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12:04:08 `q001. Part 2 includes 6 activities, some of which you might have already completed. Log into Blackboard at http://bb.vccs.edu and go to the Supervised Study Current Semester page. If have registered for your course and do not yet have a username and password you need to inform the instructor, including the date on which you did enroll and of the fact that you have not yet been able to access your username and password. If you do not yet have a username and password use 'vhstudent' and 'college' as before.on Supervised Study Current Semester. Briefly describe what you see on the Announcements page that appears with the Supervised Study Current Semester.
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RESPONSE --> ALREADY COMPLETED
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12:05:22 If you have not already done so follow the instructions under the Announcement entitled First Steps. Since those steps culminate with the instruction to run this program you have probably already done so; if so indicate that this is the case. If not describe the process you have followed. If you run into difficulties with these instructions or with the programs you should immediately email the instructor with a full description, keystroke by keystroke, of what were doing when you encountered those difficulties. If you don't know how to browse you can email the instructor for further instructions on browsing.
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RESPONSE --> I THINK I DID THIS BUT NOT CERTAIN
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12:05:35 `q002. Get the instructor's email addresses: You should still have your browser on the Supervised Study page. Click on Staff Information and copy BOTH of the instructor's email addresses. Put them BOTH into the Address Book of your email program. In the Answer Box explain what you have done, and include a copy of the instructor's addresses.
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RESPONSE --> I DID THIS
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12:06:30 In contrast to many distance courses you will do most of your computer-related work offline, using programs you download to your computer. It takes an hour or so to set up and get used to the procedures, but after that you won't have to spend much time online. You will now download the Query program and certain other programs used in your course: 1. Click on the Course Documents button to go to the Course Documents section of the Supervised Study Current Semester pages, which you have likely visited already. 2. When the Course Documents page appears scroll down to the Downloads heading and note the instructions for downloading programs. Copy and paste these instructions into the Answer Box, but don't hit Enter Answer yet. 3. Click on Downloads. Locate the program file entitled 'q_a_rates'. Download this program to the c:\vhmthphy folder using the instructions you just copied. If necessary you can go back to the previous page and again look at the instructions. 4. Locate the Query program for your course and download it to the c:\vhmthphy folder on your computer, following the same instructions as before. 5. Using the same procedures download any other programs you see under your course, especially the q_a_ programs, using the same procedure as before. Describe in the Answer Box what happened and fully describe any difficulties you encountered, and if necessary include a request for a clarification of the instructions (the instructor will reply after you have emailed the SEND file that is being created by this program). Having done so go ahead and click on Enter Answer.
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RESPONSE --> I THINK I DID THIS ALREADY
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12:08:02 `q003. Briefly run the Query program: 1. Browse to your c:\vhmthphy folder and double-click on the Query program. The program will ask you on which assignment you wish to be queried. Choose Assignment 14. 2. Click on Next Question/Answer. A question, or the beginning of a question, will probably appear. Click again on Next Question/Answer, and repeat until you first encounter something that requires a response. 3. As soon you encounter a question to which you can respond, give a response, even if you don't know the answer ('I don't know yet' would be a perfectly good answer), and click on the Enter Answer button of the Query program. 4. Click until the next question appears, and answer as before, remembering to click on Enter Answer. 5. Repeat once more. Once you have entered the answer to the third question, quit the program. Your answers will be in a the c:\vhmthphy folder in a SEND**** file similar to that being created by this program, but the file won't include your name. Attach this file to an email and send it to the instructor. 6. Warning: In the future don't do what you did here. That is, don't look at the questions in the Query program for an assignment before you have completed the assignment. You just had a brief preview of the Assignment 14 query, but don't attempt to preview other Queries. Don't use the Query until you have completed the corresponding assignment. IMPORTANT NOTE: Never open a SEND file from vhmthphy. You are welcome to view the contents of the SEND file and use them in any way you wish, but first copy it to another folder. Never tamper with the SEND file in vhmthphy. Always send the file esactly as written by the query or q_a_ program. When you have completed this task, give a brief description of what you saw what you did. Did the Query program seem to work properly?
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RESPONSE --> I DID NUMBER 1. AND NUMBER 2. AND NUMBER 3.ITHINK I DID THE REST TOO.
