# Engineering

1. Suppose that *u *= 1 and *v = *3. Evaluate the following expressions using MATLAB. Choose only TWO expressions to calculate. SHOW ALL YOUR WORK.

a) 4u3v

b) 2v−2(u+v)2

c) v3v3−u3

d) 43πv2

2. Use the MATLAB Edit Window to create a new empty M-file, type these statements into the file, and save the file with the name type your statements into the file, and save the file with the name *your first name_plot.m*. Then execute the program by typing the name in the command window. SHOW ALL YOUR WORK.

*y(x) = *2*e *-0.2x for the range 0 <= *x *<= 10 with intervals of 0.1.

Hint: ex is written as exp(x) in MATLAB

3. A trough of length *L* as a cross section in the shape of a semicircle with radius r. When filled with water to within a distance *h*of water, the volume *V *of water is

*V = L*[0.5πr2−r2sin−1(hr)−h(r2−h2)2]

Suppose *L = *10 ft, *r = *1 ft, *h = * 0.1620 ft. Find the volume of the water in the trough. SHOW ALL YOUR WORK using MATLAB.

Hint: Use asin(h/r) in MATLAB for the arcsine in the formula.

4. Show that the following equation has at least one solution in the given intervals. You may use MATLAB to solve or Symbolab.com. SHOW ALL YOUR WORK.

ln (*x) – x2 + (5/2)x *– 1 = 0, [1/2, 1]

Hint: in MATLAB use log(x) for ln(x).

5. Use the bisection method to find *p2 *for

*f(x) = x4 – *2*x3 * – 4*x2 * + 4*x + *4 = 0 on the following intervals. Choose ONLY ONE of the four intervals below to calculate. After you find *p2* write down the last interval found that may contain a solution. You may use MATLAB to solve. SHOW ALL YOUR WORK.

a) [-2, -1] b) [0, 2] c) [2, 3] d) [-1, 0]