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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 frXX XXX list that XXXXXXX. </li><li>Select <em>Zoom XX XXXXX </em>above the XXXX to XXXX XXX full hurricane XXXX. </li><li> </li><li>Make a table XX XXX storm’s horizontal XXX XXXXXXXX XXXXXXXX with XXXXXXX to XXXX. XXXXX over a XXXXXXXX point XX the path XXX note the XXXXXXXXXXX date in XXX table on the left. Make XXXX date <em>t </em>= 0. Note the position coordinates XXXX the XXXXX left corner of XXX XXX XXXX and record XXXX in Table X. Since latitude XXXXXXXX XXXXX/XXXXX XXX XXXXXXXXX XXXXXXXX east/west, XXX first coordinate will XX <em>y </em>XXX the second XXXXXXXXXX XXXX be <em>x</em>. XXX progress <XX> </li><li>XXXXXX XXXX worksheet XXXX the XXXX XXX. </li><li>If you did not paste a copy XX your XXXXX into the XXXXXXXXX, be sure to also upload the graph XXXX the Drop XXX. </li></ul> <p><u>Historical Hurricane Tracks</u> </p> <p> </p> <h1>Step X: XXXX XXX hurricane path.</h1> <p> <img XXX="file:///X:\Users\XXXXX\XXXXXXX\Local\Temp\XXXXXXXXXXXX\XX\clip_image003.jpg" width="XXX" height="XXX"><XX></p> <table> <tbody><tr> <td> <XX></td></tr> <tr> </tr> </tbody></table> <p> XXXX a XXXXXX shot XX XXX hurricane path and XXXXXXX it below: <br></p> <p>XXXXXXX the XXXX along the path. XXXX that you XXXXX need XX XXX XXX XXXXXX arrow closest XX XXX XXXX information. In XXX table XXXXX, XXXXXX and record XXX point from XXXX XXX of XXX storm. Mark each XXXXX <em>t </em>= X, <em>t </em>= X, etc. </p> <p>Track XXX storm for a XXXXX of XX least XXXX days so XXXX you XXXX a XXXXXXX XX XXXX points in XXX table. Use the example XXXXX to XXXX you XXXX the date, XXXXXXXX, and XXXXXXXXX. </p> <p> </p> <XX>XXXXX 1</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>(longitude) </p></td><td> <p><em>y</em> </p><p>(latitude) </p></td></tr> <tr> <td> <p>Aug XX, 2017 </p></td><td> <p>X </p></td><td> <p>-XX.XX </p></td><td> <p>XX.XX </p></td></tr> <tr> <td> <p>Aug XX, 2017 </p></td><td> <p>X </p></td><td> <p>-XX.06 </p></td><td> <p>27.02 </p></td></tr> <tr> <td> <p>XXX XX, 2017 </p></td><td> <p>2 </p></td><td> <p>-XX.04 </p></td><td> <p>XX.80 </p></td></tr> <tr> <td> <p>XXX XX, 2017 </p></td><td> <p>X </p></td><td> <p>-XXX.XX </p></td><td> <p>XX.XX </p></td></tr> <tr> <td> <p>XXX XX, 2017 </p></td><td> <p>4 </p></td><td> <p>-XX.61 </p></td><td> <p>XX.XX </p></td></tr> </tbody></table> <p> </p> <p><XXXXXX>XXXX X: XXXXXX a Mathematical Model.</XXXXXX> </p> <p>XXXX XXXXXXX XXX XXXXXXXXX XXXXX XX XXXXXX two parametric equations where <em>x </em>XX a XXXXXXXX XX <em>t </em>XXX <em>y </em>XX a XXXXXXXX XX <em>t</em>. </p> <ul><li>First XXXX <em>t </em>versus <em>x</em>, XXXX XXXX <em>t </em>XXXXXX <em>y</em>. XXXX XXXX of regression should you XXX XXX each XXX XXXXX XX XXXX XXXXXX? </li><li>XXX your XXXXXXXXXX XX create a formula XXX the model you XXXX chosen. Enter XXX ordered XXXXX XXXX lists and have XXX calculator XXXXXX XXX line of best fit for your XXXXX. XXX XXXXXXX, if XXXX XXXX appears XX XX XXXXXXXXXXX, you will </li><li>XXXXX XXXX final XXXXXXXXX: <XX><li><em>y</em>(<em>t</em>) = 2.8x+24. <br> </li></ul></li></ul> <p>have a XXXXX of XXX form <em>y </em>= <em>ab<sup>x</XXX> </em>XXXXX XXX XXXXXX feature on XXX calculator. </p> <p>· <em>x</em>(<em>t</em>) =X.XX^3 - 1.1x^2 - 3.1x - XX. </p> <h1>Step X: XXXXX XXXX XXXXX.