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ظ߷}vɐ Student Name: assignment #003 003. Blackboard pages for your course, Locating the 'Real' page and assts page
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12:10:33 `q001. There are five activities in this assignment. Check out Announcement in the course for which you are registered: 1. If you are not already logged in, go to http://bb.vccs.edu and login using your username and password (use 'vhstudent' and 'college' if you do not yet have your user information). Look to see if the course (e.g., Liberal Arts Mathematics, Calculus, Physics) for which you enrolled shows under Courses You Are Taking. If you are using the 'vhstudent' login the course will appear, but you need to make a note that when you get your own user information you will need to confirm that the appropriate courses do appear when you log in with your own username and password. There might be more than one listing for your course. This is being addressed and should not be a problem after the second week of May, 2003; if it is please notify the instructor. Click on that course. 2. You will probably see a single announcement but you might see more than one. You should briefly read all announcements Were you able to access the Announcements? If so copy and paste each Announcement into the Answer Box before you click on Enter Answer.
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RESPONSE --> I THINK I DID THIS
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12:26:34 Check out Course Information, Staff Information, Course Documents, Assignments and External Links in the course for which you are registered: 1. Click in turn on Course Information, Staff Information and Course Documents. Some of these folders might be empty. 2. Click on Assignments and note the link there, which will take you directly to the Assignments page for your course. Don't bother following that link at this time; you will end up in the same place shortly. 3. Click on External Links. 4. You will see a link to the actual homepage for your course. Click on that link, and look at the headings on the page. You should also bookmark this page as the 'real' homepage. Remain on your 'real' homepage for the next instruction. What are the headings on your actual homepage?
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RESPONSE --> INITIAL COURSE INFORMATION REGISTRATION PROCESS COMMUNICATING WITH THE INSTRUCTOR TEXTBOOK AND COURSE MATERIALS STARTUP/ORIENTATION INSTRUCTIONS INSTRUCTOR EMAIL CHECKING YOUR GRADES
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12:38:21 `q002. Check out Assignments and Due Dates in the course for which you are registered (note that these assignments may be modified prior to the first week of classes): 1. Click on the Assignments link or the Assts button, depending on which is visible on the homepage for your course. Your assignments may include due dates with each assignment, or there might be a Due Dates button at the top of the Assignments page. For convenience you might wish to bookmark your Assignments page. 2. If there is a Due Dates button, click on it; you might want to bookmark this page for quick reference. This page indicates the Due Dates for the current term (if you are starting early due dates for your term might not yet be posted). You will periodically check the Due Dates to be sure you are on schedule for your course. 3. Note that the Due Dates are organized by tests. This tells you when you should take tests; these tests are also often indicated as part of the appropriate assignments. 4. If there is no Due Dates button, the due dates are indicated as you scroll down through your assignment. Which assignments are assigned for each of the first three weeks (give the numbers of the assignments, e.g., 1, 2 for first week, 4,5,6 for second, etc.,).
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RESPONSE --> Week 01: Week of 05/31/05 - 06/05/05. Assignments 0, 1 and associated class notes Week 02: Week of 06/06/05 - 06/12/05. Assignments 2, 3, 4, 5 and associated class notes Week 03: Week of 06/13/05 - 06/19/05. Assignments 6, 7, 8, 9, 10 and associated
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12:43:12 Check out Assignments in the course for which you are registered: You should already be on the 'real' page for your course. If you are on the Due Date page just hit the 'Back' button on your browser. Copy and paste the instructions for Assignment 2 into the Answer box and click on Enter Answer.
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RESPONSE --> Assignment 2 q_a_assts_1_14 exercise: Do Assignment 2 on velocity and submit the corresponding Send file. OVERVIEW ASSIGNMENT: Read everything under Idea 1, Idea 2 and Idea 3 in the synopsis.htm. You won't understand everything you read but digest as much of it as possible, and make brief notes on these ideas. You will revisit this synopsis in about a week to gauge your progress.
