document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=414069>Question 414069</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you please help me find the formulas to this word problems?\r<BR>\n" );
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document.write( "An old pump requires 6h longer to empty a pool than does a new pump. With both pumps working, the pool can be emptied in 4 h. find the time required for the new pump, working alone, to empty the pool.\r<BR>\n" );
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document.write( "The height s, in feet, of a rocket, after t seconds is given by the formula s(t) = 192t – 16t2. Find the maximum height of the rocket.\r<BR>\n" );
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document.write( "A courtyard at the corner of two buildings is to be enclosed using 100 ft of redwood fencing. Find the dimensions of the courtyard that will maximize the area.<BR>\n" );
document.write( "thank you very much </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #290426 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=290426\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> An old pump requires 6h longer to empty a pool than does a new pump. With both pumps working, the pool can be emptied in 4 h. find the time required for the new pump, working alone, to empty the pool. <BR>\n" );
document.write( "Let x= hours it takes new pump to empty pool<BR>\n" );
document.write( "then<BR>\n" );
document.write( "x+6 = hours for old pump<BR>\n" );
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document.write( "4(1/x + 1/(x_6)) = 1<BR>\n" );
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document.write( "The height s, in feet, of a rocket, after t seconds is given by the formula s(t) = 192t – 16t2. Find the maximum height of the rocket. <BR>\n" );
document.write( "s(t) = 192t – 16t^2<BR>\n" );
document.write( "s(t) = –16t^2 + 192t <BR>\n" );
document.write( "vertex is at maximum<BR>\n" );
document.write( "t = -b/(2a) = -192/(-32) = 6<BR>\n" );
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document.write( "max height = –16(6)^2 + 192(6)<BR>\n" );
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document.write( "A courtyard at the corner of two buildings is to be enclosed using 100 ft of redwood fencing. Find the dimensions of the courtyard that will maximize the area.<BR>\n" );
document.write( "Let x = width<BR>\n" );
document.write( "and y = length<BR>\n" );
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document.write( "from perimeter info:<BR>\n" );
document.write( "2(x+y) = 100 (equation 1)<BR>\n" );
document.write( "from area info:<BR>\n" );
document.write( "area = xy  (equation 2)<BR>\n" );
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document.write( "solving equation 1 for y:<BR>\n" );
document.write( "y = 50-x<BR>\n" );
document.write( "plug into equation 2:<BR>\n" );
document.write( "area =x(50-x)<BR>\n" );
document.write( "area = -x^2+50x<BR>\n" );
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document.write( "vertex gives max:<BR>\n" );
document.write( "max width = -b/(2a) = -50/(-2) = 25 feet<BR>\n" );
document.write( "max length = 50-25 = 25 feet\r<BR>\n" );
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