document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209251>Question 1209251</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A Ferris wheel with a radius of 45 meters is elevated on a platform 5 meters above the ground. One full rotation takes 40 minutes. The height h(t) of a passenger is given by h(t) = 45sin(pi/20​t) + 50. What is the first time t (in minutes) when the height is 72.5 meters? </SPAN>\n" );
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document.write( "Let w = sin(pi*t/20​)\r<BR>\n" );
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document.write( "45sin(pi*t/20​) + 50 becomes 45w + 50\r<BR>\n" );
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document.write( "Solving 45w + 50 = 72.5 leads to w = 0.5 and it leads back to sin(pi*t/20​) = 0.5\r<BR>\n" );
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document.write( "If sin(x) = 0.5 in radian mode, then x = pi/6 and x = 5pi/6 are two possibilities when considering the interval <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+%3C=+x+%3C+2pi ALIGN=MIDDLE  ALT=\"0+%3C=+x+%3C+2pi\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is something to memorize since it comes up a lot in trig. Alternatives are to use a reference sheet, unit circle, or a calculator.<BR>\n" );
document.write( "We use the smaller of those x values since we're interested when the passenger reaches 72.5 meters the first time. If we changed \"first time\" to \"second time\", then we'd use 5pi/6 instead.\r<BR>\n" );
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document.write( "So,<BR>\n" );
document.write( "sin(pi*t/20​) = 0.5<BR>\n" );
document.write( "sin(pi*t/20​) = sin(pi/6)<BR>\n" );
document.write( "pi*t/20​ = pi/6<BR>\n" );
document.write( "t/20​ = 1/6<BR>\n" );
document.write( "t = (1/6)*20<BR>\n" );
document.write( "t = 20/6<BR>\n" );
document.write( "t = 10/3<BR>\n" );
document.write( "t = 3.3333... where the '3's go on forever<BR>\n" );
document.write( "This is the number of minutes it takes to arrive at the first instance of being 72.5 meters above the ground.<BR>\n" );
document.write( "Round that decimal value however your teacher instructs.<BR>\n" );
document.write( "Or you can stick with the fraction form.\r<BR>\n" );
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document.write( "Extra info:<BR>\n" );
document.write( "(10/3) minutes = (10/3)*60 = 200 seconds<BR>\n" );
document.write( "200 seconds = 180 seconds + 20 seconds = 3 minutes + 20 seconds<BR>\n" );
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