// (c) Link-Systems International, Inc. (1999)
parent.chld=false;function makedb()
{parent.mkdb=false;var ch=1;var ss=new Array();var tp,to,tq,ts,ta,th,tw,tl,st,np;var NA="";tp=new Array();tv=new Array();ts=new Array(3,20);tv[0]=new parent.Val("I",ts);ts=new Array("V.0+1",25);tv[1]=new parent.Val("I",ts);ts=new Array(1,10);tv[2]=new parent.Val("I",ts);ts=new Array(1,10);tv[3]=new parent.Val("I",ts);ts=new Array("V.2*Math.abs(V.0-V.1)",NA);tv[4]=new parent.Val("I",ts);ts=new Array("V.3*Math.abs(V.0-V.1)",NA);tv[5]=new parent.Val("I",ts);ts=new Array("a,b,c,d,f,m,n,r,q,p,w,x,y,z",NA);tv[6]=new parent.Val("L.14",ts);ts=new Array("V.0-V.1",NA);tv[7]=new parent.Val("I",ts);ts=new Array("V.4+V.5",NA);tv[8]=new parent.Val("I",ts);ts=new Array("V.8/V.7",NA);tv[9]=new parent.Val("I",ts);
tq="If V.0V.6 - V.4 = V.5 + V.1V.6, what does V.6 equal?";th="chap1/sect1/prob1/hint.gif";tw="V.0V.6 - V.4 = V.5 + V.1V.6.<br><br> Adding V.4 "+"to both sides gives:<br> V.0V.6 = V.4 + V.5 + V.1V.6.<br><br> "+"Subtracting V.1V.6 from both sides "+"yields:<br> V.0V.6 - V.1V.6 = V.4 + V.5.<br><br> "+"Simplifying both sides:<br> V.7V.6 = V.8.<br><br> "+"Dividing both sides by (V.7) gives:<br> V.6 "+"= V.8 <img src=\"chars/div.gif\" align=bottom alt=\"div\"> "+"(V.7) = V.9. <p> (<i>See pages 75-77 "+"of your text for more details.)</i>";
ts=new Array("V.9",NA);ta=new parent.Val("I",ts);tp[0]=new parent.Problem("S",10,tv,0,NA,tq,ta,th,tw);tv=new Array();ts=new Array(1,9);tv[0]=new parent.Val("I",ts);ts=new Array(3,12);tv[1]=new parent.Val("I",ts);ts=new Array("V.0+1",12);tv[2]=new parent.Val("I",ts);ts=new Array(1,"V.1-1");tv[3]=new parent.Val("I",ts);ts=new Array(1,10);tv[4]=new parent.Val("I",ts);ts=new Array(1,10);tv[5]=new parent.Val("I",ts);ts=new Array("V.0-V.2-V.4",NA);tv[6]=new parent.Val("I",ts);ts=new Array("Math.abs(V.1*V.6)",NA);tv[7]=new parent.Val("I",ts);ts=new Array("Math.abs(V.3*V.6)",NA);tv[8]=new parent.Val("I",ts);ts=new Array("Math.abs(V.5*V.6)",NA);tv[9]=new parent.Val("I",ts);ts=new Array("V.0-V.2",NA);tv[10]=new parent.Val("I",ts);ts=new Array("V.7-V.8",NA);tv[11]=new parent.Val("I",ts);ts=new Array("V.9-V.11",NA);tv[12]=new parent.Val("I",ts);ts=new Array("V.10-V.4",NA);tv[13]=new parent.Val("I",ts);ts=new Array("V.12/V.13",NA);tv[14]=new parent.Val("R.2",ts);ts=new Array("V.4*V.14 + V.9",NA);tv[15]=new parent.Val("R.2",ts);
