College Algebra Chapter 10 Part 2 Take Home Quiz
Due: Odds: Tuesday January 31st
Evens: Monday January 30th
Name _____________________________________________
Period:________
Directions: Show all work and reasoning to receive full credit.
For Questions 1 & 2, set up the partial fraction decomposition of each rational expression. DO NOT SOLVE!!
1)
3x 2  10 x  17
( x  5)( x  1) 2
3) Write the partial fraction decomposition of
2)
5 x 2  2 x  15
x 4  3x 2
x 2  15 x  4
. (This means solve!)
x 3  3x 2  4 x
For Questions 4-6, use the following scenario:
A sports drink company has two popular flavors, grape and citrus. Besides water, each contains two important ingredients: potassium
and sodium. Grape contains 6 grams of potassium and 2 grams of sodium per gallon. Citrus contains 3 grams of potassium and 6
grams of sodium per gallon. The company has 360 grams of potassium and 480 grams of sodium available for production. Each gallon
of grape produces a profit of $2 and each gallon of citrus produces a profit of $2.50.
4) Define variables and write an objective function; then, write inequalities to model your constraints.
5) Graph the constraints to find the feasible region and identify all corner points.
6) Maximize the objective function and identify the number of gallons of each flavor that should be produced in order to obtain the
maximum profit.
For Questions 7 & 8, graph the systems of inequalities below.
7)
2 x  5 y  10

4 x  3 y  12
8)
 x 2  y 2  36

2
 y  x  4
9) Graph the feasible region to maximize the objective function z = 9x + 6y subject to the constraints.
x  0
y  0

x  4
x  y  5

 x  2 y  8
10) Write the slope intercept equation of the line parallel to 2𝑥 − 4𝑦 = 16 that contains (-6, 8).
11) Write the general form of the line perpendicular to 3𝑥 + 2𝑦 = 7 that contains (5, -1).
12) Find the average rate of change of 𝑓(𝑥) = 2𝑥 2 + 2𝑥 − 3 from -5 to -1.
13) Find the difference quotient for 𝑓(𝑥) = 3𝑥 2 + 𝑥 − 3.
4
14) Solve for x. |
−3
𝑥
| = 11
8
(𝑟𝑒𝑚𝑒𝑚𝑏𝑒𝑟:
𝑓(𝑥+ℎ)−𝑓(𝑥)
)
ℎ
15) Solve the system using any technique discussed in class. You must show all work to earn credit.
 x  3 y  z  4

 2 x  y  2 z  13
3x  2 y  z  9

16) Find the inverse of the matrix below. You must show all work for credit.
4 5 0 
1 1 1 


0 1  3