document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=92889>Question 92889</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I'm really glad you're here.  Math is just not my thing, obviously, but I'm glad its yours. Here it is:\r<BR>\n" );
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document.write( "1.  The approximate distance it takes to stop a car, based on the speed the car is traveling, is given in the following chart:\r<BR>\n" );
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document.write( "Miles per Hour           Stopping Distance (ft)\r<BR>\n" );
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document.write( "      25                           62<BR>\n" );
document.write( "      35                          106<BR>\n" );
document.write( "      45                          161<BR>\n" );
document.write( "      50                          195<BR>\n" );
document.write( "      55                          228<BR>\n" );
document.write( "      65                          306\r<BR>\n" );
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document.write( "a.  Find the quadratic function based on the stopping distance for 55 mph and 65 mph and the fact that at 0 mph the stopping distance is 0 feet.\r<BR>\n" );
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document.write( "b.  Use that equation to predict the stopping distance for 55 mph and 65 mph and compare them with the distances given in the chart.<BR>\n" );
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document.write( "c.  If the equation continues to be valid for higher speeds, how many feet would it take to stop a drag racer that reaches a speed of 230 mph?\r<BR>\n" );
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document.write( "Thanks so much for your help!  Let me know if you or someone else knows trig or calculus...that not my cup of tea either.\r<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 #67587 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=67587\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1.  The approximate distance it takes to stop a car, based on the speed the car is traveling, is given in the following chart:\r<BR>\n" );
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document.write( "Miles per Hour           Stopping Distance (ft)\r<BR>\n" );
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document.write( "      25                           62<BR>\n" );
document.write( "      35                          106<BR>\n" );
document.write( "      45                          161<BR>\n" );
document.write( "      50                          195<BR>\n" );
document.write( "      55                          228<BR>\n" );
document.write( "      65                          306\r<BR>\n" );
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document.write( "a.  Find the quadratic function based on the stopping distance for 55 mph and 65 mph and the fact that at 0 mph the stopping distance is 0 feet.<BR>\n" );
document.write( "You have two points: (55,228) and (65,306)<BR>\n" );
document.write( "You are told the intercept is 0<BR>\n" );
document.write( "EQUATION Form: y = ax^2+bx+c <BR>\n" );
document.write( "You have three points so you have three equations:<BR>\n" );
document.write( "0 =  0^2a + 0b + c   ;;;So c=0<BR>\n" );
document.write( "228 =55^2a + 55b +0 <BR>\n" );
document.write( "306 =65^2a + 65b + 0<BR>\n" );
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document.write( "Now you have two equations with two unknowns so solve for a and for b:<BR>\n" );
document.write( "Comment: I'm going to use a calculator matrix method to speed this up:<BR>\n" );
document.write( "a = 0.0562237762 and b = 1.053146853<BR>\n" );
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document.write( "So the EQUATION: f(x) =  0.056237762x^2+ 1.053146853x<BR>\n" );
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document.write( "b.  Use that equation to predict the stopping distance for 55 mph and 65 mph and compare them with the distances given in the chart<BR>\n" );
document.write( "st.dis.= f(55) = 228.04 ft<BR>\n" );
document.write( "st.dis.= f(65) = 306.06 ft.<BR>\n" );
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document.write( "c.  If the equation continues to be valid for higher speeds, how many feet would it take to stop a drag racer that reaches a speed of 230 mph?<BR>\n" );
document.write( "st.dis =f(230) = 3217.2 ft <BR>\n" );
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document.write( "Thanks so much for your help!  Let me know if you or someone else knows trig or calculus...that not my cup of tea either. <BR>\n" );
document.write( "I suggest you post your problems.  I'm sure amoung the 600 responders someone<BR>\n" );
document.write( "knows trig and/or calculus.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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