Exercise 4A Write functions to perform the following tasks efficiently. Do not change the function names in the template file, and do not import any packages besides those already indicated in the template. (1) Take x and return 2x³ - X. (2) Take two inputs x and y and return their product and the absolute value of their difference, in that order. E.g. inputs 3, 4 should return 12, 1. (3) The geometric mean of n numbers is the nth root of their product. The mid-range is the ordinary (arithmetic) mean of the maximum and minimum elements. Write a function which takes a list of numbers as input and returns True if the geometric mean is less than or equal to the midrange, and False if the geometric mean is greater than the midrange. For example, the input [3,8,9] should return True and [3,6,7,5] should return False. (4) Take an integer n and returns a list of the first n of the Padovan sequence pn. (This is a variant of the Fibonacci numbers, defined by P₁ = P2 = P3 = 1, and pn = Pn-2 + Pn-3 for n ≥ 4.) (5) Take a pair r≥ 0 and representing a point's polar coordinates and return a pair x, y representing its Cartesian coordinates. 0 (6) Take a pair x, y representing a point's Cartesian coordinates and return a pair r, representing its polar coordinates, where 0 = [0, 2π). Check that your function works for (x, y) in all quadrants.

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Program: final.py Specification First, download the template file, final.py. This file contains the function names and documentation. You are required to add a header comment block with your name, the file name, the current semester, and year. Do not change the function headers, just add your implementation for each function where indicated. Add descriptive comments to your code. Remember to indent all the code for the function. Here are the functions that you will write: • Calculating tips is a common operation and the first function you write for the final project will do exactly that. The function calculate_tip accepts two parameters, the bill amount and the percent to tip, and returns the amount of the tip to write into the bill. The function should return the string "Invalid charge amount" if the charge is not more that 0 and "Invalid tip percent" if the tip is less than 0. Function heading: def calculate tip(charge, tip_percent): Parameter Specification: charge is the total ch…

2. Fill in the for-loop below with the correct parameters to make room for the new value. saved Let's say that you have to write a function to insert an element into an ordered array. It takes an array A, a size, an index and a value. The value needs to be inserted at Aſindex] without losing values that are already in the array. // Assume that the index is found to be within array bounds and there is room to insert. for (int i = ?; ?; ?) { A[i]=A[i-1]; } A[index]=value; size++; O 0; i 0; - O size; i> index; -- O size-1; i>= index; i--

In python find_substring("It was the best of times, it was the worst of times", "i") [20, 26, 47] >>> find_substring('Episode III: Revenge of the Sith', "e ") [6, 19, 26] >>> find_substring("bobbobob", "bob") [0, 3, 5]