Assignment 7

course Mth 158

This one took me a long time to get through. There was so many little things you had to do to each problem. (I think typing that out was more of a pain than anything haha).

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.

This one took me a long time to get through. There was so many little things you had to do to each problem. (I think typing that out was more of a pain than anything haha). " "Eſ٫hžassignme ⡁L{ڏy College Algebra 03-13-2006

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11:04:30 Query R.7.10 (was R.7.6). Show how you reduced (x^2 + 4 x + 4) / (x^4 - 16) to lowest terms.

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RESPONSE --> (x^2 + 4x + 4) / (x^4 - 16) = (x + 2)(x + 2) / (x^2 + 4)(x^2 - 4) = (x + 2)(x +2) / (x^2 + 4) (x +2)(x - 2) ** (x + 2) / (x + 2) cancels out leaving... = (x + 2) / (x -2)(x^2 + 4)

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11:04:44 ** We factor the denominator to get first (x^2-4)(x^2+4), then (x-2)(x+2)(x^2+4). The numerator factors as (x+2)^2. So the fraction is (x+2)(x+2)/[(x-2)(x+2)(x^2+4)], which reduces to (x+2)/[(x-2)(x^2+4)]. **

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RESPONSE --> i got it correct

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11:13:15 Query R.7.28 (was R.7.24). Show how you simplified[ ( x - 2) / (4x) ] / [ (x^2 - 4 x + 4) / (12 x) ].

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RESPONSE --> [ ( x - 2) / (4x) ] / [ (x^2 - 4 x + 4) / (12 x) ] = [ (x - 2) / (4x) ] * [ (12x) / (x^2 - 4x + 4) ] = [(x - 2)] * [ (12x) / { 4x ( x^2 - 4x + 4)} ] = [ 12x (x -2) ] / [ 4x (x-2)(x-2) ] ** the (x-2) on numerator and denominator cancel out leaving... = 12x / 4x (x-2) = 3 / (x-2) final answer**

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11:13:31 ** [ ( x - 2) / (4x) ] / [ (x^2 - 4 x + 4) / (12 x) ] = (x-2) * / 4x * 12 x / (x^2 - 4x + 4) = (x-2) * 12 x / [ 4x ( x^2 - 4x + 4) ] = 12 x (x-2) / [4x ( x-2) ( x-2) ] = 3/(x - 2) **

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RESPONSE --> got it correct

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11:15:27 Query R.7.40 (was R.7.36). Show how you found and simplified the sum (2x - 5) / (3x + 2) + ( x + 4) / (3x + 2).

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RESPONSE --> (2x - 5) / (3x + 2) + ( x + 4) / (3x + 2) = (2x - 5) + (x + 4) / 3x + 2 = (3x - 1) / (3x + 2)

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11:15:37 ** We have two like terms so we write (2x-5)/(3x+2) + (x+4)/(3x+2) = [(2x-5)+(x+4)]/(3x+2). Simplifying the numerator we have (3x-1)/(3x+2). **

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RESPONSE --> got it correct

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11:22:36 Query R.7.52 (was R.7.48). Show how you found and simplified the expression(x - 1) / x^3 + x / (x^2 + 1).

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RESPONSE --> (x - 1) / x^3 + x / (x^2 + 1) = [(x - 1) (x^2 + 1) / (x^3) (x^2 + 1)] / [(x^4) / (x^3) (x^2 + 1)] = (x -1) (x^2 +1) + x^4 / (x^3) (x^2 +1) = (x^3 + x - x^2 -1 +x^4) / (x^3) (x^2 + 1) = (x^4 + x^3 - x^2 + x - 1) / (x^3) (x^2 + 1)

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11:23:30 ** Starting with (x-1)/x^3 + x/(x^2+1) we multiply the first term by (x^2 + 1) / (x^2 + 1) and the second by x^3 / x^3 to get a common denominator: [(x-1)/(x^3) * (x^2+1)/(x^2+1)]+[(x)/(x^2+1) * (x^3)/(x^3)], which simplifies to (x-1)(x^2+1)/[ (x^3)(x^2+1)] + x^4/ [(x^3)(x^2+1)]. Since the denominator is common to both we combine numerators: (x^3+x-x^2-1+x^4) / ) / [ (x^3)(x^2+1)] . We finally simplify to get (x^4 +x^3 - x^2+x-1) / ) / [ (x^3)(x^2+1)] **

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RESPONSE --> got it correct. This one took me a long time to figure out. I just read in the book and figured out step by step.

