course Mth 158
......!!!!!!!!...................................
18:15:48 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 --> (a) Natural Numbers: None (b) Integers: None (c) Rational Numbers: {1/2, 10.3} (d) Irrational Numbers: {sqrt(2), -sqrt(2), pi} (e) Real Numbers : all confidence assessment: 3
.................................................
......!!!!!!!!...................................
18:17:06 ** 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 --> ok self critique assessment: 1
.................................................
......!!!!!!!!...................................
18:21:12 R.1.32 (was R.1.24) Write in symbols: The product of 2 and x is the product of 4 and 6
......!!!!!!!!...................................
RESPONSE --> 2*x=4*6 confidence assessment: 3
.................................................
......!!!!!!!!...................................
18:21:34 R.1.50 (was R.1.42) Explain how you evaluate the expression 2 - 5 * 4 - [ 6 * ( 3 - 4) ]
......!!!!!!!!...................................
RESPONSE --> ok confidence assessment:
.................................................
......!!!!!!!!...................................
18:24:55 **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 --> 2-5*4-[6*(3-4)]=2-5*4-[6*(-1)]=2-5*4-[-6]=2-5*4+6=2-20+6= -12 self critique assessment: 3
.................................................
......!!!!!!!!...................................
18:26:51 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 --> (x-2)(x-4)= x^2+8-4x-2x=x^2-6x+8 confidence assessment: 3
.................................................
......!!!!!!!!...................................
18:27:23 ** 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 --> ok self critique assessment: 3
.................................................
......!!!!!!!!...................................
18:30:20 R.1.86 (was R.1.78) Explain why (4+3) / (2+5) is not equal to 4/2 + 3/5.
......!!!!!!!!...................................
RESPONSE --> (4+3)/ (2+5) is not equal to 4/2 + 3/5 because: (4+3)/(2+5)=7/10 whereas 4/2+3/5 =20/10 +6/10=26/10=13/5 confidence assessment: 3
.................................................
......!!!!!!!!...................................
18:31:13 ** 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 --> ok self critique assessment: 3
.................................................
......!!!!!!!!...................................
18:32:44 Add comments on any surprises or insights you experienced as a result of this assignment.
......!!!!!!!!...................................
RESPONSE --> I noticed that i did not do the order of operations correctly in question number 80 and it is very easy to make little mistakes. I also realized i rely on using the foil method and it can mess up a problem sometimes.
.................................................