Perfect numbers are numbers that equal the sum of their positive divisors except itself. The smallest perfect number is 6. Positive divisors of 6: The sum of the divisors of 1, 2, 3 and 6 except itself: 1 + 2 + 3 = 6 and 6 is a perfect number. Likewise, the positive divisors of 28: 1, 2, 4, 7, 14, 28 is the sum of the divisors except itself: 1 + 2 + 4 +7+ 14 = 28 and 28 is a perfect number. So, write a C program that checks if a given number is a perfect number.
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- Perfect numbers are numbers that are equal to the sum of their positive divisors except itself. The smallest perfect number is 6. The positive divisors of 6: The sum of the divisors of 1, 2, 3 and 6 except itself: 1 + 2 + 3 = 6 and 6 is a perfect number. Likewise, the positive divisors of 28: 1, 2, 4, 7, 14, 28 is the sum of the divisors except itself: 1 + 2 + 4 + 7 + 14 = 28 and 28 is a perfect number. So, write a MATLAB function that checks if a given number is a perfect number.In mathematics, a prime number is a natural number greater than 1 that is not a product of two smaller natural numbers, i.e. is it has only two factors 1 and itself. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, 1 × 5 or 5 × 1, involve 5 itself.Note that the prime number series is: 2, 3, 4, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, …a. Write a Java method named isPrime that takes a natural number as a parameter and returns the if the given number is prime or not using the following header: Public static boolean isPrime(int num) b. Write a Java class called PrimeNumbers that: o Reads from the user a natural value n (should be less than or equal 200). o Prints a list of the prime numbers from 2 to n and their number and values. o The program has to work EXACTLY as given in the following sample run.In mathematics, a prime number is a natural number greater than 1 that is not a product of two smaller natural numbers, i.e. is it has only two factors 1 and itself. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, 1 × 5 or 5 x 1, involve 5 itself. Note that the prime number series is: 2, 3, 4, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, .. a. Write a Java method named isPrime that takes a natural number as a parameter and returns the if the given number is prime or not using the following header: Public static boolean isPrime (int num) b. Write a Java class called PrimeNumbers that: Reads from the user a natural value n (should be less than or equal 200). Prints a list of the prime numbers from 2 to n and their number and values. The program has to work EXACTLY as given in the following sample run. Hints: You should create a single dimension array to store the prime…
- Java Assignment: Mathematics is the very interesting subject and for the India it is also a point of pride because Mr. Brahmagupta gives the 0 to world. So, in this series want to be great mathematician like Brahmagupta. He is keep practicing for her goal achievement. Once He knew about the Vector dot Product So He asked his friend Sammer the problem. He gave her two vectors A and B length N. He asked him to reduce the dot output of these two vectors. Sammer has the option to change the order of the objects of these two carriers i.e., in any two objects I and j at any vector can change the shape of these objects. Since Sammer is new to the program, he has asked you to resolve the issue using C++ Programming language. Input: 1 4 142-5 3 -8 5 2 Output: -50A decreasing sequence of numbers is a sequence of integers where every integer in the sequence is smaller than all other previous integers in that sequence. For example, •35, 16, 7, 2, 0, -3, -9 is a decreasing sequence of numbers. The length of this sequence is 7 (total numbers in the sequence) and the difference of this sequence is 35 - (-9) -44. • 5 is a decreasing sequence of numbers with length 1 and difference 5-5 = 0 •99,-99 is a decreasing sequence of numbers with length 2 and difference 99-(-99) = 198 •17, 23, 11, 8, -5, -3 is not a decreasing sequence of %3D numbers. Write a program that contains a main() function. The main function repeatedly asks the user to enter an integer if the previously entered integers form a decreasing sequence of numbers. This process stops as soon as the latest user input breaks the decreasing sequence. Then your function should print the length and difference of the decreasing sequence. Finally, call the main() function such that the call will be…I am what you call a perfectionist. I always strive for perfection, and I appreciate everyone and everything that is perfect. That is why I have recently acquired an appreciation for perfect numbers! I absolutely need to know which numbers from 1 to 1000 are considered perfect. From what I recall, a perfect number is a positive integer that is equal to the sum of all its divisors other than itself. Example: 6 is a perfect number because the divisors of 6 other than itself are 1, 2, and 3, and 1 + 2 + 3 = 6. c++ code
