Concept explainers
(Factorial) The factorial of a nonnegative integer n is written n ! (pronounced “n factorial”) and is defined as follows:
For example,
- Write a
program that reads a nonnegative integer and computes and prints its factorial. - Write a program that estimates the value of the mathematical constant e by using the formula:
- Write a program that computes the value of e by using the formula
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- 6.Coding-----""Euler's totient function, also known as phi-function ϕ(n),counts the number of integers between 1 and n inclusive,which are coprime to n.(Two numbers are coprime if their greatest common divisor (GCD) equals 1)."""def euler_totient(n): """Euler's totient function or Phi function. Time Complexity: O(sqrt(n)).""" result = n for i in range(2, int(n ** 0.5) + 1): if n % i == 0: while n % i == 0: n //= i.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_forward5. (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 cx + dy = f ● x = ed - bf bc ad y = af - ec ad bc - Write a program that prompts the user to enter a, b, c, d, e, and f and display the result. If ad- bc is 0, report that The equation has no solution. Enter a, b, c, d, e, f: 9.0, 4.0, 3.0, -5.0, -6.0, -21.0 Enter x is -2.0 and y is 3.0 Enter a, b, c, d, e, f: 1.0, 2.0, 2.0, 4.0, 4.0, 5.0 Enter The equation has no solutionarrow_forward
- 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_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(True/False): An identifier cannot begin with a numeric digit.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 equations: ed – bf af – ec y bc ax + by = e X = cx + dy = f ad ad – bc Write a function with the following header: void solveEquation(double a, double b, double c, double d, double e, double f, double& x, double& y, bool& isSolvable) If ad – bc is 0, the equation has no solution and isSolvable should be false. Write a program that prompts the user to enter a, b, c, d, e, and f and displays the result. If ad – bc is 0, report that "The equation has no solution." See Program- ming Exercise 3.3 for sample runs.arrow_forwardExercise 1: (Design of algorithm to find greatest common divisor) In mathematics, the greatest common divisor (gcd) of two or more integers is the largest positive integer that divides each of the integers. For example, the gcd of 8 and 12 is 4. Why? Divisors of 8 are 1, 2, 4, 8. Divisors of 12 are 1, 2, 4, 6, 12 Thus, the common divisors of 8 and 12 are 1, 2, 4. Out of these common divisors, the greatest one is 4. Therefore, the greatest common divisor (gcd) of 8 and 12 is 4. Write a programming code for a function FindGCD(m,n) that find the greatest common divisor. You can use any language of Java/C++/Python/Octave. Find GCD Algorithm: Step 1 Make an array to store common divisors of two integers m, n. Step 2 Check all the integers from 1 to minimun(m,n) whether they divide both m, n. If yes, add it to the array. Step 3 Return the maximum number in the array.arrow_forwardQ2) (Perfect Numbers) 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 6 = 1 + 2 + 3. Write a function perfect that determines if 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 factors 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
- Program thisarrow_forwardC Programming Language (Code With C Programming Language) Problem Title : Visible Trees There is a legend about a magical park with N × N trees. The trees are positioned in a square grid with N rows (numbered from 1 to N from north to south) and N columns (numbered from 1 to N from west to east). The height (in metres) of each tree is an integer between 1 and N × N, inclusive. Magically, the height of all trees is unique. Bunga is standing on the northmost point of the park and wants to count the number of visible trees for each Column. Similarly, Lestari is standing on the westmost point of the park and wants to count the number of visible trees for each Row. A tree X is visible if all other trees in front of the tree X are shorter than the tree X. For example, let N = 3 and the height (in metres) of the trees are as follows6 1 87 5 32 9 4 On the first column, Bunga can see two trees, as the tree on the third row is obstructed by the other trees. On the second column, Bunga can see…arrow_forwardcode this:arrow_forward
- C++ Programming: From Problem Analysis to Program...Computer ScienceISBN:9781337102087Author:D. S. MalikPublisher:Cengage Learning