MAS162: Foundations of Discrete Mathematics - Variable Values - Mathematics Assignment Help

Assignment Task :

1. This question addresses the representation of numbers and potential round-off errors.

(a) For each of the following equations, perform the following tasks: 

• Decide if the equation is mathematically true for the variable values provided below.

• Implement the equations in MATLAB, and test if they are true in the floating point arithmetic within MATLAB for the variable values provided. (For example, the equation 3 + 72 = 5 in matlab would correspond to the command disp(3+7^2==5) and yields, upon execution of the command, the value 0 corresponding to false. This is expected since the equation is not mathematically true.) 

(b) Write a MATLAB program that creates a vector i=0:32 and a corresponding vector x with values 40, 4−1, 4−2, . . . , 4−32. Then, for each element in x, calculate y=(-2/x+1/2)+(1/2+2/x) and store the result in a vector y. Plot y as a function of i (not y as a function of x!). Explain the result and the differences to the expected value. If there is a value i∗ of i where the result changes rapidly, discuss how the value of i∗ fits with your knowledge about the representa tion of floating point numbers in a computer.

2.  Lara is turning 9 and is having a birthday party! 

(a) There are 27 kids in Lara’s class (including herself). Her best friends Fred, Asha and Adam are in her class. For her birthday, she would like to invite 7 children from her class (not counting herself). She invites Fred, Asha and Adam and 4 other children. How many differ ent combinations are possible? 

(b) Each of the kids at the party (including the host Lara) is given one of the eight colored T shirts that Lara’s father has purchased for the kids (green, blue, orange, red, yellow, pink, 2x purple). In how many ways can the T-shirts be distributed to the children? 

(c) There is a big bucket with purple, blue, green, yellow, orange and red lollies (hundreds of each color). The green lollies are the tastiest. One after the other, the children throw a colored dice (with six faces corresponding to the colors above), until each child has rolled the dice once. What is the probability that more than 3 children get a green lolly? 

(d) The kids (including the host Lara) line up in alphabetical order. Lara’s mother comes with a bucket that has cardboard cut-out number in it; it contains exactly one copy of each of the 10 numbers 0 to 9. The children line up, and each child picks a cardboard cut-out randomly and holds it up above his or her head. What is the probability that the number that is formed is 1,234,567? What is the probability that the number that is formed is greater than or equal to 4,000,000? 

(e) Fred, Asha and Adam have brown hair; all other kids have blond hair. For a particular game, Lara’s father selects a team of 3 kids with brown hair and 2 kids with blond hair. In how many different ways can he put together this team? 

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