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Precalculus Portfolio
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Name Date </p> <p> </p> <p><strong>Storm Tracker Portfolio Worksheet</strong> </p> <p><strong>PRECALCULUS: PARAMETRIC FUNCTIONS</strong> </p> <p> </p> <p><strong>Directions: </strong>Meteorologists use sophisticated models to predict the occurrence, duration, and trajectory of weather events. They build their models based on observations that they have made in the past. By understanding how previous weather events evolved, meteorologists can apply that knowledge to future weather events. </p> <p>Parametric equations can be used to graph the path of an object in space. For example, they can be used to describe the path of a storm moving through an area. In this portfolio, you will use historical storm data to trace the path of a hurricane. From this data, you will use parametric equations to model the path of the storm. </p> <p> </p> <h1>Step 1: Find your hurricane.</h1> <ul><li>Select the link to access the NOAA’s Office for Coastal Management: Historical Hurricane Tracks website to search for a hurricane. </li><li>Type any state in the search box. (Note: Inland states do not usually have hurricanes. Type in a different state if no hurricanes are listed.) </li><li>Select one hurricane from the list that appears. </li><li>Select <em>Zoom to XXXXX </em>above the XXXX XX view the XXXX XXXXXXXXX path. </li><li> </li><li>Make a table of XXX XXXXX’s XXXXXXXXXX XXX vertical XXXXXXXX with XXXXXXX to XXXX. Hover XXXX a specific XXXXX XX XXX XXXX and note the highlighted XXXX in the table on the left. XXXX XXXX XXXX <em>t </em>= 0. XXXX XXX position XXXXXXXXXXX XXXX the XXXXX left corner XX XXX XXX XXXX and XXXXXX them in Table X. XXXXX latitude XXXXXXXX XXXXX/XXXXX and longitude measures east/west, the XXXXX XXXXXXXXXX XXXX be <em>y </em>and XXX second XXXXXXXXXX XXXX XX <em>x</em>. XXX XXXXXXXX <XX> </li><li>Upload XXXX worksheet into the XXXX XXX. </li><li>XX you XXX not paste a XXXX of your graph XXXX the XXXXXXXXX, XX XXXX XX XXXX XXXXXX the graph XXXX XXX XXXX XXX. </li></ul> <p><u>Historical XXXXXXXXX Tracks</u> </p> <p> </p> <h1>Step X: XXXX the hurricane path.</XX> <p> <img XXX="XXXX:///C:\Users\abida\XXXXXXX\Local\XXXX\msohtmlclip1\01\clip_image003.jpg" width="XXX" height="XXX"><XX></p> <table> <tbody><tr> <td> <br></td></tr> <tr> </tr> </tbody></table> <p> Take a XXXXXX XXXX XX XXX XXXXXXXXX path and include it XXXXX: <XX></p> <p>XXXXXXX XXX days along the XXXX. Note XXXX you XXXXX XXXX to XXX the scroll arrow XXXXXXX to the date XXXXXXXXXXX. XX XXX table below, choose and record one point XXXX each day of XXX storm. XXXX each XXXXX <em>t </em>= 1, <em>t </em>= 2, XXX. </p> <p>Track XXX XXXXX for a total XX XX least five XXXX so XXXX you have a XXXXXXX XX XXXX points in the table. Use the XXXXXXX below XX help you find XXX date, XXXXXXXX, XXX XXXXXXXXX. </p> <p> </p> <XX>XXXXX X</XX> <p> </p> <table> <tbody><tr> <td> <p>XXXX </p></td><td> <p><em>t</em> </p></td><td> <p><em>x</em> </p><p>(XXXXXXXXX) </p></td><td> <p><em>y</em> </p><p>(latitude) </p></td></tr> <tr> <td> <p>Aug XX, XXXX </p></td><td> <p>X </p></td><td> <p>-XX.XX </p></td><td> <p>XX.25 </p></td></tr> <tr> <td> <p>Aug 16, XXXX </p></td><td> <p>1 </p></td><td> <p>-96.06 </p></td><td> <p>XX.02 </p></td></tr> <tr> <td> <p>XXX XX, 2017 </p></td><td> <p>2 </p></td><td> <p>-XX.XX </p></td><td> <p>XX.80 </p></td></tr> <tr> <td> <p>Aug 18, 2017 </p></td><td> <p>3 </p></td><td> <p>-101.XX </p></td><td> <p>XX.XX </p></td></tr> <tr> <td> <p>Aug 19, 2017 </p></td><td> <p>4 </p></td><td> <p>-XX.XX </p></td><td> <p>35.42 </p></td></tr> </tbody></table> <p> </p> <p><XXXXXX>Step X: Create a XXXXXXXXXXXX Model.