document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1119329>Question 1119329</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A Ferris wheel with a diameter of 59 meters rotates at a rate of 3 minutes per revolution. Riders board the Ferris wheel 4 meters above the ground at the bottom of the wheel. A couple boards the Ferris wheel and the ride starts.\r<BR>\n" );
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document.write( "Write a formula for the height of the couple t seconds after the ride begins.<BR>\n" );
document.write( "How many seconds after the ride starts will the couple be 18 meters above the ground for the second time? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #734838 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=734838\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "The diameter is 59 meters and the bottom is 4 meters off the ground, so the center of the circle is at 29.5 + 4 = 33.5 meters.  The amplitude of the sinusoidal variation is the radius, 29.5.  The period of revolution is 3 minutes, and one revolution is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 2\pi\"> radians.  So the radian measure of the rotation of the wheel at time <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large t\"> is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{2}{3}\pi{t}\">.  The measurement of the height starts at one of the extremes, hence the cosine is the correct model.  Further, since it starts at the low extreme point, the opposite of the cosine must be used.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ h(t)\ =\ -29.5\cos\(\frac{2}{3}\pi{t}\)\ +\ 33.5\">\r<BR>\n" );
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document.write( "The first time that the riders reach 18 meters is before they reach the maximum height of 63 meters at time 1.5 minutes.  The second time is between 1.5 minutes and the time they reach the low point again at 3 minutes.\r<BR>\n" );
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document.write( "Solve\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ -29.5\cos\(\frac{2}{3}\pi{t}\)\ +\ 33.5\ =\ 18\">\r<BR>\n" );
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document.write( "For <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large t\"> on the interval <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 1.5\ <\ t\ <\ 3.0\">\r<BR>\n" );
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document.write( "If you are using degrees instead of radians, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 1\text{ radian }=\ \frac{180}{\pi}\text{ degrees}\"><BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src=\"http://c0rk.blogs.com/gr0undzer0/darwin-fish.jpg\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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