Ass2_JaclynTrout

course Math 158

ڕwNassignment #001

Your work has been received. Please scroll through the document to see any inserted notes (inserted at the appropriate place in the document, in boldface) and a note at the end. The note at the end of the file will confirm that the file has been reviewed; be sure to read that note. If there is no note at the end, notify the instructor through the Submit Work form, and include the date of the posting to your access page.

001. `Query 1

College Algebra

06-08-2008

......!!!!!!!!...................................

21:41:53

query 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?

......!!!!!!!!...................................

RESPONSE -->

Square root of two is irrational.

Pi+Square root of two is irrational.

1/2+10.3 is irrational.

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

......!!!!!!!!...................................

21:42:03

** 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.. **

......!!!!!!!!...................................

RESPONSE -->

Ok.

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

......!!!!!!!!...................................

21:43:34

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

......!!!!!!!!...................................

RESPONSE -->

2x=4+6

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

......!!!!!!!!...................................

21:44:20

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

......!!!!!!!!...................................

RESPONSE -->

Ok.

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

......!!!!!!!!...................................

21:46:40

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

......!!!!!!!!...................................

RESPONSE -->

Always do parenthesis first. Calculate (3-4) which equals -1. Then multiply that by 6 which is -6. Make that positive. Then do 2-5, which equals -3*4= -12. -12*-6 equals 72.

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

......!!!!!!!!...................................

21:46:58

**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. **

......!!!!!!!!...................................

RESPONSE -->

Ok.

&#

Your response did not agree with the given solution in all details, and you should therefore have addressed the discrepancy with a full self-critique, detailing the discrepancy and demonstrating exactly what you do and do not understand about the given solution, and if necessary asking specific questions (to which I will respond).

&#

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

......!!!!!!!!...................................

21:47:56

query 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).

......!!!!!!!!...................................

RESPONSE -->

FOIL. First, outer, inner, last. x^2-4x-2x+8.

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

......!!!!!!!!...................................

21:48:37

** 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. *

......!!!!!!!!...................................

RESPONSE -->

Ok.

&#

This also requires a self-critique.

&#

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

......!!!!!!!!...................................

21:48:59

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

......!!!!!!!!...................................

RESPONSE -->

Because we're adding instead of dividing.

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

......!!!!!!!!...................................

21:49:13

** 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 **

......!!!!!!!!...................................

RESPONSE -->

Ok.

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

......!!!!!!!!...................................

21:49:26

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

......!!!!!!!!...................................

RESPONSE -->

It wasn't as bad as I thought it would be.

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

þލQѰysBL

&#I believe you submitted this as part of a previous submission. Let me know if I'm wrong about that; if I'm right, then be sure to avoid this sort of redundancy. &#

assignment #001

001. `Query 1

College Algebra

06-08-2008

靺DŽΨgࠗ

assignment #002

002. `query 2

College Algebra

06-08-2008

......!!!!!!!!...................................

21:56:13

query R.2.46 (was R.2.36) Evaluate for x = -2, and y = 3 the expression (2x - 3) / y and explan how you got your result.

......!!!!!!!!...................................

RESPONSE -->

-2.3 repeating.

Just plug in the numbers for x and y.

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

......!!!!!!!!...................................

21:56:57

** Starting with (2x-3)/y we substitute x=-2 and y=3 to get

(2*(-2) - 3)/3 =

(-4-3)/3=

-7/3. **

......!!!!!!!!...................................

RESPONSE -->

Ok.

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

......!!!!!!!!...................................

22:02:47

query R.2. 55 (was R.2.45) Evaluate for x = 3 and y = -2: | |4x| - |5y| | and explan how you got your result.

......!!!!!!!!...................................

RESPONSE -->

2. Absolute value just makes is positive. 4*3 - 5*2 equals 12-10 which equals 2.

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

......!!!!!!!!...................................

22:02:53

** Starting with | | 4x |- | 5y | | we substitute x=3 and y=-2 to get

| | 4*3 | - | 5*-2 | | =

| | 12 | - | -10 | | =

| 12-10 | =

| 2 | =

2. **

......!!!!!!!!...................................

RESPONSE -->

Ok.

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

......!!!!!!!!...................................

22:08:48

query R.2.64 (was R.2.54) Explain what values, if any, must not be present in the domain of the expression (-9x^2 - x + 1) / (x^3 + x)

......!!!!!!!!...................................

