A square number is an integer number whose square root is also an integer. For example 1, 4, 81 are some square numbers. Given two numbers a and b you will have to find out how many square numbers are there between a and b (inclusive). Input Each line contains two integers a and b (0 < a
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Please note that the input should be taken from a txt file you can create one with the information provided in the sample input and the output should be written in another txt file. Use python to solve this problem. Please answer as instructed.
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- P1 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) -> 12Q3: Interplanetary Spaceflight Milan Tusk is the richest person in the universe. After devoting decades of his life to further our space exploration technologies, he’s finally ready to retire. Being a space enthusiast, the first thing he wants to do is visit n planets p1, p2, …, pn, in this order. He’s currently on planet p0. Milan knows that the distance between planets pi and pi + 1 (for 0 ≤ i < n) is d[i]light years. His spaceship uses 1 tonne of fossil fuels per light year. He starts with a full tank and can fill up his tank at any of the n planets (but he must not run out in between two planets). There’s a huge cost to set up the spaceship for refuelling. Due to financial constraints (he’s not THAT rich), he can fill up his tank at most ktimes. In order to save money and make his spaceship lighter, Milan is looking for the smallest possible fuel tank that enables him to complete his space travel and reach planet pn. What is the smallest tank capacity that enables him to do so?…Ex: Let A1 ={x, y}, A2 ={1, 2}, and A3 ={a, b}, Find A1 × A2, (A1 × A2) × A3, A1 × A2 × A3.
- Complete the function below that takes in three integers (a,b,c) and returns the number of integers between a and b (inclusive of the endpoints) that are divisible by c. Make sure it tests a and b for divisibility by c! In [ ]: defhow_many_divisible(a,b,c):counter=0# YOUR CODE HEREraiseNotImplementedError()returncounter In [ ]: assert how_many_divisible(10,20,5) == 3 assert how_many_divisible(30,77,7) == 7 PYTHON jYPYTERLet A = {a, b, c} and B = {u, v}. Write a. A × B b. B × AExercise III: Catalan numbers For n e N, denote by c, to be the number of ways to form a "mountain range" with n upstrokes (U) and n downstrokes (D) that all stay above a horizontal line. For instance: for n = 1, only UD is allowed, so c = 1; • for n = 2, only UUDD and UDUD are allowed, so c2 = 2. 1. Check that c3 = 5 by writing down or drawing all possible options. 2. Consider the power series +00 g(x) = 2 n=0 (by definition co = 1) called the generating function of the sequence (en). Justify that cn < 4" for each n, and deduce that the radius of convergence of g is at least 1/4. 3. It can be show that for r E (-1/4, 1/4), g(x) = 1+ xg(r)? and therefore 1- VI 4.x g(x) = 2.x Use this formula and the known power series of V1+ x to write the first terms of the power series expansion of g, in the form g(x) = co + c1x + c2x2 + C3x + c4x* + ·.. Show how you obtain a few terms, but you do not need to show all computations and you can use a calculator for fractions. Check that you recover co,…
- A prime number is called a Mersenne prime if it can be writtenin the form 2p - 1 for some positive integer p. Write a program that findsall Mersenne primes with p ≤100 and displays the output as shown below.(Hint: You have to use BigInteger to store the number because it is too big tobe stored in long. Your program may take several hours to run.) p 2^p – 1---------------------2 33 75 31...Assuming that you have the functions "drawPolygon(int[] x, int[] y, int n)" for drawing polygon, "drawRectangle(int x, int y, int width, int height)" for drawing rectangle and "drawCircle(int xc, intyc, int radius)" for drawing circle; draw the given shape. Where: R(300,250), T1(325,275), T2(475,275), T3(400,400), Pı(285.250), P2(225.275), P3(200,450), P4(285, 300), Q1(515,250), Q2(575,275), Q3(600,450), Q4(515,300) C6: (300,75), R=50 C7: (500,75), R=50 C1: (400,150), R=100 С4: (350,150), R-10 C5: (450,150), R=10 C2: (400,195), R=50 C3: (400,175), R=30 C8: (400,225), R=15 P1 R P2, T2 P4 Q2 Q4 T3 Pa 200Knight'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
- 4 -A mathematician and discovered a number which have unique properties. As he is not decided any name to that number, so for the time being we call that number ‘Cuboid’. A unique property of Cuboid is that, if we break that number into individual units like breaking 153 into 1, 5 and 3 and take their individual cube, then the sum would be the same as original number being given. Your task is to ask the user an integer and print weather the digit entered is Cuboid or not. (Python program)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: -50Most 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)