Equations of Straight Lines

1. Graph line with equation y=-4x-2. 2. 2x=8y=17=0 3. Graph the line with slope -2 passing through the point (-3,4). 4. Find slope of the line graphed (-44, 28) (9, -12). 5. x=9 graph the line 6. 6x-9y+7=0. 7. 2x=5y+3 8. Write an equation of line (0, -4). 9. A line passes through the point (6, -6 ...continues

Seasonalize Trends

The Costello Music Company has been in business for 5 years, selling electric organs. Below are the quarterly sales by year, with annual totals. Year Quarter 1 Quarter 2 Quarter 3 Quarter 4 Total 1 4 2 1 5 12 2 6 ...continues

A refinery blends four petroleum components into three grades of gasoline

A refinery blends four petroleum components into three grades of gasoline - regular, premium and low lead.... (See attached file for full problem description)

Finding the eigenvalues and eigenvectors of a linear transformation represented by a 3 x 3 matrix, and using them to diagonalise the matrix.

Please show all steps and workings clearly and explain in detail how you derive the answers. 1) This question concerns the linear transformation represented by a 3x3 matrix of real numbers. With respect to the standard basis in both the domain and codomain. (a) Determine t ...continues

What would be the difficulties associated with modeling this situation?

After contacting all of the professionals, you set up a "blog" (weblog) for you and them to share. You'll use this "blog" as the weeks go by to ask the group questions, raise issues for discussion and encourage networking among this diverse group. You decide to start your article with a math example that the readers can unde ...continues

Integer Programming Models : Maximizing Profits

A boat company manufactures three kinds of boats. Bass boats, ski boats and speed boats. Profit: Bass boat = 20,500 Ski boat = 12,000 Speed boat = 22,300 The company believes it will sell more bass boats than the other two boats combined, but no more than twice as many. Ski boats are it's standard model, bass boats and ...continues

Linear Transformations : The composition of any two reflections, whose lines of reflection are orthogonal, is a half-turn.

Matrix Theory – Homework 7 Prove the following in several stages: The composition of any two reflections,whose lines of reflection are orthogonal,is a half-turn. We will work in the vector space ℝ .... First Stage Refer to the diagram provided.The line l makes some angle with the x-axis. Let us suppose that ...continues

Vectors : Linear Transformations, Eigenvectors and Eigenvalues

Given the plane: x-y in 3-space do the following: a) show the normal vector b) construct a matrix that will reflect points across this plane c) Compute the eigenvalues for this matrix d) compute the eigenvectors for these eigenvalues

Vectors : Linear Transformations, Eigenvectors and Eigenvalues

Given the plane (x, -y, 0). This is the plane that is parallel with the Z axis and intersects the x,y plane through the line x-y=0 in 3 space do the following: a) show the normal vector b) construct a matrix that will reflect points across this plane c) Compute the eigenvalues for this matrix d) compute the eig ...continues

Linear Operations

Need to figure out how to do this type of problem. Using A =[ Cos alpha - Sin alpha ] Sin alpha Cos alpha (1) Find A^-1 =[ ] E SO sub 2 (1R) (2) Check A inverse is in SO sub2 (R) Check A inverse * A = Identity and A * ...continues