## Description

1. (a) Write a Python class Sphere for representing spheres. The class has a data attribute radius indicating the radius of the sphere. It also provides the following methods:

(i) getRadius(self) for returning the radius of the sphere, (ii) surfaceArea(self) for returning the surface area of the sphere, (iii) volume(self) for returning the volume of the sphere.

(b) Write a Python class Quadratic for representing the quadratic function f(x) = ax2 + bx + c. The class has three data attributes for the coefficients a, b, and c called a, b, and c. It also has the following methods:

(i) value(self, x) for computing a value of f at a point x,

(ii) table(self, n, L, R) for printing a table of x and f values at n values of x in the interval [L,R],

(iii) roots(self) for computing the roots of f(x) = 0.

2. (a) Write a Python class Card for representing a playing card. The class has two data attributes rank and suit where rank is an int in the range 1-13 indicating the ranks Ace to King and suit is a single character “d”, “c”, “h”, or “s” indicating the suit (diamonds, clubs, hearts, or spades). It also has the following methods:

(i) getRank(self) for returning the rank of the card,

(ii) getSuit(self) for returning the suit of the card,

(iii) value(self) for returning the Blackjack value of the card where numeral cards 2 to 10 count at their face values, face cards (Jacks, Queens, Kings) count as 10, and Aces count as 1,

(iv) str (self) for returning a string that names the card such as โโAce of Spadesโ.

(v) repr (self) for returning a string such that eval applied to the string recreates the instance.

(b) Write a Python class RationalNumber for performing arithmetics with fractions. The class has two data attributes num and den which are the numerator and denominator of the fraction expressed in reduced form, e. g. 2/4 is stored as the fraction 1/2. It also provides the following methods:

(i) add (self, other) for returning the sum of two rational numbers in reduced form,

(ii) sub (self, other) for returning the difference of two rational numbers in reduced form,

(iii) mul (self, other) for returning the product of two rational numbers in reduced form,

(iv) truediv (self, other) for returning the quotient of two rational numbers in reduced form,

(v) display(self) for printing the fraction in the form a/b where a is the numerator and b is the denominator.

3. Write a Python class Employee for storing the data of the employee in a company. The class has four data attributes for the last name, first name, staff number, and salary of the employee called lastname, firstname, staffnum and salary where the first two are of type string and the last two are of type int. It also has a class attribute called count for counting the number of Employee objects created. Moreover, it provides the method display(self) for printing the information of the employee as well as the static method getcount() for returning the total number of employees.

4. (a) Write a Python class Vec3D for representing vectors in three-dimensional space by inheriting from class Vec2D in section 3.2.2 of the notes. In this derived class, you should override the methods defined in the base class appropriately. Moreover, add a new method cross(self, other) to this class for returning the cross product of two vectors in three-dimensional space.

(b) Write a Python class Point for representing geometric points. This class has two data attributes x and y for the x- and y-coordinates of the point which are of type int. It also provides the method str (self) for returning a string representation of the point in the form (x, y). Next, write a Python class Circle for representing circles by inheriting from class Point. This class has two data attributes (x, y) and radius where (x, y) is a Point object indicating the center of the circle and radius is a float indicating the radius of the circle. Moreover, it adds a method area for returning the area of the circle and overrides the method str (self) for returning a string representation of the circle in the form of

Center = (x, y), Radius = radius. Finally, write a Python class Cylinder for representing cylinders by inheriting from class Circle. This class adds a data attribute height which is a float indicating the height of the cylinder and a method volume for returning the volume of the cylinder. (For this class, (x, y) refers to the base center of the cylinder.) It also overrides the method area for returning the surface area of the cylinder and the method str (self) for returning a string representation of the cylinder in the form of Center = (x, y), Radius = radius, Height = height.

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