</XX> <p>Plug in the XXXXXX <em>t </em>= X, X, 2, X, XXX X XXXX XXXX parametric equations and insert your values XXX <em>x </em>and <em>y </em>in XXX table below. </p> <p> </p> <XX>XXXXX X</h2> <table> <tbody><tr> <td> <p><em>t</em> </p></td><td> <p><em>x</em> </p><p>(XXXXXXXXX) </p></td><td> <p><em>y</em> </p><p>(XXXXXXXX) </p></td></tr> <tr> <td> <p>0 </p></td><td> <p>-XX.X </p></td><td> <p>24.X </p></td></tr> <tr> <td> <p>1 </p></td><td> <p>-XX.8 </p></td><td> <p>XX.8 </p></td></tr> <tr> <td> <p>X </p></td><td> <p>-XX.4 </p></td><td> <p>XX.6 </p></td></tr> <tr> <td> <p>X </p></td><td> <p>-100.4 </p></td><td> <p>XX.4 </p></td></tr> <tr> <td> <p>4 </p></td><td> <p>-XX.X </p></td><td> <p>35.X </p></td></tr> </tbody></table> <p> </p> <p>Now XXXXX XXX <em>x- </em>XXX <em>y</em>-XXXXXXXXXXX from XXXXX 1 onto XXXXX XXXXX XXXXX XXX color, and XXXXX XXX <em>x- </em>XXX <em>y</em>-XXXXXXXXXXX XXXX XXXXX 2 XXXX XXX same graph paper using a different color. You XXX XXXXXX copy and paste XXXX graph XXXX or upload it along with this worksheet. </p> <p><XXX src="file:///X:\Users\abida\XXXXXXX\Local\Temp\msohtmlclip1\XX\clip_image005.jpg" width="337" XXXXXX="XXX"> <img src="XXXX:///C:\Users\abida\XXXXXXX\XXXXX\XXXX\msohtmlclip1\XX\XXXXXXXXXXXXX.jpg" width="XXX" height="204"> </p> <p>Compare XXX model points with XXX XXXXXXXX XXXXXX and answer XXX XXXXXXXXX XXXXXXXXX: </p> <ul><li>How does XXXX model XXXXXXX XX the actual path? </li><li>XXX XXX you XXXXXX XXX graph family that you XXX? XXX you XXXXXX well? XXX or why XXX? </li><li>XX it possible XX solve <em>x</em>(<em>t</em>) for <em>t</em>, XXXXXXXXXX it into <em>y</em>(<em>t</em>) XX eliminate XXX </li></ul> <p>XXX plot XXXX Table 2 XX XXXXXXXX XXXX that of Table X. XXXXXXX that, they are XXXXXXXXXX. </p> <p> </p> <p>I XXXXX the XXXXX XXXXX XXXXXX because it XX a common XXXXX XXXX is easier XX observe </p> <p>and XXXX its XXXXXXXXXXXXXXX. XXX XXXXXX XX well as XXX graph XX reproducible and XXXXXX </p> <p>parameter, <em>t</em>, XXX XXXXX it XX a rectangular XXXXXXXX with <em>x </em>XXX <em>y </em>XXXXXXX? Why or why not? </p> <p>No, it is not possible. Because x(t) XXXXXXXX has a coefficient XX 3 (XXXX XXXX in y(t)). </p> <p>Hence, there is XX XXXXXXXXXXXX manipulation that XXX XX done XX remove the <XX> </p> <XX>XXXX it in:</h2> <p><XX></p><p><br></p><p><XXXXXX>Step X: XXXXXX a Mathematical XXXXX.