RESPONSE -->

I can't divide a number by 0, so x^3=x cannot equal zero.

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

......!!!!!!!!...................................

22:08:56

** The denominator of this expression cannot be zero, since division by zero is undefined.

Since x^3 + x factors into (x^2 + 1) ( x ) we see that x^3 + x = 0 only if x^2 + 1 = 0 or x = 0.

Since x^2 cannot be negative x^2 + 1 cannot be 0, so x = 0 is indeed the only value for which x^3 + x = 0. **

......!!!!!!!!...................................

RESPONSE -->

Ok.

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

......!!!!!!!!...................................

22:11:54

query R.2.76 \ 73 (was R.4.6). What is -4^-2 and how did you use the laws of exponents to get your result?

......!!!!!!!!...................................

RESPONSE -->

I get -.0625. I have a negative, so I move it to the denominator.

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

......!!!!!!!!...................................

22:12:26

** order of operations implies exponentiation before multiplication; the - in front of the 4 is not part of the 4 but is an implicit multiplication by -1. Thus only 4 is raised to the -2 power.

-4^(-2) Since a^-b = 1 / (a^b), we have

4^-2 = 1 / (4)^2 = 1 / 16.

The - in front then gives us -4^(-2) = - ( 1/ 16) = -1/16.

If the intent was to take -4 to the -2 power the expression would have been written (-4)^(-2).**

......!!!!!!!!...................................

RESPONSE -->

Ok.

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

......!!!!!!!!...................................

22:17:03

query Extra Problem. What is (3^-2 * 5^3) / (3^2 * 5) and how did you use the laws of exponents to get your result?

......!!!!!!!!...................................

RESPONSE -->

The law of negative exponents says I need to make the exponent positive by moving the negative numbers to the denominator.

&#

You need a detailed self-critique here.

&#

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

......!!!!!!!!...................................

22:17:13

** (3^(-2)*5^3)/(3^2*5). Grouping factors with like bases we have

3^(-2)/3^2 * 5^3 / 5. Using the fact that a^b / a^c = a^(b-c) we get

3^(-2 -2) * 5^(3-1), which gives us

3^-4 * 5^2. Using a^(-b) = 1 / a^b we get

(1/3^4) * 5^2. Simplifying we have

(1/81) * 25 = 25/81. **

......!!!!!!!!...................................

RESPONSE -->

Ok.

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

......!!!!!!!!...................................

22:23:03

query R.2.94. Express [ 5 x^-2 / (6 y^-2) ] ^ -3 with only positive exponents and explain how you used the laws of exponents to get your result.

......!!!!!!!!...................................

RESPONSE -->

Put one in the numerator on both negative exponents making them positive. Dividing is like multiplying by the reciprocal.

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

......!!!!!!!!...................................

22:23:10

[ 5 x^-2 / (6 y^-2) ] ^ -3 = (5 x^-2)^-3 / (6 y^-2)^-3, since (a/b)^c = a^c / b^c. This simplifies to

5^-3 (x^-2)^-3 / [ 6^-3 (y^-2)^-3 ] since (ab)^c = a^c b^c. Then since (a^b)^c = a^(bc) we have

5^-3 x^6 / [ 6^-3 y^6 ] . We rearrange this to get the result

6^3 x^6 / (5^3 y^6), since a^-b = 1 / a^b.

......!!!!!!!!...................................

RESPONSE -->

Ok.

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

......!!!!!!!!...................................

22:26:34

query Extra Problem. Express (-8 x^3) ^ -2 with only positive exponents and explain how you used the laws of exponents to get your result.

......!!!!!!!!...................................

RESPONSE -->

1/(-8x^3)^-2. Move the negative to the denominator.

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

......!!!!!!!!...................................

22:26:50

** ERRONEOUS STUDENT SOLUTION: (-8x^3)^-2

-1/(-8^2 * x^3+2)

1/64x^5

INSTRUCTOR COMMENT:1/64x^5 means 1 / 64 * x^5 = x^5 / 64. This is not what you meant but it is the only correct interpretation of what you wrote.

Also it's not x^3 * x^2, which would be x^5, but (x^3)^2.

There are several ways to get the solution. Two ways are shown below. They make more sense if you write them out in standard notation.

ONE CORRECT SOLUTION: (-8x^3)^-2 =

(-8)^-2*(x^3)^-2 =

1 / (-8)^2 * 1 / (x^3)^2 =

1/64 * 1/x^6 =

1 / (64 x^5).

