Numerical Methods

Problem Produce a report that contains written descriptions, analysis and mathematics that shows how calculus can be used to solve an engineering problem. The tasks are to: Use thinking methods to analyse the given engineering problem, e.g. break the problem down into a series of manageable elements, and produce a specification • Prepare a valid proposal for solving the problem and present it • Produce mathematical models for the identified elements of the problem • Apply calculus methods to produce answers for each of the elements • Bring the elements together in a formal presentation

An object following a quadratic trajectory h(t) = t^2 – 7t + 6 hits the ground at two times. Find the latest time it hits the ground a. t=6 b. t=16 c. t=0 d. t=1

Find the transform. Show the details of your work. Assume that a, b, w, 0 are constants.

1) Which of the following points satisfy the linear inequality 2x + 4y <= 7? A) (1, 1) В) (-1, 3) C) (2, 4) D) (0, 2) E) none of these

Find the transform. Show the details of your work. Assume that a, b, w, 0 are constants.

The graph off over the interval [1, 9] is shown inthe figure. Using the data in the figure, find a midpointapproximation with 4 equal subdivisions forn \int_{i}^{9} f(x) d x

6) Determine whether the point (7, 8) is in the feasible set of the system of inequalities: \left\{\begin{array}{l} 2 x+6 y \leq 66 \\ 4 x+2 y \leq 48 \\ x+y \leq 14 \\ x \geq 0, y \geq 0 \end{array}\right. A) Yes B) No

A sample of 370 people is selected. The people are classified according to place of residence ("urban", "suburban", or "rural"). They are also classified according to highest educational degree earned ("no college degree", "two-year degree", "four-year degree", or "advanced degree"). The results are given in the contingency table below. What is the relative frequency of people in the sample whose place of residence is suburban?

5.17. The equation of state for a gas is given by the van der Waals equation \left(P+\frac{a}{v^{2}}\right)(v-b)=R T where P is the pressure, v is the specific volume, T'is the temperature,R is the gas constant, and a, b are constants that depend on the gas. For P= 70 atm, T= 200 K, R =0.08205 liter atm/mole K, a = 3.59, and b =0.0427, the specific volume is given in liters/mole. Find this value using the Newton-Raphson method, after obtaining the approximate value by the search method. Also, use the roots function in MATLAB to obtain the solution and compare the result with that obtained earlier.

Given F(s) = L(f), find f(r). a, b, L, n are constants. Show the details of your work. \text { 30. } \frac{4 s+32}{s^{2}-16}