- Quadratic Root Solver For a general quadratic equation y = ax? + bx + c, the roots can be classified into three categories depending upon the value of the discriminant which is given by b2 - 4ac First, if the discriminant is equal to 0, there is only one real root. Then, if the discriminant is a positive value, there are two roots which are real and unequal. The roots can be computed as follows: -b+ Vb? – 4ac 2a Further, if the discriminant is a negative value, then there are two imaginary roots. In this case, the roots are given by b ь? - 4ас 2a 2a Programming tasks: A text file, coeff.txt has the following information: coeff.txt 3 4 4 4 1 4 Each line represents the values of a, b and c, for a quadratic equation. Write a program that read these coefficient values, calculate the roots of each quadratic equation, and display the results. Your program should perform the following tasks: • Check if the file is successfully opened before reading • Use loop to read the file from main…Tiling: The precondition to the problem is that you are given threeintegers n, i, j, where i and j are in the range 1 to 2n. You have a 2n by 2n squareboard of squares. You have a sufficient number of tiles each with the shape . Your goalis to place nonoverlapping tiles on the board to cover each of the 2n × 2n tiles except forthe single square at location i, j. Give a recursive algorithm for this problem in whichyou place one tile yourself and then have four friends help you. What is your base case?Computer Science There is an n × n grid of squares. Each square is either special, or has a positive integer costassigned to it. No square on the border of the grid is special.A set of squares S is said to be good if it does not contain any special squares and, starting fromany special square, you cannot reach a square on the border of the grid by performing up, down,left and right moves without entering a cell belonging to S. 5 3 4 9 4 X 3 6 1 9 X 4 1 2 3 5 - Design an algorithm which receives an arbitrary n × n grid, runs in time poly-nomial in n and determines a good set of squares with minimum total cost.
- CCC '13 J1 - Next in line Canadian Computing Competition: 2013 Stage 1, Junior #1 You know a family with three children. Their ages form an arithmetic sequence: the difference in ages between the middle child and youngest child is the same as the difference in ages between the oldest child and the middle child. For example, their ages could be 5, 10 and 15, since both adjacent pairs have a difference of 5 years. Given the ages of the youngest and middle children, what is the age of the oldest child? Input Specification The input consists of two integers, each on a separate line. The first line is the age Y of the youngest child (0Blackout Math is a math puzzle in which you are given an incorrect arithmetic equation. The goal of the puzzle is to remove two of the digits and/or operators in the equation so that the resulting equation is correct. For example, given the equation 6 - 5 = 15 ^ 4/2 we can remove the digit 5 and the / operator from the right-hand side in order to obtain the correct equality 6 - 5 = 1 ^ 42. Both sides of the equation now equal to 1. Observe how removing an operator between two numbers (4 and 2) causes the digits of the numbers to be concatenated (42). Here is a more complicated example: 288 / 24 x 6 = 18 x 13 x 8 We can remove digits and operators from either side of the equals sign (either both from one side, or one on each side). In this case, we can remove the 2 from the number 24 on the left-hand side and the 1 from the number 13 on the right-hand side to obtain the correct equality 288 / 4 x 6 = 18 x 3 x 8 Both sides of the equation now equal to 432. Here is another puzzle for you…Knight's Tour: The Knight's Tour is a mathematical problem involving a knight on a chessboard. The knight is placed on the empty board and, moving according to the rules of chess, must visit each square exactly once. There are several billion solutions to the problem, of which about 122,000,000 have the knight finishing on the same square on which it begins. When this occurs the tour is said to be closed. Your assignment is to write a program that gives a solution to the Knight's Tour problem recursively. You must hand in a solution in C++ AND Java. The name of the C++ file should be "main.cc" and the name of the Java file should be "Main.java". Write C++ only with a file name of main.cc Please run in IDE and check to ensure that there are no errors occuring Output should look similar to: 1 34 3 18 49 32 13 16 4 19 56 33 14 17 50 31 57 2 35 48 55 52 15 12 20 5 60 53 36 47 30 51 41 58 37 46 61 54 11 26 6 21 42 59 38 27 64 29 43 40 23 8 45 62 25 10 22 7 44 39 24 9 28 63SEE MORE QUESTIONS