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ESC 251 HW 11 Due: Sep. 28

Remember to indent the bodies of your IF-THEN statements.



1)
(2 pts) Enter the following commands into a script file and run it.
    a = 1.1;
    b = 2.2; 
    c = 3.3;
    if(c == a+b) 
       disp('c = a+b is true')
    else
       disp('c = a+b is false')
    end
Does it give the correct output? What do you think is the reason for this behavior?
2)
(6 pts) Write a script that does the following:
a)
Asks the user to input three lengths a, b, and c
b)
Tests to determine if these lengths are capable of forming a triangle.
c)
If a triangle cannot be formed, an error message should be printed out. If (and only if) a triangle can be formed, your program should compute the area of the triangle using Heron's formula

\begin{displaymath}A = \sqrt{s(s-a)(s-b)(s-c)}\end{displaymath}

where s is the semi-perimeter of the triangle

\begin{displaymath}s = \frac{a+b+c}{2}.\end{displaymath}

Test your program with the 2 sets of data: a = 4.1, b = 6.4, c = 10.1; a = 7.8, b = 12.0, c = 3.4.
3)
(5 pts) The income tax in Australia is computed according to the following table:
Taxble Income Tax Owed
$0 - $6,000 $0
$6,001 - $20,000 $0.17 for each $1 over $6,000
$20,001 - $50,000 $2,380 plus $0.30 for each $1 over $20,000
$50,001 - $60,000 $11,380 plus $0.42 for each $1 over $50,000
over $60,000 $15,580 plus $0.47 for each $1 over $60,000

In addition, a 1.5% tax is charged on all income regardless of the taxable amount.

Write a script that will compute the income tax owed given the amount of taxable income. Test your program for income amounts of $5,015, $14,678, $55,784 and $75,000.

3)
(6 pts) When a light ray pssses from one medium to another, the light ray gets bent. Snell's Law of Refraction is the relationship that determines how much a light ray will bend. It states

\begin{displaymath}\frac{\sin(\theta_1)}{\sin(\theta_2)} = \frac{n_2}{n_1}\end{displaymath}

where $\theta_1$ is the angle of incidence through a medium with a refractive index of n1 and $\theta_2$ is the angle of refraction through a medium with a refractive index of n2.



Write a script that will ask the user to input values of $\theta_1$ (in degrees), n1 and n2 and computes the value of $\theta_2$ (provided the calculation is feasible). The value of $\theta_2$ should be printed out in degrees. In the event that the calculation is not feasible, an error message should be printed out.



Test your program using the 2 cases

a)
$\theta_1 = 45^{\circ}, n_1 = 0.73, n_2 = 1.44$
b)
$\theta_1 = 45^{\circ}, n_1 = 0.58, n_2 = 0.13$



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2018-09-26