course Mth 174
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.YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
$72.00/ $8.00 per hour = 9 hours
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Question: `q004. Calculate (8 + 3) * 5 and 8 + 3 * 5, indicating the order of your steps. Explain, as best you can, the reasons for the difference in your results.
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Your solution:
(8+3) * 5
First start with parenthesis: (8+3) = 11
Next 11 * 5 = 55
So, (8+3)*5 = 55
8 + 3 * 5
Start with multiplication 3 * 5 = 15
Next 8 +15 = 23
So, 8 + 3 * 5 = 23
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Self-critique rating #$&* 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 rising 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
(2^4) = 16
16 * 3 = 48
So, (2^4) *3 = 48
2^(4*3)
(4*3) = 12
Thus it would then be 2^12 or 2 raised to the twelfth power.
2^12 = 4096
So, 2^(4*3) = 4096
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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.
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Your solution:
3 * 5 - 4 * 3 ^ 2
Exponent- ( 3^2 ) = 9
Then (3*5) & (4*9)
Which = 15-36
So, 15-36= -21
3 * 5 - 4 * 3 ^ 2 = -21
3 * 5 - (4 * 3)^2
First parenthesis: (4*3)=12
Next exponent 12^2 = 144
Then (3*5) =15
Finally 15-144= -129
3 * 5 - (4 * 3)^2 = -129
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Self-critique rating #$&* OK
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Question: `q007. Let y = 2 x + 3. (Note: Liberal Arts Mathematics students are encouraged to do this problem, but are not required to do it).
• Evaluate y for x = -2. What is your result? In your solution explain the steps you took to get this result.
• Evaluate y for x values -1, 0, 1 and 2. Write out a copy of the table below. In your solution give the y values you obtained in your table.
x y
-2
-1
0
1
2
• Sketch a graph of y vs. x on a set of coordinate axes resembling the one shown below. You may of course adjust the scale of the x or the y axis to best depict the shape of your graph.
• In your solution, describe your graph in words, and indicate which of the graphs depicted previously your graph most resembles. Explain why you chose the graph you did.
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Your solution:
If x= -2 then, y = 2 (-2) + 3 = -1
x= -1 then, y = 2 (-1) + 3 = 1
x = 0 then, y = 2 (0) + 3 = 3
x = 1 then, y = 2 (1) + 3 = 5
x = 2 then, y = 2 (2) + 3 = 7
In x vs. y, when plotted you see a line. Which means the graph is linear.
Confidence rating #$&* OK
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Self-critique rating #$&* I feel as if I’m slower at graphs than just working out plain equations. I remember going over graphs in the classroom however, I still struggle with them. The solution can be so simple to find, but I sit and think that it’s going to be complicated and that’s where I go blank and struggle the most.
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Question: `q008. Let y = x^2 + 3. (Note: Liberal Arts Mathematics students are encouraged to do this problem, but are not required to do it).
• Evaluate y for x = -2. What is your result? In your solution explain the steps you took to get this result.
• Evaluate y for x values -1, 0, 1 and 2. Write out a copy of the table below. In your solution give the y values you obtained in your table.
x y
-2
-1
0
1
2
• Sketch a graph of y vs. x on a set of coordinate axes resembling the one shown below. You may of course adjust the scale of the x or the y axis to best depict the shape of your graph.
• In your solution, describe your graph in words, and indicate which of the graphs depicted previously your graph most resembles. Explain why you chose the graph you did.
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Your solution:
If x = -2 then, y = -2^2 + 3 = 7
If x = -1 then, y = -1^2 +3 = 2
If x = 0 then, y = 0^2 +3 = 3
If x = 1 then, y = 1^2 + 3 = 4
If x = 2 then, y = 2^2 + 3 = 7
This graph is a parabola.
confidence rating #$&*
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Question: `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
1
2
3
4
• 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
If x = 1 then y = 2^1 +3 = 5
If x = 2 then y = 2^2 + 3 = 7
If x = 3 then y = 2^3 + 3 = 11
If x = 4 then y = 2^4 + 3 = 19
This graph increases from left to right, getting steeper along the way. It is exponential.
confidence rating #$&*
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Question: `q010. If you divide a certain positive number by 1, is the result greater than the original number, less than the original number or equal to the original number, or does the answer to this question depend on the original number?
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Your solution:
The result would be equal to the original number.
Ex.
2/1 = 2
3/1 = 3
4/1 = 4
20/1 = 20
confidence rating #$&*
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Question: `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:
The result is less than the original number.
Ex.
4/2 = 2
9/3 = 3
12/4 = 3
15/5 = 3
confidence rating #$&*
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Question: `q012. If you divide a certain positive number by a positive number less than 1, is the result greater than the original number, less than the original number or equal to the original number, or does the answer to this question depend on the original number?
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Your solution:
Dividing by a number bigger than 1 gives a small number. Thus dividing by a number smaller than 1 will give you a larger number.
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Self-critique rating #$&* OK
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Question: `q013.
Answer:
q’007.
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Self-critique rating #$&* I feel as if I’m slower at graphs than just working out plain equations. I remember going over graphs in the classroom however, I still struggle with them. The solution can be so simple to find, but I sit and think that it’s going to be complicated and that’s where I go blank and struggle the most.
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&#Good responses. Let me know if you have questions. &#
#$&*