document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=171926>Question 171926</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A bakery sells cheesecakes having diameters 6 in, 8 in, 10 in; all the same height. Suppose that they cost $8, $12, and $20 respectively.\r<BR>\n" );
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document.write( "A. Which size gives you the most cheesecake per dollar?<BR>\n" );
document.write( "please explain.\r<BR>\n" );
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document.write( "B. Find a quadratic equation that models how the ocst of a cheesecake varies with diameter.\r<BR>\n" );
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document.write( "I would appreciate any help I can get.<BR>\n" );
document.write( "Please help soon! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #127027 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=127027\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A bakery sells cheesecakes having diameters 6 in, 8 in, 10 in; all the same height. Suppose that they cost $8, $12, and $20 respectively. <BR>\n" );
document.write( "A. Which size gives you the most cheesecake per dollar?<BR>\n" );
document.write( "please explain.<BR>\n" );
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document.write( "The volume of each pie is (pi)r^2h; pi and h are the same for each pie<BR>\n" );
document.write( "so the volume depends on r^2 for each pie<BR>\n" );
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document.write( "The 6\" has r^2 = 9 and the cost is (9/8)pih = 1.125 pih/dollar<BR>\n" );
document.write( "The 8\" has r^2 = 16 and the cost is (16/12)pih = 1.3333..pih/dollar<BR>\n" );
document.write( "The 10\" has r^2 = 25 and the cost is (25/20pih = 1.25 pih/dollar<BR>\n" );
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document.write( "So the best buy is the 8\" pie which gives you more volume per dollar<BR>\n" );
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document.write( "B. Find a quadratic equation that models how the cost of a cheesecake varies <BR>\n" );
document.write( "You have three points: (6,8), (8,12), (10,20)<BR>\n" );
document.write( "The quadratic form is ax^2 + bx + c = y<BR>\n" );
document.write( "Substitute to get three equations in a,b, and c<BR>\n" );
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document.write( "36a + 6b + c = 8<BR>\n" );
document.write( "64a + 8b + c = 12<BR>\n" );
document.write( "100a + 10b +c = 20<BR>\n" );
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document.write( "Solve by any method you know to get:<BR>\n" );
document.write( "a = 1/2<BR>\n" );
document.write( "b = -5<BR>\n" );
document.write( "c = 20<BR>\n" );
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document.write( "Equations: <BR>\n" );
document.write( "y = (1/2)x^2 -5x + 20<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
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