Starting Out with Python (4th Edition)
4th Edition
ISBN: 9780134444321
Author: Tony Gaddis
Publisher: PEARSON
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Chapter 4, Problem 12PE
Calculating the Factorial of a Number
In mathematics, the notation n! represents the factorial of the nonnegative integer n. The factorial of n is the product of all the nonnegative integers from 1 to n. For example.
7! = 1x2x3x4x5x6x7 = 5,040
and
|4! = 1x2x3x4 = 24
Write a
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A complex number is a number in the form a + bi, where a and b are real numbers and i is sqrt( -1). The numbers a and b are known as the real part and imaginary part of the complex number, respectively.You can perform addition, subtraction, multiplication, and division for complex numbers using the following formulas:a + bi + c + di = (a + c) + (b + d)ia + bi - (c + di) = (a - c) + (b - d)i(a + bi) * (c + di) = (ac - bd) + (bc + ad)i(a+bi)/(c+di) = (ac+bd)/(c^2 +d^2) + (bc-ad)i/(c^2 +d^2)You can also obtain the absolute value for a complex number using the following formula:| a + bi | = sqrt(a^2 + b^2)(A complex number can be interpreted as a point on a plane by identifying the (a, b) values as the coordinates of the point. The absolute value of the complex number corresponds to the distance of the point to the origin, as shown in Figure 13.10.)Design a class named Complex for representing complex numbers and the methods add, subtract, multiply, divide, and abs for performing complex…
A complex number is a number in the form a+bi, where a and b are real numbers and i is √(-1)
The numbers a and b are known as the real part and imaginary part of the complex number, respectively. You can perform addition, subtraction, multiplication, and division for complex numbers using the following formulas:
a + bi + c + di = (a+c) + (b+d)i (addition)
a + bi − (c + di) = (a−c) + (b−d)i (subtraction)
(a + bi) * (c + di) = (ac−bd) + (bc+ad)i (multiplication)
(a + bi) / (c + di) = (ac+bd) / (c2+d2) + (bc−ad)i / (c2+d2) (division)
You can obtain the Absolute Value for a complex number using the following formula:
|a + bi| = √(a2 + b2)
A Complex number can be interpreted as a point on a plane by identifying the (a,b) values as the coordinates of the point. The absolute value of the complex number corresponds to the distance of the point to the origin, as shown in the example below.
(1) Design a class named Complex for representing complex numbers
Include…
Collatz Sequence: In 1937, Lothar Collatz proposed that no matter what number you begin with, the
sequence eventually reaches 1. This is widely believed to be true but has never been formally proved.
Write a program that inputs a number from the user, and then displays the Collatz Sequence starting
from that number. Stop when you reach 1.
If n is even, divide it by 2 to get n / 2.
If n is odd, multiply it by 3 and add 1 to get 3n + 1.
Repeat the process indefinitely.
Find out and print the maximum number that you can get in these calculations. '
Part-3:
Please enter a number: 2051
6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70
35 106 53 160 80 40 20 10 5 16 8 4 2 1
The maximum number you get: 9232
Chapter 4 Solutions
Starting Out with Python (4th Edition)
Ch. 4.1 - What is a repetition structure?Ch. 4.1 - What is a condition-controlled loop?Ch. 4.1 - What is a count-controlled loop?Ch. 4.2 - What is a loop iteration?Ch. 4.2 - Does the while loop test its condition before or...Ch. 4.2 - How many times will 'Hello world' be printed in...Ch. 4.2 - What is an infinite loop?Ch. 4.3 - Rewrite the following code so it calls the range...Ch. 4.3 - What will the following code display? For number...Ch. 4.3 - What will the following code display? for number...
Ch. 4.3 - What will the following code display? for number...Ch. 4.3 - What will the following code display? for number...Ch. 4.4 - Prob. 13CPCh. 4.4 - Should an accumulator be initialized to any...Ch. 4.4 - What will the following code display? total - 0...Ch. 4.4 - What will the following code display? number 1 =...Ch. 4.4 - Rewrite the following statements using augmented...Ch. 4.5 - Prob. 18CPCh. 4.5 - Why should you take care to choose a distinctive...Ch. 4.6 - What does the phrase garbage in, garbage out mean?Ch. 4.6 - Give a general description of the input validation...Ch. 4.6 - Describe the steps that are generally taken when...Ch. 4.6 - Prob. 23CPCh. 4.6 - If the input that is read by the priming read is...Ch. 4 - A_________-controlled loop uses a true/false...Ch. 4 - A _____-controlled loop repeats a specific number...Ch. 4 - Each repetition of a loop is known as a(n) a cycle...Ch. 4 - The while loop is a _______ type of loop. a....Ch. 4 - A(n) ______ loop has no way of ending and repeats...Ch. 4 - The -= operator is an example of a(n) _________...Ch. 4 - Prob. 7MCCh. 4 - A(n) ____________ is a special value that signals...Ch. 4 - Prob. 9MCCh. 4 - The integrity of a programs output is only as good...Ch. 4 - The input operation that appears just before a...Ch. 4 - Validation loops are also known as _________. a....Ch. 4 - A condition-controlled loop always repeats a...Ch. 4 - The while loop is a pretest loop.Ch. 4 - The following statement subtracts 1 from x: x = x ...Ch. 4 - It is not necessary to initialize accumulator...Ch. 4 - In a nested loop, the inner loop goes through all...Ch. 4 - To calculate the total number of iterations of a...Ch. 4 - The process of input validation works as follows:...Ch. 4 - What is a condition-controlled loop?Ch. 4 - What is a count-controlled loop?Ch. 4 - What is an infinite loop? Write the code for an...Ch. 4 - Why is it critical that accumulator variables are...Ch. 4 - What is the advantage of using a sentinel?Ch. 4 - Prob. 6SACh. 4 - What does the phrase garbage in, garbage out mean?Ch. 4 - Give a general description of the input validation...Ch. 4 - Write a while loop that lets the user enter a...Ch. 4 - Write a while loop that asks the user to enter two...Ch. 4 - Write a for loop that displays the following set...Ch. 4 - Write a loop that asks the user to enter a number....Ch. 4 - Write a loop that calculates the total of the...Ch. 4 - Rewrite the following statements using augmented...Ch. 4 - Write a set of nested loops that display 10 rows...Ch. 4 - Write code that prompts the user to enter a...Ch. 4 - Write code that prompts the user to enter a number...Ch. 4 - Bug Collector The Bug Collector Problem A bug...Ch. 4 - Calories Burned Running on a particular treadmill...Ch. 4 - Budget Analysis Write a program that asks the user...Ch. 4 - Distance Traveled The distance a vehicle travels...Ch. 4 - Average Rainfall Write a program that uses nested...Ch. 4 - Celsius to Fahrenheit Table Write a program that...Ch. 4 - Pennies for Pay Write a program that calculates...Ch. 4 - Sum of Numbers Write a program with a loop that...Ch. 4 - Ocean Levels Assuming the ocean's level is...Ch. 4 - Tuition Increase At one college, the tuition for a...Ch. 4 - Weight Loss If a moderately active person cuts...Ch. 4 - Calculating the Factorial of a Number In...Ch. 4 - Population Write a program that predicts the...Ch. 4 - Prob. 14PECh. 4 - Prob. 15PECh. 4 - Turtle Graphics: Repeating Squares In this...Ch. 4 - Turtle Graphics: Star Pattern Use a loop with the...Ch. 4 - Turtle Graphics: Hypnotic Pattern Use a loop with...Ch. 4 - Turtle Graphics: STOP Sign In this chapter, you...
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