task is to find Kth smallest GCD among h that 1
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- 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.Computer science questionJAVA Coding Problem Holi is celebrated in India as a festival of colours and your friend Khan from India has gifted you X packets of colours. Now you are planning to make a beautiful rangoli, to make it you need to map all colours pairwise distinct, so that they look attractive. To do so, you can mix the colours zero or more times: Pick any two random colours. Let's denote their weight by t and u. Mix the colour with second colour. After the process, the value of the first colour remains t, but the weight of the second colour changes to t+ u. Now you have to develop the code to find the minimum number of mixing operations you needs to perform to make a beautiful Rangoli. Sample Test Case Scenario: 1 3 321 Output:
- Let A = {a, b, c} and B = {u, v}. Write a. A × B b. B × AF4Q3: Superheroes Supervillains are tired of Toronto condo rental prices, so they are leaving Toronto for Mississauga. Luckily, we have valiant superheroes that can deal with them. The superhero () has a name , an intelligence score , and a strength score .ni-th0 = gin[x] + s[x] Detective Zingaro has asked for your help. For each of the supervillains, tell him the name of the superhero that should deal with that supervillain. Note: A superhero can be assigned to multiple supervillains (or none at all). Note: whenever there are multiple superheroes that satisfy the given requirements for a supervillain, report the one whose name is lexicographically smallest (i.e. the one that’s the smallest according to Python’s ordering of strings). It’s guaranteed that superheroes have distinct names. Hint: Tuples of multiple elements may be helpful here. In python, you can compare two tuples and . If and are different, the result is the same as comparing and . If and are equal, the result is the same…
- nbm.m//,//Tiling: The precondition to the problem is that you are given threeintegers n, i, j, where i and j are in the range 1 to 2n. You have a 2n by 2n squareboard of squares. You have a sufficient number of tiles each with the shape . Your goalis to place nonoverlapping tiles on the board to cover each of the 2n × 2n tiles except forthe single square at location i, j. Give a recursive algorithm for this problem in whichyou place one tile yourself and then have four friends help you. What is your base case?Little Frank loves mathematics. Every day, he solves some mathematical problems to improve his skill. A few days ago, he found a popular problem about turtles. The problem is as follows. Little Frank is given R rectangles, numbered 1 through R. The width and height of the i-th rectangle are Ni and M¡ unit respectively. There is a turtle located on the top-left corner of each rectangle. For each rectangle, count the number of ways the turtle can reach the bottom-right corner, if each turtle can only move right or down 1 unit at any time. The turtle is not allowed to move outside the rectangle, but, of course, the turtle can move on the boundary of the rectangle. In less than one second, this problem was solved for all rectangles. He felt that the problem was too easy. This morning, Little Frank wanted more challenges. Thus, for each rectangle į, he cut and removed a rectangle of A¡ x Bị unit from the top-right corner. See the following figure for detail. Bị Mi He could not solve this…
- [Unbalanced Rod] Given a set of n weights {w₁,..., wn} and a rod of length n - 1 inches, we can attach the weights to the rod at hooks placed at one inch distances apart as shown in the figure below. -1". /10 2 3 12 2 4 We can attach a weight to any hook but no two weights can be attached to the same hook and we have to attach all the weights. For any given assignment of weights to hooks, we can compute the location of the center of mass of the rod and the weights according to the following equation (neglecting the weights of the rod and the hooks). where 0 ≤ Pi≤n-1 is the position of weight along the rod. For example, in the figure shown above, the center of mass is computed as C= C = i Wi Pi Σi Wi 10 0+2 1+3·2+4·3+12.4 +2.5 10+2+3+4+12+2 78 33 The problem is to find an assignment of weights to hooks that makes the center of mass as far as possible to the left, i.e., minimize the value of c. Answer the following questions. 1. Describe a greedy algorithm that finds the assignments that…python please thank youHeat capacity of a solid: Debye's theory of solids gives the heat capacity of a solid at temperature T to be 3 T rOp/T Cy = 9VpkB (e* – 1)2 dx, - where V is the volume of the solid, p is the number density of atoms, kg is Boltzmann's constant, and 0D is the so-called Debye temperature, a property of solids that depends on their density and speed of sound. Develop a computer code to evaluate Cy (T) for a given value of the temperature, for a sample consisting of 1000 cubic centimeters of solid aluminum, which has a number density of p = 6.022 x 1028m-3 and a Debye temperature of 0p = 428K. The Boltzmann's constant kg = 1.380649 x 10-23 J · K-1. Please evaluate the integral with the following methods: (a) MATLAB adaptive Simpson quadrature, [Q.FCNT] = QUAD(FUN,A,B,TOL) with TOL =le-10.