AD, BE, CF of a triangle ABC have a common point of intersection, which divides each median in the ratio 2:1.

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