query 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?

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution: 1/2+10.3 are rational numbers and {-sqrt(2), pi + sqrt(2), are irrational numbers. There are not any counting numbers in this problem.

confidence rating: 3

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

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

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):none

------------------------------------------------

Self-critique Rating:3

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

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

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution: The product of 2 and x is 2 * x. the product of 4 and 6 is 4 * 6. So if they are the same then 2*x=4*6

confidence rating:3

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

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

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):none

------------------------------------------------

Self-critique Rating:3

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

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

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

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

= 2-5*4-[6*-1] multiply inside the brackets

= 2-5*4 +1 the multiply 5*4

= 2-20+6 next add and subtract in order

= -12

confidence rating: 3

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

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

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*-1] . Then do the multiplication to get

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

-12. **

confidence rating: 3

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

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

Question:** 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).

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

(x-2)(x-4) using foil

=x^2-4x-2x+8

=x^2-6x+8

confidence rating: 3

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

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

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):Ok I got the right answer but I did use the FOIL method. I am unsure of the why you do not want us to use FOIL if it gives you the same answer. Could you go into more detail or give me and example of a problem in which FOIL would give you the wrong answer. Thank you.

*&$*&$

In the first place the question asked you explain how to to use the distributive law. FOIL doesn't explain how the distributive law is used, so it simply doesn't answer the question.

FOIL won't give the wrong answer if it applies. It just doesn't always apply, while the distributing law does.

For example you can't multiply

(x^2 - 3 x + 7) by (x^3 + 2 - 4) using FOIL.

But if you understand the distributive law it's not hard to multiply, though it's a little tedious. However there's no alternative.

------------------------------------------------

Self-critique Rating:3

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

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

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution: Cause in order of operation you would to the addition inside the ( ) first so this would give you 7/ 7

confidence rating: 3

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

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

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

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

* Add comments on any surprises or insights you experienced as a result of this assignment.

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

Self-critique (if necessary):none

------------------------------------------------

Self-critique Rating:3"

query 1

&#This looks good. See my notes. Let me know if you have any questions. &#