assignments 1  2

course MTH 158

should this be taking so long to finish. around 4 hours per section

m???????????assignment #002

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.

002. `query 2

College Algebra

01-21-2007

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

13:40:17

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 -->

I think this is the place i left off .

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

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

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

= x^-1 y^3

This is as far as i could get with the book.

my brotherinlaw told me somthing to try so lets see

(x^-2 y) / (x y^2) = (x^-2 y) / (x yy)

= y / (xxx yy) = 1 / (x^3 y)

confidence assessment: 2

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

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

13:45:12

** (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 -->

I should have used the law a^-B = 1/a^B

bUT I STILL GOT IT

self critique assessment: 2

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

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

14:29:18

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 -->

4 x^-2 (y z)^-1 / [ (-5)^2 x^4 y^2 z^-5 ]

=ZZZZZ / 4 XXXXXX YYY Z 25

=Z^4/ 4*X^6*Y^3*25

confidence assessment: 2

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

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

14:31:46

** 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 -->

I moved the 4 to the denominater.

self critique assessment: 2

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

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

14:47:54

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

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

RESPONSE -->

4.21*10-3

confidence assessment: 2

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

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

14:48:33

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

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

RESPONSE -->

ok

self critique assessment: 3

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

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

14:49:35

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

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

RESPONSE -->

9700

confidence assessment: 2

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

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

14:49:51

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

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

RESPONSE -->

ok

self critique assessment: 3

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

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

15:34:27

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?

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

RESPONSE -->

| T - 98.6 | > 1.5

add 98.6 = T> 100.1

-| T - 98.6 | > 1.5

= ( -T + 98.6) > 1.5

- 98.6 = -t > -97.1

= T < 97.1

T = 97 is unhealthy T = 100 is not unhealthy

confidence assessment: 2

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

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

15:36:03

** 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

self critique assessment: 2

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

????wd??O??????assignment #003

003. `query 3

College Algebra

01-21-2007

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

15:43:26

R.3.12 (was R.3.6) What is the hypotenuse of a right triangle with legs 14 and 48 and how did you get your result?

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

RESPONSE -->

A^2 + b^2 = c^2

so

14^2 + 48^2 = x^2

196 + 2304 = 2500

the hypotenuse is 50

confidence assessment: 2

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

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

15:44:09

** The Pythagorean Theorem tells us that

c^2 = a^2 + b^2, where a and b are the legs and c the hypotenuse. Substituting 14 and 48 for a and b we get

c^2 = 14^2 + 48^2, so that

c^2 = 196 + 2304 or

c^2 = 2500.

This tells us that c = + sqrt(2500) or -sqrt(2500). Since the length of a side can't be negative we conclude that c = +sqrt(2500) = 50. **

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

RESPONSE -->

ok

self critique assessment: 2

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

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

15:51:27

R.3.18 (was R.3.12). Is a triangle with legs of 10, 24 and 26 a right triangle, and how did you arrive at your answer?

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

RESPONSE -->

10 24 26

10^2 + 24^2 = 26^2

100 + 576 = 676

So yrs this is a right triangle

confidence assessment: 3

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

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

15:51:44

** Using the Pythagorean Theorem we have

c^2 = a^2 + b^2, if and only if the triangle is a right triangle. Substituting we get

26^2 = 10^2 + 24^2, or

676 = 100 + 576 so that

676 = 676

This confirms that the Pythagorean Theorem applies and we have a right triangle. **

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

RESPONSE -->

ok

self critique assessment: 2

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

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

16:05:07

R.3.30 (was R.3.24). What are the volume and surface area of a sphere with radius 3 meters, and how did you obtain your result?

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

RESPONSE -->

v = 4/3)*3.141592654*r^3

so v = 113.097 meters

surface area = 4* 3.141592654* r^2

so surface area = 37.70 meters

confidence assessment: 2

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

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

16:11:54

** To find the volume and surface are a sphere we use the given formulas:

Volume = 4/3 * pi * r^3

V = 4/3 * pi * 3^3

V = 4/3 * pi * 27

V = 36pi m^3

Surface Area = 4 * pi * r^2

S = 4 * pi * 3^2

S = 4 * pi * 9

S = 36pi m^2. **

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

RESPONSE -->

Surface Area = 4 * pi * r^2 Got this

S = 4 * pi * 3^2 this

S = 4 * pi * 9 and even this.

