Mathematics Homework Solutions

Greatest Common Factors

Find the GCF: (12,18), (16,20) (44,153) I tried to do on my own, I'm not sure if I understand what I am doing. If you can would it be possible to describe in details exactly what I should be doing. Thanks.

Uniform Distributions and Probability Density Functions

Let A be a random variable that is uniformly distributed over (0,1). Find the pdf of B = A^(1/n)

Iterative method

Please see the attached file. Iterative method - Two bodies are connected by springs of stiffness, K1, K¬2 and K3 and of natural lengths l1, l2 and l3 as shown in figure 1 Task Develop an iterative method to solve X1,X2 and X3 and implement this in Excel

Euler's Method

The function of y(x) satisfies the differential equation and the initial condition y(1)=1. Firstly solve the equation to get an exact value then use Euler's method to obtain the value of y(2). Compare this value with the analytical value and discuss how the approximate value obtained by Euler’s method may be improved. ...continues

A certain engineering system can be represented by mass in a spring, as shown in Figure 1. If the mass is pulled downwards and then released, it oscillates on the spring. Using Newton¡¯s second law, a homogeneous second-order differential equation can be set up as below: If the mass m is 1kg and the spring¡¯s stiffness k is 100N/m, find an expression for the displacement x with respect to time t, when t=0, x(0)=0 and x`(0)=1 ...........Diagram .....

A certain engineering system can be represented by mass in a spring, as shown in Figure 1. If the mass is pulled downwards and then released, it oscillates on the spring. Using Newton¡¯s second law, a homogeneous second-order differential equation can be set up as below: If the mass m is 1kg and the spring¡¯s stiffness k is 1 ...continues

The manger of the Carpet City outlet needs to make an accurate forecast of the demand of Soft Shag carpet

2. The manger of the Carpet City outlet needs to make an accurate forecast of the demand of Soft Shag carpet (its biggest seller). If the manger does not order enough carpet from the carpet mill, customer will their carpet from one of Carpet City’s many competitors. The manager has collected the following demand data for the pas ...continues

This posting provides solution to Linear Programming and Integer Programming problems.

1. Consider the following linear programming model: Maximize Z=5 x1 + 4x2 Subject to 3x1+4x2≤10 X1, x2≥0 and integer Demonstrate the graphical solution of this model. ...continues

Consider a capital budgeting example with 5 projects from which to select.

Consider a capital budgeting example with 5 projects from which to select. Let x1 = 1 if project a is selected, 0 if not, for a = 1, 2, 3, 4, 5. Projects cost $100, $200, $150, $75, and $300 respectively. The budget is $450. Write the appropriate constraint for the following conditions: Choose no fewer than 3 projects. If proj ...continues

Lagrange

Please see attachment.

Newton's interpolating polynomial

see attachment Use Newton’s interpolating polynomial to approximate the function: f (x) = e^ (–ax2) a = 1.1125 Construct approximation using the values f (x) at x= -2, -1, 0, 1, 2. Call this approximation N(x). ii) Compute the value of the integral accurate to 1 decimal place. iii) Compute sufficient ...continues

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