course Mth 158 YQ噩ыѲassignment #001
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12:15:25 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?
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RESPONSE --> Counting numbers- 1/2+10.3 Rational- 1/2+10.3 Irrational numbers- -sqrt(2) & pi+sqrt(2) Real numbers- pi + sqrt (2), 1/2+10.3
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12:16:21 06-07-2009 12:16:21 ** 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.. **
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12:16:23 ** 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.. **
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RESPONSE -->
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12:16:25 06-07-2009 12:16:25 ** 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.. **
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assignment #001 001. `query 1 College Algebra 06-07-2009
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12:19:07 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?
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RESPONSE --> Counting numbers- any whole numbers , there are no given counting numbers Rational numbers- 1/2+10.3 Irrational numbers- -Sqrt(2), pi + sqrt (2) confidence assessment: 2
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12:20:21 ** 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.. **
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RESPONSE --> self critique assessment: 3
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12:21:05 R.1.32 (was R.1.24) Write in symbols: The product of 2 and x is the product of 4 and 6
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RESPONSE --> 2*x=4*6 confidence assessment: 3
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12:21:28 ** 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. **
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RESPONSE --> self critique assessment: 3
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12:23:49 R.1.50 (was R.1.42) Explain how you evaluate the expression 2 - 5 * 4 - [ 6 * ( 3 - 4) ]
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RESPONSE --> To evaluate this eexpression you first complete the problem in the brackets, but within in brackets do the paranthesis first [6*(3-4)] 6*(-1) -6 2-5*4-(-6) you then do the multiplication 2-20-(-6) -18-(-6) =-24 confidence assessment: 3
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12:27:01 **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. **
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RESPONSE --> When I did this I completely overlooked the fact that you would be subtracting a negative number which makes that cancel out to actually be adding that number so instead of subtracting -6 i should have added 6 2-20+6 -18+6 -12 self critique assessment: 3
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12:33:43 R.1.80 (was R.1.72) Explain how you use the distributive property to remove the parentheses from the express (x-2)(x-4).
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RESPONSE --> (x-2)(x-4) =(x-2) you first take out what both sets have in common and in this case it is x and 2 x-2*-2 x+4 confidence assessment: 2
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12:37:34 ** 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. *
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RESPONSE --> My teachers throughtout highschool always stressed how college professors did not like using FOIL so, I tried not to and I did the only way it seemed correct but if I would have done this problem using FOIL I could have came out witht he correct answer (x-2)(x-4) X^2*-4x*-2x+8 x^2-6x+8 self critique assessment: 2
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12:39:10 R.1.86 (was R.1.78) Explain why (4+3) / (2+5) is not equal to 4/2 + 3/5.
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RESPONSE --> In this case you need to do each set of paranthesis so you get the answer of 7/7 which gives you one, when a set of paranthesis is given you must complete that step first confidence assessment: 3
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12:39:31 ** 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 **
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RESPONSE --> self critique assessment: 3
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12:40:31 Add comments on any surprises or insights you experienced as a result of this assignment.
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RESPONSE --> I was surprised that there is so many different ways to get a result and each remain correct. confidence assessment: 3
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12:51:09 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 --> (2*(-2)-3)/3 (-4-3)/3 -7/3 = -2 1/3 I got this by first completing what is in the paranthesis confidence assessment: 3
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12:51:18 ** 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 --> self critique assessment: 3
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12:56:29 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 --> x=3 y=-2 | |4*3| - |5*-2| | | |12| -|-10| | | 12- 10 | 2 confidence assessment: 3
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12:56:36 ** 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 --> self critique assessment: 3
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12:59:42 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 --> (-9x^2-x+1)/(x^3+x) x can not be equal to zero confidence assessment: 2
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13:00:43 ** 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 --> self critique assessment:
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13:02:45 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 --> (-4)^-2 =-4*-4*-4 =-64 confidence assessment: 3
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13:05:30 **Since a^-b = 1 / (a^b), we have (-4)^-2 = 1 / (-4)^2 = 1 / 16. **
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RESPONSE --> I do not seem to understand this concept self critique assessment: 1
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13:13:05 ** (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 believe somehow I skipped the problem and answer but this is how I would have thought to solve the equation (3^-2*5^3)/(3^2*5) (-9-125)/(9*5) (-134)/(45) =-2.978 And clearly I did this a totally different way because I did not group the factors with like bases but this solution makes sense and if given a problem again with factors with the same bases i would realize how to correctly solve the problem self critique assessment: 2
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13:20:23 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 --> (5x)(^-2*-3)/(6y)(^-2*-3) (5x^6)/(6y^6) confidence assessment: 2
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13:24:22 [ 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 do not see how you can take and seperate the problem down like this has it seems to just have reversed the problem around in a different ordering and I do not see how this changed the exponets from being negative Is there anyway you can explain this problem in a little more depth
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13:28:30 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 --> (-8)x^(3+-2) (-8x)^1 you do not raise any problem to the first power confidence assessment: 0
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13:29:52 ** 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 do not seem to understand the negative exponets being turned into positive exponets self critique assessment: 0
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13:32:45 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 --> x (y^-2) / x (y^2) (xy)^(-2*2) -1(xy)^(2*2) -1(xy)^4 confidence assessment: 0
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13:33:02 ** (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 --> self critique assessment: 0
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13:33:15 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 --> confidence assessment: 0
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13:33:36 ** 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 do not understand self critique assessment: 0
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13:36:06 R.2.122 (was R.4.72). Express 0.00421 in scientific notation.
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RESPONSE --> 4.21*10^-3 confidence assessment: 3
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13:36:18 ** 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 --> self critique assessment: 3
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13:36:58 R.2.128 (was R.4.78). Express 9.7 * 10^3 in decimal notation.
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RESPONSE --> 9700 confidence assessment: 3
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13:37:04 ** 9.7*10^3 in decimal notation is 9.7 * 1000 = 9700 **
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RESPONSE --> self critique assessment: 3
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13:40:18 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 --> T=97 |97-98.6| |-1.6| 1.6>1.5 which makes this an unhealthy temperature T=100 |100-98.6| |1.4| 1.4 1.4 is not greater than 1.5 so you can not prove this to be an unhealthy temperature confidence assessment: 3
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13:40:24 ** 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 --> self critique assessment: 3
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