Assignment 1

course MTH 158

If your solution to stated problem does not match the given solution, you should self-critique per instructions at http://vhcc2.vhcc.edu/dsmith/geninfo/labrynth_created_fall_05/levl1_22/levl2_81/file3_259.htm.

Your solution, attempt at solution:

If you are unable to attempt a solution, give a phrase-by-phrase interpretation of the problem along with a statement of what you do or do not understand about it. This response should be given, based on the work you did in completing the assignment, before you look at the given solution.

001. `* 1

*********************************************

Question: * R.1.26 \ was R.1.14 (was R.1.6) Of the numbers in the set {-sqrt(2), pi + sqrt(2), 1 / 2 + 10.3} which are counting numbers, which are rational numbers, which are irrational numbers and which are real numbers?

*********************************************

Your solution:

Counting numbers-there are none.

Rational numbers- { ½ + 10.3 }

Irrational numbers – { - sqrt(2), pi + sqrt(2)}

Real Numbers – All of them are real numbers

Confidence Assessment:

.............................................

Given Solution:

* * ** Counting numbers are the numbers 1, 2, 3, .... . None of the given numbers are counting numbers

Rational numbers are numbers which can be expressed as the ratio of two integers. 1/2+10.3 are rational numbers.

Irrational numbers are numbers which can be expressed as the ratio of two integers. {-sqrt(2)}, pi+sqrt(2) are irrational numbers.. **

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):

0

Self-critique Rating: 0

*********************************************

Question: * R.1.44 \ 32 (was R.1.24) Write in symbols: The product of 2 and x is the product of 4 and 6

*********************************************

Your solution:

2*x=4*6

Confidence Assessment:

.............................................

Given Solution:

* * ** The product of 2 and x is 2 * x and the product of 4 and 6 is 4 * 6. To say that these are identical is to say that 2*x=4*6. **

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):

0

Self-critique Rating:

*********************************************

Question:

* R.1.62 \ 50 (was R.1.42) Explain how you evaluate the expression 2 - 5 * 4 - [ 6 * ( 3 - 4) ]

*********************************************

Your solution:

You will follow the order of operations.

First you will do the inner most parentheses. Witch is 3-4. = -1

Then you will do the outer parentheses. That will be [6*-1]= -6

Next multiply. 5*4 witch is 20.

Finally add and subtract. Putting the answers together it would be

2-20-(-6)

-12

Now put the whole problem together:

2-5*4-[6*(3-4)]

2-5*4-[6*(-1)]

2-5*4-(-6)

2-20-(-6)

-12

Confidence Assessment:

.............................................

Given Solution:

* * **Starting with

2-5*4-[6*(3-4)]. First you evaluate the innermost group to get

2-5*4-[6*-1] . Then multiply inside brackets to get

2-5*4+6. Then do the multiplication to get

2-20+6. Then add and subtract in order, obtaining

-12. **

* R.1.98 \ 80 (was R.1.72) Explain how you use the distributive property to remove the parentheses from the express (x-2)(x-4).

*********************************************

Your solution:

X(x-4) First take the x from (x-2) and multiply it by the (x – 4)

-2(x-4) Then you take the -2 from (x-2) and multiply it by the (x-4)

X^2-4x Then you will distribute the x in x(x-4)

-2x-8 Next you will distribute the -2 in -2(x-4)

Finally you will add or subtract like terms.

X^2-4x-8

Put the whole problem together.

(x-2)(x-4)

X(x-2)-2(x-4)

X^2-2x-2x-8

X^2-4x-8

Confidence Assessment:

.............................................

Given Solution:

* * ** COMMON ERROR: Using FOIL. FOIL is not the Distributive Law. FOIL works for binomial expressions. FOIL follows from the distributive law but is of extremely limited usefulness and the instructor does not recommend relying on FOIL.

Starting with

(x-2)(x-4) ; one application of the Distributive Property gives you

x(x-4) - 2(x-4) . Applying the property to both of the other terms we get

x^2 - 4x - (2x -8). Simplifying:

x^2 - 4x - 2x + 8 or

x^2 - 6x + 8. *

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):

0

Self-critique Rating: 0

*********************************************

Question:

&&& In your answer x(x-4) - 2(x-4) witch is from x(x-4) - 2(x-4) . Applying the property to both of the other terms we get. Would the -4 in x(x-4) be a -2. Because in the original problem it says(x-2)(x-4)&&&&

* R.1.102 \ 86 (was R.1.78) Explain why (4+3) / (2+5) is not equal to 4/2 + 3/5.

*********************************************

Your solution:

Because of the order of operations. In the first problem to follow the order of operations you would do what in parentheses then divide. In the second problem you would divde then add.

Confidence Assessment:

.............................................

Given Solution:

* * ** Good answer but at an even more fundamental level it comes down to order of operations:

(4+3)/(2+5) means

7/7 which is equal to

1.

By order of operations, in which multiplications and divisions precede additions and subtractions,

4/2+3/5 means

(4/2) + (3/5), which gives us

2+3/5 = 2 3/5

Your work looks very good.

Do include confidence assessments.