tag:blogger.com,1999:blog-38620704665818468732024-02-19T17:35:51.612-07:00CRMS Calculus 2010Bruhttp://www.blogger.com/profile/00445757737038941900noreply@blogger.comBlogger144125tag:blogger.com,1999:blog-3862070466581846873.post-50524793433598658302010-06-30T01:02:00.002-06:002010-06-30T01:09:44.315-06:00Capstone PresentationHello All,<br />
Here are the slides that I presented today to the MSU capstone committee on the work we did during the 3rd quarter of our calculus class. I hope that it honestly depicts the time and effort we all put into our online adventure. Thank you again for your commitment to the project. I hope that it benefited you as much as it did me.<br />
<br />
<div style="width:425px" id="__ss_4648057"><strong style="display:block;margin:12px 0 4px"><a href="http://www.slideshare.net/dbrudzinski/my-capstone-presentation-june-29-2010" title="My Capstone Presentation, June 29, 2010">My Capstone Presentation, June 29, 2010</a></strong><object id="__sse4648057" width="425" height="355"><param name="movie" value="http://static.slidesharecdn.com/swf/ssplayer2.swf?doc=mycapstonepresentationmsu17-100630013945-phpapp01&stripped_title=my-capstone-presentation-june-29-2010" /><param name="allowFullScreen" value="true"/><param name="allowScriptAccess" value="always"/><embed name="__sse4648057" src="http://static.slidesharecdn.com/swf/ssplayer2.swf?doc=mycapstonepresentationmsu17-100630013945-phpapp01&stripped_title=my-capstone-presentation-june-29-2010" type="application/x-shockwave-flash" allowscriptaccess="always" allowfullscreen="true" width="425" height="355"></embed></object><div style="padding:5px 0 12px">View more <a href="http://www.slideshare.net/">presentations</a> from <a href="http://www.slideshare.net/dbrudzinski">Colorado Rocky Mountain School</a>.</div></div><br />
Cheers and Thanx<br />
BruBruhttp://www.blogger.com/profile/00445757737038941900noreply@blogger.com0tag:blogger.com,1999:blog-3862070466581846873.post-54254784768532843092010-05-30T21:32:00.004-06:002010-05-30T21:36:11.661-06:00Light Bulb Project<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgQ1lF-woz5XGbwe1OZse4ZhxjkCIaGpeXz79FHgrMjLfgHsY4vIFC51NT7YlStw-0tpgNsFU_g01X8WwhLho4CILEW_tlyHJ9aak-TceyKsaxcm5M6ajBaccFdvvUtxS3Z_FJ9h95uZJtK/s1600/Picture+2.png"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 303px; height: 400px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgQ1lF-woz5XGbwe1OZse4ZhxjkCIaGpeXz79FHgrMjLfgHsY4vIFC51NT7YlStw-0tpgNsFU_g01X8WwhLho4CILEW_tlyHJ9aak-TceyKsaxcm5M6ajBaccFdvvUtxS3Z_FJ9h95uZJtK/s400/Picture+2.png" border="0" alt="" id="BLOGGER_PHOTO_ID_5477272386818263794" /></a><br /><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi5oXl9SS2mcM_lmu0yJ9PgZXd4z_d2NdFHOVqJpW4EiC25jhH73KVYOIt61Xt8eyRxz9HXMwg4bXH1K1IaGhVWn8f8ZAIeJynS7iWixktQta4VwWDzBUIXQthbzbK7apoJmaFxOVaJVbI2/s1600/Picture+3.png"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 346px; height: 400px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi5oXl9SS2mcM_lmu0yJ9PgZXd4z_d2NdFHOVqJpW4EiC25jhH73KVYOIt61Xt8eyRxz9HXMwg4bXH1K1IaGhVWn8f8ZAIeJynS7iWixktQta4VwWDzBUIXQthbzbK7apoJmaFxOVaJVbI2/s400/Picture+3.png" border="0" alt="" id="BLOGGER_PHOTO_ID_5477272385176183218" /></a><br /><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjR10_RspewZqxslfPEiwSVuAFTn_GO9NmVvmiSCgSiajf1i1uVQPi7KDJBTJEOPAppBZjvJtWRoW6kfE90aY5NJWYK4UiGYYlvuGq178b2p98be2FL6ghO8go6V2BcnNGbIr8ISReN6mSb/s1600/Picture+4.png"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 353px; height: 400px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjR10_RspewZqxslfPEiwSVuAFTn_GO9NmVvmiSCgSiajf1i1uVQPi7KDJBTJEOPAppBZjvJtWRoW6kfE90aY5NJWYK4UiGYYlvuGq178b2p98be2FL6ghO8go6V2BcnNGbIr8ISReN6mSb/s400/Picture+4.png" border="0" alt="" id="BLOGGER_PHOTO_ID_5477272374979768050" /></a>flying slughttp://www.blogger.com/profile/07817015602372891184noreply@blogger.com0tag:blogger.com,1999:blog-3862070466581846873.post-5211642757032129042010-05-30T21:06:00.003-06:002010-05-30T21:15:43.253-06:00Calculus Final Project 2010<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhAuafQu8B2ie-SEQTaYn12Vt96B88EOS-8CUxek9Eku2QHXMyIo3snhbUMWjc13jV3_2cRpX5q3SBiB-Spyf15hZLoirhtO4uJUrGWSjQL3YmDkEIsM4hFcOgtOcdVvnppyx_0t68uU-Pn/s1600/JayLukeCalculusFinalProject2010_1.jpg"><img style="cursor:pointer; cursor:hand;width: 400px; height: 300px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhAuafQu8B2ie-SEQTaYn12Vt96B88EOS-8CUxek9Eku2QHXMyIo3snhbUMWjc13jV3_2cRpX5q3SBiB-Spyf15hZLoirhtO4uJUrGWSjQL3YmDkEIsM4hFcOgtOcdVvnppyx_0t68uU-Pn/s400/JayLukeCalculusFinalProject2010_1.jpg" border="0" alt="" id="BLOGGER_PHOTO_ID_5477266902786207986" /></a><br /><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjLuL_R0sD8zEO49HpBjJHRn4_WnoiuxRkg2T2PoSIY5CaF4xPd2w9S-wTOvUZ17AfZMqnKFJf_w2ws_zdPSHtHRPHpNSahOlPU02UQ8Px8e0qYc4k5hxTRG85GpqI5M8bmUVHXpT8vnGu1/s1600/JayLukeCalculusFinalProject2010_2.jpg"><img style="cursor:pointer; cursor:hand;width: 294px; height: 400px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjLuL_R0sD8zEO49HpBjJHRn4_WnoiuxRkg2T2PoSIY5CaF4xPd2w9S-wTOvUZ17AfZMqnKFJf_w2ws_zdPSHtHRPHpNSahOlPU02UQ8Px8e0qYc4k5hxTRG85GpqI5M8bmUVHXpT8vnGu1/s400/JayLukeCalculusFinalProject2010_2.jpg" border="0" alt="" id="BLOGGER_PHOTO_ID_5477266894285809282" /></a><br /><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgXW-F7WGqC6kD3End1McR1p8Oo9YRzrsITDWpqdsas25OQH7Z9EIoUQ7RW9Kkkqvp-u1067EdvBPyNZboUYYMx2mWAad-uPy6RC3sgiDxrXQTSmrl5_n5Q-65Gbhn7W_D0gzfBHj1Ecb6z/s1600/JayLukeCalculusFinalProject2010_3.jpg"><img style="cursor:pointer; cursor:hand;width: 343px; height: 400px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgXW-F7WGqC6kD3End1McR1p8Oo9YRzrsITDWpqdsas25OQH7Z9EIoUQ7RW9Kkkqvp-u1067EdvBPyNZboUYYMx2mWAad-uPy6RC3sgiDxrXQTSmrl5_n5Q-65Gbhn7W_D0gzfBHj1Ecb6z/s400/JayLukeCalculusFinalProject2010_3.jpg" border="0" alt="" id="BLOGGER_PHOTO_ID_5477266890313786066" /></a><br /><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjNP2dAluGktVnWzMAUhca3syU-_J_57V2dt7cqh9VIvfyCNyc6LHCkgCWuT_e9YRw-LbGuYEnsTgk0Vz4nME6izh-sjTqvJtwEBpYQhaeWx5gY4OTnipYBt4MQhyphenhyphenVXkq3_TcbwUYuTC4l1/s1600/JayLukeCalculusFinalProject2010_4.jpg"><img style="cursor:pointer; cursor:hand;width: 291px; height: 400px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjNP2dAluGktVnWzMAUhca3syU-_J_57V2dt7cqh9VIvfyCNyc6LHCkgCWuT_e9YRw-LbGuYEnsTgk0Vz4nME6izh-sjTqvJtwEBpYQhaeWx5gY4OTnipYBt4MQhyphenhyphenVXkq3_TcbwUYuTC4l1/s400/JayLukeCalculusFinalProject2010_4.jpg" border="0" alt="" id="BLOGGER_PHOTO_ID_5477266885759142434" /></a><br /><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiqoVo7dx8NN3ikgxwGt4Y0YDzxhchbsT7p23FcZifO-L0IjG668b5Q9HNti7DVD7nM9FPtFbrXj-q2zSqTFN6R8JVpIlgsmEwGqGH7FGDkQirMB56Le5XQW7RfpEO-tQEIyaOjHZbzzkeu/s1600/JayLukeCalculusFinalProject2010_5.jpg"><img style="cursor:pointer; cursor:hand;width: 400px; height: 334px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiqoVo7dx8NN3ikgxwGt4Y0YDzxhchbsT7p23FcZifO-L0IjG668b5Q9HNti7DVD7nM9FPtFbrXj-q2zSqTFN6R8JVpIlgsmEwGqGH7FGDkQirMB56Le5XQW7RfpEO-tQEIyaOjHZbzzkeu/s400/JayLukeCalculusFinalProject2010_5.jpg" border="0" alt="" id="BLOGGER_PHOTO_ID_5477266876698009218" /></a>Hyunhwahttp://www.blogger.com/profile/07311561114746029422noreply@blogger.com0tag:blogger.com,1999:blog-3862070466581846873.post-50759774560764085512010-05-28T12:50:00.007-06:002010-05-31T10:09:18.229-06:00Final Review Slides: May 31, 2010Hello All,<br />
Here is an overview of what we covered this year in Calculus. It can serve as an initial review for the final exam.<br />
<div style="width:425px" id="__ss_4364980"><strong style="display:block;margin:12px 0 4px"><a href="http://www.slideshare.net/dbrudzinski/crms-calculus-may-31-2010-4364980" title="CRMS Calculus May 31, 2010">CRMS Calculus May 31, 2010</a></strong><object id="__sse4364980" width="425" height="355"><param name="movie" value="http://static.slidesharecdn.com/swf/ssplayer2.swf?doc=finalexamreview10-100531103415-phpapp02&stripped_title=crms-calculus-may-31-2010-4364980" /><param name="allowFullScreen" value="true"/><param name="allowScriptAccess" value="always"/><embed name="__sse4364980" src="http://static.slidesharecdn.com/swf/ssplayer2.swf?doc=finalexamreview10-100531103415-phpapp02&stripped_title=crms-calculus-may-31-2010-4364980" type="application/x-shockwave-flash" allowscriptaccess="always" allowfullscreen="true" width="425" height="355"></embed></object><div style="padding:5px 0 12px">View more <a href="http://www.slideshare.net/">presentations</a> from <a href="http://www.slideshare.net/dbrudzinski">Colorado Rocky Mountain School</a>.</div></div>Cheers, BruBruhttp://www.blogger.com/profile/00445757737038941900noreply@blogger.com0tag:blogger.com,1999:blog-3862070466581846873.post-9262528054021431712010-05-24T14:11:00.000-06:002010-05-24T14:11:25.258-06:00Today's Slides: May 21, 2010Hello All,<br />
