document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=68140>Question 68140</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For f(x)=1/x^2-2x-8, find the interval(s) where f(x)<0.\r<BR>\n" );
document.write( "\n" );
document.write( "Express the following statement as a formula with the value of the constant of proportionality determined with the given conditions: w varies directly as x and inversely as the square of y. If x=15 and y=5, then w=36.\r<BR>\n" );
document.write( "\n" );
document.write( "The electrical resistance R of a wire varies directly as its length L and inversely as the square of its diameter. A wire 20 meters long and 0.6 centimeters in diameter made from a certain alloy has a resistance of 36 ohms. What is the resistance of a piece of wire 60 meters long and 1.2 centimeters in diameter made from the same material?\r<BR>\n" );
document.write( "\n" );
document.write( "The period of a simple pendulum is directly proportional to the square root of its length. If a pendulum has a length of 6 feet and a period of 2 seconds, to what length should it be shortened to achieve a 1 swcond period?\r<BR>\n" );
document.write( "\n" );
document.write( "Thanks for asssiting me in studying for my final exam. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #48430 by </B><A HREF=/tutors/aboutme.mpl?userid=funmath><B>funmath(2933)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=funmath><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=48430\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For f(x)=1/x^2-2x-8, find the interval(s) where f(x)<0.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=1%2F%28x%5E2-2x-8%29 ALIGN=MIDDLE  ALT=\"f%28x%29=1%2F%28x%5E2-2x-8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=1%2F%28%28x-4%29%28x%2B2%29%29 ALIGN=MIDDLE  ALT=\"f%28x%29=1%2F%28%28x-4%29%28x%2B2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x-4=0 when x=4 and x+2=0 when x=-2<BR>\n" );
document.write( "So your possible intervals are (-infinity,-2), (-2,4), or (4, infinity)<BR>\n" );
document.write( "for (-infinity,-2) test -3<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-3%29=1%2F%28%28-3%29%5E2-2%28-3%29-8%29 ALIGN=MIDDLE  ALT=\"f%28-3%29=1%2F%28%28-3%29%5E2-2%28-3%29-8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-3%29=1%2F%289%2B6-8%29 ALIGN=MIDDLE  ALT=\"f%28-3%29=1%2F%289%2B6-8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-3%29=1%2F7 ALIGN=MIDDLE  ALT=\"f%28-3%29=1%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" > 1/7 is not <0 so reject this interval.<BR>\n" );
document.write( "for (-2,4) test 0<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%280%29=1%2F%280%5E2-2%280%29-8%29 ALIGN=MIDDLE  ALT=\"f%280%29=1%2F%280%5E2-2%280%29-8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%280%29=-1%2F8 ALIGN=MIDDLE  ALT=\"f%280%29=-1%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > -1/8 is <0 so accept this interval.<BR>\n" );
document.write( "for (4,infinity) test 5<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%285%29=1%2F%285%5E2-2%285%29-8%29 ALIGN=MIDDLE  ALT=\"f%285%29=1%2F%285%5E2-2%285%29-8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%285%29=1%2F%2825-10-8%29 ALIGN=MIDDLE  ALT=\"f%285%29=1%2F%2825-10-8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%285%29=1%2F7 ALIGN=MIDDLE  ALT=\"f%285%29=1%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" > 1/7 is not <0 so reject this interval.<BR>\n" );
document.write( "Therefore the interval where f(x)<0 is (-2,4)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Express the following statement as a formula with the value of the constant of proportionality determined with the given conditions: w varies directly as x and inversely as the square of y. If x=15 and y=5, then w=36.