College Algebra K /DC Wednesday, 10 September 2014

1. College Algebra K/DCWednesday, 10 September 2014 • OBJECTIVETSW solve problems involving sets of numbers, absolute value, and substitution. • ASSIGNMENT DUE (wire basket) • WSMean, Median, Mode • TESTS are not graded.

2. Set of Numbers and Absolute Value R.2:

3. Sets of Numbers s s s s s

4. Sets of Numbers Decide whether the statement is true or false. If false, give one counterexample. a) Every whole number is an integer. true b) Every integer is a rational number. true c) Every rational number is an integer. false: ½

5. Absolute Value • Absolute value is the distance on the number line from a number to 0. • The absolute value of a number is always positive or 0.

6. Evaluating Absolute Values • Evaluate each expression: (a) (b) (c) (d)

7. Evaluating Absolute Value Expressions • Let m = 13 and n = –9. Evaluate each expression. (a) (b)

8. Assignment: 09/10/2014 • Sec. R.2: pp. 18-20 (3-14 all, 31-39 odd, 61-66 all, 71-76 all) • Due in 45 minutes. • QUIZ over Mean, Median, Mode, Absolute Value on MONDAY, 09/15/2014.

9. Assignment: pp. 18-20 (3-14 all, 31-39 odd, 61-66 all, 71-76 all) • Decide whether each statement is true or false. If it is false, tell why. • 3. Every integer is a whole number. • 4. Every natural number is an integer. • 5. Every irrational number is an integer. • 6. Every integer is a rational number. • 7. Every natural number is a whole number. • 8. Some rational numbers are irrational. • 9. Some rational numbers are whole numbers. • 10. Some real numbers are integers. • Let set B = { 6, 12/4, 5/8, 3, 0, ¼, 1, 2π, 3, 12 }. List all elements of B that belong to each set. • 11. Natural #’s 12. Whole #’s 13. Integers 14. Rational #’s • Evaluate. • 31.

10. Assignment: pp. 18-20 (3-14 all, 31-39 odd, 61-66 all, 71-76 all) • If p = 4, q = 8, and r = 10, evaluate each expression. • 33.35. • 37.39. • Simplify each expression. • 61.62. 63. • 64. 65. 66. • Decide whether each statement is true or false. If false, correct the statement so it is true. • 71. | 6 – 8 | = | 6 | − | 8 | 72. | (−3)3 | = −| 33 | • 73. | −5 | ∙ | 6 | = | −5 ∙ 6 | 74. • 75. | a – b | = | a | − | b |, if b > a > 0. • 76. If a is negative, then | a | = −a, You have until 2:00 to finish. Turn into the wire basket.

11. Working with Absolute Value Ex: Find all values for x such that | x | = 14. Solution:x = 14 or x = 14

12. Working with Absolute Value Ex: Find all values for x such that | x 18 | = 23. Solution:x 18 = 23 or x 18 = 23 x = 41 x = 5

13. Working with Absolute Value Ex: Find all values for x such that | 25 x | = 1. Solution:25  x = 1 or 25  x = 1 x = 24 x = 26 x = 24 x = 26

14. Absolute Value Applications You will not have to write the whole problem, but you will have to show all work.

15. Absolute Value Applications Systolic blood pressure is the maximum pressure produced by each heartbeat. Both low blood pressure and high blood pressure may be cause for medical concern. Therefore, health care professionals are interested in a patient’s “pressure difference from normal,” or Pd. If 120 is considered a normal systolic pressure, then Pd = |P – 120|, where P is the patient’s recorded systolic pressure. Find Pd for a patient with a systolic pressure, P, of 113.

16. Absolute Value Applications Systolic blood pressure is the maximum pressure produced by each heartbeat. Both low blood pressure and high blood pressure may be cause for medical concern. Therefore, health care professionals are interested in a patient’s “pressure difference from normal,” or Pd. If 120 is considered a normal systolic pressure, Pd = |P – 120|, where P is the patient’s recorded systolic pressure. Find Pd for a patient with a systolic pressure, P, of 113. Pd = |P – 120| = |113 – 120| = |–7| = 7

17. Absolute Value Applications If a problem asks you to find a value and answer a question, use complete sentences. “What does this represent?” “What does this mean?” “Why or why not?” (What follows is part of the assignment so you should follow along.)