Here are the slides from our introduction into solids of revolution and using a definite integral to calculate their volume.<br />
<div style="width:425px" id="__ss_4204642"><strong style="display:block;margin:12px 0 4px"><a href="http://www.slideshare.net/dbrudzinski/crms-calculus-2010-may-21-2010" title="CRMS Calculus 2010 May 21, 2010">CRMS Calculus 2010 May 21, 2010</a></strong><object id="__sse4204642" width="425" height="355"><param name="movie" value="http://static.slidesharecdn.com/swf/ssplayer2.swf?doc=classnotes-exploration5-9a10-100521131646-phpapp01&stripped_title=crms-calculus-2010-may-21-2010" /><param name="allowFullScreen" value="true"/><param name="allowScriptAccess" value="always"/><embed name="__sse4204642" src="http://static.slidesharecdn.com/swf/ssplayer2.swf?doc=classnotes-exploration5-9a10-100521131646-phpapp01&stripped_title=crms-calculus-2010-may-21-2010" type="application/x-shockwave-flash" allowscriptaccess="always" allowfullscreen="true" width="425" height="355"></embed></object><div style="padding:5px 0 12px">View more <a href="http://www.slideshare.net/">presentations</a> from <a href="http://www.slideshare.net/dbrudzinski">Colorado Rocky Mountain School</a>.</div></div>Cheers, BruBruhttp://www.blogger.com/profile/00445757737038941900noreply@blogger.com0tag:blogger.com,1999:blog-3862070466581846873.post-55323118982043362462010-05-17T19:53:00.001-06:002010-05-17T19:57:07.323-06:00Today's Slides: May 17, 2010Hello All,<br />
Here are the slides from our Exploration into 2D apps of the definite integral. (3D apps coming soon!)<br />
<div style="width:425px" id="__ss_4133567"><strong style="display:block;margin:12px 0 4px"><a href="http://www.slideshare.net/dbrudzinski/crms-calculus-2010-may-17-2010" title="CRMS Calculus 2010 May 17, 2010">CRMS Calculus 2010 May 17, 2010</a></strong><object id="__sse4133567" width="425" height="355"><param name="movie" value="http://static.slidesharecdn.com/swf/ssplayer2.swf?doc=classnotes-sec-5-8c-applicationsofdefiniteintegralsintwodimensions-100517204813-phpapp01&stripped_title=crms-calculus-2010-may-17-2010" /><param name="allowFullScreen" value="true"/><param name="allowScriptAccess" value="always"/><embed name="__sse4133567" src="http://static.slidesharecdn.com/swf/ssplayer2.swf?doc=classnotes-sec-5-8c-applicationsofdefiniteintegralsintwodimensions-100517204813-phpapp01&stripped_title=crms-calculus-2010-may-17-2010" type="application/x-shockwave-flash" allowscriptaccess="always" allowfullscreen="true" width="425" height="355"></embed></object><div style="padding:5px 0 12px">View more <a href="http://www.slideshare.net/">presentations</a> from <a href="http://www.slideshare.net/dbrudzinski">Colorado Rocky Mountain School</a>.</div></div>Cheers, BruBruhttp://www.blogger.com/profile/00445757737038941900noreply@blogger.com0tag:blogger.com,1999:blog-3862070466581846873.post-90370302705334218262010-05-14T09:29:00.003-06:002010-05-14T09:30:37.798-06:00Today's Slides: May 14, 2010Hello All,<br />
Here are today's slides on finding the area between curves.<br />
<div style="width:425px" id="__ss_4097770"><strong style="display:block;margin:12px 0 4px"><a href="http://www.slideshare.net/dbrudzinski/crms-calculus-2010-may-14-2010" title="CRMS Calculus 2010 May 14, 2010">CRMS Calculus 2010 May 14, 2010</a></strong><object id="__sse4097770" width="425" height="355"><param name="movie" value="http://static.slidesharecdn.com/swf/ssplayer2.swf?doc=classnotes-sec-5-8a-areabetweencurves-100514101856-phpapp01&stripped_title=crms-calculus-2010-may-14-2010" /><param name="allowFullScreen" value="true"/><param name="allowScriptAccess" value="always"/><embed name="__sse4097770" src="http://static.slidesharecdn.com/swf/ssplayer2.swf?doc=classnotes-sec-5-8a-areabetweencurves-100514101856-phpapp01&stripped_title=crms-calculus-2010-may-14-2010" type="application/x-shockwave-flash" allowscriptaccess="always" allowfullscreen="true" width="425" height="355"></embed></object><div style="padding:5px 0 12px">View more <a href="http://www.slideshare.net/">presentations</a> from <a href="http://www.slideshare.net/dbrudzinski">Colorado Rocky Mountain School</a>.</div></div>Cheers, BruBruhttp://www.blogger.com/profile/00445757737038941900noreply@blogger.com0tag:blogger.com,1999:blog-3862070466581846873.post-50055588512541604502010-05-13T11:47:00.000-06:002010-05-13T11:47:44.524-06:00Today's Slides: May 12, 2010Hello All,<br />
Here are the slides from our exploration of some properties of definite integrals.<br />
<div style="width:425px" id="__ss_4086347"><strong style="display:block;margin:12px 0 4px"><a href="http://www.slideshare.net/dbrudzinski/crms-calculus-2010-may-12-2010" title="CRMS Calculus 2010 May 12, 2010">CRMS Calculus 2010 May 12, 2010</a></strong><object id="__sse4086347" width="425" height="355"><param name="movie" value="http://static.slidesharecdn.com/swf/ssplayer2.swf?doc=classnotes-exploration5-7somepropertiesofdefiniteintegrals-100513115741-phpapp01&stripped_title=crms-calculus-2010-may-12-2010" /><param name="allowFullScreen" value="true"/><param name="allowScriptAccess" value="always"/><embed name="__sse4086347" src="http://static.slidesharecdn.com/swf/ssplayer2.swf?doc=classnotes-exploration5-7somepropertiesofdefiniteintegrals-100513115741-phpapp01&stripped_title=crms-calculus-2010-may-12-2010" type="application/x-shockwave-flash" allowscriptaccess="always" allowfullscreen="true" width="425" height="355"></embed></object><div style="padding:5px 0 12px">View more <a href="http://www.slideshare.net/">presentations</a> from <a href="http://www.slideshare.net/dbrudzinski">Colorado Rocky Mountain School</a>.</div></div>Cheers, BruBruhttp://www.blogger.com/profile/00445757737038941900noreply@blogger.com0tag:blogger.com,1999:blog-3862070466581846873.post-48178584875515795032010-05-06T13:37:00.000-06:002010-05-06T13:37:20.764-06:00Today's Slides: May 5, 2010Hello All,<br />
Here are today's slides from our discovery of the Fundamental Theorem of Calculus.<br />
<div style="width:425px" id="__ss_3997950"><strong style="display:block;margin:12px 0 4px"><a href="http://www.slideshare.net/dbrudzinski/crms-calculus-2010-may-5-2010-3997950" title="CRMS Calculus 2010 May 5, 2010">CRMS Calculus 2010 May 5, 2010</a></strong><object id="__sse3997950" width="425" height="355"><param name="movie" value="http://static.slidesharecdn.com/swf/ssplayer2.swf?doc=classnotes-sec5-6b-fundamentaltheorem-100506143050-phpapp02&stripped_title=crms-calculus-2010-may-5-2010-3997950" /><param name="allowFullScreen" value="true"/><param name="allowScriptAccess" value="always"/><embed name="__sse3997950" src="http://static.slidesharecdn.com/swf/ssplayer2.swf?doc=classnotes-sec5-6b-fundamentaltheorem-100506143050-phpapp02&stripped_title=crms-calculus-2010-may-5-2010-3997950" type="application/x-shockwave-flash" allowscriptaccess="always" allowfullscreen="true" width="425" height="355"></embed></object><div style="padding:5px 0 12px">View more <a href="http://www.slideshare.net/">presentations</a> from <a href="http://www.slideshare.net/dbrudzinski">Colorado Rocky Mountain School</a>.</div></div>Cheers, BruBruhttp://www.blogger.com/profile/00445757737038941900noreply@blogger.com0tag:blogger.com,1999:blog-3862070466581846873.post-60272358497511284022010-05-03T12:11:00.002-06:002010-05-03T12:14:01.284-06:00Today's Slides: May 3, 2010Hello All,<br />
Here are the slides from constructing some very special Riemann sums.<br />