Typewriter Notation: Distance Students: As you have been instructed, you should have run the program q_a_initial_pbs.exe, which you were instructed to download from The Supervised Study page into your c:\vhmthphy folder. You should have been instructed to do the Typewriter Notation problems and send the SEND file to the instructor. If you have not done this, do so now. In-class students: You will be instructed regarding the Typewriter Notation assignment. Randomized Problems: Assignment 2, Problem 1. Randomly choose a version of the problem , solve it and submit it. (There are 40 versions for Problem 1, 9 versions for Problem 2). Submit your solution directly by email. Introductory Problem Sets, Set 2, #'s 1-3. See also Uniformly Accelerated Motion on CD #0. Do Mini-Experiment 3 on Drawing Your Own Calibration Graph under Mini-Experiments and submit your results as instructed in bold red letters just under the heading of that page. Not Currently Assigned: Do Introductory Force Experiment. Distance Students: Complete q_a_area_volumes_misc.exe asst 2 on Volumes. Go to Memorize This and memorize all statements under Idea 1, Rates. These statements, along with the problems you have solved, should help you organize your thinking about the idea of rates and should help you over the next several assignments as you apply these ideas to velocity and acceleration. `gGeneral College Physics Students Do Text Chapter 1 Problems 1-10. You need not submit these problems, or any assigned text problems, though you may if you wish do so (in word-processed form). When you do the Query you should have your work on these problems in front of you; the Query will ask you questions about your solutions. [ 3, 5, 8, 10] Explore the Giancoli Homepage, which is associated with your text. Specifically, do the following: (note: Giancoli page is not working properly; assignment will be modified when the page is working) Not currently assigned: Randomized Problems: Assignment 2, Problem 2. Follow same directions as for Assignment 2, Problem 1. `uUniversity Physics Students Text Chapter 1 Even Numbered Exercises 2-20. You need not submit these problems, or any assigned text problems though you may if you wish do so (in word-processed form). When you do the Query you should have your work on these problems in front of you; the Query will ask you questions about your solutions. [8, 10, 12] Randomized Problems: Assignment 2, Problem 2. Follow same directions as for Assignment 2, Problem 1. When you have completed the entire assignment run the Query program..................................................
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12:43:48 `q003. Scroll down to the end of the listing of assignments and note how many assignments there are for your course. How many assignments are there?
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RESPONSE --> THERE ARE 40 ASSIGNMENTS
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zyvJƤ Student Name: assignment #004 004. 'Real' page: read syllabus; orientation CD and other CDs
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14:43:53 `q001. Part 4 includes 4 activities. Estimated time: 30 minutes - 2 hours depending on familiarity with computer and time required to read and follow instructions. Return to the 'real' homepage for your course. If you have failed to bookmark it you can access it by first typing 164.106.222.236 into your browser's Addess box then clicking on the appropriate course. If you were able to successfully access your 'real' homepage, indicate that you have; if not indicate exactly what you did and what happened.
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RESPONSE --> I KNOW HOW TO OPEN THE HOMEPAGE FOR PHYSICS 121. HOWEVER, WHEN I TYPED IN 164. 106.122.236 INTO THE BROWSER ON MY COMPUTER- THE BROWSER COULD NOT FIND IT.
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14:59:54 Read your course syllabus: 1. Your browser should be showing the homepage for your course. If not, click on your bookmark to access it, or enter 164.106.222.236 into the Address box on your browser. 2. Your course syllabus gives an official description of course and prerequisites, an indication of instructional methods, expectations, what text is used (however see the Textbooks listing under Supervised Study Current Semester, Course Documents for the official list), how you are graded, and other important information. 3. If there are buttons marked info, assts, etc., at the top of your page, click on Info to access the Information page, then on the Syllabus or rCourse of Study for your course. If you do not have the indicated buttons near the top of your page, there will be a link directly to Course of Study. Click on that link. 2. Thoroughly read your course of study. 3. Copy and paste into the Answer Box the information related to prerequisites for your course, and include an affirmation that you do indeed have the necessary prerequisites. Then click on Enter Answer.
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RESPONSE --> BOOKMARK? WHAT AND WHERE IS THAT?
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x}Iwt~Z̏薿K Student Name: assignment #004 004. 'Real' page: read syllabus; orientation CD and other CDs
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15:26:21 `q001. Part 4 includes 4 activities. Estimated time: 30 minutes - 2 hours depending on familiarity with computer and time required to read and follow instructions. Return to the 'real' homepage for your course. If you have failed to bookmark it you can access it by first typing 164.106.222.236 into your browser's Addess box then clicking on the appropriate course. If you were able to successfully access your 'real' homepage, indicate that you have; if not indicate exactly what you did and what happened.
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RESPONSE --> YES
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15:26:41 Read your course syllabus: 1. Your browser should be showing the homepage for your course. If not, click on your bookmark to access it, or enter 164.106.222.236 into the Address box on your browser. 2. Your course syllabus gives an official description of course and prerequisites, an indication of instructional methods, expectations, what text is used (however see the Textbooks listing under Supervised Study Current Semester, Course Documents for the official list), how you are graded, and other important information. 3. If there are buttons marked info, assts, etc., at the top of your page, click on Info to access the Information page, then on the Syllabus or rCourse of Study for your course. If you do not have the indicated buttons near the top of your page, there will be a link directly to Course of Study. Click on that link. 2. Thoroughly read your course of study. 3. Copy and paste into the Answer Box the information related to prerequisites for your course, and include an affirmation that you do indeed have the necessary prerequisites. Then click on Enter Answer.