tq="Solve the following equation:<br> V.0r + V.7 - V.2r "+"- V.8 = V.4r + V.9<br> rounding your solution "+"to two decimal places.";th="chap1/sect1/prob2/hint.gif";tw="We are given<br> V.0r + V.7 - V.2r - V.8 = V.4r "+"+ V.9. <br><img src=\"chars/space.gif\" align=bottom "+"alt=\"space\"><br> Step 1 : Combine like terms<br> "+"(V.0 - V.2)r + (V.7 - V.8) = V.4r + V.9 "+"<br> V.10r + V.11 = V.4r + V.9. <br><img src=\"chars/space.gif\" "+"align=bottom alt=\"space\"><br> "+"Step 2: Addition property<br> subtract V.11 from "+"both sides <br> V.10r + V.11 - V.11 = V.4r + V.9 "+"- V.11 <br> V.10r = V.4r + V.12 <br> subtract "+"V.4r from both sides <br> V.10r - V.4r = V.4r - "+"V.4r + V.12 <br> (V.10 - V.4)r = V.12<br> V.13r "+"= V.12. <br><img src=\"chars/space.gif\" align=bottom "+"alt=\"space\"><br> Step 3: Multiplication "+"property <br> Divide both sides by V.13<br> V.13r/V.13 "+"= V.12/V.13<br> r = V.14.<br><img src=\"chars/space.gif\" align=bottom alt=\"space\"><br> "+"Step 4: Checking the answer<br> V.0(V.14) + V.7 "+"- V.2(V.14) - V.8 = V.15 = V.4(V.14) + V.9<br> "+"so the solution checks out. <p> (<i>See pages 74-76 "+"of your text for more details.</i>)";
ts=new Array("V.14",NA);ta=new parent.Val("I",ts);tp[1]=new parent.Problem("S",16,tv,0,NA,tq,ta,th,tw);tv=new Array();ts=new Array("1,2,5,7,11,13",NA);tv[0]=new parent.Val("L.6",ts);ts=new Array("1,3,5,7,9",NA);tv[1]=new parent.Val("L.5",ts);ts=new Array("Math.abs(2*V.0-3*V.1)+1",30);tv[2]=new parent.Val("I",ts);ts=new Array("V.2%2==0?V.2+1:V.2",NA);tv[3]=new parent.Val("I",ts);ts=new Array("V.3%3==0?V.3+2:V.3",NA);tv[4]=new parent.Val("I",ts);ts=new Array(1,10);tv[5]=new parent.Val("I",ts);ts=new Array("0:V.0:3",NA);tv[6]=new parent.Val("M",ts);ts=new Array("0:V.1:2",NA);tv[7]=new parent.Val("M",ts);ts=new Array("0:V.4:6",NA);tv[8]=new parent.Val("M",ts);ts=new Array("0:2:2",NA);tv[9]=new parent.Val("M",ts);ts=new Array("0:3:3",NA);tv[10]=new parent.Val("M",ts);ts=new Array("2*V.0",NA);tv[11]=new parent.Val("I",ts);ts=new Array("3*V.1",NA);tv[12]=new parent.Val("I",ts);ts=new Array("V.11-V.12",NA);tv[13]=new parent.Val("I",ts);ts=new Array("V.13+V.4",NA);tv[14]=new parent.Val("I",ts);ts=new Array("-V.5*6",NA);tv[15]=new parent.Val("I",ts);ts=new Array("0:V.11:6",NA);tv[16]=new parent.Val("M",ts);ts=new Array("0:V.12:6",NA);tv[17]=new parent.Val("M",ts);ts=new Array("0:V.13:6",NA);tv[18]=new parent.Val("M",ts);ts=new Array("0:V.14:6",NA);tv[19]=new parent.Val("M",ts);ts=new Array("0:6:V.14",NA);tv[20]=new parent.Val("M",ts);ts=new Array("0:V.15:V.14",NA);tv[21]=new parent.Val("M",ts);ts=new Array("V.15/V.14",NA);tv[22]=new parent.Val("R.2",ts);ts=new Array("V.15/parent.gcd(V.15,V.14)",NA);tv[23]=new parent.Val("I",ts);ts=new Array("V.14/parent.gcd(V.15,V.14)",NA);tv[24]=new parent.Val("I",ts);ts=new Array("0:V.23:V.24",NA);tv[25]=new parent.Val("M",ts);ts=new Array("-1*V.4*V.23 - V.5*6*V.24",NA);tv[26]=new parent.Val("I",ts);ts=new Array("6*V.24",NA);tv[27]=new parent.Val("I",ts);ts=new Array("Math.abs(V.26)",NA);tv[28]=new parent.Val("I",ts);ts=new Array("V.26<0?'-':' '",NA);tv[29]=new parent.Val("SE",ts);ts=new Array("V.29:V.28:V.27",NA);tv[30]=new parent.Val("M",ts);
