Functions Exercises

Question-1: Harmonic Mean

Write a function that takes three numbers as parameters and returns the harmonic mean of these numbers using the formula: \(\displaystyle H(x, y, z) = \frac{3}{\frac{1}{x}+\frac{1}{y}+\frac{1}{z}}\).

Question-2: Circle

Write a function that takes two parameters: radius (\(r\)) with a default value of 1, and calculation_type with a default value of “area”.

• If calculation_type is area (\(\pi r^2\)) the function returns the area of the circle, rounded to the nearest hundredth.

• If calculation_type is perimeter(\(2\pi r\)) the function returns the perimeter of the circle, rounded to the nearest hundredth.

• If calculation_type is both the function returns a tuple containing both the perimeter and the area of the circle, each rounded to the nearest hundredth.

• If calculation_type is anything else, it prints a “not valid type” warning.

Question-3: Algebraic Operations

Write a function that takes two numbers as parameters and returns the results of the four basic operations.

• If the second number is zero for division, print a warning message about division by zero.

• Round the result of the division to the nearest hundredth.

Sample Output: alg_operation(3,7)

3 + 7 = 10
3 - 7 = -4
3 x 7 = 21
3 / 7 = 0.43

Question-4: Letters

Write a function that takes a number as its input and returns the first corresponding number of lowercase letters from the alphabet.

• If the input number exceeds the total number of letters in the alphabet, the function returns all letters.

• If the input is zero or negative, it returns an empty string.

Sample Output

print(letter_func(4))
abcd

print(letter_func(-5))
(No Output)

print(letter_func(40))
abcdefghijklmnopqrstuvwxyz

Question-5: Distance

Write a function that takes four parameters: the (x, y) coordinates of two points, A and B.

• Plot a red line connecting these two points on a graph.

• Label points A and B by adding texts next to each point.

• Calculate the distance between these points and display it as text in the middle of the line.

• Rotate the text for better visibility.

Sample Output

Question-6: Password Check

Select a 4-digit password. Then, write a function that takes a 4-digit number as its parameter.

• If the provided number is within 10 units of the chosen password, the function should print a message granting permission to enter; otherwise, it should print a message denying entrance.

Sample Output

password_check(1234)
DENY!

password_check(4325)
ACCEPT!

Question-7: Random Points

Write a function that takes a parameter representing the number of points to plot in green.

• This function should generate random points, each with random sizes and transparencies, and plot them on a graph.

• The sizes of the points should be integers ranging from 5 to 800.

• The transparencies should be decimal numbers between 0 and 1.

• The x and y coordinates of the points should be decimal numbers ranging from 5 to 10.

Sample Output

Question-8: Pyramid

Write a function that takes five parameters representing:

1. The x-coordinate of the right upper corner of the rectangle.

2. The y-coordinate of the right upper corner of the rectangle.

3. The width of the rectangle.

4. The length of the rectangle.

5. The color of the rectangle.

The function should:

• Plot the corresponding rectangle.

• Plot the point (0,0) in blue color.

• Draw four dotted blue lines from the point (0,0) to each corner of the rectangle.

• Remove the axis.

Sample plot:

Question-9: Equation of a Line

Write a function that takes four parameters representing:

1. The x-coordinate of the first point.

2. The y-coordinate of the first point.

3. The x-coordinate of the second point.

4. The y-coordinate of the second point.

The function should return the equation of the line that passes through these two points using the slope-intercept form \(y=mx+b\) , where:

• \(m\) is the slope, calculated as \(m=\frac{y_2-y_1}{x_2-x1}\)

• \(b\) is the y-intercept, calculated as \(b = y_2 - mx_2\).

Warning: If \(x_2=x_1\) , the equation of the line is \(x=x_2\).

Question-10: Pitch Monitor

Write a function that takes a list of whole numbers representing pitches and visualize the pitches, using the print() function and * characters.

• The length of the pitch list is the number of * columns.

• The numbers in the list represent the number of * characters in each column.

• For example, if pitch_list = [2, 5, 3, 4], then:

  • The first column has 2 stars.

  • The second column has 5 stars.

  • The third column has 3 stars.

  • The fourth column has 4 stars.

Sample Output for pitch_list = [2,5,3,4]:

Business Application

Question: Simple Interest

Write a function that takes the principal amount, annual interest rate, and time period in years as parameters and returns the interest amount and final amount as a tuple.

• The annual interest rate is in decimal form.

Question: Cost

Total cost (C) has two parts:

1. Variable Costs: Expense that changes in proportion to number of items produced.

   • Variable Cost = Number of items produced \(\cdot\) Cost of producing one item

2. Fixed Costs: Does not depend on the number of the items produced.

   • Examples: rent, lease costs, salaries, utility bills, insurance

It costs a company 80 dollars to produce one item, and the company has fixed costs of 850 dollars and \(n\) represents the number of items produced.

• Write a function which has the paramter \(n\) and returns the total cost.

• Find the cost of producing 6 items.

Question: Linear Depreciation

The value of a new machine is \(100,000\) dollars and its values is depreciated by \(7500\) dollars per year.

• Write a function which has only one parameter \(t\) that represents the year and returns the value of the machine after \(t\) years.

• Find the value of the machine after 6 years.

Question: Exponential Depreciation

The value \(V\) of a truck in dollars is given by the formula \(140000(1.35)^{-0.6t}\) where \(t\) is the age of the truck in years.

• Write a function which has only one parameter \(t\) that represents the year and returns the value of the truck after \(t\) years.

• Find the value of the truck after 6 years.

Question: Plumber Charge

A plumber charges a fixed fee of 150 dollars if the working time does not exceed 2 hours. If it exceeds 2 hours, he charges an extra 80 dollars for each additional hour. Write a function that takes one parameter, hours, and calculates the total cost based on the hours provided.

Question: Monthly Plan

A gym company offers two plans: Basic and Professional. The details for each plan are as follows:

• Basic Plan:

  • Fixed fee: 5 dollars

  • Cost per hour: 5 cents

• Professional Plan:

  • Fixed fee: 10 dollars

  • Cost per hour: 6 cents

Write a function that takes two parameters, plan (either “Basic” or “Professional”) and hours, and calculates the total cost based on the plan and hours provided.