#$&* course MTH 158 Here are the remaining ten questions:*********************************************
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Given Solution: Many students simply know, at the level of common sense, that if we divide $72 by $8 / hour we get 9 hours, so 9 hours are required. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK ------------------------------------------------ Self-critique Rating: 3 ********************************************* 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. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: You follow the rule of PEMDAS. First you start with the parentheses. So 8+3=11*5 =55. Then 3*5. The answer is 23. Confidence Rating:3
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Given Solution: (8 + 3) * 5 and 8 + 3 * 5 To evaluate (8 + 3) * 5, you will first do the calculation in parentheses. 8 + 3 = 11, so (8 + 3) * 5 = 11 * 5 = 55. To evaluate 8 + 3 * 5 you have to decide which operation to do first, 8 + 3 or 3 * 5. You should be familiar with the order of operations, which tells you that multiplication precedes addition. The first calculation to do is therefore 3 * 5, which is equal to 15. Thus 8 + 3 * 5 = 8 + 15 = 23 The results are different because the grouping in the first expression dictates that the addition be done first. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK Self-critique Rating: 3 ********************************************* 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. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: You would need to find out whats in the parenthesis first which would be 16, then you would do the other equation which would be 2^12 or 4096 Confidence Rating:1
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Given Solution: To evaluate (2^4) * 3 we first evaluate the grouped expression 2^4, which is the fourth power of 2, equal to 2 * 2 * 2 * 2 = 16. So we have (2^4) * 3 = 16 * 3 = 48. To evaluate 2^(4 * 3) we first do the operation inside the parentheses, obtaining 4 * 3 = 12. We therefore get 2^(4 * 3) = 2^12 = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 = 4096. It is easy to multiply by 2, and the powers of 2 are important, so it's appropriate to have asked you to do this problem without using a calculator. Had the exponent been much higher, or had the calculation been, say, 3^12, the calculation would have become tedious and error-prone, and the calculator would have been recommended. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary):OK ********************************************* 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. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: Do the parentheses first - (4 * 3)^2. = 4*9Then do the exponent, 144, then multiplication 15-36= -21 &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary):2 ------------------------------------------------ Self-critique Rating:2 In the next three problems, the graphs will be of one of the basic shapes listed below. You will be asked to construct graphs for three simple functions, and determine which of the depicted graphs each of your graphs most closely resembles. At this point you won't be expected to know these terms or these graph shapes; if at some point in your course you are expected to know these things, they will be presented at that point. Linear: Quadratic or parabolic: Exponential: Odd power: Fractional positive power: Even negative power: partial graph of polynomial of degree 3 more extensive graph of polynomial of degree 3 ********************************************* 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. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: First you plug in the numbers to evaluate the expression. -if x=-2: y=2x+3=2 * (-2) + 3 = -4 + 3 = -1. -if x=-1: y=2x+3=2 * (-1) + 3 = -2 + 3 = 1. -if x=0: y=2x+3=2 * (0) + 3 = 0 + 3 = 3. -if x=1:y=2x+3=2 * (1) + 3 = 2 + 3 = 5 -if x=2:y=2x+3=2 * (2) + 3 = 4 + 3 = 7. This would give us the coordinates of (-2, -1), (-1, 1), (0, 3), (1, 5), (2, 7) When graphed, you get a straight line. This is a linear graph. confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary):OK ------------------------------------------------ Self-critique Rating:3 Question: `q008. 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 • 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. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: you need to plug in -2, -1, 0, 1, and 2 in the equation If x = -2 : y = x^2 + 3 = (-2)^2 + 3 = 4 + 3 = 7. If x = -1 : y = x^2 + 3 = (-1)^2 + 3 = ` + 3 = 4. If x = 0 :y = x^2 + 3 = (0)^2 + 3 = 0 + 3 = 3. If x = 1 : y = x^2 + 3 = (1)^2 + 3 = 1 + 3 = 4. If x = 2 : y = x^2 + 3 = (2)^2 + 3 = 4 + 3 = 7. Then we get coordinates of (-2, 7), (-1, 4), (0, 3), (1, 4), (2, 7). After plotting these points, we are shown to have a right-left symmetry and is a quadratic graph. Confidence Rating:3 &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK Self-critique Rating: 3 ********************************************* 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. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: Plug in the numbers and solve: When x = 1 : y = 2^1 + 3 = 2 + 3 = 5. When x = 2 : y = 2^2 + 3 = 4 + 3 = 7. When x = 3 : y = 2^3 + 3 = 8 + 3 = 11. When x = 4 : y = 2^4 + 3 = 16 + 3 = 19. Our coordinates are now: (1, 5), (2, 7), (3, 11), (4, 19). When plotted we see an exponential graph. confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK ------------------------------------------------ Self-critique Rating:3 ********************************************* Question: `q010. If you divide a certain positive number by 1, is the result greater than the original number, less than the original number or equal to the original number, or does the answer to this question depend on the original number? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: If you divide any number by 1, the answer is the same as the number you dicvided it by. Confidence Rating: 3 &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary):Ok ------------------------------------------------ Self-critique Rating:3 ********************************************* Question: `q011. If you divide a certain positive number by a number greater than 1, is the result greater than the original number, less than the original number or equal to the original number, or does the answer to this question depend on the original number? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: The answer will always be less than the original. confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary):OK ------------------------------------------------ Self-critique Rating:3 ********************************************* 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? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: Well, the smaller the number you divide, the more you get confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK ------------------------------------------------ Self-critique Rating:3 ********************************************* Question: ####Q008, In question 8, although I gave my answer, I didn’t quite explain all of the points. I understood the question and the equations, however, I couldn’t quite grasp how to explain plotting the points without copying what you had given as an answer. " Self-critique (if necessary): ------------------------------------------------ Self-critique rating: ********************************************* Question: ####Q008, In question 8, although I gave my answer, I didn’t quite explain all of the points. I understood the question and the equations, however, I couldn’t quite grasp how to explain plotting the points without copying what you had given as an answer. " Self-critique (if necessary): ------------------------------------------------ Self-critique rating: #*&!