document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1097414>Question 1097414</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The stopping distance d of a car after the brakes are applied varies directly as the square of the speed r. If a car traveling 50 mph can stop in 110 &#8203;ft, how many feet will it take the same car to stop when it is traveling 100 &#8203;mph?  It will take how many feet?  Please give exact answer!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #711846 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=711846\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> When a variable (like braking distance, d, in feet)<BR>\n" );
document.write( "varies directly with some other variable (like the square of the speed, with r=speed measured in mph),<BR>\n" );
document.write( "as one variable changes by a factor, so does the other.<BR>\n" );
document.write( "As the speed doubles, from 50 mph to 110 mph,<BR>\n" );
document.write( "the square of the speed quadruples.<BR>\n" );
document.write( "It changes from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50%5E2=2500 ALIGN=MIDDLE  ALT=\"50%5E2=2500\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100%5E2=10000 ALIGN=MIDDLE  ALT=\"100%5E2=10000\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "but we do not need to calculate to know<BR>\n" );
document.write( "that when one number doubles its square quadruples.<BR>\n" );
document.write( "The square of the speed quadrupled,<BR>\n" );
document.write( "and so does the breaking distance,<BR>\n" );
document.write( "from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=110ft ALIGN=MIDDLE  ALT=\"110ft\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2A%28110ft%29=highlight%28440ft%29 ALIGN=MIDDLE  ALT=\"4%2A%28110ft%29=highlight%28440ft%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Easy mental math.<BR>\n" );
document.write( " <BR>\n" );
document.write( "If you were asked to write it as a function,<BR>\n" );
document.write( "you would define <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" > as a positive constant,<BR>\n" );
document.write( "say that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=k%2Ar%5E2 ALIGN=MIDDLE  ALT=\"d=k%2Ar%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and substituting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=110 ALIGN=MIDDLE  ALT=\"110\"   DISABLED_style= \"max-width:90%; height:auto;\" > for the distance and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50 ALIGN=MIDDLE  ALT=\"50\"   DISABLED_style= \"max-width:90%; height:auto;\" > for the speed,<BR>\n" );
document.write( "you would find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" > :<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=110=k%2A50%5E2 ALIGN=MIDDLE  ALT=\"110=k%2A50%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=110=k%2A2500 ALIGN=MIDDLE  ALT=\"110=k%2A2500\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=110%2F2500=k ALIGN=MIDDLE  ALT=\"110%2F2500=k\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=0.044 ALIGN=MIDDLE  ALT=\"k=0.044\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Then, the function,would be<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=0.044%2Ar%5E2 ALIGN=MIDDLE  ALT=\"d=0.044%2Ar%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Then, you could use that function,<BR>\n" );
document.write( "substituting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100 ALIGN=MIDDLE  ALT=\"100\"   DISABLED_style= \"max-width:90%; height:auto;\" > for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "to calculate the answer as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=0.044%2A100%5E2=0.044%2A10000=440 ALIGN=MIDDLE  ALT=\"d=0.044%2A100%5E2=0.044%2A10000=440\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "That would require a lot more writing and calculating. </SPAN>\n" );
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