Suppose a company has fixed costs of $47,600 and variable cost per unit of 4/9x + 333 dollars,

where x is the total number of units produced. Suppose further that the selling price of its product is

1767 −5/9x dollars per unit.

(a) Find the break-even points. (Enter your answers as a comma-separated list.)
x =  

  

(b) Find the maximum revenue. (Round your answer to the nearest cent.)
$  

(c) Form the profit function P(x) from the cost and revenue functions.
P(x) =  

  

Find maximum profit.
$  

(d) What price will maximize the profit? (Round your answer to the nearest cent.)
$

Julie recently drove to visit her parents who live 200200 miles away. On her way there her average speed was 99 miles per hour faster than on her way home (she ran into some bad weather). If Julie spent a total of 1010 hours driving, find the two rates.

Writing Equations of Lines

Write the slope-intercept form of the equation of the line given the slope and y-intercept.

Slope = -5, y-intercept = -3

Write the slope-intercept form of the equation of the line given the slope and y-intercept.

Slope = -1, y-intercept = 5

Write the slope-intercept form of the equation of the line.

y – 5 = -10(x – 4)

Write the slope-intercept form of the equation of the line.

Write the slope-intercept form of the equation of the line through the given point with the             given slope.

Through: (4,-4), slope = 2

Write the slope-intercept form of the equation of the line through the given point with the             given slope.

Through: (-5,1), slope = undefined

Write the slope-intercept form of the equation of the line through the given points.

Through: (3,-3) and (4,0)

Write the slope-intercept form of the equation of the line through the given points.

Through: (3,5) and (0,1)

Write the standard form of the equation of the line given the slope and y-intercept.

Slope = -2, y-intercept = -2

Write the standard form of the equation of the line given the slope and y-intercept.

Through: (1,2), slope = 6

Find the equation of the ellipse of the form Ax^2+Cy^2+Dx+Ey+F=0 with major axis of lenght 10 and foci have coordinates (8,2) and (0,2).

Suppose a total of 15 ounces of medicine is added to the original mixture (so that the total volume is now 25 ounces with 18 ounces of medicine and 7 ounces of water). How much water must now be added so that the mixture has the same proportion of medicine and water as the original mixture?

_________ ounces

A, B, C, D are all matricies
A = 2x3
1 2 −3
−1 4 5
,
B = 2x3
3 0 −1
1 2 1

, C = 2x2
2 5
1 2

,
D = 3x3
1 −1 1
2 −1 2
4 −3 4

Find each of the following or explain why it does not exist.
1) A + B,
2) 2A − 3B,
3) A + C,
4) A − C,
5) AC,
6) CA,
7) AD,
8) DA,
9) C
10) D−1
.
11) Solve the matrix equation CX = B

Find the two scalars (in C) λ1 and λ2 so that A − λI is singular. For

A = [₁^{1 ₁ -1}]

Use the fact that A − λI is singular iff det(A − λI) = 0.

For each λi find a basis for RS(A−λ_iI). Each basis will consist of a single vector, verify that the two vectors you found are orthogonal.

Match each table with its equation.

OPTIONS -Linear, Square Root, Quadratic, Absolute Value, Cubic, Reciprocal

OPTIONS -Linear, Square Root, Quadratic, Absolute Value, Cubic, Reciprocal

OPTIONS -Linear, Square Root, Quadratic, Absolute Value, Cubic, Reciprocal

OPTIONS -Linear, Square Root, Quadratic, Absolute Value, Cubic, Reciprocal

OPTIONS -Linear, Square Root, Quadratic, Absolute Value, Cubic, Reciprocal

OPTIONS -Linear, Square Root, Quadratic, Absolute Value, Cubic, Reciprocal

1. Plot each point. Label them A,B,C , and D.

A. (2,-2) B. (-4,0 C. (1.5 5/2) D. ),5)

2. Find the x and Y intercepts of the gien equation and write answers in ordered pair form (x,y). Then graph the equation using these intercepts.

4x-3y=12

X-interceptis:______

Y-Intercepts is:_______

3. Find the slope of the line passing through the given points using the slope formula, then graph the line using the slope found. (3,5) and (-5,6)

m=_________

5. Find the slope and the y-intercept of the line with the given equation. Remember you must first solve this equation for y.

2x=3y=6

M=_________

6. Solve the system of equations by the elimination mehtod. If the lines intersect, identify the point of intersection, if the lines are parallel or coincindent, indicate the appropriate solution.

2x=11y=-10

5x=4y=22

7. Use the point-slope form of a linear equation y-y₁=m(x-x_{1 ) to write the equation of the line with the given slope and point. Write your final answer in the slope-intercept form of a linear.equation y=mx+b.}

_{Slopee=2 and passes through (3,5)}

Let T and S be linear transformations of a vector space V, and TS=ST

(a) Show that T preserves the generalized eigenspace and eigenspace of S.

(b) Suppose V is a vector space on R and dimV = 4. S has a minimal polynomial of (t-2)² (t-3)²?. What is the jordan canonical form of S.

(c) Show that the characteristic polynomial of T has at most 2 distinct roots and splits completely.

show that a 2x2 complex matrix A is nilpotent if and only if Tr(A)=0 and Tr(A^2)=0. give an example of a complex 2x2 matrix which is not nilpotent but whose trace is 0

If equilateral triangles are constructed on the sides of any triangle, prove that the distances between the vertices of the original triangle and the opposite vertices of the equilateral triangles are equal.

5a. Write the equation of the polynomial with leading coefficient 3 that has degree 4, with x-intercepts at -2 and 1, both having a multiplicity of 2.

b. Write the equation of the polynomial which goes through the following points. (-2,0),(-1,0),(5,0), and (0,10).

c. (1+i) is a zero of f(x)=x^4 - 2x^3 - x^2+ 6x - 6. Find the other zeros

Please show all the work. Expert and correct answers only.