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RESPONSE --> ALREADY DID
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15:34:17 `q002. If you do not have your CDs yet you will have to skip this instruction for now, and you will need to return to this assignment when you receive them. If that is the case you may close this assignment after first entering in the Answer box a statement that you do not yet have the CDs (be sure to click Enter Answer after typing in your statement). Otherwise run one of the CDs for your course: CD #0, #1 or #2 would be a good choice, depending on your course (the Lib1 Logic or Lib2 Counting CD would be a good choice for Mth 151 or 152, respectively). 1. Insert the CD you have selected into your drive. 2. Browse to the CD and look for the file named disk2 or something very similar. This file gives you the easiest access to the information on your CD. Double-click to run the file. 3. You will either get a menu of Class Notes or a series of direct links to video clips. a. If you get a menu of Class Notes, click on one of the links (#3 would be a good choice but any will do). Otherwise go to the instruction #4. b. You will see a page containing notes. If you scroll down the page you will see links to video clips embedded within the notes. c. Click on several of these links to see how they work. 4. If you got a series of direct links, click on one of them in order to see how they work. Click on several more so you will be familiar with the format of these video clips. Describe what you did and what you saw.
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RESPONSE --> I HAVE TWO CD'S WHICH CAME WITH MY LAB PACKED WITH IT. THE TITLE'S FOR THEM WHERE: Phy I Part A Phy I Part B However my computer's browser told me that there was nothing on them. Now I do not know what to do.
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15:39:14 Check the rest of your CDs: Each CD is most easily accessed by browsing to the CD and running the file whose name most closely matches the name of the CD. Insert each CD in turn into your CD drive, browse to the appropriate file, and run it. If all your CDs work, indicate that they do. If you have trouble with any of them, or with these instructions, describe your problems in detail. This completes Part 4. If you are done for the day send the SEND&&&&**** file in c:\vhmthphy to the instructor; otherwise send it when you have completed your day's work.
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RESPONSE --> O.K. I inserted Phy I Part A into my computer's E drive. I went to Run on the Start Menu. Then I clicked on Browse. Then I clicked on All files from the bottom of the little screen. Then I clicked OK. Old Batch came up from 2002. When I clicked on that, a blank screen appeared. I did that for Phy I Part B too. I do not know what to do now.
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__________________________________________________ Do You Yahoo!? Tired of spam? Yahoo! Mail has the best spam protection around http://mail.yahoo.com
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21:05:59 06-24-2005 21:05:59 Since a liter is a cube 10 cm on a side, we need 10 such cubes to span 1 meter. So we visualize 10 layers each of 10 rows each of 10 ten-centimeter cubes, for a total of 1000 10-cm cubes. Again each 10-cm cube is a liter, so there are 1000 liters in a cubic meter.
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NOTES -------> OK
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21:06:03 06-24-2005 21:06:03 `q013. Summary Question 3: How can we calculate the number of cubic centimeters in a cubic meter?
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NOTES ------->
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21:06:06 06-24-2005 21:06:06 One way is to know that there are 1000 liters in a cubic meters, and 1000 cubic centimeters in a cubic meter, giving us 1000 * 1000 = 1,000,000 cubic centimeters in a cubic meter. Another is to know that it takes 100 cm to make a meter, so that a cubic meter is (100 cm)^3 = 1,000,000 cm^3.
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NOTES ------->
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21:06:09 06-24-2005 21:06:09 `q014. Summary Question 4: There are 1000 meters in a kilometer. So why aren't there 1000 cubic meters in a cubic kilometer? Or are there?
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NOTES ------->
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21:06:13 06-24-2005 21:06:13 A cubic kilometer is a cube 1000 meters on a side, which would require 1000 layers each of 1000 rows each of 1000 one-meter cubes to fill. So there are 1000 * 1000 * 1000 = 1,000,000,000 cubic meters in a cubic kilometer. Alternatively, (1 km)^3 = (10^3 m)^3 = 10^9 m^3, not 1000 m^3.
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NOTES ------->
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21:06:16 06-24-2005 21:06:16 `q015. Explain how you have organized your knowledge of the principles illustrated by the exercises in this assignment.
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NOTES ------->
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__________________________________________________ Do You Yahoo!? Tired of spam? Yahoo! Mail has the best spam protection around http://mail.yahoo.com
їS\cz°e Student Name: assignment #001 001. typewriter notation......!!!!!!!!...................................
20:13:40 `q001. Explain the difference between x - 2 / x + 4 and (x - 2) / (x + 4).
