document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1208738>Question 1208738</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A circular pool measures 10 feet across. One cubic yard of concrete is to be used to create a circular border of uniform width around the pool. If the border is to have a depth of 3 inches. How wide should the border be? \r<BR>\n" );
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document.write( "Note: 1 cubic yard = 27 cubic feet\r<BR>\n" );
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document.write( "Let me see.\r<BR>\n" );
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document.write( "I need A =  πr^2.\r<BR>\n" );
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document.write( "I need the area of the pool.\r<BR>\n" );
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document.write( "A = π(5)^2\r<BR>\n" );
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document.write( "A = 25π ft^2\r<BR>\n" );
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document.write( "I need to find the total area including the border.\r<BR>\n" );
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document.write( "A = π(x + 5)^2\r<BR>\n" );
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document.write( "A = π(x^2 + 10x + 25)\r<BR>\n" );
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document.write( "A πx^2 + 10πx + 25π ft^2\r<BR>\n" );
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document.write( "Area of border = volume ÷ depth.\r<BR>\n" );
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document.write( "The depth is given in inches. I must concert to feet.\r<BR>\n" );
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document.write( "Let me see\r<BR>\n" );
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document.write( "3 inches of a foot = 3/12 = 1/4 feet.\r<BR>\n" );
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document.write( "Area of border = 27 feet ÷ (1/4) feet\r<BR>\n" );
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document.write( "Area of border = 108 feet^2.\r<BR>\n" );
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document.write( "Stuck here....\r<BR>\n" );
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document.write( "You say?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #847155 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=847155\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "x = width of the border walkway in feet<BR>\n" );
document.write( "x > 0\r<BR>\n" );
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document.write( "The circular pool has diameter 10 feet. <BR>\n" );
document.write( "That cuts in half to 5 feet which is the radius.<BR>\n" );
document.write( "A = area of the pool only<BR>\n" );
document.write( "A = pi*r^2 = pi*5^2 = 25pi square feet<BR>\n" );
document.write( "B = combined area of the pool and walkway <BR>\n" );
document.write( "B = pi*r^2 = pi*(x+5)^2 = pi*(x^2+10x+25) square feet\r<BR>\n" );
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document.write( "C = area of just the walkway only<BR>\n" );
document.write( "C = B - A<BR>\n" );
document.write( "C = pi*(x^2+10x+25) - pi*25<BR>\n" );
document.write( "C = pi*(x^2+10x+25 - 25)<BR>\n" );
document.write( "C = pi*(x^2+10x)\r<BR>\n" );
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document.write( "Multiplying the walkway's area with its height gives the volume of this concrete ring.<BR>\n" );
document.write( "volume = area*height<BR>\n" );
document.write( "27 cubic feet = pi*(x^2+10x)*(3/12 of a foot)<BR>\n" );
document.write( "27 = pi*(x^2+10x)*(0.25)<BR>\n" );
document.write( "0.25pi*x^2 + 2.5pi*x - 27 = 0\r<BR>\n" );
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document.write( "Use the quadratic formula to solve that equation. <BR>\n" );
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document.write( "Plug in a = 0.25pi, b = 2.5pi, c = -27<BR>\n" );
document.write( "I'll let the student do the scratch work.<BR>\n" );
document.write( "An alternative approach is to use a graphing calculator like a TI83, <a  rel=nofollow HREF=\"https://www.geogebra.org/calculator\">GeoGebra</a> or <a  rel=nofollow HREF=\"https://www.desmos.com/calculator\">Desmos</a> (to name a few options).\r<BR>\n" );
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document.write( "When solving 0.25pi*x^2+2.5pi*x - 27 = 0, you should get these approximate solutions<BR>\n" );
document.write( "{x = -12.705678, x = 2.705678}<BR>\n" );
document.write( "I used the calculator's stored version of pi to get the most accuracy possible.\r<BR>\n" );
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document.write( "Ignore the negative result since a negative width makes no sense. <BR>\n" );
document.write( "Recall that x > 0.\r<BR>\n" );
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document.write( "Answer: 2.705678 feet approximately<BR>\n" );
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