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=kx%2Fy%5E2 ALIGN=MIDDLE  ALT=\"w=kx%2Fy%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36=k%2815%29%2F%285%29%5E2 ALIGN=MIDDLE  ALT=\"36=k%2815%29%2F%285%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36=15k%2F25 ALIGN=MIDDLE  ALT=\"36=15k%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36=3k%2F5 ALIGN=MIDDLE  ALT=\"36=3k%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2F3%29%2836%29=%285%2F3%29%283k%2F5%29 ALIGN=MIDDLE  ALT=\"%285%2F3%29%2836%29=%285%2F3%29%283k%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60=k ALIGN=MIDDLE  ALT=\"60=k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Therefore, the formula is: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28w=60x%2Fy%5E2%29 ALIGN=MIDDLE  ALT=\"highlight%28w=60x%2Fy%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "The electrical resistance R of a wire varies directly as its length L and inversely as the square of its diameter. A wire 20 meters long and 0.6 centimeters in diameter made from a certain alloy has a resistance of 36 ohms. What is the resistance of a piece of wire 60 meters long and 1.2 centimeters in diameter made from the same material?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R=kL%2Fd%5E2 ALIGN=MIDDLE  ALT=\"R=kL%2Fd%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Convert 20 m to cm's: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20m%2A100cm%2Fm=2000cm ALIGN=MIDDLE  ALT=\"20m%2A100cm%2Fm=2000cm\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36=k%282000cm%29%2F%28.6cm%29 ALIGN=MIDDLE  ALT=\"36=k%282000cm%29%2F%28.6cm%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36%2A.6%2F2000=2000k%2F.6%2A%28.6%2F2000%29 ALIGN=MIDDLE  ALT=\"36%2A.6%2F2000=2000k%2F.6%2A%28.6%2F2000%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.0108=k ALIGN=MIDDLE  ALT=\".0108=k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R=.0108L%2Fd%5E2 ALIGN=MIDDLE  ALT=\"R=.0108L%2Fd%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "60m=6000cm<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R=.0108%286000cm%29%2F%281.2cm%29%5E2 ALIGN=MIDDLE  ALT=\"R=.0108%286000cm%29%2F%281.2cm%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28R=45%29 ALIGN=MIDDLE  ALT=\"highlight%28R=45%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ohms<BR>\n" );
document.write( ": <BR>\n" );
document.write( "The period of a simple pendulum is directly proportional to the square root of its length. If a pendulum has a length of 6 feet and a period of 2 seconds, to what length should it be shortened to achieve a 1 swcond period?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Period=T Length=L<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T=k%2Asqrt%28L%29 ALIGN=MIDDLE  ALT=\"T=k%2Asqrt%28L%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2=k%2Asqrt%286%29 ALIGN=MIDDLE  ALT=\"2=k%2Asqrt%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Fsqrt%286%29=k%2Asqrt%286%29%2Fsqrt%286%29 ALIGN=MIDDLE  ALT=\"2%2Fsqrt%286%29=k%2Asqrt%286%29%2Fsqrt%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Asqrt%286%29%2F%28sqrt%286%29%2Asqrt%286%29%29=k ALIGN=MIDDLE  ALT=\"2%2Asqrt%286%29%2F%28sqrt%286%29%2Asqrt%286%29%29=k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Asqrt%286%29%2F6=k ALIGN=MIDDLE  ALT=\"2%2Asqrt%286%29%2F6=k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%286%29%2F3=k ALIGN=MIDDLE  ALT=\"sqrt%286%29%2F3=k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T=sqrt%286L%29%2F3 ALIGN=MIDDLE  ALT=\"T=sqrt%286L%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1=sqrt%286L%29%2F3 ALIGN=MIDDLE  ALT=\"1=sqrt%286L%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%281%29=3sqrt%286L%29%2F3 ALIGN=MIDDLE  ALT=\"3%281%29=3sqrt%286L%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3=sqrt%286L%29 ALIGN=MIDDLE  ALT=\"3=sqrt%286L%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E2=%28sqrt%286L%29%29%5E2 ALIGN=MIDDLE  ALT=\"3%5E2=%28sqrt%286L%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9=6L ALIGN=MIDDLE  ALT=\"9=6L\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2F6=6L%2F6 ALIGN=MIDDLE  ALT=\"9%2F6=6L%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F2=L ALIGN=MIDDLE  ALT=\"3%2F2=L\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "L=1.5 ft<BR>\n" );
document.write( "Good Luck on Your Final!<BR>\n" );
document.write( "Happy Calculating!!!! </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );