document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1149303>Question 1149303</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A Ferris wheel is 45 meters in diameter and boarded from a platform that is 2 meters above the ground. The six o'clock position on the Ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 10 minutes. How many minutes of the ride are spent higher than 28 meters above the ground?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #770639 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13203)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=770639\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The height above the ground is a sinusoidal function.<br><BR>\n" );
document.write( "The minimum height is 2; the maximum height is 2+45 = 47; the midline is (2+47)/2 = 24.5.<br><BR>\n" );
document.write( "We can model a revolution of the Ferris wheel as starting at the loading platform, which is the minimum height of the ride; so we can model the height with a negative cosine function:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24.5-22.5%2Acos%28x%29 ALIGN=MIDDLE  ALT=\"24.5-22.5%2Acos%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "For this problem, we don't need to use the 10-minute rotation time of the Ferris wheel in our function; we can use a \"plain\" cosine function and simply determine what fraction of one revolution is spent above 28 feet.<br><BR>\n" );
document.write( "Here is a graph of a bit more than one period of the function, along with the constant function 28, showing the ride at its minimum height at 0 degrees of revolution and again at 360 degrees:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-60%2C420%2C-5%2C50%2C24.5-22.5%2Acos%28%28pi%2F180%29x%29%2C28%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-60%2C420%2C-5%2C50%2C24.5-22.5%2Acos%28%28pi%2F180%29x%29%2C28%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "To find the fraction of a period during which the height of the ride is above 28 feet, you can use a graphing calculator to find the points of intersection of the two graphs.<br><BR>\n" );
document.write( "Algebraically, you can find the two angles when the height of the ride is 28 feet by solving the equation<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24.5-22.5%2Acos%28x%29+=+28 ALIGN=MIDDLE  ALT=\"24.5-22.5%2Acos%28x%29+=+28\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-22.5%2Acos%28x%29+=+3.5 ALIGN=MIDDLE  ALT=\"-22.5%2Acos%28x%29+=+3.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28x%29+=+arccos%28-3.5%2F22.5%29 ALIGN=MIDDLE  ALT=\"cos%28x%29+=+arccos%28-3.5%2F22.5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "You can find those angles by either of those methods; I leave that to you.<br><BR>\n" );
document.write( "The final answer is that the ride is at or above 28 feet for approximately 162.1 degrees of every 360-degree revolution.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=162.1%2F360+=+0.450 ALIGN=MIDDLE  ALT=\"162.1%2F360+=+0.450\"   DISABLED_style= \"max-width:90%; height:auto;\" > to 3 decimal places.<br><BR>\n" );
document.write( "Then, since the period of revolution is 10 minutes, the ride is above 28 feet for 4.5 minutes each revolution.<br><BR>\n" );
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