Step 3

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course mth158

1/17/2011 around 23:40

Question: `q001. If you are earning money at the rate of 8 dollars / hour and work for 4 hours, how much money do you make during this time? Answer in such a way as to explain your reasoning as fully as possible. A solution to this problem appears several lines below, but enter your own solution before you look at the given solution. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution: (type in your solution starting in the next line)

($8/1hr) * 4hr= $ 32

8 dollars per hour times 4 hours equals 32 dollars because the hour units cancels out and 8 times 4 gives you a product of 32.

confidence rating #$&*:

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Self-critique (if necessary): OK

Question: `q002. If you work 12 hours and earn $168, then at what rate, in dollars / hour, were you making money?

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Your solution: (type in your solution starting in the next line)

X=$14/hr.

Confidence Rating: 2

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Self-critique (if necessary): OK

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Question: `q003. If you are earning 8 dollars / hour, how long will it take you to earn $72? The answer may well be obvious, but explain as best you can how you reasoned out your result.

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Your solution: (type in your solution starting in the next line)

8 dollars /hour times what gives you 72 dollars?

9hr times $8/hr =$72. The hour units cancel out leaving you with dollars.

confidence rating #$&*:

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Self-critique (if necessary): OK

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Question: `q004. Calculate (8 + 3) * 5 and 8 + 3 * 5, indicating the order of your steps. Explain, as best you can, the reasons for the difference in your results.

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Your solution: (type in your solution starting in the next line)

(8+3)*5= 11*5= 55

8+3*5= 8+15= 23

Orders of operations say( p e m d a s) Parentheses(or grouping symbol first) ,than exponents, than multiply and divide whichever comes first from left to right and, then add or subtract whichever comes first from left to right.

(8+3)*5 I have to add first because it inside the parentheses next I take the sum of 8+3 (11) and multiply it by 5 . 11*5=55

8+3*5 I see that there are no parentheses so I have to multiply or divide whichever comes first from left to right. I have 3*5 so I now use the product I have with adding 8+15 which equals 23.

confidence rating #$&*:

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Self-critique (if necessary): OK

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Question: `q005. Calculate (2^4) * 3 and 2^(4 * 3), indicating the order of your steps. Explain, as best you can, the reasons for the difference in your results. Note that the symbol '^' indicates raising to a power. For example, 4^3 means 4 raised to the third power, which is the same as 4 * 4 * 4 = 64.

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Your solution: (2^4)*3= 48

(2*2*2*2)*3

16*3= 48 Orders of operations (PEMDAS)

2^(4*3)= 2^(12)=4,096 orders of operations (Parenthesis than exponents)

2^(12)= 2*2*2*2*2*2*2*2*2*2*2*2= 4,096

Confidence Rating :2

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Self-critique (if necessary): ok, I need to remember that 2^(12)= 4096 is not 2*12=24

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Question: `q006. Calculate 3 * 5 - 4 * 3 ^ 2 and 3 * 5 - (4 * 3)^2 according to the standard order of operations, indicating the order of your steps. Explain, as best you can, the reasons for the difference in your results.

Your solution

3* 5 – 4 *3 ^2

3 * 5 – 4*9

15-4*9

15-36= -21

3*5-(4*3)^2

3*5-(12)^2

3*5-144

15-144= -129

Confidence Rating :2

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Self-critique (if necessary): ok, I need to remember that 15-36 is -21 not -6

`q007. Let y = 2 x + 3. (Note: Liberal Arts Mathematics students are encouraged to do this problem, but are not required to do it).

Evaluate y for x = -2. What is your result? In your solution explain the steps you took to get this result.

Evaluate y for x values -1, 0, 1 and 2. Write out a copy of the table below. In your solution give the y values you obtained in your table.

x y

-2 2(x)+3= -1

-1 2(x)+3= 1

0 2(x)+3= 3

1 2(x)+3= 5

2 2(x)+3= 7

Sketch a graph of y vs. x on a set of coordinate axes resembling the one shown below. You may of course adjust the scale of the x or the y axis to best depict the shape of your graph. In your solution, describe your graph in words, and indicate which of the graphs depicted previously your graph most resembles. Explain why you chose the graph you did.

