#$&* course PHY 202 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 $8 / hour we get 9 hours, so 9 hours are required. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK ------------------------------------------------ Self-critique Rating: OK ********************************************* Question: `q004. Calculate (8 + 3) * 5 and 8 + 3 * 5, indicating the order of your steps. Explain, as best you can, the reasons for the difference in your results. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: Following the order of operations: (8 + 3) * 5 Step 1. Parentheses first (11)*5 Step 2. Multiplication second 55 8 + 3 *5 Step 1. Multiplication first 8+15 Step 2. Addition second 23 confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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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: OK ********************************************* 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: (2^4) * 3 Step 1. 16*3 Step 2. 48 2^(4 * 3) Step 1. 2^(12) Step 2. 4,096 confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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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 ------------------------------------------------ Self-critique Rating: OK 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. y= 2 (-2) +3 = -1 • 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 y = 2 ( -2 ) + 3 = -1 -1 y = 2 ( -1 ) + 3 = 1 0 y = 2 ( 0 ) + 3 = 3 1 y = 2 ( 1 ) + 3 = 5 2 y = 2 ( 2 ) + 3 = 7 x y -2 -1 -1 1 0 3 1 5 2 7 • • 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: This is a linear solution for a linear function. The Linear Graph best depicts the similarities between these two functions. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK ------------------------------------------------ Self-critique Rating: OK ********************************************* 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. y= -2^2 + 3 y= 4+3 y= 7 • 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 7 -1 4 0 3 1 4 2 7 y = -2^2+3 y = -1^2+3 y = 0^2+3 y = 1^2+3 y = 2^2+3 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: This graph is parabolic. The exponential function best resembles this graph as it is seen that at a point (0,3) the graph changes direction similar in nature to a parabola. confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK ------------------------------------------------ Self-critique Rating: OK ********************************************* 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. y = 2^ 1 + 3 y = 2+3 y = 5 • 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 5 2 7 3 11 4 19 y = 2^ 1 + 3 y = 2^ 2 + 3 y = 2^ 3 + 3 y = 2^ 4 + 3 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: This graph is exponential in nature as depicted the values are increasing at an exponential rate. This graph was chosen as this is the best fit for this scenario. confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK ------------------------------------------------ Self-critique Rating: OK ********************************************* Question: `q010. If you divide a certain positive number by 1, is the result greater than the original number, less than the original number or equal to the original number, or does the answer to this question depend on the original number? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: The number would be the same as the original number. confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK ------------------------------------------------ Self-critique Rating: OK ********************************************* 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: If you divide a certain positive number by a number greater than the result is less than the original number. confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK ------------------------------------------------ Self-critique Rating: OK ********************************************* Question: `q012. If you divide a certain positive number by a positive number less than 1, is the result greater than the original number, less than the original number or equal to the original number, or does the answer to this question depend on the original number? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: If you divide a certain positive number by a positive number less than one, the result is greater than the original number. confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK Understanding the concept is fairly simple; however, I do not wish to seem trivial. But, thinking in relation to working past mathematics problems if this concept is not understood I could possible obscure the answer one is searching for ####. ------------------------------------------------ Self-critique Rating: OK " end document Self-critique (if necessary): ------------------------------------------------ Self-critique rating: " end document Self-critique (if necessary): ------------------------------------------------ Self-critique rating: #*&!