<div style="width:425px" id="__ss_3950730"><strong style="display:block;margin:12px 0 4px"><a href="http://www.slideshare.net/dbrudzinski/crms-calculus-may-3-2010" title="CRMS Calculus May 3, 2010">CRMS Calculus May 3, 2010</a></strong><object id="__sse3950730" width="425" height="355"><param name="movie" value="http://static.slidesharecdn.com/swf/ssplayer2.swf?doc=classnotes-exploration5-6a-100503130355-phpapp02&stripped_title=crms-calculus-may-3-2010" /><param name="allowFullScreen" value="true"/><param name="allowScriptAccess" value="always"/><embed name="__sse3950730" src="http://static.slidesharecdn.com/swf/ssplayer2.swf?doc=classnotes-exploration5-6a-100503130355-phpapp02&stripped_title=crms-calculus-may-3-2010" type="application/x-shockwave-flash" allowscriptaccess="always" allowfullscreen="true" width="425" height="355"></embed></object><div style="padding:5px 0 12px">View more <a href="http://www.slideshare.net/">presentations</a> from <a href="http://www.slideshare.net/dbrudzinski">Colorado Rocky Mountain School</a>.</div></div>Cheers, BruBruhttp://www.blogger.com/profile/00445757737038941900noreply@blogger.com0tag:blogger.com,1999:blog-3862070466581846873.post-480718111221169452010-04-21T14:44:00.003-06:002010-04-21T14:47:23.545-06:00Today's slides: April 21, 2010Hello All,<br />
Here are today's slides of our "road trip" to discover the Mean Value Theorem.<br />
<div style="width:425px" id="__ss_3807092"><strong style="display:block;margin:12px 0 4px"><a href="http://www.slideshare.net/dbrudzinski/crms-calculus-april-21-2010" title="CRMS Calculus April 21, 2010">CRMS Calculus April 21, 2010</a></strong><object width="425" height="355"><param name="movie" value="http://static.slidesharecdn.com/swf/ssplayer2.swf?doc=classnotes-section5-5b-meanvaluetheorem-100421143309-phpapp02&stripped_title=crms-calculus-april-21-2010" /><param name="allowFullScreen" value="true"/><param name="allowScriptAccess" value="always"/><embed src="http://static.slidesharecdn.com/swf/ssplayer2.swf?doc=classnotes-section5-5b-meanvaluetheorem-100421143309-phpapp02&stripped_title=crms-calculus-april-21-2010" type="application/x-shockwave-flash" allowscriptaccess="always" allowfullscreen="true" width="425" height="355"></embed></object><div style="padding:5px 0 12px">View more <a href="http://www.slideshare.net/">presentations</a> from <a href="http://www.slideshare.net/dbrudzinski">Colorado Rocky Mountain School</a>.</div></div>Cheers, BruBruhttp://www.blogger.com/profile/00445757737038941900noreply@blogger.com0tag:blogger.com,1999:blog-3862070466581846873.post-86581246217493020332010-04-19T13:46:00.008-06:002010-04-19T19:18:41.959-06:00Today's Slides: April 19, 2010Hello All,<br />
We have two sets of slides today. The first one is our review of the entire year of Calculus (to date) in just 7 minutes, all on a single slide!<br />
<div style="width:425px" id="__ss_3777604"><strong style="display:block;margin:12px 0 4px"><a href="http://www.slideshare.net/dbrudzinski/crms-calculus-2010-april-192010" title="CRMS Calculus 2010 April 19,2010">CRMS Calculus 2010 April 19,2010</a></strong><object width="425" height="355"><param name="movie" value="http://static.slidesharecdn.com/swf/ssplayer2.swf?doc=classnotes-sec5-5-calculusin7minutes-100419131036-phpapp02&stripped_title=crms-calculus-2010-april-192010" /><param name="allowFullScreen" value="true"/><param name="allowScriptAccess" value="always"/><embed src="http://static.slidesharecdn.com/swf/ssplayer2.swf?doc=classnotes-sec5-5-calculusin7minutes-100419131036-phpapp02&stripped_title=crms-calculus-2010-april-192010" type="application/x-shockwave-flash" allowscriptaccess="always" allowfullscreen="true" width="425" height="355"></embed></object><div style="padding:5px 0 12px">View more <a href="http://www.slideshare.net/">presentations</a> from <a href="http://www.slideshare.net/dbrudzinski">Colorado Rocky Mountain School</a>.</div></div>The second set of slides is our recreation of Rolle's Theorem.<br />
<div style="width:425px" id="__ss_3778148"><strong style="display:block;margin:12px 0 4px"><a href="http://www.slideshare.net/dbrudzinski/rolles-theorem" title="Rolle's Theorem">Rolle's Theorem</a></strong><object width="425" height="355"><param name="movie" value="http://static.slidesharecdn.com/swf/ssplayer2.swf?doc=classnotes-sec5-5-rollestheorem-100419141555-phpapp02&stripped_title=rolles-theorem" /><param name="allowFullScreen" value="true"/><param name="allowScriptAccess" value="always"/><embed src="http://static.slidesharecdn.com/swf/ssplayer2.swf?doc=classnotes-sec5-5-rollestheorem-100419141555-phpapp02&stripped_title=rolles-theorem" type="application/x-shockwave-flash" allowscriptaccess="always" allowfullscreen="true" width="425" height="355"></embed></object><div style="padding:5px 0 12px">View more <a href="http://www.slideshare.net/">presentations</a> from <a href="http://www.slideshare.net/dbrudzinski">Colorado Rocky Mountain School</a>.</div></div>Cheers, BruBruhttp://www.blogger.com/profile/00445757737038941900noreply@blogger.com0tag:blogger.com,1999:blog-3862070466581846873.post-3521512755536208432010-04-13T14:37:00.006-06:002010-04-13T22:07:01.894-06:00Today's Slides: April 13, 2010Hello All,<br />
Here are today's slides on the definition of the definite integral.<br />
<div style="width:425px" id="__ss_3716698"><strong style="display:block;margin:12px 0 4px"><a href="http://www.slideshare.net/dbrudzinski/crms-calculus-2010-april-13-2010-3716698" title="CRMS Calculus 2010 April 13, 2010">CRMS Calculus 2010 April 13, 2010</a></strong><object width="425" height="355"><param name="movie" value="http://static.slidesharecdn.com/swf/ssplayer2.swf?doc=classnotessec5-4b-definitionofdefiniteintegral-100413221139-phpapp02&stripped_title=crms-calculus-2010-april-13-2010-3716698" /><param name="allowFullScreen" value="true"/><param name="allowScriptAccess" value="always"/><embed src="http://static.slidesharecdn.com/swf/ssplayer2.swf?doc=classnotessec5-4b-definitionofdefiniteintegral-100413221139-phpapp02&stripped_title=crms-calculus-2010-april-13-2010-3716698" type="application/x-shockwave-flash" allowscriptaccess="always" allowfullscreen="true" width="425" height="355"></embed></object><div style="padding:5px 0 12px">View more <a href="http://www.slideshare.net/">presentations</a> from <a href="http://www.slideshare.net/dbrudzinski">Colorado Rocky Mountain School</a>.</div></div>Cheers, BruBruhttp://www.blogger.com/profile/00445757737038941900noreply@blogger.com0tag:blogger.com,1999:blog-3862070466581846873.post-35655891557411141012010-04-12T13:46:00.001-06:002010-04-12T13:46:39.818-06:00Today's Slides: April 12, 2010Hello All,<br />
Here are the slides from today's class which introduced you to Riemann sums.<br />
<div style="width:425px" id="__ss_3701423"><strong style="display:block;margin:12px 0 4px"><a href="http://www.slideshare.net/dbrudzinski/crms-calculus-2010-april-12-2010" title="CRMS Calculus 2010, April 12, 2010">CRMS Calculus 2010, April 12, 2010</a></strong><object width="425" height="355"><param name="movie" value="http://static.slidesharecdn.com/swf/ssplayer2.swf?doc=classnotes-sectionexploration5-4riemannsumsthedefiniteintegral-100412140634-phpapp01&stripped_title=crms-calculus-2010-april-12-2010" /><param name="allowFullScreen" value="true"/><param name="allowScriptAccess" value="always"/><embed src="http://static.slidesharecdn.com/swf/ssplayer2.swf?doc=classnotes-sectionexploration5-4riemannsumsthedefiniteintegral-100412140634-phpapp01&stripped_title=crms-calculus-2010-april-12-2010" type="application/x-shockwave-flash" allowscriptaccess="always" allowfullscreen="true" width="425" height="355"></embed></object><div style="padding:5px 0 12px">View more <a href="http://www.slideshare.net/">presentations</a> from <a href="http://www.slideshare.net/dbrudzinski">Colorado Rocky Mountain School</a>.</div></div>Cheers, BruBruhttp://www.blogger.com/profile/00445757737038941900noreply@blogger.com0tag:blogger.com,1999:blog-3862070466581846873.post-22360695516687033152010-04-08T21:46:00.049-06:002010-04-09T06:39:05.960-06:00Forum: A Tale of Two IntegralsWe have been working with<i> Auntie Derivative and her Family of Functions</i>, also known as the indefinite integral. We have also worked with the definite integral. Which image below illustrates which type of integral?<br />
<br />
<div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgS8-Nc6Rq-2i4X0-B92haNm16iy7Od190q2tgs_Z_oCuKMmBOQpPFCWZT5enoOdAgqDcH8tZGSCLvv-vAbkBbYcO9uIhCDjc2FU1e7AJ2nujIJpOAh4a95SsJmq3RZt95j7Ja5NAvuDgg/s1600/both_integrals_2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgS8-Nc6Rq-2i4X0-B92haNm16iy7Od190q2tgs_Z_oCuKMmBOQpPFCWZT5enoOdAgqDcH8tZGSCLvv-vAbkBbYcO9uIhCDjc2FU1e7AJ2nujIJpOAh4a95SsJmq3RZt95j7Ja5NAvuDgg/s320/both_integrals_2.png" /></a></div><br />
