course mth 158 躡щ~PO젓assignment #001
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23:36:24 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) none rational) 1/2+10.3 irrational) pi+sqrt(2); -sqrt(2) real)1/2+10.3; pi+sqrt(2); -sqrt(2) confidence assessment: 2
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23:37:15 ** 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 --> I understand about the different types of numbers and what they all mean. I also have the notes to review later. self critique assessment: 3
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23:37:50 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: 2
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23:38:21 ** 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 --> I understood and know how to interpret words into symbols. self critique assessment: 3
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23:40:51 R.1.50 (was R.1.42) Explain how you evaluate the expression 2 - 5 * 4 - [ 6 * ( 3 - 4) ]
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RESPONSE --> 2 - 5 * 4 - [ 6 * ( 3 - 4 ) ] 2 - 5 * 4 - [ 6 *( - 1) ] 2 - 5 * 4 - [ -6 ] 2 - 20 + 6 18 + 6 24 confidence assessment: 3
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23:41:57 **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 --> I didn't give 20 the negitive sign and then added 6 to it instead of adding it to make it less of a negitive number. self critique assessment: 3
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23:43:40 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 ) 2 x^2 - 4 x- 2 x + 8 2 x^2 - 6 x + 8 confidence assessment: 3
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23:44:48 ** 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 --> I wrote it correctly in my notebook, but instead of multiplying the two xs together, I added them. I do understand this process, but it was a stupidity error. self critique assessment: 3
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23:47:26 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 --> These two equations are not alike because the first one tells us to add the two numbers in the numerator and denominator before we do anything. Then those numbers will be the fraction: 7/7= 1. The second equation is telling us to add these equations together with a LCD: 13/5. confidence assessment: 3
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23:48:01 ** 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 --> I understand and I guess I just went around it a harder way. self critique assessment: 3
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23:48:45 Add comments on any surprises or insights you experienced as a result of this assignment.
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RESPONSE --> I remember this information from a class I had in high school and I never knew I would actually use it again. confidence assessment: 3
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