# Mathemtics

## Real-Life Examples of Parabolic Shapes

Select and discuss two examples of real life objects that incorporate the parabolic shape. Explain why the parabolic shape was used for the objects. Parabolic shape is used in dish antennas that collect wireless signals from television/ internet signal transmitters on household tops. The parabolic surface of the dish … Solution Summary Real-life examples of […]

## Normal distribution

1)Which choice is another term that can be used to describe a normal distribution: A) discrete distribution B) negatively or positively skewed C) bell curve D) independent variable 2) If a normal distribution has a mean of 30 and a standard deviation of 5, then A) the median is 35 and the mode is 25. […]

## Lagrangian Interpolation

3) If e^1.3 is approximated by Langrangian interpolation from the values of e0=1, e1=2.7183, and e2 =7.3891., what are the minimum and maximum estimates for the error? Compare to the actual error. use MATLAB using “polyfit” and “polyval” functions 4) Repeat above problem but now extra polate to get e^2.7. NOTE: Find Lagrange p6(x) by […]

## Use Parseval’s equality

We are using the book Methods of Real Analysis by Richard R. Goldberg (See attached file for full problem description) — 12.5-2 Show that the Fourier series for is a) Use 12.5E to show that Fourier series at t=0 converges to . Deduce that 12.5E: Theorem. Let ( this means the function f and the […]

## Matrices and Pivot Positions : Solutions for Ax+0 and Ax=b

In problems 1-4 (a) does the equation Ax = 0 have a nontrivial solution and (b) does the equation the Ax = b have at least one solution for every possible b? 1) A is a 3×3 matrix with three pivot positions. 2) A is a 3×3 matrix with two pivot positions. 3) A is […]

## Media Selection and TV Ads

An ad campaign for a new snack chip will be conducted in a limited geographical area and can use TV time, radio time, and newspaper ads. Information about each medium is shown below. Medium Cost Per Ad # Reached Exposure Quality TV 500 10000 30 Radio 200 3000 40 Newspaper 400 5000 25 If the […]

## Systematic Elimination method

Use the Systematic Elimination method to solve the system of ordinary differential equations. See attached file for full problem description. Solution Preview Please see the attached file. Consider a system of linear differential equations with constant coefficients: where pij is a polynomial operator in , for . The three types of elementary operations are these: […]

## The following table contains the number of complaints

The following table contains the number of complaints received in a department store for the first 6 months of last year. Month Complaints January 36 February 45 March 81 April 90 May 108 June 144 Referring to the table above, if this series is smoothed using exponential smoothing with a smoothing constant of 1/3, what […]

## List the first 10 terms of each of these sequences

Please see the attached file for the fully formatted problems. Practice problem 20 List the first 10 terms of each of these sequences. a) The sequence whose nth term is the larges integer k such that k! <= n; b) The sequence whose nth term is 3^n – 2^n; c) The sequence whose nth term […]

## Slack and surplus variables

. (a) Define the slack and surplus variables. What do they represent? What is (are) the difference(s) between a slack and a surplus variable? (b) Briefly describe the important parts of each step needed to make a decision using decision sciences models. (c) What are the different types of special situations that may occur while […]

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