tq="Solve the equation<br> V.6x - V.7x = -V.8x - V.5<br> "+"(rounded to two decimal places).";th="chap1/sect1/prob3/hint.gif";tw="We\'re given<br> V.6x - V.7x = -V.8x - V.5<br><img "+"src=\"chars/space.gif\" align=bottom alt=\"space\"><br> "+"Step 1 : combine like terms<br> (V.6 "+"- V.7)x = -V.8x - V.5 <br> (V.9<img src=\"chars/times.gif\" "+"align=bottom alt=\"times\">V.6 - V.10<img "+"src=\"chars/times.gif\" align=bottom alt=\"times\">V.7)x "+"= -V.8x - V.5 <br> (V.16 - V.17)x "+"= -V.8x - V.5 <br> V.18x = -V.8x - V.5. <br><img "+"src=\"chars/space.gif\" align=bottom alt=\"space\"><br> "+"Step 2: Addition property<br> add -V.8x "+"to both sides <br> V.18x + V.8x = -V.8x + V.8x "+"- V.5 <br> V.19x = -V.5. <br><img src=\"chars/space.gif\" "+"align=bottom alt=\"space\"><br> Step "+"3: Multiplication property<br> multiply both sides "+"by V.20<br> V.20 <img src=\"chars/times.gif\" align=bottom alt=\"times\"> V.19x = -V.5 <img src=\"chars/times.gif\""+" align=bottom alt=\"times\"> "+"V.20 <br> x = V.21 = V.25 = V.22. <br><img src=\"chars/space.gif\""+" align=bottom alt=\"space\"><br> Step 4:Check your answer by plugging in V.22 "+"(or V.25) in for x <br> in the original equation.<br> "+"V.6(V.25) - V.7(V.25) = -V.8(V.25) - V.5<br> "+"V.30 = V.30<BR> so the solution satisfies "+"the equation. <p> (<i>See pages 74-76 of your text "+"for more details.</i>)";
ts=new Array("V.22",NA);ta=new parent.Val("R.2",ts);tp[2]=new parent.Problem("S",31,tv,0,NA,tq,ta,th,tw);tv=new Array();ts=new Array(2,5);tv[0]=new parent.Val("I",ts);ts=new Array(20,50);tv[1]=new parent.Val("I",ts);ts=new Array(5,15);tv[2]=new parent.Val("I",ts);ts=new Array("V.2-V.1",NA);tv[3]=new parent.Val("I",ts);ts=new Array("V.0+1",NA);tv[4]=new parent.Val("I",ts);ts=new Array("0:V.3:V.4",NA);tv[5]=new parent.Val("M",ts);ts=new Array("V.3/V.4",NA);tv[6]=new parent.Val("R.2",ts);
tq="Translate the following and solve for the number: "+"<br> V.0 times a number is added to V.1 giving "+"V.2 minus the number. <br> (rounded to two decimal "+"places)";th="chap1/sect1/prob4/hint.gif";tw="V.0 times a number is added to V.1 giving V.2 minus "+"the number translates to<br> V.1 + V.0 <img "+"src=\"chars/times.gif\" align=bottom alt=\"times\"> "+"n = V.2 - n. <br><img src=\"chars/space.gif\" "+"align=bottom alt=\"space\"><br> Subtract V.1 from "+"both sides to get <br> V.0 <img src=\"chars/times.gif\" "+"align=bottom alt=\"times\"> n = V.2 "+"- n - V.1. <br><img src=\"chars/space.gif\" align=bottom "+"alt=\"space\"><br> Add n to both sides "+"to get<br> V.4 <img src=\"chars/times.gif\" align=bottom "+"alt=\"times\"> n = V.3 to two decimal places.<br><img "+"src=\"chars/space.gif\" align=bottom "+"alt=\"space\"><br> Divide both sides by V.4 "+"to get <br> n = V.5 = V.6.<p> (<i>See pages 77-79 "+"of your text for more details.</i>)";
