Lecture 10: Solving Inequalities (continued)

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Problem of the Day

The sum of two real numbers is 14 and the product of the two is 42. What is the sum of their reciprocals?

Assignments

These are the problems you should work before today, February 5.
Review problems, page 75, 4n+1, for n=0..22;
Section 1.1, page 92, 4n+1, for n=0...24;
Section 1.2, page 102, 1-6, and 4n, for n=3...23;
Section 1.3, page 113, 4n+1, for n=0...19.

These are the problems you should work before February 12.
Section 1.4, page 120, problems 6n+1, for n=0...15;
(skip 1.5) 1.6, page 149, problems 6n+1, for n=0...16.

These are the problems you should work before February 19.
Section 1.7, page 160, 4n+1, for n=0,...,24.
Section 1.8, page 171, problems 6n+1, for n=0...8;

These are the problems you should work before February 26.
The first test, covering Chapters P and 1 and sections 2.1 and 2.2 is on February 26.
Section 2.1, page 191, problems 6n+1, for n=0...12.
Section 2.2, page 025, problems 8n+1, for n=0...11.

Outline for Monday, Sept. 14

Solving Equations and Inequalities

  1. Absolute values
    1. equalities, |x-2|=3; |x2-3x|=-4x+6
    2. inequalities |x-2|£ 3; |x2-3x|£ -4x+6
  2. Compound Interest
    1. A=P(1+r/n)nt
  3. Polynomial Expressions
    1. Equations-critical numbers
    2. Inequalities-test intervals
  4. Rational Expressions
    1. Critical numbers and test intervals
    2. (2x-7)/(x-5) £ 3.
The test below was the first test given in the Fall 1996. It is intended to give students some idea of the difficulty of test problems, and is not meant as a study guide. Problems of types not included here will certainly appear on the first test in other semesters.
    You do not need to show your work on these multiple choice problems.
  1. 4^4 x 9^4 x 4^9 x 9^9=
    A. {13^{13} B. 13^{36} C. 36^{13} D. 36^{36} E. 1296^{26}}

  2. (4^{-1}-3^{-1})^{-1}=
    A. -12 B. -1 C. 1 1/2 D. 1 E. 12

  3. |3-\pi|=
    A. 1/7 B. .14 C. 3-\pi D. 3+\pi E. \pi - 3
  4. Given that 3/2 A. 1 B. 2 C. D. 2x-4 E. 4-2x

  5. For how many real numbers x is it true that | |x|-7 |=12?
    A. 0 B. 1 C. 2 D. 3 E. 4

  6. If a>b which of the following must be true?

    A. a>0 and b<0} B. |a+b|>0 C. a-b>0 D. |a|>|b| E. a and b are rational numbers

  7. Which of the following equations have two distinct real solutions?
    a. $|x|=7$
    b. $x=\sqrt {25}$
    c. $x^2+4x+14\pi=0$
    A. a. only B. b. only C. c. only D. a. and b. only E. all three

  8. How many integers n satisfy |n|<10\pi ?
    A. 30 B. 31 C. 62 D.63 E. infintely many

  9. Seven women and five men attend a party. At this party each man shakes hands with each other person once. Each woman shakes hands only with men. How many handshakes took place at the party?
    A. 31 B. 35 C. 45 D. 56 E. 66

    On all the following problems, show all work.

  10. Find an algebraic expression which describes the volume of a cube if the area of each face of the cube is x.
  11. Express (2x-1)^4 in standard (polynomial) form.

  12. Factor completely the algebraic expression 8x^3+12x^2+6x+1.

  13. The product of a number, its reciprocal, and its square is 6. Find the absolute value of the sum of the number and its reciprocal.

  14. The demand equation for a certain product is p=60-0.0004x, where p is the price in dollars per unit and x is the number of units sold.
    The total revenue R, of course, is the given by R=px.

    A. How much revenue is produced by the sale of 3,000 units?
    B. What is the fewest number of units that can be sold to produce a revenue of at least $220,000?

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