course Mth 173 First half of orientation part III with notation questions assignment #001001. typewriter notation
......!!!!!!!!...................................
11:22:32 `q001. Explain the difference between x - 2 / x + 4 and (x - 2) / (x + 4). The evaluate each expression for x = 2.
......!!!!!!!!...................................
RESPONSE --> If the ( ) are around the numbers, then it means that they are all together, and can't be split apart. I can't remember the exact name for what it means when the ( ) are around the numbers, but I understand how it works. 2-2/2+4= 0/6 (2-2)/(2+4)= (0)/(6) confidence assessment: 1
.................................................
......!!!!!!!!...................................
11:26:02 The order of operations dictates that grouped expressions must be evaluated first, that exponentiation must be done before multiplication or division, which must be done before addition or subtraction. It makes a big difference whether you subtract the 2 from the x or divide the -2 by 4 first. If there are no parentheses you have to divide before you subtract. Substituting 2 for x we get 2 - 2 / 2 + 4 = 2 - 1 + 4 (do multiplications and divisions before additions and subtractions) = 5 (add and subtract in indicated order) If there are parentheses you evaluate the grouped expressions first: (x - 2) / (x - 4) = (2 - 2) / ( 4 - 2) = 0 / 2 = 0.
......!!!!!!!!...................................
RESPONSE --> I understand now. That makes more sense. I did not follow the order of operations, so I got the wrong answer. self critique assessment:
.................................................
......!!!!!!!!...................................
11:29:31 `q002. Explain the difference between 2 ^ x + 4 and 2 ^ (x + 4). Then evaluate each expression for x = 2. Note that a ^ b means to raise a to the b power. This process is called exponentiation, and the ^ symbol is used on most calculators, and in most computer algebra systems, to represent exponentiation.
......!!!!!!!!...................................
RESPONSE --> I understand the meaning of the ^ now. 2^2+4= 4+4= 8 2^(2+4)= 2^6= 64 confidence assessment: 3
.................................................
......!!!!!!!!...................................
11:30:44 2 ^ x + 4 indicates that you are to raise 2 to the x power before adding the 4. 2 ^ (x + 4) indicates that you are to first evaluate x + 4, then raise 2 to this power. If x = 2, then 2 ^ x + 4 = 2 ^ 2 + 4 = 2 * 2 + 4 = 4 + 4 = 8. and 2 ^ (x + 4) = 2 ^ (2 + 4) = 2 ^ 6 = 2*2*2*2*2*2 = 64.
......!!!!!!!!...................................
RESPONSE --> I got those right, but I need to remember to show all of the steps I took to get the answer. I did not write out the ^ steps in each question. I will remember to work on that. self critique assessment: 1
.................................................
......!!!!!!!!...................................
11:39:36 `q003. What is the numerator of the fraction in the expression x - 3 / [ (2x-5)^2 * 3x + 1 ] - 2 + 7x? What is the denominator? What do you get when you evaluate the expression for x = 2?
......!!!!!!!!...................................
RESPONSE --> The numerator is the top number in a fraction, and the denominator. 2-3/ [ (2*2-5)^2*3*2+1 ] -2+7*2= -1/ [ (-1)^2*6+1] -2+14= -1/ [ 1*6+1] 12= -1/ [7] 12= -1/84 confidence assessment: 1
.................................................
......!!!!!!!!...................................