</strong> </p> <p>Work through XXX XXXXXXXXX steps to create two XXXXXXXXXX equations where <em>x </em>is a function XX <em>t </em>XXX <em>y </em>XX a XXXXXXXX XX <em>t</em>. </p> <ul><li>XXXXX XXXX <em>t </em>XXXXXX <em>x</em>, XXXX XXXX <em>t </em>XXXXXX <em>y</em>. XXXX kind of regression should you use for XXXX XXX XXXXX on XXXX graphs? </li><li>XXX your calculator to XXXXXX a formula for XXX XXXXX you have chosen. Enter the ordered pairs XXXX XXXXX and XXXX the XXXXXXXXXX create XXX line of XXXX XXX XXX XXXX XXXXX. XXX XXXXXXX, XX your path XXXXXXX to be XXXXXXXXXXX, you will </li><li>XXXXX XXXX XXXXX XXXXXXXXX: <ul><li><em>y</em>(<em>t</em>) = 2.XX+24. <br> </li></XX></li></XX> <p>have a model XX the XXXX <em>y </em>= <em>ab<XXX>x</sup> </em>XXXXX the XXXXXX XXXXXXX on the calculator. </p> <p>· <em>x</em>(<em>t</em>) =X.4x^X - X.XX^X - 3.XX - 92. </p> <XX>Step 4: Check your XXXXX.</XX> <p>Plug in the values <em>t </em>= X, X, 2, 3, and 4 into your XXXXXXXXXX XXXXXXXXX XXX XXXXXX your XXXXXX for <em>x </em>XXX <em>y </em>in XXX table below. </p> <p> </p> <XX>Table X</XX> <table> <tbody><tr> <td> <p><em>t</em> </p></td><td> <p><em>x</em> </p><p>(longitude) </p></td><td> <p><em>y</em> </p><p>(latitude) </p></td></tr> <tr> <td> <p>0 </p></td><td> <p>-92.0 </p></td><td> <p>XX.0 </p></td></tr> <tr> <td> <p>1 </p></td><td> <p>-XX.X </p></td><td> <p>XX.X </p></td></tr> <tr> <td> <p>2 </p></td><td> <p>-99.X </p></td><td> <p>XX.6 </p></td></tr> <tr> <td> <p>3 </p></td><td> <p>-XXX.X </p></td><td> <p>XX.X </p></td></tr> <tr> <td> <p>4 </p></td><td> <p>-96.X </p></td><td> <p>35.X </p></td></tr> </tbody></table> <p> </p> <p>Now XXXXX the <em>x- </em>and <em>y</em>-coordinates from Table X onto XXXXX XXXXX XXXXX XXX color, XXX graph the <em>x- </em>and <em>y</em>-XXXXXXXXXXX XXXX Table 2 XXXX the XXXX graph paper XXXXX a XXXXXXXXX color. XXX XXX XXXXXX XXXX and XXXXX your graph here or upload it along with this worksheet. </p> <p><img src="XXXX:///X:\Users\abida\AppData\XXXXX\XXXX\XXXXXXXXXXXX\01\XXXXXXXXXXXXX.jpg" width="XXX" height="XXX"> <img src="XXXX:///C:\XXXXX\XXXXX\AppData\Local\XXXX\msohtmlclip1\XX\XXXXXXXXXXXXX.jpg" width="XXX" height="XXX"> </p> <p>XXXXXXX the XXXXX XXXXXX with the original XXXXXX and answer XXX following questions: </p> <XX><li>XXX XXXX your model compare XX XXX XXXXXX XXXX? </li><li>XXX did you XXXXXX the graph XXXXXX that you did? XXX you choose well? XXX or XXX XXX? </li><li>Is it possible XX XXXXX <em>x</em>(<em>t</em>) for <em>t</em>, substitute it into <em>y</em>(<em>t</em>) XX eliminate the </li></ul> <p>XXX plot XXXX Table 2 XX XXXXXXXX than that XX XXXXX 1. Besides that, XXXX are identitcal. </p> <p> </p> <p>I XXXXX XXX cubic graph XXXXXX because it XX a common XXXXX XXXX is easier XX observe </p> <p>and XXXX XXX characteristics. XXX XXXXXX is XXXX XX XXX XXXXX XX reproducible and easily </p> <p>XXXXXXXXX, <em>t</em>, XXX XXXXX it XX a XXXXXXXXXXX equation XXXX <em>x </em>XXX <em>y </em>XXXXXXX? Why or why XXX? </p> <p>No, it XX not possible. XXXXXXX x(t) XXXXXXXX XXX a XXXXXXXXXXX XX X (cube XXXX in y(t)). </p> <p>Hence, XXXXX is no mathematical XXXXXXXXXXXX XXXX XXX XX XXXX to XXXXXX the <br> </p> <XX>XXXX it in:</XX> <p><XX></p><p><br></p><p><strong>XXXX X: XXXXXX a Mathematical XXXXX.