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james rodr-guez

james r.

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Find the critical points of the following functions, and evaluate whether the critical points are maxima or minima. sin(5x) , sin(|x|) , | cos x|

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This project requires you to design a record management system for a university. The university has the following entities: 1. Students: o Attributes: Student ID, name, date of birth, contact information, program enrolled in, year of study, current grades, graduation status, disciplinary records. Relationships: o Enrolled in (many-to-many) courses with lecturers. o Advised by (one-to-one) a faculty advisor (lecturer). o Registered for (one-to-many) student organizations. 2. Lecturers: o Attributes: Lecturer ID, name, department, academic qualifications, areas of expertise, course load, research interests, publications. Relationships: o Teach (many-to-many) courses with students. o Advise (one-to-many) students. o Head (one-to-one) a research group. o Member of (one-to-many) committees. 3. Non-Academic Staff: o Attributes: Staff ID, name, job title, department, employment type, contract details, salary information, emergency contact information. 4. Courses: o Attributes: Course code, name, description, department, level, credits, prerequisites, schedule, lecturers, enrolled students, materials. 5. Departments: o Attributes: Department name, faculty, research areas, courses offered, staff members. 6. Programs: o Attributes: name, degree awarded, duration, course requirements, enrolment details. 7. Research projects: o Project title, principal investigator, funding sources, team members, publications, outcomes. • Construct a database in mysql. • Populate the database with dummy data • Build a simple interface from which the users can query the underlying database • Allow the user to execute at least 5 different queries of the database. The query must be executed within the Python code. The following are some of the suggested queries: o Find all students enrolled in a specific course taught by a particular lecturer. o Retrieve the contact information for the faculty advisor of a specific student. o Search for lecturers with expertise in a particular research area. o List all courses taught by lecturers in a specific department. o Identify lecturers who have supervised the most student research projects. o Generate a report on the publications of lecturers in the past year. o Find all staff members employed in a specific department.

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Find point on the plane $3x + 2y - 3z = -2$ that is closest to $(5, 7, 3)$. Answer: The closest point is

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5. Use Laplace Transforms to solve the following initial value problem. $y'' + 6y' + 34y = 0$ with $y(0) = 3$ and $y'(0) = 1$

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During the COVID-19 pandemic, mortgage interest rates fell to historic lows, making it less expensive for people to borrow money to buy a house. At the same time, there were production disruptions increasing costs and decreasing availability of building materials. Describe and illustrate the impact on the market for housing.

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2. Gradient of a Scalar Function (25 points): Consider the two dimensional scalar field a) Find an expression for $\nabla H$ b) Evaluate $\nabla H$ at the point x = 0, y = 0 $H(x, y) = e^{-(x^2+y^2)}$ c) Use MATLAB to produce the two figures below, which show representations of H(x,y) and $\nabla H$ You will need to use the MATLAB functions, meshgrid, surf, gradient, and quiver. For documentation on how these functions work type in doc surf or doc contour into the command window. (Hint: the figures below were created with a spatial increment of 0.2)

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1. Consider a vector \underline{A}, written in terms of orthonormal base vectors \underline{i}, \underline{j}, and \underline{k}: \underline{A} = 2\underline{i} - 2\underline{j} + \sqrt{2}\underline{k} Rewrite vector \underline{A} in terms of a new set of orthonormal base vectors \underline{a}, \underline{b}, and \underline{c}, where the angles between the two sets of base vectors are given in the table below: \begin{tabular}{|c|c|c|c|} \hline & \underline{i} & \underline{j} & \underline{k} \\ \hline \underline{a} & 60° & 120° & 135° \\ \hline \underline{b} & 60° & 120° & 45° \\ \hline \underline{c} & 135° & 135° & 90° \\ \hline \end{tabular} For example:

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Problem 13 Investigate the balancing of an eight cylinder engine with identical of mass of reciprocating m, crank radius r, distance between cylinder d and length of connecting rod L, if:- i. The engine is arranged in-line, in which the cylinders are numbered consecutively from one end of the engine and the firing order is 1-3-5-7-8-6-4-2. ii. The engine is a radial engine with a single crank with cylinders is numbered consecutively in clockwise direction. [No unbalanced primary and secondary for forces and couples; $4m\omega^2r$; $4m\omega^2r$]

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R(s) + $G_c(s)$ $G_p(s)$ Y(s) Figure 1 1. The system shown in Figure 1 has $G_p(s) = \frac{1}{(s+2)(s+4)}$. If the desired steady-state error is to be 0.01 for a unit step input, what should the lag compensator terms in $G_c(s) = \frac{(s+d)}{(s+f)}$ be?

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Find the equation for the tangent to the curve $y = \exp[7x^2]$ at the point $(4, e^{112})$. $f(x) = \exp[7x^2]$ The equation for the tangent is $y = $

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