document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1091300>Question 1091300</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 12.	Kevin is riding a mini Ferris wheel. He reaches the maximum height of 9m at 5s and then reaches the minimum height of 1m at 65s. 					<BR>\n" );
document.write( "a.	What is the period (the length of time to complete one cycle)? 				             b.	What is the radius of the wheel? 								             <BR>\n" );
document.write( "c.	Use the information given to sketch one cycle of the function. Label the graph.   <BR>\n" );
document.write( "d.the corresponding cosine equation<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #705892 by </B><A HREF=/tutors/aboutme.mpl?userid=htmentor><B>htmentor(1343)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=htmentor><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=htmentor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=705892\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a. He completes a half-cycle, from maximum to minimum height in 65 - 5 = 60s<BR>\n" );
document.write( "Therefore the time to complete a full cycle, T = 120s<BR>\n" );
document.write( "b. The diameter of the wheel is the max. height minus the min. height = 9 - 1 = 8m<BR>\n" );
document.write( "Therefore the radius = 4m.<BR>\n" );
document.write( "c. I'll leave this to you<BR>\n" );
document.write( "d. The height at a time t can be modeled as:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28t%29+=+R%2A%28cos%282pi%2FT%2At+-+phi%29%29+%2B+h0 ALIGN=MIDDLE  ALT=\"h%28t%29+=+R%2A%28cos%282pi%2FT%2At+-+phi%29%29+%2B+h0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <BR>\n" );
document.write( "where R is the radius of the wheel, T is the period, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=phi ALIGN=MIDDLE  ALT=\"phi\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the phase angle, and h0 is the height of the center of the wheel, i.e. the axis.<BR>\n" );
document.write( "The height at any time t oscillates about the center height, h0 = 5, with an amplitude R = 4.<BR>\n" );
document.write( "To find the phase angle, we note that the maximum height occurs at t = 5, <BR>\n" );
document.write( "which means <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28pi%2F60%2A5-phi%29+=+1+-%3E+pi%2F60%2A5-phi+=+0+-%3E+phi+=+pi%2F12 ALIGN=MIDDLE  ALT=\"cos%28pi%2F60%2A5-phi%29+=+1+-%3E+pi%2F60%2A5-phi+=+0+-%3E+phi+=+pi%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Putting it all together, the equation for the h(t) as a function of t is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28t%29+=+4cos%28pi%2F60%2At+-+pi%2F12%29+%2B+5 ALIGN=MIDDLE  ALT=\"h%28t%29+=+4cos%28pi%2F60%2At+-+pi%2F12%29+%2B+5\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );