BRIEF QUIZ ANSWERS FOR COLLEGE ALGEBRA STUDENTS
In this document you will find brief answers to quiz questions.
If the quiz question is a homework problem, and the answer
is in the back of the book, then the brief answer that you
will see below will be only ``See the back of the book.''
Week 1
Week 2
- See the back of the book.
- See the back of the book.
- See the back of the book.
- See the back of the book.
Week 3
- Let x = number of gallons of hydrochloric acid.
Need to solve x + .3*(12) = .4*(x+12). Answer is x = 2 gallons.
- x = 1, y = 4.
- See the back of the book.
- Let x = Barney's age. Need to solve the inequality:
5*(x-10) + 10 is less than 3*x.
Answer: x is less than 20. (Note: to be realistic, we need to
add further conditions. For example, Barney's age should not be negative.
Barney should not be older than his parents. When Barney was born
his parents should have been old enough to have a kid. These
conditions lead to: Barney's age is at least 13-14, but less than 20.)
Week 4
- See the back of the book.
- See the back of the book.
- You need to find x and y so that (x+yi) = (1+3i)/(1+2i). Since
(1+3i)/(1+2i) = (7/5) + (1/5)i, the answer is x = 7/5 and y = 1/5.
- Simplify after rewriting each negative square root as:
square_root(-n) = square_root(n)*i. The answer is 2*square_root(6)*i.
Week 5
Week 6
- (Sketch)
- length = 17
- center = (-2,-5), radius = square_root(14). (Sketch)
- (x+1)^2 + y^2 = 4
Week 7
- 5x-4y = -26
- 77 ft down
- Domain = [1,6)
- C(x) = 300 + (1.75)*x
Week 8
- y = (-1/2)(x-2)^2 + 3, so vertex is (2,3), axis of symmetry
is x = 2, increasing on (-infinity,2] and decreasing on [2,infinity).
- P(x) = (-1/20)(x-50)^2 + 80, so the price that maximizes
profit is 50 dollars.
- Shift left 2 units, stretch horizontally by a factor of 2,
then shift down 1 unit.
- Equation is y = ((-x)/3 -2)^3 - 1.
Week 9
Test 2.
Week 10
Spring Break.
Week 11
No quiz.
Week 12
- According to the Ratinal Zeros Theorem (which only
applies to polynomials with INTEGER coefficients), the
possible rational roots are +/-(1/4), +/-(1/2), +/-1, +/-2, +/-4.
The actual zeros are x = -(1/4) and 4.
- Since i is a root and the polynomial has real
coefficients, we must also have -i as a root. Dividing
P(x) by (x-i) and (x+i), and using the quadratic formula
on the remaining factor, yields that the other two
roots are (1 +/- square_root(-3))/2.
- See the back of the book.
- Discussed in class.
Week 13
- Sketch by shifting the graph of y = 3^x
three units left and five units down.
- x = -1/2.
- h = 2,400 years.
- x = 0, -3.
Week 14
- x=1. (Note: x = -3 is not a solution.)
- h = -(100/log_2(.3)) = 57.57...
- x = 2 + square_root(3). (Note: x = 2 - square_root(3)
is not a solution.)
- t = ln(2)/.03 = 23.1 years, r = ln(2)/20 = .0346... or
3.46 percent.
Week 15
Test 3.
Last modified on Jan 24, 2000.