B1

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course mth 158

9/5 1

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:

The difference between the two is the way the order of operations is caried out. The first one you will divide first before you add and subract. The second one you will do what is in the ( ) first before you divide.

2-2/2+4= 2-1+4= 5

(2-2) / (2+4)= 0/6= 0

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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:

The difference between the two is the order of operations in the first one you will do the multiplying first then the addition and then in the second one you will do the addition first because of the ( ) then the multiplication.

2^2+4= 4+4= 8

2^(2+4)= 2^6= 64

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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 is 3 because it comes before the / and it is the only one being divided.

The denominator is [(2x-5)^2*3x+1] because it is the only one dividing the 3

2-3/[(2*2-5)^2*3(2)+1]-2+7*2

2-3/[(4-5)^2*6+1]-2+14

2-3/[(-1)^2*6+1]-2+14

2-3/[1*6+1]-2+14

2-3/7-2+14

2-2+14-(3/7)

14-(3/7)= 98/7-3/7= 95/7

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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(4)-1+3/4-2

1*4-1+3/4-2

4-1+3/4-2

4-1-2+3/4

4+3/4

7/4

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Question: `q005. At the link

http://www.vhcc.edu/dsmith/genInfo/introductory problems/typewriter_notation_examples_with_links.htm

(copy this path into the Address box of your Internet browser; alternatively use the path

http://vhmthphy.vhcc.edu/ > General Information > Startup and Orientation (either scroll to bottom of page or click on Links to Supplemental Sites) > typewriter notation examples

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:

On the sites are example questions and the different forms of how the question is set up. Such as the standard form and the expressions in typewriter.

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Question: `q006 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.

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 probably have to enter expressions using a keyboard, so it is well worth the trouble to get used to this notation.

As one example take a minute and go to Wolfram Alpha at http://www.wolframalpha.com/. If this link doesn't work just search the Web for 'Wolfram Alpha'. When the page comes up, you can simply copy the expression

x - 3 / (2x + 4)

into the box. Think about what you would get were you to evaluate this expression, then click on the = sign.

Repeat the process with each of the following expressions. Be sure you think in each case about what expression you would expect to see.

(x - 3) / (2 x + 4)

x - 2 / 3

(x - 2) / 3

(x+2) ^ 2x

(x+2) ^ (2x)

(x - 3) / 3x

(x - 3) / (3 x)

x - 3 / 3x

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:

They act like more in the way of order of operations. It is important to understand this so you can do the question correctly and in the right order to come to the correct answer.

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Question: `q006 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.

You should of course write everything out in standard notation when you work it on paper.

x - 3 / (2x + 4)

into the box. Think about what you would get were you to evaluate this expression, then click on the = sign.

Repeat the process with each of the following expressions. Be sure you think in each case about what expression you would expect to see.

(x - 3) / (2 x + 4)

x - 2 / 3

(x - 2) / 3

(x+2) ^ 2x

(x+2) ^ (2x)

(x - 3) / 3x

(x - 3) / (3 x)

x - 3 / 3x

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:

They act like more in the way of order of operations. It is important to understand this so you can do the question correctly and in the right order to come to the correct answer.

confidence rating #$&*:

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B1

&#Good responses. Let me know if you have questions. &#