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RESPONSE --> IF YOU WERE GOING TO WORK OUT THE PROBLEM X -2 / X + 4 YOU WOULD SUBTRACT THE 2/X FROM THE X AND THEN ADD THE 4. IF YOU WERE GOING TO WORK OUT THE PROBLEM (X-2)/ (X+4), YOU WOULD DIVIDE (X-2) BY (X+4). THE PARENTHESES MAKES THE DIFFERENCE.
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20:14:38 The order of operations dictates that grouped expressions must be evaluated first, that exponentiation must be done before multiplication or division, which must be done before addition or subtraction. It makes a big difference whether you subtract the 2 from the 2 or divide the -2 by 4 first. If there are no parentheses you have to divide before you subtract: 2 - 2 / 2 + 4 = 2 - 1 + 4 (do multiplications and divisions before additions and subtractions) = 5 (add and subtract in indicated order) If there are parentheses you evaluate the grouped expressions first: (x - 2) / (x - 4) = (2 - 2) / ( 4 - 2) = 0 / 2 = 0.
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RESPONSE --> YES I AGREE
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20:17:31 `q002. Explain the difference between 2 ^ x + 4 and 2 ^ (x + 4). Then evaluate each expression for x = 2. Note that a ^ b means to raise a to the b power. This process is called exponentiation, and the ^ symbol is used on most calculators, and in most computer algebra systems, to represent exponentiation.
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RESPONSE --> BECAUSE (X+4) IS CONTAINED IN PARENTHESIS, EVERYTHING INSIDE IS THE WHOLE NUMBER THAT RAISES THE 2 IN 2^(X+4) TO THAT POWER. WITH 2^X + 4, ONLY X WILL BE THE EXPONENT AND THE RESULT WILL BE ADDED TO 4.
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20:18:18 2 ^ x + 4 indicates that you are to raise 2 to the x power before adding the 4. 2 ^ (x + 4) indicates that you are to first evaluate x + 4, then raise 2 to this power. If x = 2, then 2 ^ x + 4 = 2 ^ 2 + 4 = 2 * 2 + 4 = 4 + 4 = 8. and 2 ^ (x + 4) = 2 ^ (2 + 4) = 2 ^ 6 = 2*2*2*2*2*2 = 64.
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RESPONSE --> RIGHT
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20:43:16 `q003. What is the numerator of the fraction in the expression x - 3 / [ (2x-5)^2 * 3x + 1 ] - 2 + 7x? What is the denominator? What do you get when you evaluate the expression for x = 2?
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RESPONSE --> 3 IS THE NUMERATOR. THE DENOMINATOR IS EVERYTHING IN BRACKETS WHICH IS [ (2X-5)^2 * 3X + 1 ]. IF X = 2 THEN: X - 3 / [ (2X-5)^2 * 3X +1 ] - 2 + 7X = 2 - 3 / [ (2X-5)^2 * 3X +1 ] - 2 + 7X = 2 - 3 / [ (2X-5) * (2X-5) * 3X +1 ] - 2 + 7X = 2 - 3 / [ (4X^2 -10X -10X +25) * 3X + 1 ] -2 +7X = 2 - 3 / [ (4X^2 - 20X +25) * 3X + 1 ] -2 +7X = 2 - 3 / [ 12X^3 - 60X^2 + 75X + 1 ] -2 +7X = 2 - 3 / [ 12*(2)^2 - 60*(2)^2 + 75(2) + 1] -2 +7(2) = 2 - 3 / [ 12*4 - 60*4 + 150 + 1 ] -2 + 14 = 2 - 3 / [ 48 - 240 + 150 + 1] - 2 + 14 = 2 - 3 / [ - 41 ] -2 + 14 = 2 +3 / 41 - 2 + 14 = 14 + 3/ 41 = 85/41
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20:45:07 The numerator is 3. x isn't part of the fraction. / indicates division, which must always precede subtraction. Only the 3 is divided by [ (2x-5)^2 * 3x + 1 ] and only [ (2x-5)^2 * 3x + 1 ] divides 3. If we mean (x - 3) / [ (2x-5)^2 * 3x + 1 ] - 2 + 7x we have to write it that way. The preceding comments show that the denominator is [ (2x-5)^2 * 3x + 1 ] Evaluating the expression for x = 2: - 3 / [ (2 * 2 - 5)^2 * 3(2) + 1 ] - 2 + 7*2 = 2 - 3 / [ (4 - 5)^2 * 6 + 1 ] - 2 + 14 = evaluate in parenthese; do multiplications outside parentheses 2 - 3 / [ (-1)^2 * 6 + 1 ] -2 + 14 = add inside parentheses 2 - 3 / [ 1 * 6 + 1 ] - 2 + 14 = exponentiate in bracketed term; 2 - 3 / 7 - 2 + 14 = evaluate in brackets 13 4/7 or 95/7 or about 13.57 add and subtract in order. The details of the calculation 2 - 3 / 7 - 2 + 14: Since multiplication precedes addition or subtraction the 3/7 must be done first, making 3/7 a fraction. Changing the order of the terms we have 2 - 2 + 14 - 3 / 7 = 14 - 3/7 = 98/7 - 3/7 = 95/7.