Did you pick the correct one? The <b>indefinite integral is a family of functions</b> with a given derivative and the<b> definite integral is the area under a curve</b>. Incredibly, they are related to each other, as we will soon discover!<br />
<br />
What method have we used to approximate the definite integral (starts with a "t")? This method uses a strategy developed by <a href="http://www-history.mcs.st-and.ac.uk/Biographies/Archimedes.html">Archimedes</a>, considered by many to have been the greatest applied mathematician of antiquity. His method for finding areas under curves laid the groundwork for the invention of calculus by Newton and Leibniz two thousand years later. Read this recent New York Times <a href="http://opinionator.blogs.nytimes.com/2010/04/04/take-it-to-the-limit/">article</a> by Steven Strogatz, a professor of applied mathematics at Cornell University. Professor Strogatz discusses Archimedes <b>method of exhaustion</b> and many of the ideas we have covered this year: Zeno's Paradox of Motion, infinity, linear approximations, and the underlying basis for calculus - the concept of a limit. Post a short comment on one "take-away" from the article.Bruhttp://www.blogger.com/profile/00445757737038941900noreply@blogger.com15tag:blogger.com,1999:blog-3862070466581846873.post-75644303798661923852010-04-05T18:44:00.000-06:002010-04-05T18:44:28.457-06:00Today's Slides: April 5, 2010Hello All,<br />
Here are the slides from today's introduction to slope fields.<br />
<div id="__ss_3644187" style="width: 425px;"><strong style="display: block; margin: 12px 0pt 4px;"><a href="http://www.slideshare.net/dbrudzinski/crms-calculus-2010-april-5-2010-3644187" title="CRMS Calculus 2010 April 5, 2010">CRMS Calculus 2010 April 5, 2010</a></strong><object height="355" width="425"><param name="movie" value="http://static.slidesharecdn.com/swf/ssplayer2.swf?doc=classnotes-sec5-3bexplorationofslopefields10-100405193019-phpapp01&stripped_title=crms-calculus-2010-april-5-2010-3644187" /><param name="allowFullScreen" value="true"/><param name="allowScriptAccess" value="always"/><embed src="http://static.slidesharecdn.com/swf/ssplayer2.swf?doc=classnotes-sec5-3bexplorationofslopefields10-100405193019-phpapp01&stripped_title=crms-calculus-2010-april-5-2010-3644187" type="application/x-shockwave-flash" allowscriptaccess="always" allowfullscreen="true" width="425" height="355"></embed></object><div style="padding: 5px 0pt 12px;">View more <a href="http://www.slideshare.net/">presentations</a> from <a href="http://www.slideshare.net/dbrudzinski">Colorado Rocky Mountain School</a>.</div></div>Cheers, BruBruhttp://www.blogger.com/profile/00445757737038941900noreply@blogger.com0tag:blogger.com,1999:blog-3862070466581846873.post-60712560709553144912010-03-31T14:01:00.003-06:002010-03-31T14:05:10.381-06:00Today's Slides: March 31, 2010Hello All,<br />
Here are the slides from today's class on the rules of integration.<br />
<br />
<div id="__ss_3606284" style="width: 425px;"><b style="display: block; margin: 12px 0pt 4px;"><a href="http://www.slideshare.net/dbrudzinski/crms-calculus-2010-march-31-2010" title="CRMS Calculus 2010 March 31, 2010">CRMS Calculus 2010 March 31, 2010</a></b><object height="355" width="425"><param name="movie" value="http://static.slidesharecdn.com/swf/ssplayer2.swf?doc=sec5-3aclassnotesintegrationindefiniteintegralday1-100331145549-phpapp02&stripped_title=crms-calculus-2010-march-31-2010" /><param name="allowFullScreen" value="true"/><param name="allowScriptAccess" value="always"/><embed src="http://static.slidesharecdn.com/swf/ssplayer2.swf?doc=sec5-3aclassnotesintegrationindefiniteintegralday1-100331145549-phpapp02&stripped_title=crms-calculus-2010-march-31-2010" type="application/x-shockwave-flash" allowscriptaccess="always" allowfullscreen="true" width="425" height="355"></embed></object><br />
<div style="padding: 5px 0pt 12px;">View more <a href="http://www.slideshare.net/">presentations</a> from <a href="http://www.slideshare.net/dbrudzinski">Colorado Rocky Mountain School</a>.</div></div>Cheers, BruBruhttp://www.blogger.com/profile/00445757737038941900noreply@blogger.com0tag:blogger.com,1999:blog-3862070466581846873.post-7528355154178954152010-03-30T22:16:00.001-06:002010-03-30T22:17:26.235-06:00Today's Slides: March 30, 2010Hello All,<br />
Here are the slides from Exploration 5.1 and our introduction to integrals and integration.<br />
<br />
<div id="__ss_3600100" style="width: 425px;"><b style="display: block; margin: 12px 0pt 4px;"><a href="http://www.slideshare.net/dbrudzinski/crms-calculus-2010-march-30-2010" title="CRMS Calculus 2010 March 30, 2010">CRMS Calculus 2010 March 30, 2010</a></b><object height="355" width="425"><param name="movie" value="http://static.slidesharecdn.com/swf/ssplayer2.swf?doc=sec5-1classnotesexploration-100330230007-phpapp01&stripped_title=crms-calculus-2010-march-30-2010" /><param name="allowFullScreen" value="true"/><param name="allowScriptAccess" value="always"/><embed src="http://static.slidesharecdn.com/swf/ssplayer2.swf?doc=sec5-1classnotesexploration-100330230007-phpapp01&stripped_title=crms-calculus-2010-march-30-2010" type="application/x-shockwave-flash" allowscriptaccess="always" allowfullscreen="true" width="425" height="355"></embed></object><br />
<div style="padding: 5px 0pt 12px;">View more <a href="http://www.slideshare.net/">presentations</a> from <a href="http://www.slideshare.net/dbrudzinski">Colorado Rocky Mountain School</a>.</div></div>Cheers, BruBruhttp://www.blogger.com/profile/00445757737038941900noreply@blogger.com0tag:blogger.com,1999:blog-3862070466581846873.post-17732580608624702942010-03-05T08:35:00.006-07:002010-03-06T19:21:00.829-07:00Math Final Group 2<p align="center"><strong><span style="font-size:180%;color:#ff0000;">Math Final Project Group 2</span></strong><br />Group Member:<br />YDplusSB, Hyunhwa, J-tron foteen<br />Materials:</p><p align="center">A measuring cylinder<br />A right circular cone<br />A plastic bag<br />A glass<br />A timer<br />3 people….</p><p align="left"> </p><p align="left">Purpose:</p><p align="left">The purpose of our final project is to help us understand calculus espeically the related rate problems better by applying the math into a real world situation. Throughout the process of solving the problem, we could also learn how to edit a video, how to distribute work, and how to work together as a group.</p><p align="left"> </p><p align="left">Scenario:<br />There is a right circular cone with a height of 11.3cm, a radius of 4cm. Initially, there is 15ml amount of water in the cone with a height of 4.85cm. As we unlock the bottom of the cone, the water in the cone will drip with a flow rate of 1.875ml/sec. At the same time, some water is poured into the cone at a flow rate of 0.275ml/sec.<br /><br />Question:<br />What’s the rate of change of the radius after 3sec with the volume of 10.45cm3 and the height of 4.226cm?</p><p align="left">Little Video:</p><p align="left"></p><p></p><p><br /><object height="385" width="480"><param name="movie" value="http://www.youtube.com/v/4xwtNPyR1yQ&hl=zh_CN&fs=1&"><param name="allowFullScreen" value="true"><param name="allowscriptaccess" value="always"><embed src="http://www.youtube.com/v/4xwtNPyR1yQ&hl=zh_CN&fs=1&" type="application/x-shockwave-flash" allowscriptaccess="always" allowfullscreen="true" width="480" height="385"></embed></object></p><p>The actually video quality is low. We use a white backgroup to highlight the actual experiment which consists of a right circular cone, a plastic bag, one glass, and a measuring cylinder.</p><p>Check out our solution in WIKI</p><p><a href="http://crmscalc2010.pbworks.com/Final-Project">http://crmscalc2010.pbworks.com/Final-Project</a>#</p>YDplusSBhttp://www.blogger.com/profile/03133765178448567641noreply@blogger.com0tag:blogger.com,1999:blog-3862070466581846873.post-90634602980404076152010-03-05T08:25:00.005-07:002010-03-05T10:19:15.276-07:00Ski Movie Final Project<!--StartFragment--> <p class="MsoNormal">The purpose of this final project is to help us understand related rates through teaching them ourselves. We are also hoping that we can help to teach others and challenge them to a new Related Rates problem. About all everyday scenarios, such as skiing, contain some bit of calculus. We are proposing a scenario, in which two skiers are skiing away from each other. We are going to calculate the rate at which the distance between them is changing. This problem was created by skirdude, secret and Flying Slug.