course Mth 158 ꍶh_aڈҗassignment #001
......!!!!!!!!...................................
11:06:48 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?
......!!!!!!!!...................................
RESPONSE --> -sqrt (2) is an irrational number, pi is irrational, sqrt (2) is irational and 1/2 +10.3 is a rational number. confidence assessment: 2
.................................................
......!!!!!!!!...................................
11:08:03 ** 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.. **
......!!!!!!!!...................................
RESPONSE --> I know that rational numbers can be expressed as the ratio of two intergers. I also know that irrational numbers cannot be expressed this way. self critique assessment: 2
.................................................
......!!!!!!!!...................................
11:09:39 R.1.32 (was R.1.24) Write in symbols: The product of 2 and x is the product of 4 and 6
......!!!!!!!!...................................
RESPONSE --> 2x=4*6 confidence assessment: 2
.................................................
......!!!!!!!!...................................
11:10:42 ** 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. **
......!!!!!!!!...................................
RESPONSE --> I know that product means multiply and I know that is means equal to. self critique assessment: 2
.................................................
......!!!!!!!!...................................
11:15:49 R.1.50 (was R.1.42) Explain how you evaluate the expression 2 - 5 * 4 - [ 6 * ( 3 - 4) ]
......!!!!!!!!...................................
RESPONSE --> First you must do everything in parentheses. 2-5*4-[6*(3-4)]. 2 - 5*4 -[6 (-1)]. Then the brackets. 2 - 5*4 - (-6). Then do the multiplication. 2 - 20 - (-6) Then the subtraction from left to right. 2-20 equals -18. -18- (-6) or -18 +6 equals -12. confidence assessment: 1
.................................................
......!!!!!!!!...................................
11:16:18 **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. **
......!!!!!!!!...................................
RESPONSE --> I did it in the right order and got the correct answer. self critique assessment: 3
.................................................
......!!!!!!!!...................................
11:18:13 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).
......!!!!!!!!...................................
RESPONSE --> First you distribute x to the second set of parentheses. x^2 -4x. Then 2 to the second set. -2x +8. That gives you x^2 - 4x -2x +8 confidence assessment: 2
.................................................
......!!!!!!!!...................................
11:19:23 ** 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. *
......!!!!!!!!...................................
RESPONSE --> I didn't use foil. I used the distributive property and got the correct answer. self critique assessment: 2
.................................................
......!!!!!!!!...................................
11:22:13 R.1.86 (was R.1.78) Explain why (4+3) / (2+5) is not equal to 4/2 + 3/5.
......!!!!!!!!...................................
RESPONSE --> Because (4+3) is one term, it cannot be separated. (2+5) cannot be separated either, so it wouldn't be correct to say that (4+3)/ (2+5) is equal to 4/2 + 3/5 confidence assessment: 2
.................................................
......!!!!!!!!...................................
11:23:25 ** 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 **
......!!!!!!!!...................................
RESPONSE --> I didn't think about the order of operations, now I see how they can be used to determine if these two quantites are equal. self critique assessment: 2
.................................................
......!!!!!!!!...................................
11:24:09 Add comments on any surprises or insights you experienced as a result of this assignment.
......!!!!!!!!...................................
RESPONSE --> I learned how the order of operations can be used to determine if two quantities are equal. confidence assessment: 3
................................................."