course Mth 158 Sorry again for it being so late. ¦®«kqªµ àG¡Å¯g‰{ꟊ÷‹Ö ®º†assignment #001
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18:51:03 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 --> In the set of numbers there is no counting numbers. In the set of numbers: {pi+sqrt(2),1/2+10.3, and -sqrt(2)} are all rational numbers. In the set of numbers: {pi+sqrt(2), and 1/2+10.3} are irrational numbers. confidence assessment: 3
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18:51:30 01-28-2007 18:51:30 ** 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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NOTES -------> 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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18:57:43 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 --> The product of 4 and 6 is 10. To get the product of 2 and x I had to subtract 2 from 10 which gave me the answer 8. So x is eqaul to 8. confidence assessment: 2
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18:58:10 01-28-2007 18:58:10 ** 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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NOTES -------> ** 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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19:05:23 R.1.50 (was R.1.42) Explain how you evaluate the expression 2 - 5 * 4 - [ 6 * ( 3 - 4) ]
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RESPONSE --> You would have to first solve what is in the prentices (3-4) which is -1. Then you will have to work what is in the brackets [6*(-1)] which is -6 then you would have to multiply 5*4 which is 20 and then subtract 2 to get 18. Then you would take 18 and subtract it from [-6] which will give the answer which is 24. confidence assessment: 2
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19:05:41 01-28-2007 19:05:41 **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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NOTES -------> **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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19:15:26 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 --> You would take the problem (x-2)(x-4). You could the FOIL which you would multiply the first two numbers which would give you x^2. Then you would the outter portion of the parentheses which would be -4x. Then you would multiply the inner part of the parentheses which would give you -2x. Then you would multiply the last part of the parentheses which would give 8. The problem would look like this: x^2-6x+8 confidence assessment: 2
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19:16:00 01-28-2007 19:16:00 ** 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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NOTES -------> ** 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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19:22:01 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 --> The two problems are not equal because (4+3) / (2+5) equals 1. The other problem 4/2 + 3/5 equals 2.6. You have to apply the rules of signs and you also have to use the Least Common Multiple to add two fractions. confidence assessment: 2
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19:22:18 01-28-2007 19:22:18 ** 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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NOTES -------> ** 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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19:24:06 Add comments on any surprises or insights you experienced as a result of this assignment.
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RESPONSE --> This was a little challenging and it was submitted a little late on my behalf but I finally understand my assignments and what I am suppose to do. Thank you for the help you have given me this week. I am also sorry for having to do my work so late but I am working six days a week. confidence assessment: 3
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