ts=new Array("V.6",NA);ta=new parent.Val("R.2",ts);tp[3]=new parent.Problem("S",7,tv,0,NA,tq,ta,th,tw);tv=new Array();ts=new Array(1,35);tv[0]=new parent.Val("I",ts);ts=new Array("3*V.0",NA);tv[1]=new parent.Val("I",ts);ts=new Array(NA,NA);tv[2]=new parent.Val("S",ts);ts=new Array(1,3);tv[3]=new parent.Val("I",ts);ts=new Array("V.3:twice, three times, four times",NA);tv[4]=new parent.Val("L.3",ts);ts=new Array("V.3:2,3,4",NA);tv[5]=new parent.Val("L.3",ts);ts=new Array("V.5 +1",NA);tv[6]=new parent.Val("I",ts);ts=new Array("0:1:V.6",NA);tv[7]=new parent.Val("M",ts);ts=new Array("0:V.1:V.6",NA);tv[8]=new parent.Val("M",ts);ts=new Array("V.1/V.6",NA);tv[9]=new parent.Val("R.2",ts);ts=new Array("V.1/V.5",NA);tv[10]=new parent.Val("R.2",ts);ts=new Array("V.6/V.1",NA);tv[11]=new parent.Val("R.2",ts);ts=new Array("V.5/V.1",NA);tv[12]=new parent.Val("R.2",ts);
tq="The process of building a new space station involved "+"cutting a V.1 foot solar panel into two pieces. "+"The first piece is V.4 as long as the second. "+"How long is the second piece? <br>(Please round "+"your answer to two decimal places.)";to=new Array();ts=new Array("V.10",NA);to[0]=new parent.Val("S",ts);ts=new Array("V.11",NA);to[1]=new parent.Val("S",ts);ts=new Array("V.12",NA);to[2]=new parent.Val("S",ts);ts=new Array("V.1",NA);to[3]=new parent.Val("S",ts);
th="chap1/sect1/prob5/hint.gif";tw="We want to find the length of the second piece,<br> "+"so we will make that our variable, call it s.<br> "+"The first piece, therefore is V.5 <img src=\"chars/times.gif\""+" align=bottom alt=\"times\"> "+"s. The total length of the panel is V.5 <img src=\"chars/times.gif\""+" align=bottom alt=\"times\"> s + s.<br><img src=\"chars/space.gif\" align=bottom "+"alt=\"space\"><br> Translate the problem into "+"an equation. <br> V.5 <img src=\"chars/times.gif\" "+"align=bottom alt=\"times\"> s + s = V.1.<br><img "+"src=\"chars/space.gif\" align=bottom alt=\"space\"><br> "+"Now, solve it. <br> (V.5 + 1)s = "+"V.1 <br> V.6s = V.1 <br> V.7<img src=\"chars/times.gif\" "+"align=bottom alt=\"times\">V.6s = V.1<img "+"src=\"chars/times.gif\" align=bottom alt=\"times\">V.7 "+"<br> s = V.8 = V.9. <br><img src=\"chars/space.gif\" "+"align=bottom alt=\"space\"><br> "+"So, in words, the length of the second panel is "+"V.9 feet long. <br><img src=\"chars/space.gif\" "+"align=bottom alt=\"space\"><br> To check it we get,"+" <br> (V.5 + 1)(V.8) = V.1 <br> so our answer "+"checks out. <p>(<i>See pages 77-79 of your text "+"for more details.</i>)";
