Write a Python function called integrateSpectrum that uses the Trapezoidal Method to numerically estimate the bounded integral. The first few lines of its definition are outlined here. It's up to you to fill in the rest of the function with code: def integrateSpectrum (wavelengths, fluxes, w_lower, w_upper): This function performs a numerical integral of a spectrum. Arguments: wavelengths = a numpy array of wavelengths, in nanometers fluxes = a numpy array of fluxes, corresponding to w w_lower = the lower wavelength limit of the integration w_upper = the upper wavelength limit of the integration Returns:
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- Implement a function called tautology? that takes as input a fully parenthesized formula and returns true if it is a tautology and false otherwise. As was the case in the previous lab, the formula will contain at least one set of parentheses for each operator, but may contain more. The best strategy for doing is to use an insight called Quine's method. It is based on the observation that if a formula, such as (p or (not p)), is a tautology, the result of substituting p with true is a tautology and the result of substituting p with false is also a tautology. This implies a computational strategy: to evaluate whether a formula F is a tautology1. Collect all of the propositional variables.2. Substitute every occurrence of the first variable with #t and every occurrence ofthe same variable with #f3. Make two recursive calls to Tautology? “And” the results.4. When all possible substitutions have been made, i.e., the formula contains onlytruth values, evaluate the formula and return the…Implement a function called tautology? that takes as input a fully parenthesized formula and returns true if it is a tautology and false otherwise. As was the case in the previous lab, the formula will contain at least one set of parentheses for each operator, but may contain more. The best strategy for doing is to use an insight called Quine's method. It is based on the observation that if a formula, such as (p or (not p)), is a tautology, the result of substituting p with true is a tautology and the result of substituting p with false is also a tautology. This implies a computational strategy: to evaluate whether a formula F is a tautology 1. Collect all of the propositional variables. 2. Substitute every occurrence of the first variable with #t and every occurrence of the same variable with #f 3. Make two recursive calls to Tautology? “And” the results. 4. When all possible substitutions have been made, i.e., the formula contains only truth values, evaluate the formula and return…Write a program in Python with a function decimalToBinary(n) that converts a positive decimal integer n to a string representing the corresponding binary number. Do the conversion by repeatedly dividing the number n by 2 using integer division, keeping track of the remainders, until the number is reduced to 0. The remainders written in reverse order form the binary number string.
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- Your first task will be to write a simple movement simulator on a snakes and ladders board. For this questionyou can ignore the snakes and ladders and just simply assume you only have to deal with moving. You willneed to simulate rolling the die - this can be done by using the Python random module and the randint method.Your function play_game will take as input the length of the board (an integer), "play" the game by rolling the diemultiple times until the sum of rolls is larger or equal to the length of the board. (note: this is one of the possibleand simplest end rules). The function should return the total number of rolls required to finish the the particulargame that was played. Obviously this number will vary as it depends on the specific random rolls performedduring the movement simulation.***python only*** Write a function that takes a DrawingPanel as a parameter and draws the horizontal pyramid shape as shown in the following figure. There are ten rectangles of increasing sizesfilled with increasing shade of green color (increment of G by 20 while keeping R and B at 0). These rectangles should have the same width, and completely symetric with respect tothe center horizontal line of the window. Each rectangle should have a blue outline. A sample run of the following main() function should result in the following graphics. WIDTH = 300 HEIGHT = 300 ### # Your code here ### def main() : panel =Drawing Panel(WIDTH, HEIGHT) draw_objects(panel) panel.window.mainloop if_name_ == '_main_' :main()in Java Apply the Newton-Raphson's method xn+1 = xn – f '(xn) / f ''(xn) to develop a function double findMinMax(…) that returns a solution that is either a minimum value or a maximum value for z. The program finds a local minimum or a local maximum when the difference between the new solution and the previous one is smaller than 0.00001 within 10000 iterations. Otherwise, it shows Infinity as output. Let function z = x4+2y6 – xy – x + 2. Show the post-conditions for z. The preconditions for x and y are shown as below. Feel free to choose an arbitrary initial guess values x0 and y0 that meet the following precondition. |x| ≤ 6 and |y| ≤ 5