assn3 n 5

course MTH 158

assignment #003

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.

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

09-10-2006

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18:19:12

query 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?

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RESPONSE -->

14^2+48^2=50

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18:19:48

** 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. **

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RESPONSE -->

ok..I got this right and i knwo how to do it but when you right the answer like this i'm sooo lost.

I can tell what you did, but 14^2+48^2 = 196 + 2404, which is not 50.

sqrt( 14^2+48^2) = sqrt(2500) = 50.

It's a very good idea to jot down the equations in the given solution on paper. It's easier to look at and it gets you used to interpreting this notation.

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18:22:04

query 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?

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RESPONSE -->

yes, 10^2=100 24^2=576 26^2=676

100+576=676

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18:22:11

** 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. **

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18:24:55

query 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?

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RESPONSE -->

V=113.08, using the formula, i don't have a pi key

A=113.09

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18:25:15

** 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. **

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18:26:18

query R.3.42 (was R.3.36). A pool of radius 10 ft is enclosed by a deck of width 3 feet. What is the area of the deck and how did you obtain this result?

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RESPONSE -->

15 1/2ab

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18:26:36

** The deck plus the pool gives you a circle of radius 10 ft + 3 ft = 13 ft.

The area of the deck plus the pool is therefore pi * (13 ft)^2 = 169 pi ft^2.

So the area of the deck must be

deck area = area of deck and pool - area of pool = 169 pi ft^2 - 100 pi ft^2 = 69 pi ft^2. **

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RESPONSE -->

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.

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18:26:42

005. `query 4

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18:26:44

005. `query 4

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18:33:24

Query R.4.36 (was R.5.30). What is the single polynomial that is equal to 8 ( 4 x^3 - 3 x^2 - 1 ) - 6 ( 4 x^3 + 8 x - 2 )?

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RESPONSE -->

56x^3-24x^2-48x+12

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18:35:04

** ERRONEOUS STUDENT SOLUTION: To make this problem into a single polynomial, you can group like terms together. (8-6)+ (4x^3-4x^3) + (-3x^2) + (8x) + (-1+2).

Then solve from what you just grouped...2 (-3x^2+8x+1).

INSTRUCTOR CORRECTION:

8 is multiplied by the first polynomial and 6 by the second. You can't isolate them like that.

Starting with

8 ( 4 x^3 - 3 x^2 - 1 ) - 6 ( 4 x^3 + 8 x - 2 ) use the Distributive Law to get

32 x^3 - 24 x^2 - 8 - 24 x^3 - 48 x + 12. Then add like terms to get

8?^3 - 24?^2 - 48? + 4 **

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RESPONSE -->

this is pretty much what i got, but i'm confused by the u's

Something went haywire with the browser or the source file. I don't even see u's. In any case the last line should read

8x^3 - 24x^2 - 48x + 4 .

The coefficient of x^3 is 8, not 56. I believe you'll see why--you just made a simple error in signs.

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18:37:38

Query R.4.60 (was R.5.54). What is the product (-2x - 3) ( 3 - x)?

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RESPONSE -->

2x^2+3x-9

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18:38:01

** 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. **

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RESPONSE -->

sign is my only thing wrong

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18:39:37

Query R.4.66 (was R.5.60). What is the product (x - 1) ( x + 1) and how did you obtain your result using a special product formula?

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RESPONSE -->

x^2+x-x-1

x^2-1

foil

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18:39:46

** Starting with

(x-1)(x+1) use the Distributive Law once to get

x ( x + 1) - 1 ( x+1) then use the Distributive Law again to get

x*x + x * 1 - 1 * x - 1 * 1. Simplify to get

x^2 +- x - x + - 1. Add like terms to get

x^2 - 1. **

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18:40:55

Query R.4.84 (was R.5.78). What is (2x + 3y)^2 and how did you obtain your result using a special product formula?

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RESPONSE -->

4x^2+9y^2

distribute to the square

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18:41:15

** The Special Product is

(a + b)^2 = a^2 + 2 a b + b^2.

Letting a = 2x and b = 3y we get

(2x)^2 + 2 * (2x) * (3y) + (3y)^2, which we expand to get

4 x^2 + 12 x y + 9 y^2. **

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RESPONSE -->

The square does not distribute.

You need a detailed self-critique here.

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18:42:41

Query R.4.90 (was R.5.102). Explain why the degree of the product of two polynomials equals the sum of their degrees.

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RESPONSE -->

because you distribute

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18:43:04

** STUDENT ANSWER AND INSTRUCTOR COMMENTS: The degree of the product of two polynomials equals the sum of their degrees because you use the law of exponenents and the ditributive property.

INSTRUCOTR COMMENTS: Not bad.

A more detailed explanation:

The Distributive Law ensures that you will be multiplying the highest-power term in the first polynomial by the highest-power term in the second.

Since the degree of each polynomial is the highest power present, and since the product of two powers gives you an exponent equal to the sum of those powers, the highest power in the product will be the sum of the degrees of the two polynomials.

Since the highest power present in the product is the degree of the product, the degree of the product is the sum of the degrees of the polynomials. **

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18:43:13

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

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RESPONSE -->

none

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18:43:18

006. `query 6

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RESPONSE -->

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You're doing good work overall. You'll get used to the notation.

Be sure you self-critique everytime your answer doesn't completely agree with the given solution.

Let me know if you have questions.

assn3 n 5

I can tell what you did, but 14^2+48^2 = 196 + 2404, which is not 50. sqrt( 14^2+48^2) = sqrt(2500) = 50. It's a very good idea to jot down the equations in the given solution on paper. It's easier to look at and it gets you used to interpreting this notation.

Something went haywire with the browser or the source file. I don't even see u's. In any case the last line should read 8x^3 - 24x^2 - 48x + 4 . The coefficient of x^3 is 8, not 56. I believe you'll see why--you just made a simple error in signs.

The square does not distribute.

You need a detailed self-critique here.

You're doing good work overall. You'll get used to the notation. Be sure you self-critique everytime your answer doesn't completely agree with the given solution. Let me know if you have questions.

I can tell what you did, but 14^2+48^2 = 196 + 2404, which is not 50.

sqrt( 14^2+48^2) = sqrt(2500) = 50.

It's a very good idea to jot down the equations in the given solution on paper. It's easier to look at and it gets you used to interpreting this notation.

Something went haywire with the browser or the source file. I don't even see u's. In any case the last line should read

8x^3 - 24x^2 - 48x + 4 .

The coefficient of x^3 is 8, not 56. I believe you'll see why--you just made a simple error in signs.

You're doing good work overall. You'll get used to the notation.

Be sure you self-critique everytime your answer doesn't completely agree with the given solution.

Let me know if you have questions.