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RESPONSE --> I SHOULD ALWAYS DO THE ORDER OF OPERATIONS IN ORDER
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20:56:45 `q004. Explain, step by step, how you evaluate the expression (x - 5) ^ 2x-1 + 3 / x-2 for x = 4.
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RESPONSE --> WITH ( X- 5 ) ^2X - 1 + 3 / X-2 FOR X = 4 JUST DO THE PARENTHESIS FIRST. SO (4-5)^2(4)- 1 + 3 / 2 - 2
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20:57:38 We get (4-5)^2 * 4 - 1 + 3 / 1 - 4 = (-1)^2 * 4 - 1 + 3 / 4 - 2 evaluating the term in parentheses = 1 * 4 - 1 + 3 / 4 - 2 exponentiating (2 is the exponent, which is applied to -1 rather than multiplying the 2 by 4 = 4 - 1 + 3/4 - 2 noting that 3/4 is a fraction and adding and subtracting in order we get = 1 3/4 = 7 /4 (Note that we could group the expression as 4 - 1 - 2 + 3/4 = 1 + 3/4 = 1 3/4 = 7/4). COMMON ERROR: (4 - 5) ^ 2*4 - 1 + 3 / 4 - 2 = -1 ^ 2*4 - 1 + 3 / 4-2 = -1 ^ 8 -1 + 3 / 4 - 2. INSTRUCTOR COMMENTS: There are two errors here. In the second step you can't multiply 2 * 4 because you have (-1)^2, which must be done first. Exponentiation precedes multiplication. Also it isn't quite correct to write -1^2*4 at the beginning of the second step. If you were supposed to multiply 2 * 4 the expression would be (-1)^(2 * 4). Note also that the -1 needs to be grouped because the entire expression (-1) is taken to the power. -1^8 would be -1 because you would raise 1 to the power 8 before applying the - sign, which is effectively a multiplication by -1.
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RESPONSE --> OK
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CpЩkcȃɖÕƼ Student Name: assignment #002 002. Describing Graphs
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23:38:56 `q001. You will frequently need to describe the graphs you have constructed in this course. This exercise is designed to get you used to some of the terminology we use to describe graphs. Please complete this exercise and email your work to the instructor. Problem 1. We make a table for y = 2x + 7 as follows: We construct two columns, and label the first column 'x' and the second 'y'. Put the numbers -3, -2, -1, -, 1, 2, 3 in the 'x' column. We substitute -3 into the expression and get y = 2(-3) + 7 = 1. We substitute -2 and get y = 2(-2) + 7 = 3. Substituting the remaining numbers we get y values 5, 7, 9, 11 and 13. These numbers go into the second column, each next to the x value from which it was obtained. We then graph these points on a set of x-y coordinate axes. Noting that these points lie on a straight line, we then construct the line through the points. Now make a table for and graph the function y = 3x - 4. Identify the intercepts of the graph, i.e., the points where the graph goes through the x and the y axes.
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RESPONSE --> y = 3x - 4 table: x = -3, -2, -1, 0, 1, 2, 3, 4 y = -13, -10, -7, - 4, -1, 2, 5, 8 function: y = 3x - 4 function: y = 3x - 4 y = 3(-3) - 4 y = 3(-2) -4 y = -9 - 4 y = -6 - 4 y = -13 y = -10 function: y = 3x - 4 function: y = 3x - 4 y = 3(-1) - 4 y = 3(0) - 4 y = -3 - 4 y = 0 - 4 y = -7 y = - 4 function: y = 3x - 4 function: y = 3x - 4 y = 3(1) - 4 y = 3(2) - 4 y = 3 - 4 y = 6 - 4 y = -1 y = 2 function: y = 3x - 4 function: y = 3x - 4 y = 3(3) - 4 y = 3(4) -4 y = 9 - 4 y = 12 - 4 y = 5 y = 8 The graph I hope to put in the email with this attachment because I created it in paint ...
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23:39:45 The graph goes through the x axis when y = 0 and through the y axis when x = 0. The x-intercept is therefore when 0 = 3x - 4, so 4 = 3x and x = 4/3. The y-intercept is when y = 3 * 0 - 4 = -4. Thus the x intercept is at (4/3, 0) and the y intercept is at (0, -4). Your graph should confirm this.