S = 36pi m^2. **

why not go on and multiply to get 113.097 m^2 ?

self critique assessment: 2

It's OK to do that as long as you use an appropriate degree of precision. However note the following advantages to the multiple-of-pi notation:

It's easier to connect 36 to the conditions of the problem.

36 pi is exact, whereas 113.097 is not.

113.097 might or might not be rounded to an appropriate number of significant figures, depending on the situation.

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

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

16:29:13

** Many students like to use FOIL but it's much better to use the Distributive Law, which will later be applied to longer and more complicated expressions where FOIL does not help a bit.

Starting with

(-2x - 3) ( 3 - x) apply the Distributive Law to get

-2x ( 3 - x) - 3 ( 3 - x). Then apply the Distributive Law again to get

-2x(3) - 2x(-x) - 3 * 3 - 3 ( -x) and simiplify to get

-6x + 2 x^2 - 9 + 3x. Add like terms to get

2 x^2 - 3 x - 9. **

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

RESPONSE -->

My dauter just pushed somthing so I will awnser any problem she just put on the screen. sorry

find airea of pool + deck then subtract airea of pool

10+3=13 r=13

13^2*Pi = 169* Pi = 530.929

10^2*Pi = 100* Pi = 314.159

530.929 - 314.159 = 216.77 ft^2 or

69*Pi ft^2

005. `query 5 is somehow showing up so i will just ignore it if i am missing somthing just state this in your rsponse thank you.

self critique assessment: 2

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

"

You're doing good work. See my notes and let me know if you have questions.

Standard time input in a math course is about 3 hours of homework for 1 hour of class. So 4 hours on an assignment is within the realm of expectation. Some students take longer, some less. It depends on grade goals, background, aptitude etc.. Your work here is consistent with very good performance in the course.

I wouldn't expect that every assignment will take you 4 hours, but that depends on many factors. You'll get a better idea over the next few assignments. Keep me posted.

assignments 1  2

course MTH 158

should this be taking so long to finish. around 4 hours per section

m???????????assignment #002

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.

002. `query 2

College Algebra

01-21-2007

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

13:40:17

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 -->

I think this is the place i left off .

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

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

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

= x^-1 y^3

This is as far as i could get with the book.

my brotherinlaw told me somthing to try so lets see

(x^-2 y) / (x y^2) = (x^-2 y) / (x yy)

= y / (xxx yy) = 1 / (x^3 y)

confidence assessment: 2

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

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

13:45:12

** (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 -->

I should have used the law a^-B = 1/a^B

bUT I STILL GOT IT

self critique assessment: 2

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

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

14:29:18

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 -->

4 x^-2 (y z)^-1 / [ (-5)^2 x^4 y^2 z^-5 ]

=ZZZZZ / 4 XXXXXX YYY Z 25

=Z^4/ 4*X^6*Y^3*25

confidence assessment: 2

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

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

14:31:46

** 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 -->

I moved the 4 to the denominater.

self critique assessment: 2

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

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

14:47:54

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

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

RESPONSE -->

4.21*10-3

confidence assessment: 2

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

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

14:48:33

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

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

RESPONSE -->

ok

self critique assessment: 3

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

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

14:49:35

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

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

RESPONSE -->

9700

confidence assessment: 2

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

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

14:49:51

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

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

RESPONSE -->

ok

self critique assessment: 3

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

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

15:34:27

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?

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

RESPONSE -->

| T - 98.6 | > 1.5

add 98.6 = T> 100.1

-| T - 98.6 | > 1.5

= ( -T + 98.6) > 1.5

- 98.6 = -t > -97.1

= T < 97.1

T = 97 is unhealthy T = 100 is not unhealthy

confidence assessment: 2

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

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

15:36:03

** 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

self critique assessment: 2

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

????wd??O??????assignment #003

003. `query 3

College Algebra

01-21-2007

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

15:43:26

R.3.12 (was R.3.6) What is the hypotenuse of a right triangle with legs 14 and 48 and how did you get your result?

