Find a matrix P that diagonalizes the matrix A = [ 2 0 ?2 / 0 3 0 / 0 0 3 ] and compute P ?1AP.

Resource allocation. A coffee manufacturer uses Colombian and Brazilian coffee beans to produce two? blends, robust and mild. A pound of the robust blend requires 12 ounces of Colombian beans and 4 ounces of Brazilian beans. A pound of the mild blend requires 6 ounces of Colombian beans and 10 ounces of Brazilian beans. Coffee is shipped in 138pound burlap bags. The company has 65 bags of Colombian beans and 30 bags of Brazilian beans on hand. How many pounds of each blend should they produce in order to use all the available? beans?

1. A living room is 15 ft x 19 ft. The walls of the room are 8.5 ft tall.

Calculate the total area of the West wall?

How many rolls of wallpaper will you need to cover the wall. One roll will cover 44 square feet

What will be the cost of the wallpaper? ($14.99 for a pack of 2 rolls)

2. Calculate the following for the remaining walls

Calculate the total area of the North Wall. (Note: You are not painting the Kitchen door.) Kitchen door is 3.5 ft wide by 7 ft tall

Calculate the total area of the East Wall.

Calculate the total area of the South Wall. (Note: You are not painting the Front Door or the Window.) Front door is 3.5 ft wide by 7 ft tall and the window is 8 ft by 4 ft tall

Calculate the total area of the North, East, and South Walls combined.

How many cans of paint do you need? Why? (Remember, you are doing a double coating.) one can of paint will cover 400 square feet and is $17.99 per can

Calculate the total cost of paint.

3.When looking at your dingy carpet, you noticed the dirt trail leading from the Front Door to the Kitchen Door. In order to negate this problem you decided to create a 4 ft laminate tile walkway from the Front Door to the Kitchen Door. Then the rest of the room would be re-carpeted.

Calculate the following for the new walkway.

What are the dimensions of the new walkway?

Calculate the total area of the new walkway.

Calculate how many boxes of laminate tiles you need. Laminate tiles one box will cover 12 square feet and is $24.99 per sq yd

Calculate the total cost of creating the new walkway.

4. Calculate the following for the recarpeted area.

What is the dimension of the area that will be recarpeted?

Calculate the total area that will be recarpeted in sq ft.

Calculate the total area that will be recarpeted in sq yd.

Calculate the total cost of the recarpeted area.Carpet is sold by the square yard and is $29.99 per sq yd

4. Calculate the total cost of the recarpeted floor and making a new walkway.

5.Next, it is time to fix the ceiling. After all the other work you have done, you decided it was best to keep the ceiling uniform with a single type of tile.

Calculate the total area of the ceiling.

Calculate the total amount of boxes of ceiling tiles you need. One box of tile will cover 20 square ft and it is $19.99 per box

Calculate the total cost of the ceiling tiles.

6. Finally, you are finished! All that is left is to calculate how much money you spent on your wonderful renovations.

What was the total cost of fixing the entire living room? Give an itemized list.

How many methods are there for solving quadratic equations? And which is a preferred method?

the number of bacteria in millions in a petri dish t seconds after an antibiotic is added is given by the function b(t) Assume b(t) is an exponential function first point (1,12) second point (2,2) What is the 1 unit growth factor? what is the 1 unit percent change? How many bacteria in millions are there in the petri dish at the moment the antibiotic is added? Find the function of B(t) How long does it take the number of bacteria to decrease by 50%? include units

Find the values of the 5 remaining trigonometric functions given the value and constraints.

csc = 3/2 where cos < 0

Chelsea took out three loans for a total of ?$78000 to start an organic orchard. Her? business-equipment loan was at an interest rate of? 11%, the? small-business loan was at an interest rate of 5?%, and her? home-equity loan was at an interest rate of 4.5?%. The total simple interest due on the loans in one year was ?$4605. The annual simple interest on the? home-equity loan was ?$105 more than the interest on the? business-equipment loan. How much did she borrow from each? source?

A Population Model The population of the world in 2013
was 7.13 billion people and was growing at a rate of 1.1% per
year. Assuming that this growth rate continues, the model
P(t) = 7.1311.0112^(t-2013) represents the population P (in
billions of people) in year t.
(a) According to this model, when will the population of the
world be 10 billion people?
(b) According to this model, when will the population of the
world be 12.2 billion people?

A saleswoman sells a? dried-fruit mixture for

?$5.90

per pound and nuts for

?$14.55

per pound. She wants to blend the two to get a

10?-lb

mixture that she will sell for

?$9.36

per pound. How much of each should she? use? Solve using matrices.

Solve for x

x^4 + 2x^3 + 2x^2 + 3x + 1 = 0

Let x ∈ R³ be nonzero and let A be the matrix whose columns are x, 2x, 3x in this order. Show that x is an eigenvector of A and find a basis for the null space of A.

Orca J-43 is sighted in Pudget Sound at the following depths (in feet) at certain times t (in minutes) measured from sea level. D(t) =    59 0 ≤ t < 5 t 2 − 22t + 144 5 ≤ t < 10 24 10 ≤ t < 18 8(t − 15) 18 ≤ t ≤ 22 (a) What is the range of the function D? Strategy then final result, no algebra steps (b) Another orca, K-97, also shows her presence in Pudget sound. If her depths (measured at the same time as above) is given by g(t) = 2t + 1, at which times are both whales at the same depth? Strategy then final result, no algebra steps

P(x) = x6 − 7x3 − 8

(a) Find all zeros of P, real and complex.

(b) Factor P completely.

In many cities and towns across the United States, the numbering system of the roads is based on a grid, similar to the latitude and longitude lines on a globe. Suppose the green lines in the following graph represent two east-west and two north-south running roads in a Midwestern town.

Write equations for the two horizontal and two vertical lines that represent roads in the town.






2. The Willis Tower (formerly known as the Sears Tower) in Chicago, Illinois, is the tallest building in the United States. Measuring 1,450 feet, the tower contains 110 stories filled with a combination of office and retail space. The base of the tower is made up of nine 75’ × 75’ squares. Suppose the square graphed on the coordinate plane below represents the base of the Willis Tower.

Write equations for the two horizontal and two vertical lines that pass through the square.



3. Think of another real-world situation that might involve horizontal and vertical lines. Write a description of the situation and draw the graph of a coordinate plane with two horizontal and two vertical lines to represent your situation. Draw the lines so that two of them pass through positive values and the other two pass through negative values on the coordinate plane. Then write equations for all four of the lines on your graph.

Did you drive to work or school today? When you are driving at a constant speed, the amount of gas left in the tank can typically be modeled by a linear equation. The equation y = -2x + 15 would represent a car that has a full 15-gallon tank and burns 2 gallons of gas an hour when x is the number of hours driven and y is the amount of gas in the tank. Find a linear relationship (equation) that you would use or rely on in your field when you receive your degree, and explain what it is and how it is used. Identify the initial condition, such as the full tank of gas above, and the rate of change. For a linear equation, the rate of change (slope) needs to be constant. If you can’t find one in your field, broaden your research to include any real-world application.