Hello Class:

Please remember to complete your DLAs and have a nice weekend.

They are due Wednesday on December 2.  There will be no DLA on the final week.  Therefore, complete them as soon as possible no exception.

Study guide for Chapter 7 Exam:

1. Logic:  propositions, and statement, or statement, make sure you know the truth table for each of the statements.  The converse, contrapositive statement, logical implication, logical equivalence statement.

2. When are the statement a : tautology, contradiction, contingency?

3. What is/are

a)      Set

b)      Elements

c)      Empty set

d)      Subset of

e)      Union of a set

f)        Intersection of a set

g)      Venn Diagram

h)      Disjoint

i)        Complement

4. Factorial, permutation, combination.  Study various examples given in class, and the questions from the homework sets.

October 21:

Note on permutation, combination, factorial, and examples on those topic and completion of ch 7.3 and 7.4.

October 26:  Questions and answers and review for exam 3.

October 28: Flex Day.  

No School.

Exam3: November2.

1. not real

2. irrational

3. irrational

4. c = square root of 89

5. y = square root of 95

6. -4

7. -10

8. 5d¹⁰ (square root of 2)  

9.  (square root of 14) / z⁶

10. 2⁶ / 3² 

*Note the distinction between square root of and square of *

For Question: 82:

Answer: 700

Question 81:

Answer: 200

Determine if the following is rational or irrational:

For questions 1, 2, 3 do the following:

pg. 556.  48 45 50

4. Do pg 557  #75                   5. Do pg 557. # 76

Find each root:

6. do pg 558 # 106

7. do pg 558 #108

Simplify:

8. do pg 565 #74. 

9. do pg 565 #86 

10. 10. do pg 565 #62 

1. 2a² b / 3

2.  q²+1  /  q²+4

3. -m / m+2

4. 4r² -16  /  (5r+12)(r-1)

5.  8/5

7.  -10, 3

8. 0

9. dn(a+l) / 2

10. p= (-4s)/ 3(2+st)

11. x=8 mph

12. 4.42 hrs.

2. 21 r³s⁶

3. z(z-4)(z+1)

4. (7k-9)/ k(k+3)(k-1)

5. (p+2m²) / m(4m+p)

6.  -m/( 2+m)

7. (a-2)/2a

8.  4(r-2)(r+2) / ( 5r+12) (r-1)

Hw 6.2   Q29

There are total of 15 steps.  I will only post those procedures since it will be too long to post the entire solution.

Pivot element: 1 fourth row and second colm.  Basic Var: S1,S2,S3,S4,P.

Step I:

5R₄ +R₅ ->  R₅

 Step II:

-4R₄ +R₃ -> R₃

Step III:

-3R₄ +R₂ ->R₂ 

Step IV:

-2R₄ +R₁ ->R₁   

Second Pivot:

Pivot Element: 1 first col and third row.  Basic element: S1,S2,S3, X2,P.

Step V:

-R₃ +R₁->R₁

Step VI:

-R₃ +R₂ ->R₂

Step VII:

2R₃ +R₅ ->R₅

Third Pivot:

Pivot element: 1 sixth colm and second row.  Basic var: S1,S2,X1,X2,P.

Step VIII:

-2R₂ +R₁ -> R₁

Step IX:

4R₂ +R₃ ->R₃

Step X:

-R₂ +R₄ ->R₄

Step XI:

3R₂ + R₅ -> R₅

 Fourth Pivot:

Pivot element: 1, fifth col and first row.

Basic Var: S3,S4,X1,X2, P.

Step XII:

R₁ + R₂ ->R₂

 Step XIII:

3R₁ +R₃ -> R₃

Step XIV:

-R₁ + R₄ ->R₄

Step XV:

R1+ R5 -> R5.

Then set: S1=0 and S2=0.

Solve the following with the above conditions:

S₁ - 2S₂ + S₃  =4

S₁ + S₄ =6

X₁ +3S₁ =24

X₂ - S₁ =8

S₁  + S₂ + P = 88