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

RESPONSE -->

A^2 + b^2 = c^2

so

14^2 + 48^2 = x^2

196 + 2304 = 2500

the hypotenuse is 50

confidence assessment: 2

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

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

15:44:09

** The Pythagorean Theorem tells us that

c^2 = a^2 + b^2, where a and b are the legs and c the hypotenuse. Substituting 14 and 48 for a and b we get

c^2 = 14^2 + 48^2, so that

c^2 = 196 + 2304 or

c^2 = 2500.

This tells us that c = + sqrt(2500) or -sqrt(2500). Since the length of a side can't be negative we conclude that c = +sqrt(2500) = 50. **

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

RESPONSE -->

ok

self critique assessment: 2

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

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

15:51:27

R.3.18 (was R.3.12). Is a triangle with legs of 10, 24 and 26 a right triangle, and how did you arrive at your answer?

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

RESPONSE -->

10 24 26

10^2 + 24^2 = 26^2

100 + 576 = 676

So yrs this is a right triangle

confidence assessment: 3

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

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

15:51:44

** Using the Pythagorean Theorem we have

c^2 = a^2 + b^2, if and only if the triangle is a right triangle. Substituting we get

26^2 = 10^2 + 24^2, or

676 = 100 + 576 so that

676 = 676

This confirms that the Pythagorean Theorem applies and we have a right triangle. **

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

RESPONSE -->

ok

self critique assessment: 2

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

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

16:05:07

R.3.30 (was R.3.24). What are the volume and surface area of a sphere with radius 3 meters, and how did you obtain your result?

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

RESPONSE -->

v = 4/3)*3.141592654*r^3

so v = 113.097 meters

surface area = 4* 3.141592654* r^2

so surface area = 37.70 meters

confidence assessment: 2

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

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

16:11:54

** To find the volume and surface are a sphere we use the given formulas:

Volume = 4/3 * pi * r^3

V = 4/3 * pi * 3^3

V = 4/3 * pi * 27

V = 36pi m^3

Surface Area = 4 * pi * r^2

S = 4 * pi * 3^2

S = 4 * pi * 9

S = 36pi m^2. **

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

RESPONSE -->

Surface Area = 4 * pi * r^2 Got this

S = 4 * pi * 3^2 this

S = 4 * pi * 9 and even this.

S = 36pi m^2. **

why not go on and multiply to get 113.097 m^2 ?

self critique assessment: 2

It's OK to do that as long as you use an appropriate degree of precision. However note the following advantages to the multiple-of-pi notation:

It's easier to connect 36 to the conditions of the problem.

36 pi is exact, whereas 113.097 is not.

113.097 might or might not be rounded to an appropriate number of significant figures, depending on the situation.

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

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

16:29:13

** Many students like to use FOIL but it's much better to use the Distributive Law, which will later be applied to longer and more complicated expressions where FOIL does not help a bit.

Starting with

(-2x - 3) ( 3 - x) apply the Distributive Law to get

-2x ( 3 - x) - 3 ( 3 - x). Then apply the Distributive Law again to get

-2x(3) - 2x(-x) - 3 * 3 - 3 ( -x) and simiplify to get

-6x + 2 x^2 - 9 + 3x. Add like terms to get

2 x^2 - 3 x - 9. **

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

RESPONSE -->

My dauter just pushed somthing so I will awnser any problem she just put on the screen. sorry

find airea of pool + deck then subtract airea of pool

10+3=13 r=13

13^2*Pi = 169* Pi = 530.929

10^2*Pi = 100* Pi = 314.159

530.929 - 314.159 = 216.77 ft^2 or

69*Pi ft^2

005. `query 5 is somehow showing up so i will just ignore it if i am missing somthing just state this in your rsponse thank you.

self critique assessment: 2

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

"

You're doing good work. See my notes and let me know if you have questions.

Standard time input in a math course is about 3 hours of homework for 1 hour of class. So 4 hours on an assignment is within the realm of expectation. Some students take longer, some less. It depends on grade goals, background, aptitude etc.. Your work here is consistent with very good performance in the course.

I wouldn't expect that every assignment will take you 4 hours, but that depends on many factors. You'll get a better idea over the next few assignments. Keep me posted.