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RESPONSE --> Yes it does.
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23:41:35 `q002. Does the steepness of the graph in the preceding exercise (of the function y = 3x - 4) change? If so describe how it changes.
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RESPONSE --> YES. IT SEEMS TO GO IN THE OPPOSITE DIRECTION.
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23:43:02 The graph forms a straight line with no change in steepness.
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RESPONSE --> Enter, as appropriate, an answer to the question, a critique of your answer in response to a given answer, your insights regarding the situation at this point, notes to yourself, or just an OK. I THINK THAT YOUR POINTS MUST DIFFER FROM MINE. YOU WILL SEE THIS HOPEFULLY IN MY EMAIL.
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23:57:00 `q003. What is the slope of the graph of the preceding two exercises (the function ia y = 3x - 4;slope is rise / run between two points of the graph)?
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RESPONSE --> THE X- INTERCEPT = (4/3,0) AND I WILL LABEL IT X1, Y1 THE Y- INTERCEPT = (0, - 4) AND LABELED... X2, Y2 THE SLOPE FORMULA IS X2-X1 M = ---------- Y2-Y1 IF I REPLACE THE COORDINATES INTO THE FORMULA, I OBTAIN THIS: 0 - 4/3 M= ----------- SO - 4/3 - 4 - 0 M= ------ - 4 -4/3 * - 1/ 4 = 1/3 SO M= 1/3 AND THAT IS THE SLOPE.
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23:58:18 Between any two points of the graph rise / run = 3. For example, when x = 2 we have y = 3 * 2 - 4 = 2 and when x = 8 we have y = 3 * 8 - 4 = 20. Between these points the rise is 20 - 2 = 18 and the run is 8 - 2 = 6 so the slope is rise / run = 18 / 6 = 3. Note that 3 is the coefficient of x in y = 3x - 4. Note the following for reference in subsequent problems: The graph of this function is a straight line. The graph increases as we move from left to right. We therefore say that the graph is increasing, and that it is increasing at constant rate because the steepness of a straight line doesn't change.
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RESPONSE --> THE STEEPNESS OF A STRAIGHT LINE NEVER CHANGES.
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00:14:42 `q004. Make a table of y vs. x for y = x^2. Graph y = x^2 between x = 0 and x = 3. Would you say that the graph is increasing or decreasing? Does the steepness of the graph change and if so, how? Would you say that the graph is increasing at an increasing rate, increasing at a constant rate, increasing at a decreasing rate, decreasing at an decreasing rate, decreasing at a constant rate, or decreasing at a decreasing rate?
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RESPONSE --> X = 0, 1, 2, 3 Y = 0, 1, 4, 9 Y= X^2 Y = X^2 Y = X^2 Y= X^2 Y=(0)^2 Y =(1)^2 Y =(2)^2 Y=(3)^2 Y= 0 Y = 1 Y = 4 Y= 9 INCREASING AT A CONSTANT RATE
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00:15:04 Graph points include (0,0), (1,1), (2,4) and (3,9). The y values are 0, 1, 4 and 9, which increase as we move from left to right. The increases between these points are 1, 3 and 5, so the graph not only increases, it increases at an increasing rate.
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RESPONSE --> YES. I THINK SO.
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00:40:38 `q005. Make a table of y vs. x for y = x^2. Graph y = x^2 between x = -3 and x = 0. Would you say that the graph is increasing or decreasing? Does the steepness of the graph change and if so, how? Would you say that the graph is increasing at an increasing rate, increasing at a constant rate, increasing at a decreasing rate, decreasing at an decreasing rate, decreasing at a constant rate, or decreasing at a decreasing rate?
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RESPONSE --> Y = X^2 X = -3, -2, -1, 0 Y = 9, 4, 1, 0 Y= X^2 Y= X^2 Y = X^2 Y = X^2 Y =(-3)^2 Y= (-2)^2 Y= (-1)^2 Y =(0)^2 Y = 9 Y= 4 Y= 1 Y = 0 IT IS DECREASING AT A DECREASING RATE
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00:41:01 From left to right the graph is decreasing (points (-3,9), (-2,4), (-1,1), (0,0) show y values 9, 4, 1, 0 as we move from left to right ). The magnitudes of the changes in x from 9 to 4 to 1 to 0 decrease, so the steepness is decreasing. Thus the graph is decreasing, but more and more slowly. We therefore say that the graph is decreasing at a decreasing rate.
