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(Pythagorean Triples) A right triangle can have sides whose lengths are all integers. The set or three integer values for the lengths or the sides of a right triangle is called a Pythagorean triple. The lengths of the three sides must satisfy the relationship that the sum of the squares of two of the sides is equal to the square of the hypotenuse. Write an application that displays a table of the Pythagorean triples for side1, Side2 and the hypotenuse, all no larger than 500. Use a triple-nested for loop that tries all possibilities. This method is an example of “brute-force” computing. You’ll learn in more advanced computer-science courses that for many interesting problems there’s no known
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Java How to Program, Early Objects (11th Edition) (Deitel: How to Program)
- Programming Language : R programming (R Studio) A twin prime is a prime that has a prime gap of two. Sometimes the term twin prime isused for a pair of twin primes. For example, the five twin prime pairs are (3, 5), (5, 7),(11, 13), (17, 19) and (29, 31). Write a function that returns the number of all twin primepairs between 1 and a given number n.arrow_forwarddef winning_card(cards, trump=None): Playing cards are again represented as tuples of (rank,suit) as in the cardproblems.pylecture example program. In trick taking games such as whist or bridge, four players each play one card from their hand to the trick, committing to their play in clockwise order starting from the player who plays first into the trick. The winner of the trick is determined by the following rules:1. If one or more cards of the trump suit have been played to the trick, the trick is won by the highest ranking trump card, regardless of the other cards played.2. If no trump cards have been played to the trick, the trick is won by the highest card of the suit of the first card played to the trick. Cards of any other suits, regardless of their rank, are powerless to win that trick.3. Ace is the highest card in each suit.Note that the order in which the cards are played to the trick greatly affects the outcome of that trick, since the first card played in the trick…arrow_forward(Algebra: solve 2 x 2 linear equations) You can use Cramer's rule to solve the following 2 x 2 system of linear equation: ax + by = e ed – bf af- ec ad - bc cx + dy = f ad – bc y = Write a program that prompts the user to enter a and f and display the result. If ad - bc is 0 b, c, d , e, , report that The equation has no solution.arrow_forward
- (Area of a convex polygon) A polygon is convex if it contains any line segment that connects two points of the polygon. Write a program that prompts the user to enter the number of points in a convex polygon, then enter the points clockwise, and display the area of the polygon. Sample Run Enter the number of points: 7 Enter the coordinates of the points: -12 0 -8.5 10 0 11.4 5.5 7.8 6 -5.5 0 -7 -3.5 -5.5 The total area is 244.575arrow_forward(Factorials) Factorials are used frequently in probability problems. The factorial of a positive integer n (written n! and pronounced “n factorial”) is equal to the product of the positive integers from 1 to n. Write an application that calculates the factorials of 1 through 20. Use type long . Display the results in tabular format. What difficulty might prevent you from calculating the factorial of 100?arrow_forward(Perfect Numbers) An integer is said to be a perfect number if the sum of its divisors, including 1 (but not the number itself), is equal to the number. For example, 6 is a perfect number, because 6=1+2+3. Write a functionisPerfect that determines whether parameter number is a perfect number. Use this function in a program that determines and prints all the perfect numbers between 1 and 1000. Print the divisors of each perfect number to confirm that the number is indeed perfect. Challenge the power of your computer by testing numbers much larger than 1000.arrow_forward
- (Airline Reservations System) A small airline has just purchased a computer for its new automated reservations system. The president has asked you to program the new system. You’ll write a program to assign seats on each flight of the airline’s only plane (capacity: 10 seats). Your program should display the following menu of alternatives: Please type 1 for "first class" Please type 2 for "economy" If the person types 1, then your program should assign a seat in the first class section (seats 1– 5). If the person types 2, then your program should assign a seat in the economy section (seats 6– 10). Your program should then print a boarding pass indicating the person's seat number and whether it’s in the first class or economy section of the plane. Initialize all the elements of the array to 0 to indicate that all seats are empty. As each seat is assigned, set the corresponding element of the array to 1 to indicate that the seat is no longer available. Your program should, of course,…arrow_forward## MP (Machine Problem) Details The bulls and cows game is a code-breaking game designed for two or more players. Each player chooses a secret code of 4 digits from 0 – 9. The digits must be all different. The goal of the game is for each player to guess the other player's secret code. The players in turn present their guesses to the opponents. The opponents respond by telling the players: 1. The number of bulls, i.e. the number of matching digits in their right positions, and 2. The number of cows, i.e. the number of matching digits but in different positions. ### Requirements The main goal of this assignment is to develop the bulls and cows game that allows a single player to play interactively against the computer. The game stores two secret codes, one from the player and one from the computer. The player and the computer will try to guess each other’s secret code. Both the player and the computer only have seven attempts for guessing the secret code. If the player enters invalid…arrow_forward(GREATEST COMMON DIVISOR) The greatest common divisor of integers x and y is the largest integer that evenly divides into both x and y. Write and test a recursive function gcd that returns the greatest common divisor of x and y. The gcd of x and y is defined recursively as follows: If y is equal to 0, then gcd (x, y) is x; otherwise, gcd (x, y) is gcd (y, x % y), where % is the remainder operator.arrow_forward
- (Geometry: area of a regular polygon) A regular polygon is an n-sided polygon in which all sides are of the same length and all angles have the same degree (i.e., the polygon is both equilateral and equiangular). The formula for computing the area of a regular polygon is n x s? Area 4 X tan Here, s is the length of a side. Write a program that prompts the user to enter the number of sides and their length of a regular polygon and displays its area. Here is a sample run:arrow_forwardwrite code for :arrow_forwardpython nMath: pentagonal numbers) A pentagonal number is defined as n(3n-1)/2 for n=1,2,..., and so on. So, the first few numbers are 1, 5, 12, 22, .... Write a function with the following header that returns a pentagonal number: def getPentagonalNumber(n): Write a test program that uses this function to display the first 100 pentagonal numbers with 10 numbers on each line.arrow_forward
- C++ Programming: From Problem Analysis to Program...Computer ScienceISBN:9781337102087Author:D. S. MalikPublisher:Cengage Learning