</strong> </p> <p>Work through XXX XXXXXXXXX steps XX create two parametric XXXXXXXXX where <em>x </em>is a XXXXXXXX of <em>t </em>XXX <em>y </em>XX a XXXXXXXX of <em>t</em>. </p> <ul><li>First plot <em>t </em>XXXXXX <em>x</em>, XXXX plot <em>t </em>XXXXXX <em>y</em>. XXXX XXXX XX XXXXXXXXXX should you XXX for each one based XX XXXX XXXXXX? </li><li>XXX XXXX calculator to XXXXXX a XXXXXXX XXX XXX model you XXXX XXXXXX. Enter XXX XXXXXXX pairs into XXXXX and XXXX the XXXXXXXXXX XXXXXX the XXXX of best fit XXX your XXXXX. XXX XXXXXXX, XX XXXX path XXXXXXX to be XXXXXXXXXXX, you will </li><li>Write XXXX XXXXX XXXXXXXXX: <ul><li><em>y</em>(<em>t</em>) = X.8x+XX. </li></XX></li></ul> <p>XXXX a XXXXX XX XXX form <em>y </em>= <em>ab<XXX>x</sup> </em>XXXXX the XXXXXX feature XX XXX calculator. </p> <p>· <em>x</em>(<em>t</em>) =X.4x^3 - 1.XX^X - X.1x - 92. </p> <h1>XXXX 4: Check your XXXXX.</h1> <p>Plug in XXX values <em>t </em>= 0, X, 2, X, and 4 into XXXX XXXXXXXXXX equations XXX insert your values for <em>x </em>XXX <em>y </em>in XXX table below. </p> <p> </p> <XX>XXXXX 2</h2> <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>0 </td><td>-XX.0 </td><td>XX.0 </td></tr> <tr> <td>X </td><td>-95.8 </td><td>26.X </td></tr> <tr> <td>X </td><td>-99.X </td><td>29.6 </td></tr> <tr> <td>X </td><td>-XXX.X </td><td>XX.X </td></tr> <tr> <td>X </td><td>-96.X </td><td>35.X </td></tr> </tbody></table> <p> </p> <p>Now XXXXX the <em>x- </em>XXX <em>y</em>-coordinates from XXXXX X XXXX XXXXX XXXXX XXXXX one color, XXX XXXXX XXX <em>x- </em>and <em>y</em>-XXXXXXXXXXX from Table X onto XXX XXXX graph XXXXX using a XXXXXXXXX color. You may XXXXXX copy and XXXXX your graph XXXX or XXXXXX it along with XXXX XXXXXXXXX. </p> <p><XXX XXX="file:///C:\Users\abida\XXXXXXX\Local\Temp\XXXXXXXXXXXX\01\clip_image005.jpg" width="XXX" height="XXX"> <img XXX="file:///X:\Users\abida\XXXXXXX\XXXXX\Temp\msohtmlclip1\XX\clip_image007.jpg" width="XXX" height="204"> </p> <p>XXXXXXX XXX XXXXX XXXXXX XXXX the XXXXXXXX points and XXXXXX XXX XXXXXXXXX questions: </p> <XX><li>How XXXX XXXX model compare XX the actual path? </li><li>Why did you XXXXXX XXX graph XXXXXX XXXX you did? XXX you XXXXXX well? Why or why XXX? </li><li>Is it XXXXXXXX XX XXXXX <em>x</em>(<em>t</em>) XXX <em>t</em>, substitute it into <em>y</em>(<em>t</em>) to XXXXXXXXX the </li></XX> <p>XXX XXXX XXXX XXXXX 2 XX smoother XXXX that XX Table 1. XXXXXXX XXXX, they XXX XXXXXXXXXX. </p> <p> </p> <p>I XXXXX the XXXXX XXXXX XXXXXX XXXXXXX it XX a common XXXXX XXXX is easier XX observe </p> <p>and plot its XXXXXXXXXXXXXXX. The choice XX well XX XXX graph is reproducible XXX XXXXXX </p> <p>parameter, <em>t</em>, and XXXXX it XX a XXXXXXXXXXX equation with <em>x </em>XXX <em>y </em>instead? Why or why XXX? </p> <p>No, it is not possible. Because x(t) equation has a XXXXXXXXXXX of X (cube XXXX in y(t)). </p> <p>Hence, there is no XXXXXXXXXXXX manipulation that XXX XX done to XXXXXX XXX </p> <h2>Turn it in:</h2> <p><XX></p>">
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