Square of 13 is 169. 31, which is a reverse of 13 has a square 961. Here are few numbers which have this property. Write a program to find out whether any more such numbers exist in the range 10 to 100.
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- Find the numbers that can be expressed as the product of two nonnegative integers insuccession and print them in increasing order. (For example, 30 is such a number as it can bewritten as the product of 5 and 6 (30=5x6), which are two numbers in succession.) The user shouldspecify a maximum value and the program should print all said numbers smaller than or equal tothat value. The program should keep a count of how many numbers were printed and shouldoutput that count, as well as the numbers. creat a git bash script for the problem aboveP1 P2 P3 P4 A pentagonal number is one that corresponds to dots arranged into a pentagon. Above are the first four pentagonal numbers and their pentagons. The pentagonal number PN has sides made of N dots. When you count the dots for a pentagonal number, include the dots for the inner pentagons. So to figure out how many dots PN has, find out how many P(N-1) has and add the dots for the new sides of size N. P1 = 1, P2 = 5, P3 = 12, P4 = 22 Figure out a recursive formula for PN and then write a function that implements it. That is, implement pentagonal() using recursion. pentagonal(1) -> 1 pentagonal(2) -> 5 pentagonal(3) -> 1223. A perfect number is a positive integer that is equal to the sum of its positive divisorsexcept the number itself. The first two perfect numbers are 6 and 28 since 6=1+2+3and 28=1+2+4+7+14. Write a computer program that finds thefirst four perfect numbers
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- 7) The ideal gas law allows the calculation of volume of a gas given the pressure(P), amount ofthe gas (n), and the temperature (T). The equation is:V = nRT / PSince we only have used integer arithmetic, all numbers will be integer values with nodecimal points. The constant R is 8.314 and will be specified as (8314/1000). This givesthe same result. Implement the idea gas law program where the user is prompted for andenters values for n, T, and P, and V is calculated and printed out. Be careful toimplement an accurate version of this program. Your program should include a properand useful prompt for input, and print the results in a meaningful mannerWrite the following function to draw a regular polygon:def drawPolygon(x = 0, y = 0, radius = 50, numberOfSides = 3):The polygon is centered at (x, y) with a specified radius for the bounding circle for the polygon and the number of sides. Write a test program that displays a triangle, square, pentagon, hexagon, heptagon, and octagon, as shown in Figure 6.12a.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 63
- Assume that a, b, c are numbers.Return 'increasing' if they are in increasing order, 'decreasing' if they are in decreasing order, 'both' if they are both increasing and decreasing, and 'neither' otherwise.Here, 'increasing' means that each value is at least as largeas its predecessor. Similarly for decreasing.The sequence 3, 4, 4 is increasing. whereasthe sequence 4, 4, 4 is both increasing and decreasing.For example,lenient(3, 4, 5) returns 'increasing'lenient(3, 4, 4) returns 'increasing'lenient(4, 4, 4) returns 'both'lenient(4, 3, 2) returns 'decreasing'lenient(4, 3, 3) returns 'decreasing'lenient(4, 2, 3) returns 'neither'Write a program that finds five prime numbers largerthan Long.MAX_VALUE.Most of the children in the kindergarten have been picked up by their parents, and there are only a few children left. The teacher has some candy in his hand, and now he wants to give the children a point, but he does not want the children to eat too much sugar. The teacher came up with the idea of adding 1 to the remainder of each child's age divided by 2. Enter: Number of children n(1<=n<=10) and age of n children Output: Total number of candies Sample input: 3 656 Example output: 4 | Try to write a program(C)