Calculate the running time of the following program. for i in range(n): a=5 a += 1 for i in range(n): for j in range(n): b 5 b += 1
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- Write a Python (or R) program that asks the user to enter an integer (X), then: Determines if X is prime or not • If X is not prime, compute and print the factors of that integer X • Evaluate and print the equation Y=8X²+ 1, for X values from -5 to 5 using the range function and for loopT can be approximated by using the following infinite series: +-+...) Write a program that prints out two versions of the approximation one that goes out to a denominator of 13 and one that goes out of a denominator of 15. T=4 1 3 5 7 9 Note you will want to use 1.0 for your numerators. In my code I used a decimal version for all of these integers.The binomial coefficient (n, k) is an integer equal to (n, k) = n! / [k! (n – k)!] Note that n! = n(n – 1)(n – 2) … (1) and that 0! = 1. a) Using this form for the binomial coefficient, write a Python user-defined function binomial(n,k) that calculates the binomial coefficient for given n and k. Make sure your function returns the answer in the form of an integer (not a float) and gives the correct value of 1 for the case where k = 0. Use phyton code to answer,
- Given the recursive function below where n is an integer: if n = 0 or n = 1 or n = 2 f(n) = {f(n – 2) + f(n – 4) otherwise Which of the following statements is true? IMPORTANT: There is no "Check" button for this question. You can change the answer as many times as you like. Select one: O a. The function terminates if and only if n is 1 or even. O b. The function terminates if and only if n24. O . The function terminates if and only if n=1 or n is even and greater or equal to 0. O d. The function terminates if and only if n is 0, 1 or 2. O e. The function terminates if and only if n20.2√2 TU 1 1 + 22 1 222 1 1 + 2 1 + 1 + 2 2 2 1 + This equation can be used in a recursive function to compute to a large number of decimal places. In the above 1 1 2 equation, consider the base case as Write a Python code (and show its output) using recursive functions to compute the value of accurate up to 8 decimal places as 3.14159265. How many times do you need to recurse so that you can get the accuracy of up to 8 decimal places? Upload a .py file of your source code. Include your answer to the follow-up question in a comment block.Practicing Loops. Einstein Private Elementary school has three classes in each of its 9 grades. 27 classes in total. It has kindergarten (grade 0) though 8th grade. The school allows parents to pay tuition over the nine-month school year. Tuition for kindergarten is $90 dollars every month. Tuition for the other grades is $50 times the grade level every month. (1st grade is $50 a month, second grade is $100 a month, etc.) Design a programming solution that outputs nine tuition payment bills for each of the 27 classrooms. Each bill must contain the grade number (0 through 8), the classroom number (1 through 3), the month (1 through 9) and the amount of the tuition due. Your output should look something like: Grade Classroom Month Tuition 0 1 1 90 0 1 2 90 0 1 3 90 0 1 4 90 ... 8 3 7 400 8 3…
- A typical NMR peak after Fourier transform has a Lorentzian absorptive line shape. This line shape is represented by the function below, where x is in Hz 1 f (x) : x2 + 1 Write a program to calculate the integral of this function using Riemann sums on the range from [-10, 10] (inclusive) with dx = 0.01. In other words, estimate the following integral with a Riemann sum. 10 1 x2 + 1 -10The Taylor’s series for cos(x) is given as cos(x)=∑∞ n=0(-1)^n x^2n/2n!= 1-x^2/2!+x^4/4!-x^6/6!+…. The program to calculate cos(x) should use three recursive functions:float power (float x, float n);float fact (float n);float cosine (float x, float n); Write a c programπ can be computed using the following series: m(i) = 4(1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 + . . . + (-1)i+1/(2i - 1) ) Write a function that returns m(i) for a given i and write a test program that displays the following table: i m(i)1 4.0000101 3.1515201 3.1466301 3.1449401 3.1441501 3.1436601 3.1433701 3.1430801 3.1428901 3.1427
- Write a python function that takes a positive integer n as an argument. This function will return the number of positive integers less than n that are co-prime to n. Co-prime Numbers: Two numbers are coprime to each other if they don't have any common divisor except 1. Sample Input 1: 1 Sample Output 1: Reason: Since 1 is the smallest positive integer, there exists no positive integer that is less than and coprime to 1. Sample Input 2: 2 Sample Output 2: 1 Reason: Only 1 doesn't share any common divisor (except 1 itself) with 2. Also, 1 < 2. Sample Input 3: Sample Output 3: Reason: Namely, the two coprime numbers to 6 are 1 and 5. Sample Input 4: 36 Sample Output 4: 12 Reason: The numbers coprime to 36 are 1, 5, 7, 11, 13, 17, 19, 23, 25, 29, 31 and 35Convert Newton’s method for approximating square roots in Project 1 to a recursive function named newton. (Hint: The estimate of the square root should be passed as a second argument to the function.) An example of the program input and output is shown below: Enter a positive number or enter/return to quit: 2 The program's estimate is 1.4142135623746899 Python's estimate is 1.4142135623730951 Enter a positive number or enter/return to quit Given Code: # Modify the code below """ File: newton.py Project 6.1 Compute the square root of a number (uses function with loop). 1. The input is a number, or enter/return to halt the input process. 2. The outputs are the program's estimate of the square root using Newton's method of successive approximations, and Python's own estimate using math.sqrt. """ import math # Initialize the tolerance TOLERANCE = 0.000001 def newton(x): """Returns the square root of x.""" # Perform the successive approximations estimate = 1.0…Convert Newton’s method for approximating square roots in Project 1 to a recursive function named newton. (Hint: The estimate of the square root should be passed as a second argument to the function.) An example of the program input and output is shown below: Enter a positive number or enter/return to quit: 2 The program's estimate is 1.4142135623746899 Python's estimate is 1.4142135623730951 Enter a positive number or enter/return to quit