#$&*
course Mth 277
6/7 10:30 am
Question 3: 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.72/8= 9 hours
Confidence=3
OK
Question 4: 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.
PEMDAS
(8+3)=11 * 5 =55
8+15=23
Confidence=3
OK
Question 5: 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.
PEMDAS
2^4=16*3=48
no parenthesis, so we do the exponent first then we multiply.
(4*3)=12 --> 2^(12) = 4096
parenthesis first, then exponent.
Confidence:3
OK
Question 6: 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.
PEMDAS
3^2=9
3*5=15 and 4*9=36
15-36= -21
PEMDAS
(4*3)=12^2=144
3*5=15
15-144= -129
Confidence=3
OK
Question 7: Let y = 2 x + 3. 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.
x=-2 --> y=2(-2)+3=-4+3=-1
x=-1 --> y=2(-1)+3=-2+3=1
x=0 --> y=2(0)+3=0+3=3
x=1 --> y=2(1)+3=2+3=5
x=2 --> y=2(2)+3=4+3=7
Now we have both x and y points:
(-2,-1)
(-1,1)
(0,3)
(1,5)
(2,7)
When we graph these points, we see that they line up in a straight line which means that we would use the linear graph. It's the only one with a straight line also. The rest of the graphs curve.
Confidence=3
OK
Question 8: Let y = x^2 + 3.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
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. 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.
x=-2 --> y=(-2)^2+3=4+3=7
x=-1 --> y=(-1)^2+3=1+3=4
x=0 --> y=(0)^2+3=0+3=3
x=1 --> y=(1)^2+3=1+3=4
x=2 --> y=(2)^2+3=4+3=7
Points: (-2,7) (-1,4) (0,3) (1,4) (2,7)
As we can see when we plot the points, it forms a curve. This is a parabola. We will graph it accordingly.
Confidence:3
OK
Question 9: Let y = 2 ^ x + 3. 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.
x=1 --> y=2^(1)+3=2+3=5
x=2 --> y=2^(2)+3=4+3=7
x=3 --> y=2^(3)+3=8+3=11
x=4 --> y=2^(4)+3=16+3=19
Points: (1,5) (2,7) (3,11) (4,19)
The main thing to notice is that as the x increases so does the y. We see that the y increases each time by a little more. If we look closely, the increase in the y is actually doubled each time (2,4,8). When we graph the points, we see that it rises positively, which makes us first think it is linear, but as we graph the last two points, we see that it rises faster and faster and starts to curve upward. This leads us to the conclusion that the graph is exponential.
Confidence:3
OK
Question 10: 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?
If you divide any number by 1, it is always equal to that original number. It doesn't matter what the original number is, positive or negative, it will always equal the same original number.
Confidence=3
OK
Question 11: 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?
If you divide a positive number by a number that is greater than 1, it is always going to be smaller than the original number because you are taking the original number and splitting it up in that many different ways. It doesn't matter what the original number is as long as it is positive. For example:
12/1=12
12/2=6
12/-2=-6
Confidence=3
OK
Question 12: 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?
Assuming that ""less than 1"" means a positive fraction and not 0, then when you divide a positive number by a positive number less than 1 then the result is greater than the original number. For example:
12/1=12
12/.5=24
Confidence=3
OK
Question 13: The one problem I would think I had problems with if any at all would be Question 9. At first glance, I just saw that the x and y was both increasing and assumed it was another linear graph. Then, once I graphed it on paper, I saw that it was exponential. Sometimes these are hard for me to see at first, but once drawing it out with a better scale I was able to see it.
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