11:41:52 The numerator is 3. x isn't part of the fraction. / indicates division, which must always precede subtraction. Only the 3 is divided by [ (2x-5)^2 * 3x + 1 ] and only [ (2x-5)^2 * 3x + 1 ] divides 3. If we mean (x - 3) / [ (2x-5)^2 * 3x + 1 ] - 2 + 7x we have to write it that way. The preceding comments show that the denominator is [ (2x-5)^2 * 3x + 1 ] Evaluating the expression for x = 2: - 3 / [ (2 * 2 - 5)^2 * 3(2) + 1 ] - 2 + 7*2 = 2 - 3 / [ (4 - 5)^2 * 6 + 1 ] - 2 + 14 = evaluate in parenthese; do multiplications outside parentheses 2 - 3 / [ (-1)^2 * 6 + 1 ] -2 + 14 = add inside parentheses 2 - 3 / [ 1 * 6 + 1 ] - 2 + 14 = exponentiate in bracketed term; 2 - 3 / 7 - 2 + 14 = evaluate in brackets 13 4/7 or 95/7 or about 13.57 add and subtract in order. The details of the calculation 2 - 3 / 7 - 2 + 14: Since multiplication precedes addition or subtraction the 3/7 must be done first, making 3/7 a fraction. Changing the order of the terms we have 2 - 2 + 14 - 3 / 7 = 14 - 3/7 = 98/7 - 3/7 = 95/7. COMMON STUDENT QUESTION: ok, I dont understand why x isnt part of the fraction? And I dont understand why only the brackets are divided by 3..why not the rest of the equation? INSTRUCTOR RESPONSE: Different situations give us different algebraic expressions; the situation dictates the form of the expression. If the above expression was was written otherwise it would be a completely different expression and most likely give you a different result when you substitute. If we intended the numerator to be x - 3 then the expression would be written (x - 3) / [(2x-5)^2 * 3x + 1 ] - 2 + 7x, with the x - 3 grouped. If we intended the numerator to be the entire expression after the / the expression would be written x - 3 / [(2x-5)^2 * 3x + 1 - 2 + 7x ].
......!!!!!!!!...................................
RESPONSE --> I read the question wrong. I thought was supposed to answer what a denominator was. I will have to work at these. I got the answer wrong, but I understand/remember more now. self critique assessment: 1
.................................................
......!!!!!!!!...................................
11:46:51 `q004. Explain, step by step, how you evaluate the expression (x - 5) ^ 2x-1 + 3 / x-2 for x = 4.
......!!!!!!!!...................................
RESPONSE --> (4-5)^2(4)-1 +3/4-2 First i replaced x with 4 (-1)^8-1 +3/2 Then i slove for x (-1)^7 +3/2 2/2=1 Work out the problem to get the solution confidence assessment: 2
.................................................
......!!!!!!!!...................................
11:48:42 We get (4-5)^2 * 4 - 1 + 3 / 1 - 4 = (-1)^2 * 4 - 1 + 3 / 4 - 2 evaluating the term in parentheses = 1 * 4 - 1 + 3 / 4 - 2 exponentiating (2 is the exponent, which is applied to -1 rather than multiplying the 2 by 4 = 4 - 1 + 3/4 - 2 noting that 3/4 is a fraction and adding and subtracting in order we get = 1 3/4 = 7 /4 (Note that we could group the expression as 4 - 1 - 2 + 3/4 = 1 + 3/4 = 1 3/4 = 7/4). COMMON ERROR: (4 - 5) ^ 2*4 - 1 + 3 / 4 - 2 = -1 ^ 2*4 - 1 + 3 / 4-2 = -1 ^ 8 -1 + 3 / 4 - 2. INSTRUCTOR COMMENTS: There are two errors here. In the second step you can't multiply 2 * 4 because you have (-1)^2, which must be done first. Exponentiation precedes multiplication. Also it isn't quite correct to write -1^2*4 at the beginning of the second step. If you were supposed to multiply 2 * 4 the expression would be (-1)^(2 * 4). Note also that the -1 needs to be grouped because the entire expression (-1) is taken to the power. -1^8 would be -1 because you would raise 1 to the power 8 before applying the - sign, which is effectively a multiplication by -1.
......!!!!!!!!...................................
RESPONSE --> I did not do the problem right. I continue to work the problem without changing it up. self critique assessment: 1
.................................................
......!!!!!!!!...................................
23:10:14 *&*& Standard mathematics notation is easier to see. On the other hand it's very important to understand order of operations, and students do get used to this way of doing it. You should of course write everything out in standard notation when you work it on paper. It is likely that you will at some point use a computer algebra system, and when you do you will have to enter expressions through a typewriter, so it is well worth the trouble to get used to this notation. Indicate your understanding of the necessity to understand this notation.
......!!!!!!!!...................................
RESPONSE --> I understand the necessity of notation, and that I need to work on it self critique assessment: 1
................."