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course Phy 201
I was confused on where to type my answer. The first question, I put the answer in the box to the right and I clicked save to notes. I then clicked next question and I think I skipped the second question accidentally. Questions 3,4, and 5, I answered directly below the question in the same box and typed
Ans:
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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.`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?
Ans: The numerator is the top half of the fraction, which is 3.
The denominator is ( (2x-5)^2 * 3x + 1 )
When the expression is evaluated at x=2,
2- 3 / [ (2*2-5)^2 * 3*2 + 1 ] - 2 + 7*2 =
2- 3/(1*6+1) -2 +14 =
2- 3/7 -2 +14 =
14 - 3/7 = 95/17 = 13.5714
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 ].`q004. Explain, step by step, how you evaluate the expression (x - 5) ^ 2x-1 + 3 / x-2 for x = 4.
Ans: First, 4-5=-1, then you square -1, which gives you one. One times 4 = 4. Then you subtract 1, which gives you 3. 3 plus (3 divided by four) = (15/4) or 3.75. The last step is to subtract 2 from 3.75, which gives you 1.75 for the solution.
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. *&*& 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.
It's hard for me to see the problems and understand them on the computer. I have to write them out in order to visualize the steps. However, I realize that it is important for me to understand the notation used. More than likely I will have to use it in the future. `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.
Ans: The page is called ""Typewriter Notation Practice"". I Clicked on the first link, which brought me to a page that had examples of different expressions shown in typewriter notation and standard notation. There was also a link that explained the steps in both notations.
You should see a brief set of instructions and over 30 numbered examples. If you click on the word Picture you will see the standard-notation format of the expression. The link entitled Examples and Pictures, located in the initial instructions, shows all the examples and pictures without requiring you to click on the links. There is also a file which includes explanations.
The instructions include a note indicating that Liberal Arts Mathematics students don't need a deep understanding of the notation, Mth 173-4 and University Physics students need a very good understanding, while students in other courses should understand the notation and should understand the more basic simplifications.
There is also a link to a page with pictures only, to provide the opportunity to translated standard notation into typewriter notation.end program
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assignment #001
001. typewriter notation
qa initial problems
06-02-2007
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17:48:22
06-02-2007 17:48:22
`q001. Explain the difference between x - 2 / x + 4 and (x - 2) / (x + 4). The evaluate each expression for x = 2.
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NOTES -------> The two equations produce different solutions. With the first equation, you subtract (2/x) from x. You then add four. In the second equation, you divide (x-2) by (x+4). The first equation evaluated at x=2 is 2-(2/2)+4 = 5. The second equation evaluated at x=2 is (2-2)/(2+4) = 0/6 which = 0.
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