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course phy 201
Question: `q001. Explain the difference between x - 2 / x + 4 and (x - 2) / (x + 4). Then evaluate each expression for x = 2.
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Your solution:
Because division is before addition and subtraction, parentheses are needed if 2 is supposed to be subtracted from x and 4 added to x.
(2-2) / (2+4) = 0
Confidence: 3
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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:
With the parentheses x + 4 is added first instead of 2^x plus 4.
2^(2+4)
2^6
64
Confidence: 3
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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:
3 is the numerator and the denominator is [(2x-5)^2 x 3x +1].
2-3/[(4-5)^2 x 6 + 1] -2 +14
98/7 - 3/7 = 95/7
Confidence: 3
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Question: `q004. Explain, step by step, how you evaluate the expression (x - 5) ^ 2x-1 + 3 / x-2 for x = 4.
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Your solution:
(4 - 5) ^ 2(4)-1 + 3 / 4-2
(-1)^2 x 4-1+3/4-2 Square -1 and multiply by 4
4-1+3/4-2 subtract and add
1+3/4 Use 4 as common denominator
7/4
Confidence: 3
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Question: `q005. Evaluate the expression x^3x+2/x-1 for x = 2, according to the order of operations. Show all your steps.
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Your solution:
8 x 2 + 2 / 2 -1
16 + 1 -1
16
Confidence: 3
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Question: `q006. At the link
http://www.vhcc.edu/dsmith/genInfo/introductory problems/typewriter_notation_examples_with_links.htm
and you will find a page containing a number of additional exercises and/or examples of typewriter notation.Locate this site, click on a few of the links, and describe what you see there.
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Your solution:
There are 35 practice problems with pictures. The pictures show the problem with actual fractions.
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Question: `q007. Standard mathematics notation is easier to look at; it's easier to see the meaning of the expressions.
However it's very important to understand order of operations, and students do get used to this way of doing it.
Do these expressions act the way most people would expect, or do they act in the way dictated by the order of operations?
Indicate your understanding of why it is important to understand this notation.
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Your solution:
These follow the order of operations. Most people may not expect them to come out like this.
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Very good.
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