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11:26:26 Query R.7.58 (was R.7.54). How did you find the LCM of x - 3, x^3 + 3x and x^3 - 9x, and what is your result?

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RESPONSE --> x - 3 , x^3 + 3 , x^3 - 9x = x - 3 , x(x^2 + 3) , x (x-3)(x+3) = LCM is x -3 , x , x^2 + 3 , x + 3

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11:27:15 ** x-3, x^3+3x and x^3-9x factor into x-3, x(x^2+3) and x(x^2-9) then into (x-3) , x(x^2+3) , x(x-3)(x+3). The factors x-3, x, x^2 + 3 and x + 3 'cover' all the factors of the three polynomials, and all are needed to do so. The LCM is therefore: x(x-3)(x+3)(x^2+3) **

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RESPONSE --> got it correct but i didn't put it in the order shown at the bottom.... x(x-3)(x+3)(x^2+3)

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11:31:04 Query R.7.64 (was R.7.60). Show how you found and simplified the difference3x / (x-1) - (x - 4) / (x^2 - 2x + 1).

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RESPONSE --> 3x / (x-1) - (x - 4) / (x^2 - 2x + 1) = x^2 -2x +1 equals (x -1)^2 = 3x (x-1) / (x-1)^2 - x-4 / (x-1)^2 = 3x^2 - 3x - x -4 / (x-1)^2 = (3x^2 - 4x -4) / (x-1)^2

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11:31:18 ** Starting with 3x / (x-1) - (x-4) / (x^2 - 2x +1) we factor the denominator of the second term to obtain (x - 1)^2. To get a common denominator we multiply the first expression by (x-1) / (x-1) to get 3x(x-1)/(x-1)^2 - (x-4)/(x-1)^2, which gives us (3x^2-3x-x-4) / (x-1)^2 = (3x^2 - 4x - 4) / (x-1)^2. DRV**

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RESPONSE --> got it correct

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11:33:44 QUESTION FROM STUDENT: On the practice test I'm having problems with problem #5 I don't know where to start or how to set it up. I'm probably missing something simple and will probably feel stupid by seeing the solution. Could you help with this problem. A retailer is offering 35% off the purchase price of any pair of shoes during its annual charity sale. The sale price of the shoes pictured in the advertisement is $44.85. Find the original price of the shoes by solving the equation p-.35p = 44.85 for p. INSTRUCTOR RESPONSE: It's very easy to get ahold of the wrong idea on a problem and then have trouble shaking it, or to just fail to look at it the right way. Nothing stupid about it, just human nature. See if the following makes sense. If not let me know. p - .35 p = 44.85. Since p - .35 p = 1 p - .35 p = (1 - .35) p = .65 p we have .65 p = 44.85. Multiplying both sides by 1/.65 we get p = 44.85 / .65 = etc. (you can do the division on your calculator); you'll get something near $67).

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RESPONSE --> that was a little confusing. i don' t really get the part p - .35 p = 44.85. Since p - .35 p = 1 p - .35 p = (1 - .35) p = .65 p we have .65 p = 44.85

Take each step in turn.

p - .35 p = 1 p - .35 p. The only difference between the sides is that p has been expressed as 1 p.

1 p - .35 p = (1 - .35) p. In this step p is treated as a monomial, which is factored out of the two expressions. This is the distributive law, since (1 - .35) p = 1 p - .35 p by that law.

(1 - .35) p = .65 p. This follows: since 1 - .35 = .65, so (1 - .35) p = .65 p.

What this boils down to is that if you take 35% off the original price, you are left with 65% of the original price. It's important to see the formal algebra involved in the process.

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You did well on these problems. See my note on your question at the end. Let me know if you have questions on that or on anything else.