assign2

course MTH 158

assignment #001001. Only assignment: prelim asst

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????????p???s??assignment #002

??b????-?????College Algebra

09-10-2006

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17:39:18

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.

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RESPONSE -->

4-(-2)-3/3=-4-3/3=-1/3

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17:40:07

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

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

(-4-3)/3=

-7/3. **

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RESPONSE -->

mathematical error, i forgot the neg sign

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17:41:03

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

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RESPONSE -->

4*3-5*-2

12-10

2

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17:41:08

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

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

| | 12 | - | -10 | | =

| 12-10 | =

| 2 | =

2. **

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RESPONSE -->

ok

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17:42:23

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)

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RESPONSE -->

i don't understand, the values of x that were in the book aren't here

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17:43:21

** 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. **

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RESPONSE -->

oh so i should have found out how it would have equaled 0

Specifically, when the denominator is 0.

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17:45:03

query R.2.73 (was R.4.6). What is (-4)^-2 and how did you use the laws of exponents to get your result?

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RESPONSE -->

a negative times a neg is a positive, so -4^2 would be a positive 16

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17:45:39

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

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

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RESPONSE -->

where did the one come from?

a^-b = 1 / (a^b), meaning a^(-b) is the reciprocal of a^b.

The reciprocal of a number is 1 divided by that number.

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17:48:25

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?

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RESPONSE -->

3^2=9, 5^3=125, 3^2=9

must do square roots first.

9*125/9*5=1125/45=25

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17:49:46

** (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. **

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RESPONSE -->

i thought there was just a division in there, i dind't know it was a fraction. honestly, it's hard to understand this on the computer.

You did fine except that you didn't do the negative exponent correctly.

It takes a little getting used to the computer notation, and it's a good idea to transcribe any expression you don't immediately understand onto paper, being careful to follow the order of operations.

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17:54:44

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.

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RESPONSE -->

If you switch the numerator and denominator it becomes positive.

6^3y^6/5^3x^6

216y^6/125x^6

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17:55:22

[ 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.

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RESPONSE -->

i think this is what i put....

It is equivalent. Good work.

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17:57:47

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.

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RESPONSE -->

x^5/-8^2

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17:58:39

** 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 ). **

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RESPONSE -->

i'm completely confused

You appear to know the rules, so I can't identify what is confusing you here, though I don't question your statement that something is.

Can you be specific about which step or steps in the given solution you do not understand? You're welcome to submit a copy of the problem with the specifics--I'll be glad to respond.

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17:59:43

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.

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RESPONSE -->

xy/y^2

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18:00:48

** (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).**

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RESPONSE -->

ok

In a good self-critique you need identify the specific things you do and do not understand in the given solution, and either demonstrate your understanding or ask specific questions about what you don't understand. It doesn't accomplish the intended learning goals to simply say that you understand.

That way, once you have defined your difficulties I can help you address them.

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18:08:19

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.

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RESPONSE -->

4z^4/-5x^2y

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18:09:29

** 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 ) **

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RESPONSE -->

i don't see where x^6 and y^3 came from

x^-6 in the numerator is equivalent to x^6 in the denominator, by the laws of exponents. Similarly for y^-3 being equivalent to y^3 in the denominator.

Do you see where the x^-6 and y^-3 come from?

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18:10:24

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

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RESPONSE -->

4.21*10^ -3

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18:10:42

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

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RESPONSE -->

ok

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18:11:24

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

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RESPONSE -->

9700

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18:11:29

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

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RESPONSE -->

k

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18:12:59

query R.2.150 (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?

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RESPONSE -->

97-98.6>1.5

1.6>1.5

100-98.6>1.5

2.6>1.5

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18:13:14

** 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. **

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RESPONSE -->

ok

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"

Your work on this assignment is good overall. You generally do a good job with self-critique, though I noted a couple of places where more self-critique would have been desirable.

See my notes and be sure to let me know if you have questions or further responses.