course Phy 201 8/24, 9:31PM Here are the remaining ten questions:*********************************************
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Given Solution: (8 + 3) * 5 and 8 + 3 * 5 &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): (If you believe your solution matches the given solution then just type in 'OK'. -OK. ------------------------------------------------ Self-critique Rating: (If you believe your solution matches the given solution then just type in 'OK'. -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: In the first equation, the exponent in the parenthesis gets priority due to order of operations, making the next step (16) * 3. In the second, the parenthesis gets priority, making it 2^(12). The result of the first one would end up being 48, while the second one would be 4096. confidence rating: (Type in a number from 0 to 3, indicating your level of confidence in your solution. ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ -3. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& 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. Your solution: The first equation would start out with the exponent, causing the equation to be 3*5-4*9. The second would give the priority to the parenthesis making the equation look like 3*5-(12)^2. The next step for number one would be to do multiplication from left to right, making it 15-36. The second step for the other equation would be to raise the number in the parenthesis to the corresponding power, making it 3*5-144. For the first equation, the problem ends up being -21. To finish up the second equation, you multiply 3*5 to get 15, and then subtract the remaining 144 from 15 to get -129. confidence rating: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ -3. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& 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. 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: x Y -2 -1 -1 1 0 3 1 5 2 7 Y = 2(-2) + 3 = -1 Y = 2(-1) + 3 = 1 Y = 2(0) + 3 = 3 Y = 2(1) + 3 = 5 Y = 2(2) + 3 = 7 -When you graph the lines, you will see that theyre in a straight line. So the appropriate graph would be the linear graph. confidence rating: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ -3. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& 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. 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: Y = X ^2 + 3 Y = -2 ^2 + 3 = 7 Y = -1^2 + 3 = 4 Y = 0 ^2 + 3 = 3 Y = 1^2 + 3 = 4 Y = 2^2 + 3 = 7 x y -2 7 -1 4 0 3 1 4 2 7 -When you graph the lines, they form a parabola. The (+ 3) at the end of the equation means that the parabola will be at least 3 units above the X-Axis, so when you substitute X with a 1, it will move over to the right one, as well as go up one. This graph is caused by a quadratic equation. confidence rating: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ -3. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& 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. 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: y = 2 ^ x + 3 y = 2^1 + 3 = 5 y = 2^2 +3 = 7 y = 2^3 + 3 = 11 y = 2^4 + 3 = 19 x y 1 5 2 7 3 11 4 19 -When you graph the lines, they look similar to the previous problem, but only cut in half. This is because the higher the exponent becomes, the greater the slope will be. The slope will always be a positive number since exponents cannot make a number negative, only a decimal. The only graph up there like this is the exponential graph. confidence rating: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& 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: It will always remain the same number. Dividing by 1 will never change any number. confidence rating: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& 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: The result will always be less than the original number. If you divided 12 by 2, it will give you 6, a number less than 12. confidence rating: 3. ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& 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 positive number by another positive number less than 1, it will always make the original number greater. 12 divided by .5 makes it 24. confidence rating: 3. ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK. ------------------------------------------------ Self-critique Rating: OK.