document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=59355>Question 59355</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find an equation relating the variables for each situation described.\r<BR>\n" );
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document.write( "(1) z varies directly as b, and z = 4 when b = 16\r<BR>\n" );
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document.write( "(2) s2 varies inversely as s1, and s2= -2 when s1 = 1/2\r<BR>\n" );
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document.write( "(3) y varies jointly as a and b, and y = -24 when a = 9 and b = -4\r<BR>\n" );
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document.write( "(4) m varies directly as n and inversely as p, and p = -3 and m = 1 and n = 1/2\r<BR>\n" );
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document.write( "(5) The cost of pipe is directly proportional to its length.  If 6 feet of pipe costs $40, find he cost of 10 feet of pipe.\r<BR>\n" );
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document.write( "(6) The intensity of light is inversely prorportional to the square of its distance from its origin. An intensity of 100 lumens is registered at a distance of 5 feet.  What is the intensity of light registered at a distance of 10 feet? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #40680 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=40680\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find an equation relating the variables for each situation described.<BR>\n" );
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document.write( "(1) z varies directly as b, and z = 4 when b = 16<BR>\n" );
document.write( "  \"z varies direclty as b\" -->> z=kb<BR>\n" );
document.write( "z=4 and b=16 find k:<BR>\n" );
document.write( "4=k(16)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F16=16k%2F16 ALIGN=MIDDLE  ALT=\"4%2F16=16k%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F4=k ALIGN=MIDDLE  ALT=\"1%2F4=k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substitute that into the first step:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28z=%281%2F4%29b%29 ALIGN=MIDDLE  ALT=\"highlight%28z=%281%2F4%29b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":\r<BR>\n" );
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document.write( "(2) s2 varies inversely as s1, and s2= -2 when s1 = 1/2<BR>\n" );
document.write( "\"s2 varies inversely as s1\" -->> s2=k/s1<BR>\n" );
document.write( "s2=-2 and s1=1/2 find k:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2=k%2F%281%2F2%29 ALIGN=MIDDLE  ALT=\"-2=k%2F%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%28-2%29=%281%2F2%29k%2F%281%2F2%29 ALIGN=MIDDLE  ALT=\"%281%2F2%29%28-2%29=%281%2F2%29k%2F%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1=k ALIGN=MIDDLE  ALT=\"-1=k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substitute that into the first step:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28s2=-1%2Fs1%29 ALIGN=MIDDLE  ALT=\"highlight%28s2=-1%2Fs1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "(3) y varies jointly as a and b, and y = -24 when a = 9 and b = -4<BR>\n" );
document.write( "\"y varies jointly as a and b\" -->> y=kab<BR>\n" );
document.write( "y=-24, a=9, and b=-4, find k<BR>\n" );
document.write( "-24=k(9)(-4)<BR>\n" );
document.write( "-24=-36k<BR>\n" );
document.write( "-24/-36=-36k/-36<BR>\n" );
document.write( "2/3=k<BR>\n" );
document.write( "Substitute that into the first step:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=%282%2F3%29ab%29 ALIGN=MIDDLE  ALT=\"highlight%28y=%282%2F3%29ab%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "(4) m varies directly as n and inversely as p, and p = -3 and m = 1 and n = 1/2<BR>\n" );
document.write( "\"m varies directly as n and inversely as p\" -->> m=kn/p<BR>\n" );
document.write( "p=-3, m=1, and n=1/2 find k<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1=k%281%2F2%29%2F-3 ALIGN=MIDDLE  ALT=\"1=k%281%2F2%29%2F-3\"   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=-3k%281%2F2%29%2F-3 ALIGN=MIDDLE  ALT=\"-3%281%29=-3k%281%2F2%29%2F-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3=k%2F2 ALIGN=MIDDLE  ALT=\"-3=k%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28-3%29=2k%2F2 ALIGN=MIDDLE  ALT=\"2%28-3%29=2k%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6=k ALIGN=MIDDLE  ALT=\"-6=k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substitute that into step 1:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28m=-6n%2Fp%29 ALIGN=MIDDLE  ALT=\"highlight%28m=-6n%2Fp%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "(5) The cost of pipe is directly proportional to its length.  If 6 feet of pipe costs $40, find the cost of 10 feet of pipe.<BR>\n" );
document.write( "Let cost be:C  and Length be:L<BR>\n" );
document.write( "\"cost is directly proportional to length\" -->> C=kL<BR>\n" );
document.write( "C=40, L=6, find k:<BR>\n" );
document.write( "40=k(6)<BR>\n" );
document.write( "40/6=6k/6<BR>\n" );
document.write( "6.667=k<BR>\n" );
document.write( "Substitute that into the first step: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=%286.667%29L ALIGN=MIDDLE  ALT=\"C=%286.667%29L\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Let L=10<BR>\n" );
document.write( "C=(6.667)(10)<BR>\n" );
document.write( "C=$66.67<BR>\n" );
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document.write( "(6) The intensity of light is inversely prorportional to the square of its distance from its origin. An intensity of 100 lumens is registered at a distance of 5 feet.  What is the intensity of light registered at a distance of 10 feet?<BR>\n" );
document.write( "Let intensity be:I and distance be:d<BR>\n" );
document.write( "\"intensity of light in inversely proportional to the square of its distance\" -->> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=I=k%2Fd%5E2 ALIGN=MIDDLE  ALT=\"I=k%2Fd%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I=100, d=5, find k<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100=k%2F%285%5E2%29 ALIGN=MIDDLE  ALT=\"100=k%2F%285%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100=k%2F25 ALIGN=MIDDLE  ALT=\"100=k%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25%28100%29=25k%2F25 ALIGN=MIDDLE  ALT=\"25%28100%29=25k%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2500=k ALIGN=MIDDLE  ALT=\"2500=k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substitute that into step 1:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=I=2500%2Fd%5E2 ALIGN=MIDDLE  ALT=\"I=2500%2Fd%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If d=10<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=I=2500%2F%2810%5E2%29 ALIGN=MIDDLE  ALT=\"I=2500%2F%2810%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=I=2500%2F100 ALIGN=MIDDLE  ALT=\"I=2500%2F100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I=25 lumens<BR>\n" );
document.write( "Happy Calculating!!! </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );