10. The following triangular arrays of dots led the early Greeks to call the numbers 1,...
The numbers 1, 3, 6, 10, 15 are called triangular numbers because they represent the number of objects needed to make triangular arrays as shown below: 16. 10 15 What is the 100th triangular number? Give your rationale.
This is the sequence 1,3,6,10,15 the pattern is addin 1 more than last time but what is the name for this patternThese are called the triangular numbers The sequence is 1 3=1+2 6=1+2+3 10=1+2+3+4 15=1+2+3+4+5 You can also observe this pattern x _________ x xx __________ x xx xxx __________ x xx xxx xxxx to see why they're called triangular numbers. I think the Pythagoreans (around 700 B.C.E.) were the ones who gave them this name. I do know the...
13. (i) For each of the following equations, find all the natural numbers n that satisfy it (a) φ(n)-4 (b) o(n) 6 (c) ф(n) 8 (d) φ(n) = 10 (ii) Prove or disprove: (a) For every natural number k, there are only finitely many natural num- bers n such that ф(n)-k (b) For every integer n > 2, there are at least two distinction integers that are invertible modulo n (c) For every integers a, b,n with n > 1...
use C++ Project 6 1. Using vectors or arrays, write a function named word_rev() that reverse any given word. 2. Write a program that will: Ask the user to enter a word. Save the entry as word_entered. Call word_rev on the entry Display the reversed entry (word_entered) 3. Write a function named prime() that determine whether or not a given number n (greater than one) is prime. The algorithm: If n is even then n is not a prime number...
i need help writing these programs in c++ format 1. Enter two integer arrays: array1-129, 0, -56, 4, -7 and array2-19, 12, -36, -2, 12 3. Write the code to form and display another array array3 in which each element is the sum of numbers in the position in both arrays. Use pointers and functions: get array0. process arrays0 and show array0 (50 points) 2. Enter a positive 5-digit integer via the keyboard. Display each digit and fol- lowed by...
Question 1 (CLOI, 10 marks) a) Figure I shows a triangular element with respective node numbers and coordinates. If the modulus elasticity, E = 30 x 10 N/mm and Poisson ratio, v0.3. determine the element equation of the triangular element. (10 marks) 3 (18,9) 2 (5.7) b) Assume the triangular element has thickness of 25mm and fixed supported along node 1 to node 2. If a tension force of 200 N is applied on node 3. determine the nodal displacement...
Question 3 (10 marks) An integer number is said to be a perfect number if its factors, including 1 (but not the number itself), sum to the number. For example, 6 is a perfect number because its factors, except itself, are 3, 2, and 1, and 6 = 3+2+1, but 12 is not a perfect number because its factors, except itself, are 6, 4, 3, 2, and 1, but 12 # 6+4+3+2+1. First. Write a C function, called isperfect, that...
Assignment Develop a program to analyze one or more numbers entered by a user. The user may enter one or more numbers for analysis. Input should be limited to numbers from 1 through 1000. Determine if a number is a prime number or not. A prime number is one whose only exact divisors are 1 and the number itself (such as 2, 3, 5, 7, etc.). For non-prime numbers, output a list of all divisors of the number. Format your...
*these questions are related to Matlab The number 24 is exactly divisible by eight numbers (i.e. 1, 2, 3, 4, 6, 8, 12 and 24). The number 273 is also exactly divisible by eight numbers (i.e. 1, 3, 7, 13,21, 39, 91 and 273) There are 10 numbers in the range of 1:100 that are exactly divisible by eight numbers (i.e. 24, 30, 40, 42, 54, 56, 66, 70, 78 and 88). How many numbers in the range of n-1:20000...
Number of Numbers (10 pts) For this assignment you will be working with arrays. Open a new Java project called Nums Prompt a user to enter in the length of the array (the number of numbers). Enter the number of numbers: Use this information to declare an array of the user-specified length. Next, using a for loop, prompt the user to enter that many numbers, and store each one in your array until your array is at full capacity. Using...