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course Mth 164
4:00 9/5/12
Question: `q001. Explain the difference between x - 2 / x + 4 and (x - 2) / (x + 4). Then evaluate each expression for x = 2.YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
If you have x-2 / x+4 then the order of operations says you divide first. if you have (x-2) / (x+4) then you must subtract and add the integers in the parenthesis first.
So if you substitute 2 for x in x-2 / x+4
You get 2-2 / 2+4 and you must do division first. getting 2-1+4 then evaluating this you end with the answer of 5.
In (x-2) / (x+4) after you substitute in 2 you get (2-2) / (2+4) and order of operations say you must do whats in the parenthesis first. (0)/ (6) ending with 0.
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Given Solution:
`aThe 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) / ( 2 + 4 ) = 0 / 6 = 0.
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Self-critique (if necessary):
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Question: `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.
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Your solution:
2^x+4 means you raise 2 to the x power then add 4
2^(x+4) means you raise 2 to the x+4 power
If x=2 then
2^2 +4 = 8
2^(2+4) = 2^(6) = 64
confidence rating #$&*:
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Given Solution:
`a2 ^ 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.
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Self-critique (if necessary):
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Self-critique Rating:
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Question: `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?
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Your solution:
The numerator in the expression x - 3 / [ (2x-5)^2 * 3x + 1 ] - 2 + 7x = x-3
Denominator is {(2x-5)^2*3x+1] - 2 + 7x
If x = 2 then
2 - 3 / [ (2(2)-5)^2 * 3(2) + 1 ] - 2 + 7(2)
-1 / [-1^2 *7] +12 = -1 / 5 = -5
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Self-critique (if necessary):
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Self-critique rating:
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&#Your response did not agree with the given solution in all details, and you should therefore have addressed the discrepancy with a full self-critique, detailing the discrepancy and demonstrating exactly what you do and do not understand about the parts of the given solution on which your solution didn't agree, and if necessary asking specific questions (to which I will respond).
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Question: `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?
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Your solution:
The numerator in the expression x - 3 / [ (2x-5)^2 * 3x + 1 ] - 2 + 7x = x-3
Denominator is {(2x-5)^2*3x+1] - 2 + 7x
If x = 2 then
2 - 3 / [ (2(2)-5)^2 * 3(2) + 1 ] - 2 + 7(2)
-1 / [-1^2 *7] +12 = -1 / 5 = -5
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Self-critique (if necessary):
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Self-critique rating:
@&
&#Your response did not agree with the given solution in all details, and you should therefore have addressed the discrepancy with a full self-critique, detailing the discrepancy and demonstrating exactly what you do and do not understand about the parts of the given solution on which your solution didn't agree, and if necessary asking specific questions (to which I will respond).
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Question: `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?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
The numerator in the expression x - 3 / [ (2x-5)^2 * 3x + 1 ] - 2 + 7x = x-3
Denominator is {(2x-5)^2*3x+1] - 2 + 7x
If x = 2 then
2 - 3 / [ (2(2)-5)^2 * 3(2) + 1 ] - 2 + 7(2)
-1 / [-1^2 *7] +12 = -1 / 5 = -5
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Self-critique (if necessary):
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Self-critique rating:
@&
&#Your response did not agree with the given solution in all details, and you should therefore have addressed the discrepancy with a full self-critique, detailing the discrepancy and demonstrating exactly what you do and do not understand about the parts of the given solution on which your solution didn't agree, and if necessary asking specific questions (to which I will respond).
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