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RESPONSE --> YES I AGREE
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01:09:42 `q006. Make a table of y vs. x for y = `sqrt(x). [note: `sqrt(x) means 'the square root of x']. Graph y = `sqrt(x) between x = 0 and x = 3. Would you say that the graph is increasing or decreasing? Does the steepness of the graph change and if so, how? Would you say that the graph is increasing at an increasing rate, increasing at a constant rate, increasing at a decreasing rate, decreasing at an decreasing rate, decreasing at a constant rate, or decreasing at a decreasing rate?
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RESPONSE --> Y = `SQRT(X) AND THIS ~MEANS APPROXIMATELY X = 0, 1, 2, 3 Y = 0, 1, 14/10, 17/10 Y= `SQRT(X) Y= `SQRT(X) Y = `SQRT(X) Y= `SQRT(0) Y= `SQRT(1) Y = `SQRT(2) Y= 0 Y= 1^1/2 Y = 1.4 Y= 1^0.5 Y ~ 1 + 4/10 Y= 1 Y~ 14/10 Y= `SQRT(X) Y= `SQRT(3) Y~ 1.7 Y~ 1 + 7/10 Y~ 17/10 THIS GRAPH IS INCREASING AT A DECREASING RATE
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01:11:22 If you use x values 0, 1, 2, 3, 4 you will obtain graph points (0,0), (1,1), (2,1.414), (3. 1.732), (4,2). The y value changes by less and less for every succeeding x value. Thus the steepness of the graph is decreasing. The graph would be increasing at a decreasing rate.{}{} If the graph respresents the profile of a hill, the hill starts out very steep but gets easier and easier to climb. You are still climbing but you go up by less with each step, so the rate of increase is decreasing. {}{}If your graph doesn't look like this then you probably are not using a consistent scale for at least one of the axes. If your graph isn't as desribed take another look at your plot and make a note in your response indicating any difficulties.
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RESPONSE --> MY GRAPH LOOKS PRETTY FAIR AND ACCURATE.
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01:45:41 `q007. Make a table of y vs. x for y = 5 * 2^(-x). Graph y = 5 * 2^(-x) between x = 0 and x = 3. Would you say that the graph is increasing or decreasing? Does the steepness of the graph change and if so, how? Would you say that the graph is increasing at an increasing rate, increasing at a constant rate, increasing at a decreasing rate, decreasing at an decreasing rate, decreasing at a constant rate, or decreasing at a decreasing rate?
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RESPONSE --> Y = 5 * 2^(-X) X = 0, 1, 2, 3 Y= 0, 2.5, 5, 7.5 Y= 5 * 2^(-0) Y= 5 * 2^(-X) Y= 5 * 2^(-X) Y= 5 * 0 Y= 5 * 2^(-1) Y= 5 * 2^(-2) Y= 0 Y= 5 * 1/2 Y= 5 * 2/2 Y= 5/2 Y= 5 * 1 Y= 2.5 Y= 5 Y= 5 * 2^(-X) Y= 5 * 2^(-3) Y= 5 * 3/2 Y= 15/2 Y= 7.5
THE STEEPNESS OF THE GRAPH APPEARS TO BE INCREASING AT A CONSTANT RATE.................................................
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01:47:15 ** From basic algebra recall that a^(-b) = 1 / (a^b). So, for example: 2^-2 = 1 / (2^2) = 1/4, so 5 * 2^-2 = 5 * 1/4 = 5/4. 5* 2^-3 = 5 * (1 / 2^3) = 5 * 1/8 = 5/8. Etc. The decimal equivalents of the values for x = 0 to x = 3 will be 5, 2.5, 1.25, .625. These values decrease, but by less and less each time. The graph is therefore decreasing at a decreasing rate. **
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RESPONSE --> OK SO THAT IS WHAT IS HAPPENING.
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01:48:18 `q008. Suppose you stand still in front of a driveway. A car starts out next to you and moves away from you, traveling faster and faster. If y represents the distance from you to the car and t represents the time in seconds since the car started out, would a graph of y vs. t be increasing or decreasing? Would you say that the graph is increasing at an increasing rate, increasing at a constant rate, increasing at a decreasing rate, decreasing at an decreasing rate, decreasing at a constant rate, or decreasing at a decreasing rate?
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RESPONSE --> THE GRAPH WOULD BE INCREASING AT AN INCREASING RATE.
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01:48:39 ** The speed of the car increases so it goes further each second. On a graph of distance vs. clock time there would be a greater change in distance with each second, which would cause a greater slope with each subsequent second. The graph would therefore be increasing at an increasing rate. **
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RESPONSE --> YES. I THOUGHT SO.
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