document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1031362>Question 1031362</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1. the larger leg of a right triangle is 3cm longer than its smaller leg. The hypotenuse is 6 cm longer than the smaller leg. How many centimeters long is the smaller leg? \r<BR>\n" );
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document.write( "2. the function f(t)= -5t^2+20t+60 models the approximate height of an object t seconds after its launched. How many seconds does it take the object to hit the ground? \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 #646122 by </B><A HREF=/tutors/aboutme.mpl?userid=LinnW><B>LinnW(1048)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=LinnW><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=LinnW><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=646122\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. s = length of smaller leg<BR>\n" );
document.write( "l = larger leg<BR>\n" );
document.write( "h = hypotenuse<BR>\n" );
document.write( "l = s + 3<BR>\n" );
document.write( "h = s + 6<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%5E2+%2B+l%5E2+=+h%5E2 ALIGN=MIDDLE  ALT=\"s%5E2+%2B+l%5E2+=+h%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "substituting<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%5E2+%2B+%28s%2B3%29%5E2+=+%28s%2B6%29%5E2 ALIGN=MIDDLE  ALT=\"s%5E2+%2B+%28s%2B3%29%5E2+=+%28s%2B6%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "s^2 + s^2 + 6s + 9 = s^2 + 12s + 36<BR>\n" );
document.write( "add -s^2 to each side<BR>\n" );
document.write( "s^2 + 6s + 9 = 12s + 36<BR>\n" );
document.write( "add -12s to each side<BR>\n" );
document.write( "s^2 - 6s + 9 = 36<BR>\n" );
document.write( "add -36 to each side<BR>\n" );
document.write( "s^2 - 6s - 27 = 0<BR>\n" );
document.write( "(s - 9)(s + 3) = 0<BR>\n" );
document.write( "So s = 9 , s cannot be -3 since this would be a negative length.<BR>\n" );
document.write( "2. <BR>\n" );
document.write( "f(t)= -5t^2+20t+60<BR>\n" );
document.write( "We want to find the values for t where f(t) = 0 .<BR>\n" );
document.write( "0 = -5t^2+20t+60<BR>\n" );
document.write( "divide each side by -5<BR>\n" );
document.write( "0 = t^2 - 4t - 12<BR>\n" );
document.write( "0 = (t - 6)(t + 2)<BR>\n" );
document.write( "So t = 6.  t = -2 does not work since we cannot have negative time.<BR>\n" );
document.write( "Confirm by substituting in our original equation.<BR>\n" );
document.write( "0 = -5(6)^2+20(6)+60<BR>\n" );
document.write( "0 = -5(36)+20(6)+60<BR>\n" );
document.write( "0 = -180 +120 + 60<BR>\n" );
document.write( "0 = 0<BR>\n" );
document.write( "So it checks out.<BR>\n" );
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