Alternatively

(-8 x^3)^-2 =

1 / [ (-8 x^3)^2] =

1 / [ (-8)^2 (x^3)^2 ] =

1 / ( 64 x^6 ). **

......!!!!!!!!...................................

RESPONSE -->

Ok.

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

......!!!!!!!!...................................

22:27:49

query R.2.90 (was R.4.36). Express (x^-2 y) / (x y^2) with only positive exponents and explain how you used the laws of exponents to get your result.

......!!!!!!!!...................................

RESPONSE -->

Use the reciprocal by putting (xy^2)/(x^-2y) because negatives should always be in the denominator.

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

......!!!!!!!!...................................

22:27:56

** (1/x^2 * y) / (x * y^2)

= (1/x^2 * y) * 1 / (x * y^2)

= y * 1 / ( x^2 * x * y^2)

= y / (x^3 y^2)

= 1 / (x^3 y).

Alternatively, or as a check, you could use exponents on term as follows:

(x^-2y)/(xy^2)

= x^-2 * y * x^-1 * y^-2

= x^(-2 - 1) * y^(1 - 2)

= x^-3 y^-1

= 1 / (x^3 y).**

......!!!!!!!!...................................

RESPONSE -->

Ok.

&#

Self-critique should be included here.

&#

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

......!!!!!!!!...................................

22:29:12

query Extra Problem. . Express 4 x^-2 (y z)^-1 / [ (-5)^2 x^4 y^2 z^-5 ] with only positive exponents and explain how you used the laws of exponents to get your result.

......!!!!!!!!...................................

RESPONSE -->

Multiply 4x^-2(yz)^-1 by 1 making it positive then divide by the denominator.

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

......!!!!!!!!...................................

22:29:46

** Starting with

4x^-2(yz)^-1/ [ (-5)^2 x^4 y^2 z^-5] Squaring the -5 and using the fact that (yz)^-1 = y^1 * z^-1:

4x^-2 * y^-1 * z^-1/ [25 * x^4 * y^2 * z^-5} Grouping the numbers, and the x, the y and the z expression:

(4/25) * (x^-2/x^4) * (y^-1/y^2) * (z^-1/z^-5) Simplifying by the laws of exponents:

(4/25) * x^(-2-4) * y^(-1-2) * z^(-1+5) Simplifying further:

(4/25) * x^-6 * y^-3 * z^4 Writing with positive exponents:

4z^4/ (25x^6 * y^3 ) **

......!!!!!!!!...................................

RESPONSE -->

Ok.

&#

This also requires a self-critique.

&#

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

......!!!!!!!!...................................

22:30:58

query R.2.122 (was R.4.72). Express 0.00421 in scientific notation.

......!!!!!!!!...................................

RESPONSE -->

x*10^4.

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

......!!!!!!!!...................................

22:31:11

** 0.00421 in scientific notation is 4.21*10^-3. This is expressed on many calculators as 4.21 E-4. **

......!!!!!!!!...................................

RESPONSE -->

Ok.

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

......!!!!!!!!...................................

22:31:25

query R.2.128 (was R.4.78). Express 9.7 * 10^3 in decimal notation.

......!!!!!!!!...................................

RESPONSE -->

9.7

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

......!!!!!!!!...................................

22:31:32

** 9.7*10^3 in decimal notation is 9.7 * 1000 = 9700 **

......!!!!!!!!...................................

RESPONSE -->

Ok.

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

......!!!!!!!!...................................

22:32:07

query R.2.152 \ 150 (was R.2.78) If an unhealthy temperature is one for which | T - 98.6 | > 1.5, then how do you show that T = 97 and T = 100 are unhealthy?

......!!!!!!!!...................................

RESPONSE -->

T-97>1.

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

......!!!!!!!!...................................

22:32:19

** You can show that T=97 is unhealthy by substituting 97 for T to get | -1.6| > 1.5, equivalent to the true statement 1.6>1.5.

But you can't show that T=100 is unhealthy, when you sustitute for T then it becomes | 100 - 98.6 | > 1.5, or

| 1.4 | > 1.5, giving us

1.4>1.5, which is an untrue statement. **

......!!!!!!!!...................................

RESPONSE -->

Ok.

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

ޢ~˘׽h

assignment #002

002. `query 2

College Algebra

06-08-2008

Good answers on many questions. See my notes on self-critique.