</strong> </p> <p>Work XXXXXXX the following XXXXX XX XXXXXX two parametric equations where <em>x </em>is a XXXXXXXX of <em>t </em>and <em>y </em>XX a XXXXXXXX of <em>t</em>. </p> <XX><li>XXXXX plot <em>t </em>versus <em>x</em>, XXXX XXXX <em>t </em>XXXXXX <em>y</em>. What XXXX of regression should you XXX for each XXX XXXXX on XXXX XXXXXX? </li><li>Use your XXXXXXXXXX XX XXXXXX a XXXXXXX for XXX XXXXX you have chosen. XXXXX XXX ordered pairs XXXX lists and XXXX XXX calculator XXXXXX the XXXX of XXXX fit for XXXX model. XXX XXXXXXX, if XXXX path XXXXXXX XX be exponential, you will </li><li>XXXXX your final equations: <XX><li><em>y</em>(<em>t</em>) = 2.8x+XX. </li></ul></li></ul> <p>XXXX a model of XXX XXXX <em>y </em>= <em>ab<XXX>x</sup> </em>using XXX XXXXXX XXXXXXX on XXX XXXXXXXXXX. </p> <p>· <em>x</em>(<em>t</em>) =X.XX^X - X.1x^2 - 3.1x - XX. </p> <XX>XXXX 4: XXXXX XXXX XXXXX.</XX> <p>XXXX in the values <em>t </em>= X, 1, 2, X, and 4 XXXX your parametric XXXXXXXXX XXX XXXXXX your values XXX <em>x </em>XXX <em>y </em>in XXX table XXXXX. </p> <p> </p> <h2>Table 2</XX> <table> <tbody><tr> <td><em>t</em> </td><td><em>x</em> <p>(longitude) </p></td><td><em>y</em> <p>(XXXXXXXX) </p></td></tr> <tr> <td>X </td><td>-XX.0 </td><td>24.X </td></tr> <tr> <td>1 </td><td>-XX.8 </td><td>26.8 </td></tr> <tr> <td>X </td><td>-XX.X </td><td>29.6 </td></tr> <tr> <td>3 </td><td>-XXX.4 </td><td>XX.4 </td></tr> <tr> <td>X </td><td>-XX.4 </td><td>35.X </td></tr> </tbody></table> <p> </p> <p>XXX graph the <em>x- </em>and <em>y</em>-coordinates XXXX XXXXX 1 XXXX XXXXX XXXXX XXXXX one color, and graph the <em>x- </em>XXX <em>y</em>-coordinates from Table X onto the XXXX XXXXX XXXXX XXXXX a different XXXXX. XXX XXX XXXXXX XXXX and XXXXX your XXXXX XXXX or upload it XXXXX with this XXXXXXXXX. </p> <p><img XXX="XXXX:///C:\Users\XXXXX\AppData\Local\XXXX\XXXXXXXXXXXX\01\clip_image005.XXX" width="XXX" XXXXXX="XXX"> <img XXX="file:///C:\Users\XXXXX\AppData\Local\XXXX\msohtmlclip1\XX\clip_image007.XXX" width="XXX" height="XXX"> </p> <p>XXXXXXX XXX XXXXX XXXXXX with XXX original XXXXXX and XXXXXX the XXXXXXXXX questions: </p> <XX><li>How XXXX your model compare to XXX actual XXXX? </li><li>Why did you XXXXXX the XXXXX XXXXXX XXXX you XXX? XXX you choose XXXX? Why or why not? </li><li>XX it XXXXXXXX to solve <em>x</em>(<em>t</em>) XXX <em>t</em>, XXXXXXXXXX it into <em>y</em>(<em>t</em>) to XXXXXXXXX the </li></XX> <p>The plot from XXXXX 2 is XXXXXXXX than XXXX of XXXXX 1. XXXXXXX XXXX, they are identitcal. </p> <p> </p> <p>I XXXXX XXX XXXXX graph family because it XX a XXXXXX graph XXXX is XXXXXX to observe </p> <p>and XXXX its XXXXXXXXXXXXXXX. XXX XXXXXX XX well XX XXX XXXXX is XXXXXXXXXXXX and XXXXXX </p> <p>XXXXXXXXX, <em>t</em>, and write it as a rectangular XXXXXXXX with <em>x </em>XXX <em>y </em>instead? Why or XXX not? </p> <p>No, it XX XXX XXXXXXXX. Because x(t) XXXXXXXX has a XXXXXXXXXXX XX X (cube XXXX in y(t)). </p> <p>Hence, XXXXX XX no mathematical XXXXXXXXXXXX that can be XXXX to remove XXX </p> <XX>Turn it in:</XX> <p><br></p>">
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