Reference no: EM132394120

Assignment

1 Question

Given two lines defined by the equations:

y = m₁x + b₁
y = m₂x + b₂

Given the values: m₁ = 0.9, b₁ = -0.1, m₂ = -1.2 and b₂ = 1.5. Write a Python script which computes the point where these two lines intersect.

2 Question

Given the box shown in Figure 1. It has a width and height of 1. There is a boundary that bisects the box as shown. Region 1 is on the far side of the box. Write a Python script to throw 10,000 darts at the box. Print out how many land in region 1. Before you run your script use random.seed( 324 ).

Figure 1: Figure for problem 2.

3 Question

Given the box shown in Figure 2. It has a width and height of 1. Two bisectors are shown. Region 1 is marked. Throw 10,000 darts at this box. Count how many darts land in region 1. Before you run your script use random.seed( 247 ).

Figure 2: Figure for problem 3.

4 Question

Given the system shown in Figure 3. Each circle has a radius of 1. Write a script that throws 10,000 darts at the box. Count how many land inside of a circle. Before you run your script use random.seed( 231 ).

5 Question

Figure 4 shows an ellipse inside of an encompassing box. An ellipse was to foci, and the distance d1 + d2 is a constant for all points on the perimeter of the ellipse. The equation for an ellipse is that is centered on the origin is:

x²/a²+y²/b²= 1,

where the length of the major (long ) axis is 2a and the length of the minor axis is 2b. The location of the foci along the x-axis are

±√(a² - b²).

Given a = 1 and b = 0.5. Write a Python script that counts the number of darts that land inside of the ellipse. Use random.seed( 23 ).

6 Question

Given 1000 random numbers, which can be denoted by xi where i = (0, ..., 999). Given the equation:

z =Σ_i(x_i - x‾)²

where x‾ is the average of the x values. Write a Python script that computes z. Use random.seed(234).

7 Question

The equation for a standard deviation is:
σ =√(Σi(xi - x‾)²)/N - 1.

The numerator is the same equation used in the previous problem. Using the same random numbers from the previous problem, write a Python script to compute μ.

8 Question

Use the star program from the lecture. Write a Python script which counts the number of darts which land in each of these regions: 2, 4, 6, 9, 10. Note, do not sum these. Provide a count for each region. Throw 1000 darts. Use the random seed 95235.

9 Question

Create a box that has a length and width of 3. Divide this box up into 9 equally spaced regions. Throw 10,000 darts at this box. To show that the darts are randomly distributed, count the number of darts that land in each of 9 regions.

10 Question

What is the scientific name for this random dart method?