AT&T LTE 10:23 AM * 33% . 2 of 2 Execution Using Monte.Sarto integration method, calculate the area that Quianna can reach. Monte Carlo Integration methods take a random set of numbers and check to see if each of these values le within the area of interest. With this information, you can calculate the area by taking the ratio of true points divided by the total number of points 1. Start with a simpler problem. Create a circle (radus 1) and calculate the area using a Monte Carlo algorithm. a. Create the following figure for 200 random points. The ones that fall within the circle color red, and the ones that fall outside of the circle color blue b. Test the algorithm with the analytical answer (i.e. A- e. Test the algorithm with error analysis -abs(A, Aio") i. Plot the error vs number of points on a log plot 1. Number of random points should range from 10 to 10 2. 3. Generalize your algorithm to work for any size crcle Now, let's add in the horse. Create a program that takes in the stake location, rope length, and size of circle. This program will then calculate the grazing area. a. Create a figure for 100 random points. The ones that fal within the grazing area color red 2 and the ones that fall outside color blue. Usex-2,y 0, R 2, and r Test the ale rithm with error analysis e bs(Aur"-Air) b. i Plot the error vs number of points on a log plot 1 Number of random points should range from 10 to 10 c. Create an algorithm that outputs the area once error (x) is less than 10 Create a graphical user interface (GUJ using Matlab's a. Include all of the inputs for the calculation including x, y, R, r, and e b. Include a plot for the error analysis c. Include a scatter plot for the points inside and outside the grazing area 5. The farmer knows the location and the size of the desired grazing area. All he needs to know is what length of rope he needs to use. In the GUL create a need module to solve this problem. 6. In an alternate dimension, horses graze in three dimensions. Create a program that takes in the stake location [.yzi, rope length, and radius of the sphere. This program will then calculate the ganng area