document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1141816>Question 1141816</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Eric is riding a Ferris wheel. The wheel makes 1 revolution every 48 seconds. The wheel has a diameter of 60 feet. Eric stars the ride at the bottom, 3 feet above the ground.<BR>\n" );
document.write( "A)  write down a function for Eric’s height after x seconds.<BR>\n" );
document.write( "B) If the full ride last 4 minutes, how many times does it go around?<BR>\n" );
document.write( "C) List all of the times that Eric is 18 feet above the ground. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #762453 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=762453\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the equation that i get is:\r<BR>\n" );
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document.write( "y = 30 * sine (7.5 * (x - 12)) + 33.\r<BR>\n" );
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document.write( "this is based on the general equation of y = a * sine (b * (x - c)) + d\r<BR>\n" );
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document.write( "a is the amplitude which is equal to plus or minus the distance from the center line of the sine wave.\r<BR>\n" );
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document.write( "since the diameter is 60, the radius is 30, and the amplitude is therefore 30.\r<BR>\n" );
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document.write( "b = the frequency.\r<BR>\n" );
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document.write( "the formula for frequency is f = 360 / p.\r<BR>\n" );
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document.write( "f is the frequency.<BR>\n" );
document.write( "p is the period.\r<BR>\n" );
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document.write( "since the period is 48, the formula becomes f = 360 / 48 = 7.5.\r<BR>\n" );
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document.write( "what this says is there are 7.5 complete cycles of the sine wave in 360 degrees.\r<BR>\n" );
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document.write( "the formula for period is p = 360 / f.\r<BR>\n" );
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document.write( "360 / 7.5 = 48 for the period.\r<BR>\n" );
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document.write( "c = the horizontal shift.\r<BR>\n" );
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document.write( "since the sine wave normally starts at the center line, we need to shift the sine wave so that it starts at the bottom of the cycle.\r<BR>\n" );
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document.write( "if you graphed y = 30 * sine (7.5 * x), you would have seen that the sine wave hits bottom at -12 degrees.\r<BR>\n" );
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document.write( "we need to shift it to the right to that the value of the sine wave at 0 degrees is the same as the sine wave at - 12 degrees.\r<BR>\n" );
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document.write( "therefore, the value of c is equal to 12, and the formula becomes y = 30 * sine (7.5 * (x - 12)).\r<BR>\n" );
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document.write( "finally, the bottom of the sine wave needs to be 3 feet above the ground.\r<BR>\n" );
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document.write( "the ground is the x-axis, therefore d must be equal to 33, so that the bottom of the sine wave stops at 3 units above the x-axis.\r<BR>\n" );
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document.write( "the final equation is y = 30 * sine (7.5 * (x - 12)) + 33.\r<BR>\n" );
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document.write( "this is what the graph looks like.\r<BR>\n" );
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document.write( "any questions, write to dtheophilis@gmail.com.\r<BR>\n" );
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