</p><p class="MsoNormal"> Two skiers are having an extreme day on Snowmass Mountain. They have been skiing together all day, dropping fatty cliffs and schralping mad gnar. Its the end of the day, and they are getting tired, so they now decide they both want to go down different runs. They are total math buffs and decide to turn this into an awesome Related Rates problem!</p><p class="MsoNormal"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif; font-size: 10px; white-space: pre; "><object width="500" height="405"><param name="movie" value="http://www.youtube.com/v/4i9amQnm5Lg&hl=en_US&fs=1&color1=0x006699&color2=0x54abd6&border=1"></param><param name="allowFullScreen" value="true"></param><param name="allowscriptaccess" value="always"></param><embed src="http://www.youtube.com/v/4i9amQnm5Lg&hl=en_US&fs=1&color1=0x006699&color2=0x54abd6&border=1" type="application/x-shockwave-flash" allowscriptaccess="always" allowfullscreen="true" width="500" height="405"></embed></object></span></p><p class="MsoNormal"><br /></p><p class="MsoNormal">You can find our solution <a href="http://crmscalc2010.pbworks.com/Final+Project-+Luke%2C+Gus%2C+Kelsey">here!</a> </p><p class="MsoNormal">And a big shout out to the crew at Aspen for being very patient with us and giving us tons of help!</p><!--StartFragment--> <!--EndFragment--> <!--EndFragment-->skirdudehttp://www.blogger.com/profile/11691533567526109072noreply@blogger.com0tag:blogger.com,1999:blog-3862070466581846873.post-60726734966644761162010-03-04T17:06:00.013-07:002010-03-05T08:34:24.516-07:00Real World Related Rates<div style="text-align: center; color: rgb(102, 0, 0);"><span style="font-size:180%;">Final Project Group 1<br /></span></div><div style="text-align: center; color: rgb(102, 0, 0);"><span style="font-size:180%;"><span style="font-size:100%;"><span style="color: rgb(51, 51, 51);">Related Rates<br /><span style="color: rgb(204, 102, 0);">Co-Authors: <span style="color: rgb(255, 102, 102);"><span class="blsp-spelling-error" id="SPELLING_ERROR_0">Blitzen</span></span>, <span style="color: rgb(255, 102, 102);"><span class="blsp-spelling-error" id="SPELLING_ERROR_1">Dammitimmad</span></span>, and <span style="color: rgb(255, 102, 102);"><span class="blsp-spelling-error" id="SPELLING_ERROR_2">mc</span> Casper<span style="color: rgb(204, 102, 0);">.</span></span></span><br /></span></span></span><br /><div style="text-align: left;"><div style="text-align: center;"><div style="text-align: center;"><span style="color: rgb(0, 0, 102);">Materials: <span style="color: rgb(0, 0, 0);"><br />Bowling Ball</span> <span style="color: rgb(0, 0, 0);"> </span></span><br /></div><span style="color: rgb(0, 0, 102);"><span style="color: rgb(0, 0, 0);">Marble</span> <span style="color: rgb(0, 0, 0);"> Video </span></span><br /><span style="color: rgb(0, 0, 102);"><span style="color: rgb(0, 0, 0);">Camera</span> <span style="color: rgb(0, 0, 0);"></span></span><br /><span style="color: rgb(0, 0, 102);"><span style="color: rgb(0, 0, 0);">Smooth floor (with minimal friction)</span> </span><br /><span style="color: rgb(0, 0, 102);"><span style="color: rgb(0, 0, 0);">Paper and pen to do the work</span> </span><br /><span style="color: rgb(0, 0, 102);"><span style="color: rgb(0, 0, 0);">Black Box (calculator)</span> <span style="color: rgb(0, 0, 0);"> </span></span><br /><span style="color: rgb(0, 0, 102);"><span style="color: rgb(0, 0, 0);">Grey Box (brain)</span></span><br /></div><br /><span style="color: rgb(0, 0, 102);">Purpose: <span style="font-size:100%;"><span style="color: rgb(0, 0, 0);">For our final project we were asked to create a related rat</span></span></span><span style="color: rgb(0, 0, 102);"><span style="font-size:100%;"><span style="color: rgb(0, 0, 0);">es problem within the real world using a program to draw the actual data from our experiment. Using the video analysis with a program called logger pro we had all of the data needed to sol</span></span></span><span style="color: rgb(0, 0, 102);"><span style="font-size:100%;"><span style="color: rgb(0, 0, 0);"><span class="blsp-spelling-error" id="SPELLING_ERROR_3">ve</span> </span></span></span><span style="color: rgb(0, 0, 102);"><span style="font-size:100%;"><span style="color: rgb(0, 0, 0);">the problem at hand.<br /><br /><span style="color: rgb(0, 0, 102);">The Problem:</span> Our experiment consisted of rolling a b</span></span></span><span style="color: rgb(0, 0, 102);"><span style="font-size:100%;"><span style="color: rgb(0, 0, 0);"><span class="blsp-spelling-error" id="SPELLING_ERROR_4">owling</span> ball and a marble away from each other at a 90 degree angle. We executed this experiment on a smooth and level concrete floor indoors. We can assume that both balls were rolling at approximately the same speed (see next paragraph below). Our goal is to find the rate of change of that the distance between the two balls is increasing with respect to time.<br /><br /></span></span></span><span style="color: rgb(0, 0, 102);"><span style="font-size:100%;"><span style="color: rgb(0, 0, 0);"><span style="color: rgb(0, 0, 153);">The great lengths of assuring a constant velocity:</span></span></span></span><span style="color: rgb(0, 0, 102);"><span style="font-size:100%;"><span style="color: rgb(0, 0, 0);"><br /></span></span></span><span style="color: rgb(0, 0, 102);"><span style="font-size:100%;"><span style="color: rgb(0, 0, 0);">Time frame of experiment was roughly 2 seconds</span></span></span><br /><span style="color: rgb(0, 0, 102);"><span style="font-size:100%;"><span style="color: rgb(0, 0, 0);">Very smooth concrete floor used in experiment<br />No interference after the initial push off<br />Air resistance is negligible due to being indoors and</span></span></span><span style="color: rgb(0, 0, 102);"><span style="font-size:100%;"><span style="color: rgb(0, 0, 0);"> no wind</span></span></span><br /><br /><span style="color: rgb(0, 0, 102);"><span style="font-size:100%;"><span style="color: rgb(0, 0, 0);"><span style="color: rgb(0, 102, 0);">Figure 1:</span></span></span></span><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgTYYazmSPFEWrLVNdHAPv89Yl3WFsQedrYTo1OcxB9Mhu9W2N9_FHQjcz7lb1YqMTtZOhcvi_MCml89EnN4ypx9smjHiYNb3xiIGAiaS6stSskBlfzjOIr63LnsK70mlaFiBtQx7D3QCOx/s1600-h/Linnea+is+crazy+but+kat+still+likes+her+%28kinda%29+anyways.jpg"><img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer; width: 511px; height: 237px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgTYYazmSPFEWrLVNdHAPv89Yl3WFsQedrYTo1OcxB9Mhu9W2N9_FHQjcz7lb1YqMTtZOhcvi_MCml89EnN4ypx9smjHiYNb3xiIGAiaS6stSskBlfzjOIr63LnsK70mlaFiBtQx7D3QCOx/s320/Linnea+is+crazy+but+kat+still+likes+her+%28kinda%29+anyways.jpg" alt="" id="BLOGGER_PHOTO_ID_5444993807792445058" border="0" /></a><span style="color: rgb(0, 0, 102);"><span style="font-size:100%;"><span style="color: rgb(0, 0, 0);"><br /><span style="color: rgb(0, 102, 0);">Video of actual experiment!