Computers and Technology

Consider a square defined by with a circle inside it with radius . The area of the circle is (obviously) ; however, let's assume that you don't know that, and that you don't know the formula for the area of a circle (but you do know that the area of the square is 4). Instead, try to approximately calculate that area using a large number of random points . Write a function that takes in number of sample points and outputs an estimate of the area. Use this function to compute the area for , , and so on up to . Make a plot with N on the x-axis and the calculated area on the y-axis. Enter the code you created to do this into the code editor below to submit it for grading. Some hints: Generate random points that are uniformly distributed over the square (i. e., that are equally likely to fall anywhere within that square). And then count how many of those points fall within the circle. In Matlab, you can generate uniformly distributed random points using the function rand(N,1), which creates an array of random numbers between 0 and 1. We need and between -1 and 1, so we need to do: x

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Consider a square defined by with a circle inside it with radius . The area of the circle is (obviou...

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