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- Let A = {a, b, c} and B = {u, v}. Write a. A × B b. B × AQ3: Interplanetary Spaceflight Milan Tusk is the richest person in the universe. After devoting decades of his life to further our space exploration technologies, he’s finally ready to retire. Being a space enthusiast, the first thing he wants to do is visit n planets p1, p2, …, pn, in this order. He’s currently on planet p0. Milan knows that the distance between planets pi and pi + 1 (for 0 ≤ i < n) is d[i]light years. His spaceship uses 1 tonne of fossil fuels per light year. He starts with a full tank and can fill up his tank at any of the n planets (but he must not run out in between two planets). There’s a huge cost to set up the spaceship for refuelling. Due to financial constraints (he’s not THAT rich), he can fill up his tank at most ktimes. In order to save money and make his spaceship lighter, Milan is looking for the smallest possible fuel tank that enables him to complete his space travel and reach planet pn. What is the smallest tank capacity that enables him to do so?…38. The geometric mean g of n numbers x; is defined as the nth root of the product of x;: g=Vx1x2X3•…Xn (This is useful, for example, in finding the average rate of return for an investment which is something you'd do in engineering economics). If an investment returns 15% the first year, 50% the second, and 30% the third year, the average rate of return would be (1.15*1.50*1.30)") Compute this.
- def fquartic(x): return (x**4-1) Find the roots There are two real roots of this function. Even though you may immediately see what those roots are, use scipy.optimize.root_scalar to find those roots one by one: Use the default method (i.e. don't specify a specific method for root finding) Specify appropriate x0 and x1 values for each one of the roots (don't pick them right on top of the roots, but pick them close) Make sure that the converged attribute of your solutions are both True.Need help in python. Problem: 2D random walk. A two dimensional random walk simulates the behavior of a particle moving in a grid of points. At each step, the random walker moves north, south, east, or west with probability 1/4, independently of previous moves. Compose a program that takes a command-line argument n and estimates how long it will take a random walker to hit the boundary of a 2n+1-by-2n+1 square centered at the starting point. //Given codeImport stdioImport randomImport sysn = int(sys.argv[1])//write code herestdio.write('The walker took ')stdio.write(c)stdio.writeln(' steps')Q2: In this question, you will write a Python function to compute the Hadamard product of two matrices. The Hadamard product is the "component-wise" product of two matrices. That is, each entry of the product matrix is equal to the product of its corresponding entries of the input matrices. Here is an example: a11 a12 a21 a22 a23 a31 a13 SH a32 033 A b11 b12 b13 b21 b22 b23 b31 b32 b33. B = [an bu a21 b21 a31 b31 a12 b12 a22 b22 a32 b32 a13 b13 a23 b23 a33 b33. Hadamard product of A and B Write a Python function to compute the Hadamard product of two matrices as follows. a) The inputs to the function are two matrices. b) The function should check whether the two matrices have the same size. If not, it should print "The input matrices are not of the same size". c) If two matrices are of the same size, the function computes the Hadamard product and returns the answer. Use for loops to compute the Hadamard product.
- [Fish Tank] You play with a clown fish that has an initial size so. The fish can eat other fish in a tank organized in m columns and n rows. The fish at column i and row j has a positive size si,j. When your fish eats another fish, it grows by that amount. For example, if your clown fish has a size of 10 and eats a fish of size 5, it becomes of size 15. You cannot eat a fish that is bigger than your size. The game starts by eating any fish in the first (left-most) column that is not bigger than yours. After that, you advance one column at a time by moving right. You have only three allowed moves. You either stay at the same row, move one row higher or one row lower. You will always move to the right. Thus, you will make exactly m moves to advance from left to right. Your goal is to exit the fish tank from the right with the biggest possible size. The figure below shows an example with the best answer highlighted. In this case, the final fish size is 71 (10+8+7+24+22). You are required…*:To round (B) towards minus infinity the function used is roundn(A) fix(A) floor(A) ceil(A) round(A)Q3: Write a matlab program call matq3.m that returns the plot of the 2- D space defined by the following equation: (-xsin(x) y = {20 ( cos (x) - 2π ≤ x < 0 x ≥ 2π Label the x-axis and y-axis and z-axis and title to the curve.
- The "enor function"), is a special function that often occurs in the fields of probability and statistics, looks 10 55 3 ** -0.3 -10 art The definition of erfix) can be found here, but for now that is unimportant. There is a function in the Python matherary that directly evaluates the error function for any single, real-valued number. You can import it with the Ine from math inport erf Suppose we want to find the root of the function fo))+J The Newton-Raphson Method does not behave well with functions of this sort (see the lecture notes), so we will need to use the section Method You are to unite a function relatina, eta, left, right, taterace which computes and returns that root aahe (n) and bets (3) are the constants defining the function for) above,left and right define a range known to contain the root, and tolerance is the maxim error that can be tolerated for the root, defined as in the previous questions Notes: You should use your bisection retider function from the previous…sum = 0; for (int i = 1; i< n; i = sum++ || 2*i)Complete the function that calculates the sum of the first n+1 terms of the geometric series a, ar, ar² ar³, ar4 . note that the series begins with a and the last term is ar", in total there are n+1 terms. ar" ... [ ]: # complete the function given the variables a,r,n and return the value as series_sum. def sum_geometric_series(a,r,n): # your code here return series_sum