Consider a planer quad in 3d (for simplicity, you can assume it is the unit square). Which of the following sentences about the barycentric coordinates of a given point P inside the quad is correct? It is not possible to find any barycentric coordinates for P. There is a unique barycentric coordinates for P. There are two different barycentric coordinates for P. There are infinite many barycentric coordinates for P.
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- Let l be a line in the x-yplane. If l is a vertical line, its equation is x = a for some real number a. Suppose l is not a vertical line and its slope is m. Then the equation of l is y = mx + b, where b is the y-intercept. If l passes through the point (x₀, y₀), the equation of l can be written as y - y₀ = m(x - x₀). If (x₁, y₁) and (x₂, y₂) are two points in the x-y plane and x₁ ≠ x₂, the slope of line passing through these points is m = (y₂ - y₁)/(x₂ - x₁). Instructions Write a program that prompts the user for two points in the x-y plane. Input should be entered in the following order: Input x₁ Input y₁ Input x₂Implement Velocity Verlet • Bouncing test: Simulate two particles starting from some distance approaching each other with some speed. Plot x(t), v(t), V(t), K(t) and H(t). Are they bouncing? Is H conserved? • Find the longest ∆t that conserves H to high precision in the bouncing test . I want simulation in pythonGiven is a strictly increasing function, f(x). Strictly increasing meaning: f(x)< f(x+1). (Refer to the example graph of functions for a visualization.) Now, define an algorithm that finds the smallest positive integer, n, at which the function, f(n), becomes positive. The things left to do is to: Describe the algorithm you came up with and make it O(log n).
- write a computer program that will find a solution to Diophantine ax + by = g, where a,b,x,y,g are integers and g = gcf(a,b)We consider certain strings of length 6 over the alphabet S = {A,B,C}. We require that the string contains exactly two As, and exactly two B's, and exactly two C's. How many such strings are there? That is, how many strings of length 6 over the alphabet {A,B,C} contains exactly two A's, two B's and two C's?Suppose that the only currency were 3-dollar bills and 10-dollar bills. Show that every amount greater than 17 dollars could be made from a combination of these bills.
- Create a curve that uses a quadratic parametric approach with three interpolated control points. The equations which describe the curve are: $$f_x(u) = c_0 u^2 + c_1 u + c_2 $$ and $$f_y(u) = c_3 u^2 + c_4 u + c_5 $$ where $u$ ranges from 0.0 to 1.0. The first control point $$p_0$$ is for $u=0$, the second $p_1$ for $u=0.5$, and the third for $p_2$ and at $u=1.0$. Modify the code to implement your solution. It is sufficient for this task to get the program working with three control points, but you are most welcome to attempt a solution that works on four or more. Code: import java.awt.Graphics2D; import java.awt.geom.Ellipse2D; import java.awt.geom.Path2D; import java.awt.geom.Point2D; import javax.swing.JFrame; import javax.swing.JTabbedPane; import javax.swing.SwingUtilities; public class DotToDotDemo implements Runnable { /** * DotToDotDemo - A demo which draws dots between points to form a curve. * Eric McCreath 2015, 2019 - GPL * Modified by Matthew Aitchison 2022. */ JFrame…Let’s consider a long, quiet country road with houses scattered very sparsely along it. (We can picture the road as a long line segment, with an eastern endpoint and a western endpoint.) Further, let’s suppose that despite the bucolic setting, the residents of all these houses are avid cell phone users. You want to place cell phone base stations at certain points along the road, so that every house is within four miles of one of the base stations. Give an efficient algorithm that achieves this goal, using as few base stations as possible. Give the psudo code.CThere is a road, the starting coordinate is 0, and the coordinatesof the line are given to draw a black line, for example, five linesegments for drawing black lines, (5, 6), (1, 2), (4, 8), (7 , 9)and (5, 8), as shown belowOutput:Length of the black line on the road: 6Maximum number of overlaps: 3Maximum number of overlaps Length of black line: 2 The first row is a positive integer N, there are N line segments for drawing black lines.Then there are the integer values of the start point coordinates and the end point coordinates of the line segment of the black line. Sample 15160 180150 200280 300290 330190 210Output:Length of the black line on the road: 110Maximum number of overlaps: 2Maximum number of overlaps Length of black line: 40 Sample 21120 120Output:Length of the black line on the road: 0Maximum number of overlaps: 0Maximum number of overlaps Length of black line: 0
- For any program P that takes as input a string, can P ever solve a language other than Y(P)? If your answer is yes, give an example. If your answer is no, briefly justify your answerA string S consisting of uppercase English letters is given. In one move we can delete seven letters from S, forming the word "BALLOON" (one 'B' one A, two 'L's, two 'O's and one 'N'), and leave a shorter word in S. If the remaining letters in the shortened S are sufficient to allow another instance of the word "BALLOON" to be removed, next move can be done. What is the maximum number of such moves that we can apply using pythonPython This simulates the population of fish. Use this to generate a plot with a numerical solution and the exact solution on the same plot axes for model parameters, P_m = 20,000 fish with a birth rate of b=6%, a harvesting rate of h=4%, a change in t=0.5 and y_0=5000