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Your solution:

X = -2 y = 2(x)+3= -1

X = -1 y= 2(x)+3= 1

X = 0 y= 2(x)+3= 3

X = 1 y= 2(x)+3= 5

X = 2 y= 2(x)+3= 7

The graph is linear

Confidence Rating : 3

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Self-critique (if necessary): ok

q008. Let y = x^2 + 3. (Note: Liberal Arts Mathematics students are encouraged to do this problem, but are not required to do it).

Evaluate y for x = -2. What is your result? In your solution explain the steps you took to get this result.

Evaluate y for x values -1, 0, 1 and 2. Write out a copy of the table below. In your solution give the y values you obtained in your table.

x y

-2

-1

Sketch a graph of y vs. x on a set of coordinate axes resembling the one shown below. You may of course adjust the scale of the x or the y axis to best depict the shape of your graph.

Your solution:

Y = X ^2 +3

When x = -2 Y =7

When X = -1 Y = 4

When X = 0 Y = 3

When X = 1 Y = 4

When X = 2 Y =7

X Y

-2 7

-1 4

0 3

1 4

2 7

Confidence Rating : 3

The linear shape is a U shape paraba it starts off at -2,7 curves down mid-point 0,3 and back around at 2,7.

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Self-critique (if necessary): ok

`q009. Let y = 2 ^ x + 3. (Note: Liberal Arts Mathematics students are encouraged to do this problem, but are not required to do it).

Evaluate y for x = 1. What is your result? In your solution explain the steps you took to get this result.

Evaluate y for x values 2, 3 and 4. Write out a copy of the table below. In your solution give the y values you obtained in your table.

x y

Sketch a graph of y vs. x on a set of coordinate axes resembling the one shown below. You may of course adjust the scale of the x or the y axis to best depict the shape of your graph.

In your solution, describe your graph in words, and indicate which of the graphs depicted previously your graph most resembles. Explain why you chose the graph you did.

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Your solution: Y = 2^X +3

(2)^1+3

2+3 = 5

x y

1 5

2 7

3 8

4 16

Graph : Exponential

It starts off in a line than the line steepens as the line moves to the right.

Confidence Rating : 3

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Self-critique (if necessary): ok

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Question: `q010. If you divide a certain positive number by 1, is the result greater than the original number, less than the original number or equal to the original number, or does the answer to this question depend on the original number?

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Your solution: the number will all was equal itself because it the Identity property of division .

Confidence Rating : 3

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Self-critique (if necessary): ok

q011. If you divide a certain positive number by a number greater than 1, is the result greater than the original number, less than the original number or equal to the original number, or does the answer to this question depend on the original number?

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Your solution: less than the original number but still positive.

Confidence Rating : 3

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Self-critique (if necessary): ok

`q012. If you divide a certain positive number by a positive number less than 1, is the result greater than the original number, less than the original number or equal to the original number, or does the answer to this question depend on the original number?

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Your solution: less than the original. One is like 100 % anything less than 1 you will get less of.

Confidence Rating : 3

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Self-critique (if necessary): ok

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Question: `q013. Students often get the basic answers to nearly all, or even all these questions, correct. Your instructor has however never seen anyone who addressed all the subtleties in the given solutions in their self-critiques, and it is very common for a student to have given no self-critiques. It is very likely that there is something in the given solutions that is not expressed in your solution.

This doesn't mean that you did a bad job. If you got most of the 'answers' right, you did fine.

However, in order to better understand the process, you are asked here to go back and find something in one of the given solutions that you did not address in your solution, and insert a self-critique. You should choose something that isn't trivial to you--something you're not 100% sure you understand.

If you can't find anything, you can indicate this below, and the instructor will point out something and request a response (the instructor will select something reasonable, but will then expect a very good and complete response). However it will probably be less work for you if you find something yourself.

Your response should be inserted at the appropriate place in this document, and should be indicated by preceding it with ####.

As an answer to this question, include a copy of whatever you inserted above, or an indication that you can't find anything.

Self-critique (if necessary):

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Self-critique rating:

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Self-critique (if necessary): ok

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This doesn't mean that you did a bad job. If you got most of the 'answers' right, you did fine.

Your response should be inserted at the appropriate place in this document, and should be indicated by preceding it with ####.

As an answer to this question, include a copy of whatever you inserted above, or an indication that you can't find anything.

Self-critique (if necessary):

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Self-critique rating:

#(*!

Step 3

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