18. Absolute Value Applications 95. In the 2007 Masters Golf Tournament, Zach Johnson won the final round with a score that was 3 under par, while the 2006 tournament winner, Phil Mickelson, finished with a final-round score that was 5 over par. Using –3 to represent 3 under par and +5 to represent 5 over par, find the difference between these scores (in either order) and take the absolute value of the difference. What does this final number represent?

19. Absolute Value Applications 95. In the 2007 Masters Golf Tournament, Zach Johnson won the final round with a score that was 3 under par, while the 2006 tournament winner, Phil Mickelson, finished with a final-round score that was 5 over par. Using –3 to represent 3 under par and +5 to represent 5 over par, find the difference between these scores (in either order) and take the absolute value of the difference. What does this final number represent? difference = |–3 – 5| = |–8| = 8 This number represents the difference in their scores.

20. Distance on a Number Line If P and Q are points on the number line with coordinates a and b, respectively, then the distance d (P, Q) between them is REMEMBER: Distance is always positive or 0!

21. Absolute Value Applications • Assignment • Sec. R.2 – pp. 20-21 (77-88 all, 95-106 all) • Write the problem for 77-88 all, 103-106 all • Show work and answer in complete sentences 95-98 all. • Show work 99-102 all. • This assignment is due on Monday, 09/15/2014. • QUIZon Monday over MMM and Absolute Value.

22. Assignment: pp. 18-20 (77-88 all, 95-106 all) • Evaluate each expression. • Let x = −4 and y = 2. Evaluate each expression. • Solve each problem. 95) In the 2007 Masters Golf Tournament, Zach Johnson won the final round with a score that was 3 under par, while the 2006 tournament winner, Phil Mickelson, finished with a final-round score that was 5 over par. Using –3 to represent 3 under par and +5 to represent 5 over par, find the difference between these scores (in either order) and take the absolute value of the difference. What does this final number represent?

23. Assignment: pp. 18-20 (77-88 all, 95-106 all) • Solve each problem. 96) During his 16 yr in the NFL, Marcus Allen gained 12,243 yd rushing, 5411 ydreceving, and −6 yd returning fumbles. Find his total yardage (called all-purpose yards). Is this the same as the sum of the absolute values of the three categories? Why or why not? (Source: The Sports Illustrated 2003 Sports Almanac, 2003.) 97) Calculate the Pd value for a woman whose actual systolic pressure is 116 and whose normal value should be 125. (See previous example.) 98) If a patient’s Pd value is 17 and the normal pressure for his gender and age should be 130, what are the two possible values for his systolic blood pressure? (See previous example.)

24. Assignment: pp. 18-20 (77-88 all, 95-106 all) • The windchill factor is a measure of the cooling effect that the wind has on a person’s skin. It calculates the equivalent cooling temperature if there were no wind. The chart gives the windchill factor for various wind speeds and temperatures at which frostbite is a risk, and how quickly it may occur.

25. Assignment: pp. 18-20 (77-88 all, 95-106 all) • If we are interested only in the magnitude of the difference between two of these entries, then we subtract the two entries and find the absolute value. Find the magnitude of the difference for each pair of windchill factors. • 99) wind at 15 mph with a 30oF temperature and wind at 10 mph with a −10oF temperature • 100) wind at 20 mph with a −20oF temperature and wind at 5 mph with a 30oF temperature • 101) wind at 30 mph with a −30oF temperature and wind at 15 mph with a −20oF temperature • 102)wind at 40 mph with a 40oF temperature and wind at 25 mph with a −30oF temperature

26. Assignment: pp. 18-20 (77-88 all, 95-106 all) • Find the given distances between points P, Q, R, and S on a number line, with coordinates −4, −1, 8, and 12, respectively. • 103) d(P, Q) • 104) d(P, R) • 105)d(Q, R) • 102)d(Q, S)