</span><span style="color: rgb(0, 102, 0);"><br /></span></span></span></span></div></div><iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.blogger.com/video.g?token=AD6v5dx__VZBdOmwxtGjkVI-veEea1ACncB6OBsdZWyXLpFboAQ1kb_qCM-4klwH0GDlwZTmb_XAaFWILmEpmwc6GQ' class='b-hbp-video b-uploaded' frameborder='0'></iframe><br /><br /><br /><span style="color: rgb(0, 102, 0);">Data:<br /></span><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjgXh5KbPR7C5YyJBZMusGVkOmBlQBgwL6qEhZWEDeJOJP_z4HrEwa4ha_AKZZQQNZdBhX5LoDGD7Pdo9PHozEwAP8XGqzcNhZIw4frDYemOJ1Ua6clDi9m4Sd2M-dBFzkSv9iGYIlgRft5/s1600-h/data_1_31.png"><img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer; width: 467px; height: 406px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjgXh5KbPR7C5YyJBZMusGVkOmBlQBgwL6qEhZWEDeJOJP_z4HrEwa4ha_AKZZQQNZdBhX5LoDGD7Pdo9PHozEwAP8XGqzcNhZIw4frDYemOJ1Ua6clDi9m4Sd2M-dBFzkSv9iGYIlgRft5/s320/data_1_31.png" alt="" id="BLOGGER_PHOTO_ID_5445166402554387442" border="0" /></a><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi0F_r_RI3PGn4UZZfwwKAp6Zmk_yycx148_BZwg_jSZWdnpE99HZ4OWUf54Ep7_lnBLNKD1R0uBgiZgxdB6uQR_2CQiPIBoMrmsDRBK262kHzUJ6alWD6RgJDsy4Vhi7TGgpz6ta3YNMC9/s1600-h/Snapshot+2010-03-04+21-02-59.jpg"><img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer; width: 466px; height: 220px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi0F_r_RI3PGn4UZZfwwKAp6Zmk_yycx148_BZwg_jSZWdnpE99HZ4OWUf54Ep7_lnBLNKD1R0uBgiZgxdB6uQR_2CQiPIBoMrmsDRBK262kHzUJ6alWD6RgJDsy4Vhi7TGgpz6ta3YNMC9/s320/Snapshot+2010-03-04+21-02-59.jpg" alt="" id="BLOGGER_PHOTO_ID_5445166752761761570" border="0" /></a><br /><span style="color: rgb(0, 102, 0);">Graph of our data:<br /></span><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjemJb3Q6jm7otXDxDRj6RetE8qtGPU9Z1qJ8bQ0Sarg84wfkDQ2oKNMz71_A5mxJ8s8B-6NoKHliYroiJBDvRPP2RJnjAgm26fClVX0d5VdV2F6pbkhq906Yn8Eb8lePOlX7dM_0QQSEfR/s1600-h/graph_b4_lines.png"><img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer; width: 524px; height: 270px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjemJb3Q6jm7otXDxDRj6RetE8qtGPU9Z1qJ8bQ0Sarg84wfkDQ2oKNMz71_A5mxJ8s8B-6NoKHliYroiJBDvRPP2RJnjAgm26fClVX0d5VdV2F6pbkhq906Yn8Eb8lePOlX7dM_0QQSEfR/s320/graph_b4_lines.png" alt="" id="BLOGGER_PHOTO_ID_5445167156397928818" border="0" /></a><span style="color: rgb(0, 102, 0);"><span style="color: rgb(0, 0, 0);">You can see from our graph above that the velocity of the two objects is within minor human error, constant. The only part of the lines that are not constant is the beginning portion of the graph due to the ball's being stationary at the beginning of the video. The slight curve that is also apparent before the constant velocity is reached is due to the initial push from us accelerating the balls and bringing them up to speed.<br /><br />Using the linear regression on our program (called logger pro), we got the equations for the velocity and displacement of each object individually.<br /><br /><span style="color: rgb(0, 102, 0);">Graphs with the linear regression equations.</span></span></span><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh0O6xdC3ict31CQQKkN22EvxupI1YedmcgWKmzje9CNqr5Ym6oF_J6uUxl6SHBzzvSEE72M6DxSa1ZuKB2vQ4ihJyuVoULifP-jcANl8hWBzs2l9VIOC0YIfOi5vYZ9SJ_vorXEo5KlzMs/s1600-h/graph_w_lines.png"><img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer; width: 527px; height: 274px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh0O6xdC3ict31CQQKkN22EvxupI1YedmcgWKmzje9CNqr5Ym6oF_J6uUxl6SHBzzvSEE72M6DxSa1ZuKB2vQ4ihJyuVoULifP-jcANl8hWBzs2l9VIOC0YIfOi5vYZ9SJ_vorXEo5KlzMs/s320/graph_w_lines.png" alt="" id="BLOGGER_PHOTO_ID_5444996705070357426" border="0" /></a>(Because the linear equations are difficult to read, you can go to our WikiWork Problem to see the equations of these lines more clearly.)<br />http://crmscalc2010.pbworks.com/WikiWork-Problem-2<br /><br /><span style="color: rgb(0, 0, 153);">General Overview How To Solve:</span><br /><span style="color: rgb(0, 0, 0);">After obtaining the data and the linear regressions in loggerpro, we found the velocities using the data begotten from loggerpro. We used the X and Y components of object's velocity to find their total velocity.<br />Next we chose a random point somewhere from the middle of the graph.<br />To find the rate of change of the distance between the two objects we used the derivative of Pythagorean formula (see wiki). We substituted in the displacements for both objects into the formula and their velocities to find dz/dt (the related rate of the distance between the two objects with respect to time).<br /><br />We choose to repeat this process for three separate points to see how accurate and consistent our answers were.<br /><br />After completeing our project we determined that there was very little human error in our experiment because all three final answers were only one tenth different from one another.<br />***See WikiWork problem for full explination of calculations.***<br /></span><br /><span style="color: rgb(204, 0, 0);">Final Problem (one last time):</span><br />What is the rate at which the distance between the two objects is increasing? The velocity of the bowling ball is 37.957 inches per second. The velocity of the marble is 43.52 inches per second.<br /><br />***Please see our WikiWork page to see the calculations and solution to this problem***<br />http://crmscalc2010.pbworks.com/WikiWork-Problem-2mc Casperhttp://www.blogger.com/profile/11740006144235430482noreply@blogger.com1tag:blogger.com,1999:blog-3862070466581846873.post-13347181273033769592010-03-04T17:00:00.000-07:002010-03-04T17:02:28.416-07:00Final Project: The Related Rates Time MachineGroup 4<br />Nom de plumes: babar, WinnPlot, Tubby.<br /><br />The purpose of this Final Project was to create a unique related rates problem from a real world situation and then solve this problem, thus expanding our knowledge of related rates, and their application in the real world.<br /><br /><br /><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhcEbuPCm4KvdzdEdiz-PnwYhLJ64umntWkCxo7D3ZAR5nyOig3ZyoX_W75M3jLi8nAnYZMtpPptHDMVQufFTErq922xcI9-XUgMZ-PuCk71ZhB6Est8e6qlmOL5ergd6pL4iWMMgwO-jY/s1600-h/Time+Machine.png"><img style="cursor: pointer; width: 393px; height: 400px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhcEbuPCm4KvdzdEdiz-PnwYhLJ64umntWkCxo7D3ZAR5nyOig3ZyoX_W75M3jLi8nAnYZMtpPptHDMVQufFTErq922xcI9-XUgMZ-PuCk71ZhB6Est8e6qlmOL5ergd6pL4iWMMgwO-jY/s400/Time+Machine.png" alt="" id="BLOGGER_PHOTO_ID_5444476420528494386" border="0" /></a><br /><br />image source:http://www.friedpost.com/wp-content/uploads/2008/10/time-machine.jpg<br /><br /><br />Young Freddy Newton was trying to make it big in the stock market, and decided to build a time machine (see image) so he would be sure to buy the right Stock. Unfortunately the time machine malfunctioned sending Freddy into a ripple of time and space and landing him in the land of dinosaurs with only a bendy straw in his possession. Freddy was so thirsty upon arrival but could not find any clean water. Finally after three weeks of wandering the land aimlessly Freddy came upon a bowl, that we assume is a half-sphere filled with prehistoric sludge. <span style="color: rgb(153, 0, 0);">It had a volume of 355cubic centimeters and a radius at the top of 6.75centimeters. It takes him 22.65 seconds to consume the sludge</span>. Freddy uses his handy dandy bendy straw to drink the sludge for sustenance. We are going to assume that he drinks at a constant rate. Below is a video of this event:<br /><br /><object height="344" width="425"><param name="movie" value="http://www.youtube.com/v/yZeFCTT0AM0&hl=en_US&fs=1&"><param name="allowFullScreen" value="true"><param name="allowscriptaccess" value="always"><embed src="http://www.youtube.com/v/yZeFCTT0AM0&hl=en_US&fs=1&" type="application/x-shockwave-flash" allowscriptaccess="always" allowfullscreen="true" height="344" width="425"></embed></object><br /><br /><br /><span style="color: rgb(255, 0, 0);">So, the related rates question is:</span> <span style="color: rgb(0, 153, 0);"><br /><span style="color: rgb(102, 0, 204);">If a semi-sphere with a volume of 355 cubic centimeters filled with prehistoric sludge takes 22.64 seconds to consume what is the rate, in minutes, at which the height of sludge in the bowl is changing at the moment when the sludge is at 2 centimeters?</span></span><br /><br />Here is a hyperlink to the solution:<br /><a href="http://crmscalc2010.pbworks.com/Final-Project-Group-4#view=page">http://crmscalc2010.pbworks.com/Final-Project-Group-4#view=page</a>Babarhttp://www.blogger.com/profile/11141535193162686672noreply@blogger.com0tag:blogger.com,1999:blog-3862070466581846873.post-9787223560093412432010-03-03T10:43:00.012-07:002010-03-05T08:49:49.222-07:00Group 5's Final Project Presentation<div style="text-align: center;"><span style="color: rgb(102, 51, 255);font-size:180%;" >MMMhmmm....Ice Cream....</span><span style="font-size:180%;"><br /><br /><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://repossibility.com/wp-content/uploads/2009/08/Melting-Ice-Cream-Lady-300x300.jpg"><img style="cursor: pointer; width: 364px; height: 364px;" src="http://repossibility.com/wp-content/uploads/2009/08/Melting-Ice-Cream-Lady-300x300.jpg" alt="" border="0" /></a></span></div><div style="text-align: center; color: rgb(255, 102, 0);"><span style="font-weight: bold; color: rgb(51, 255, 51);font-size:130%;" ><br />Beston, Marley, and BlueElephants's Final Project Presentation</span><br /></div><br />The purpose of this final project is for us to watch, learn, and teach a real world application of calculus. Our problem involves a conical container and a volume of liquid that is flowing out of the bottom. The purpose is to find what the <span style="color: rgb(255, 0, 0);">rate of change</span> of the volume <span style="color: rgb(255, 0, 0);">with respect to time</span> is as the liquid flows out at a certain height.<br />In our problem we measured the <span style="color: rgb(255, 0, 0);">rate of change</span> of the ice cream flowing out of an ice cream cone <span style="color: rgb(255, 0, 0);">with respect to time</span>.<br /><span style="font-weight: bold;"><br /><span style="color: rgb(51, 102, 255);">RELATED RATES</span></span><span style="font-weight: bold;"> PROBLEM:</span><br />An ice cream cone has a radius of <span style="color: rgb(51, 204, 0);">2.5 cm</span> at the top and has a height of <span style="color: rgb(51, 204, 0);">10.2 cm</span>. If the height of the melted ice cream is decreasing at a rate of <span style="color: rgb(51, 204, 0);">0.35228 cm/s</span>, how fast is the volume of the melted ice cream decreasing when the height is <span style="color: rgb(51, 204, 0);">8.271cm</span>?<br /><span style="font-weight: bold;"><br />Materials:</span><br />-ice cream cone<br />-ice cream<br />-microwave<br />-knife<br /><span style="font-weight: bold;"><br />Instructions:</span><br />Take the ice cream cone and cut off the very tip so that there is a small hole. Measure radius and height of cone. Melt ice cream in microwave. Fill the ice cream cone up with melted ice cream. Film using loggerpro. Move knife down as level of ice cream decreases. Using loggerpro, plot data points based off of level of knife in relation to the base of the cone.<br /><br /><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgAGtqK8qjAN-CNv8TCBQujEfSKFz4UceARh9Py8f97J4H-yZWSAb2rGzyiWkr2f5EFp6Lq1dwA1bzo6d77dIgMYqix_YtSiTQpryaMZG7Uhhm1FSakGv4HLAU8IKMCHuqO71nCaSrCjjU/s1600-h/cones.png"><img style="cursor: pointer; width: 351px; height: 398px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgAGtqK8qjAN-CNv8TCBQujEfSKFz4UceARh9Py8f97J4H-yZWSAb2rGzyiWkr2f5EFp6Lq1dwA1bzo6d77dIgMYqix_YtSiTQpryaMZG7Uhhm1FSakGv4HLAU8IKMCHuqO71nCaSrCjjU/s320/cones.png" alt="" id="BLOGGER_PHOTO_ID_5444469964325618466" border="0" /></a><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiYmGwPOsC5pPAHtzNLfpmM3B4YnQd7PQN0DW-GMlM98hAvlQnRXYz55AObe8cUBqOlONH5ccFGRWYV0r3GjxS1uMCJ08HqJm6BR2WmyuSE9m6dVy90UQzddNXS7f6wln9aYRPJlpl3Ie8/s1600-h/2010-03-03_1103.png"><img style="cursor: pointer; width: 344px; height: 224px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiYmGwPOsC5pPAHtzNLfpmM3B4YnQd7PQN0DW-GMlM98hAvlQnRXYz55AObe8cUBqOlONH5ccFGRWYV0r3GjxS1uMCJ08HqJm6BR2WmyuSE9m6dVy90UQzddNXS7f6wln9aYRPJlpl3Ie8/s320/2010-03-03_1103.png" alt="" id="BLOGGER_PHOTO_ID_5444470217998232210" border="0" /></a><br /><br /><br />Here is a delightful video of us, showing you, our data collection...<br /><br /><br /><object height="385" width="640"><param name="movie" value="http://www.youtube.com/v/dBkHvQafEF0&hl=en_US&fs=1&"><param name="allowFullScreen" value="true"><param name="allowscriptaccess" value="always"><embed src="http://www.youtube.com/v/dBkHvQafEF0&hl=en_US&fs=1&" type="application/x-shockwave-flash" allowscriptaccess="always" allowfullscreen="true" height="385" width="640"></embed></object><br /><br /><br />To see our solution please go to <a href="http://crmscalc2010.pbworks.com/Final-Project-Group-5">the Wiki</a>.<br /><br /><div style="text-align: center;"><br /><span style="color: rgb(102, 51, 255);font-size:180%;" >MMMhmmm....Ice cream...But don't let it all melt away...<br /><br /><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://collegian.csufresno.edu/a/wp-content/uploads/2008/02/f_icecream.jpg"><img style="cursor: pointer; width: 418px; height: 592px;" src="http://collegian.csufresno.edu/a/wp-content/uploads/2008/02/f_icecream.jpg" alt="" border="0" /></a><br /><br /></span><div style="text-align: left;"><span style="color: rgb(102, 51, 255);font-size:85%;" ><span style="color: rgb(0, 0, 0);">Photo Credits:</span></span><span style="font-size:85%;"><br /><br /></span><span style="color: rgb(102, 51, 255);font-size:85%;" ><span style="color: rgb(0, 0, 0);">Lady eating ice cream:http://repossibility.com/wp-content/uploads/2009/08/Melting-Ice-Cream-Lady-300x300.jpg</span></span><span style="font-size:85%;"><br /></span><span style="color: rgb(102, 51, 255);font-size:85%;" ><span style="color: rgb(0, 0, 0);">Earth melting:http://collegian.csufresno.edu/a/wp-content/uploads/2008/02/f_icecream.jpg</span></span><br /></div></div>Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-3862070466581846873.post-69994012372131039702010-02-25T10:55:00.002-07:002010-02-25T11:14:23.440-07:00Future Math<span class="Apple-style-span" style="font-size: medium;">It seems to me that every year there is new, incredibly ground breaking technology. Math included. This technology always is portrayed as the "future." Its gonna change the world around us! Well, I believe that we do that by ourselves. We already have the technologies to change our world, how we use should be the most pressing issue. </span><div><span class="Apple-style-span" style="font-size: medium;"><br /></span></div><div><span class="Apple-style-span" style="font-size: medium;">Currently, everything we create is built in order to streamline the process. As shown in the article, shopping is included. The fact that a company has the rights to what music I'll be buying next, or my favorite author may, in fact, be quite frightening. I am a believer in the fact that the more this technology piles on, the more cautious we need to be about how we use it. Computers already have capabilities far beyond that of any human. As a race, we need to hold true to our roots. We must embrace technology in a way that we do not inhibit our natural tendencies. </span></div><div><span class="Apple-style-span" style="font-size: medium;"><br /></span></div><div><span class="Apple-style-span" style="font-size: medium;">I don't mean to be all superficial and such, but is this really that far from possible?</span>...</div><div><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif; font-size: 10px; white-space: pre; "><object width="560" height="340"><param name="movie" value="http://www.youtube.com/v/ECoPbiGfjNw&hl=en_US&fs=1&"></param><param name="allowFullScreen" value="true"></param><param name="allowscriptaccess" value="always"></param><embed src="http://www.youtube.com/v/ECoPbiGfjNw&hl=en_US&fs=1&" type="application/x-shockwave-flash" allowscriptaccess="always" allowfullscreen="true" width="560" height="340"></embed></object></span></div><div><span class="Apple-style-span" style="font-family:arial, serif;"><span class="Apple-style-span" style="font-size: medium; white-space: pre;"><span class="Apple-style-span" style="font-family:Arial, Helvetica, sans-serif;font-size:85%;"><span class="Apple-style-span" style="font-size: 10px;"><br /></span></span></span></span></div><div><span class="Apple-style-span" style="white-space: pre; "><span class="Apple-style-span" style="font-family:'times new roman';"><span class="Apple-style-span" style="font-size: medium;">Alright, maybe thats a little far fetched. But, I would say that we are likely on our way there. </span></span></span></div><div><span class="Apple-style-span" style="font-family:'times new roman', serif;"><span class="Apple-style-span" style="font-size: medium; white-space: pre;"><br /></span></span></div><div><span class="Apple-style-span" style="font-family:'times new roman', serif;"><span class="Apple-style-span" style="font-size: medium; white-space: pre;">I think that all this technology is definitely beneficial and could greatly change the world we live in. It has the opportunity to benefit all of us. However, I would stress that we should keep in mind where we would like to be, and where we are going.</span></span></div>skirdudehttp://www.blogger.com/profile/11691533567526109072noreply@blogger.com2tag:blogger.com,1999:blog-3862070466581846873.post-21316981263702990422010-02-23T21:33:00.004-07:002010-02-23T22:27:15.786-07:00Related Rates 2.0What are Related Rates?<div style="text-align: center;"><img style="cursor:pointer; cursor:hand;width: 455px; height: 550px;" src="http://www.donself.com/images/confused-baby.bmp" border="0" alt="" /></div><div style="text-align: center;"><span class="Apple-style-span" style="font-size:small;">http://www.donself.com/images/confused-baby.bmp</span></div><div><br /></div><div>A related rate problem has a few qualities:</div><div><br /></div><div><span class="Apple-tab-span" style="white-space:pre"> </span>a. 2 changing quantities</div><div><span class="Apple-tab-span" style="white-space:pre"> </span></div><div><span class="Apple-tab-span" style="white-space:pre"> </span>b. Hopefully enough information about those quantities</div><div><br /></div><div><span class="Apple-tab-span" style="white-space:pre"> </span>c. And (as with most Calculus problems) asks you to figure out the rate at which on is <span class="Apple-tab-span" style="white-space:pre"> </span>changing</div><div><br /></div><div><br /></div><div>There are a few tricks to helping you solve these most complex problems:</div><div><br /></div><div><span class="Apple-tab-span" style="white-space:pre"> </span><span class="Apple-style-span" style="color:#FF0000;">1. DRAW A PICTURE!</span></div><div><span class="Apple-style-span" style="color:#FF0000;"><span class="Apple-tab-span" style="white-space:pre"> </span><span class="Apple-style-span" style="color:#000000;">You might think your too cool for school... but guess what? Your not.</span></span></div><div><span class="Apple-tab-span" style="white-space:pre"> </span>Drawing a picture gives you time to organize and think, which could help with a <span class="Apple-tab-span" style="white-space:pre"> </span>breakthrough.</div><div><br /></div><div><span class="Apple-tab-span" style="white-space:pre"> </span><span class="Apple-style-span" style="color:#FF6600;">2. Identify the quantities </span></div><div><span class="Apple-style-span" style="color:#FF6600;"><span class="Apple-tab-span" style="white-space:pre"> </span><span class="Apple-style-span" style="color:#000000;">Determine and label, which quantities can change (variables) and which are constants?</span></span></div><div><span class="Apple-tab-span" style="white-space:pre"> </span>Again, keeping these organized is your road to success. </div><div><br /></div><div><span class="Apple-tab-span" style="white-space:pre"> </span><span class="Apple-style-span" style="color:#33FF33;">3. Algebra, Algebra, Algebra...</span></div><div><span class="Apple-tab-span" style="white-space:pre"> </span>Write your equation... remember what you learned in Algebra? You should!</div><div><br /></div><div><span class="Apple-tab-span" style="white-space:pre"> </span><span class="Apple-style-span" style="color:#00CCCC;">4. Calculus... your new friend</span></div><div><span class="Apple-style-span" style="color:#00CCCC;"><span class="Apple-tab-span" style="white-space:pre"> </span><span class="Apple-style-span" style="color:#000000;">Use your newly sharpened Calculus skills to differentiate the equation. This should be <span class="Apple-tab-span" style="white-space:pre"> </span>easy as pie... right?</span></span></div><div><br /></div><div><span class="Apple-style-span" style="color:#00CCCC;"><span class="Apple-style-span" style="color:#000000;"><span class="Apple-tab-span" style="white-space:pre"> </span><span class="Apple-style-span" style="color:#CC33CC;">5. Find the rates of change</span></span></span></div><div><span class="Apple-style-span" style="color:#00CCCC;"><span class="Apple-style-span" style="color:#000000;"><span class="Apple-tab-span" style="white-space:pre"> </span>Dissect the problem. Find out what quantities could be rates of change (I'm talking <span class="Apple-tab-span" style="white-space:pre"> </span>about units here!)</span></span></div><div><br /></div><div><span class="Apple-tab-span" style="white-space:pre"> </span><span class="Apple-style-span" style="color:#6600CC;">6. Substitute!</span></div><div><span class="Apple-tab-span" style="white-space:pre"> </span>Here comes the fun. Now you can work with your sweet equation to answer the <span class="Apple-tab-span" style="white-space:pre"> </span>problem.</div><div><br /></div><div><span class="Apple-style-span" style="color:#3366FF;">Wait! Don't forget... this was a word problem if I remember correctly. Which means......?</span></div><div><span class="Apple-style-span" style="color:#3366FF;"><br /></span></div><div><span class="Apple-style-span" style="color:#3366FF;">Answer in a complete sentence, with units of course. </span></div><div><span class="Apple-style-span" style="color:#3366FF;"><br /></span></div><div>This is a good <a href="http://oregonstate.edu/instruct/mth251/cq/Stage9/Practice/ratesProblems.html"><span class="Apple-style-span" style="color:#000000;">site</span></a> to practice... in case you feel you need to work on your skills.</div><div><br /></div><div>I know that this is the kind of problems we were doing last week, but just a little play by play to help anyone who is still confused out.</div><div><br /></div><div><span class="Apple-style-span" style=" white-space: pre; font-family:Arial, Helvetica, sans-serif;font-size:10px;"><object width="425" height="344"><param name="movie" value="http://www.youtube.com/v/8M11k0WPcMc&hl=en_US&fs=1&"><param name="allowFullScreen" value="true"><param name="allowscriptaccess" value="always"><embed src="http://www.youtube.com/v/8M11k0WPcMc&hl=en_US&fs=1&" type="application/x-shockwave-flash" allowscriptaccess="always" allowfullscreen="true" width="425" height="344"></embed></object></span></div><div><span class="Apple-style-span" style="font-family:Arial, Helvetica, sans-serif;font-size:85%;"><span class="Apple-style-span" style=" white-space: pre;font-size:10px;"><br /></span></span></div><div><span class="Apple-style-span" style="font-family:Arial, Helvetica, sans-serif;font-size:85%;"><span class="Apple-style-span" style=" white-space: pre;font-size:10px;"><br /></span></span></div><div><span class="Apple-style-span" style="font-family:Arial, Helvetica, sans-serif;"><span class="Apple-style-span" style=" white-space: pre;font-size:medium;">Don't forget the take home quiz assigned in class... all about Related Rates.</span></span></div><div><span class="Apple-style-span" style="font-family:Arial, Helvetica, sans-serif;"><span class="Apple-style-span" style=" white-space: pre;font-size:medium;"><br /></span></span></div><div><span class="Apple-style-span" style="font-family:Arial, Helvetica, sans-serif;"><span class="Apple-style-span" style=" white-space: pre;font-size:medium;">And we have a new final project about Related Rates coming up, so start brainstorming and coming up with fun creative ideas.</span></span></div><div><span class="Apple-style-span" style="font-family:Arial, Helvetica, sans-serif;"><span class="Apple-style-span" style=" white-space: pre;font-size:medium;"><br /></span></span></div><div><span class="Apple-style-span" style="font-family:Arial, Helvetica, sans-serif;"><span class="Apple-style-span" style=" white-space: pre;font-size:medium;">The next scribe will be Blitzen.</span></span></div><div><span class="Apple-style-span" style="font-family:Arial, Helvetica, sans-serif;"><span class="Apple-style-span" style=" white-space: pre;font-size:medium;"><br /></span></span></div><div><span class="Apple-style-span" style="font-family:Arial, Helvetica, sans-serif;"><span class="Apple-style-span" style="white-space: pre;"><span class="Apple-style-span" style=" white-space: normal; font-family:Georgia, serif;"><img src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgJT-U06tjns7WJk0TzBu8Ezo034k1IKMhh_VtsZ56wQrlsUsMntUvqdL8pwHQU8wxrZPYlllr0ulk2A0joBvfrwUaQViSTxMVn9GAC_zSMz_9xnOBHvlrMsF8M5r5MpxKegp5qPjIYNA4g/s320/skierdude.png" border="0" alt="" id="BLOGGER_PHOTO_ID_5441676514385455186" style="cursor: pointer; width: 78px; height: 79px; " /></span></span></span></div><div><span class="Apple-style-span" style="font-size: x-small;">http://www.timtim.com/public/images/drawings/large/Skier.gif</span></div><div><span class="Apple-style-span" style="font-family:Arial, Helvetica, sans-serif;"><span class="Apple-style-span" style=" white-space: pre;font-size:medium;">-Skirdude-</span></span></div><div><span class="Apple-style-span" style="font-family:Arial, Helvetica, sans-serif;font-size:85%;"><span class="Apple-style-span" style=" white-space: pre;font-size:10px;"><br /></span></span></div>skirdudehttp://www.blogger.com/profile/11691533567526109072noreply@blogger.com9