ts=new Array("V.9",NA);ta=new parent.Val("S",ts);tp[4]=new parent.Problem("M",13,tv,4,to,tq,ta,th,tw);np=5;st="Section 2.1 &nbsp; Linear Equations and Applications";tl="help/sec2_1.html";ss[0]=new parent.Section(st,np,tp,tl,"sounds/sec2_1.wav","avi/sec2_1.avi");parent.hist[ch][0].max_questions=np;parent.hist[ch][0].title=st;
tp=new Array();tv=new Array();ts=new Array(-5,5);tv[0]=new parent.Val("I",ts);ts=new Array(-6,6);tv[1]=new parent.Val("I",ts);ts=new Array(2,6);tv[2]=new parent.Val("I",ts);ts=new Array(2,5);tv[3]=new parent.Val("I",ts);ts=new Array("V.3+1",NA);tv[4]=new parent.Val("I",ts);ts=new Array("V.2*V.0-V.3*V.1",NA);tv[5]=new parent.Val("I",ts);ts=new Array("V.0+V.4*V.1",NA);tv[6]=new parent.Val("I",ts);ts=new Array("parent.term('V.6','')",NA);tv[7]=new parent.Val("SE",ts);ts=new Array("-V.2*V.4",NA);tv[8]=new parent.Val("I",ts);ts=new Array("V.2*V.6",NA);tv[9]=new parent.Val("I",ts);ts=new Array("parent.term('V.9','')",NA);tv[10]=new parent.Val("SE",ts);ts=new Array("-V.9",NA);tv[11]=new parent.Val("I",ts);ts=new Array("parent.term('V.11','')",NA);tv[12]=new parent.Val("SE",ts);ts=new Array("V.8-V.3",NA);tv[13]=new parent.Val("I",ts);ts=new Array("V.5-V.9",NA);tv[14]=new parent.Val("I",ts);ts=new Array("Math.abs(V.14)",NA);tv[15]=new parent.Val("I",ts);ts=new Array("Math.abs(V.13)",NA);tv[16]=new parent.Val("I",ts);ts=new Array("((V.13<0&&V.14>0)||(V.13>0&&V.14<0))?'-':'0'",NA);tv[17]=new parent.Val("SE",ts);ts=new Array("V.17:V.15:V.16",NA);tv[18]=new parent.Val("M",ts);ts=new Array("-V.4*V.1",NA);tv[19]=new parent.Val("I",ts);ts=new Array("V.2*V.0",NA);tv[20]=new parent.Val("I",ts);ts=new Array("V.3*V.1",NA);tv[21]=new parent.Val("I",ts);ts=new Array("-4,-3,-2,-1,1,2,3,4",NA);tv[22]=new parent.Val("L.8",ts);ts=new Array("-4,-3,-2,-1,1,2,3,4",NA);tv[23]=new parent.Val("L.8",ts);ts=new Array("-4,-3,-2,-1,1,2,3,4",NA);tv[24]=new parent.Val("L.8",ts);ts=new Array("-4,-3,-2,-1,1,2,3,4",NA);tv[25]=new parent.Val("L.8",ts);ts=new Array("V.4*V.1",NA);tv[26]=new parent.Val("I",ts);ts=new Array("V.0+V.23",NA);tv[27]=new parent.Val("I",ts);ts=new Array("V.0+V.24",NA);tv[28]=new parent.Val("I",ts);ts=new Array("V.1+V.25",NA);tv[29]=new parent.Val("I",ts);ts=new Array("V.1+V.22",NA);tv[30]=new parent.Val("I",ts);tq="Solve the system of linear equations by the substitution "+"method.<br> V.2x - V.3y = V.5<br> x + V.4y "+"= V.6";
to=new Array();ts=new Array("(V.27,V.29)",NA);to[0]=new parent.Val("S",ts);ts=new Array("(V.28,V.30)",NA);to[1]=new parent.Val("S",ts);ts=new Array("(V.28,V.1)",NA);to[2]=new parent.Val("S",ts);ts=new Array("(V.0,V.29)",NA);to[3]=new parent.Val("S",ts);ts=new Array("(V.27,V.30)",NA);to[4]=new parent.Val("S",ts);
th="chap1/sect2/prob1/hint.gif";tw="To avoid fractions, solve the second equation for "+"x:<br> x + V.4y = V.6 => x = -V.4y V.7. <p><img "+"src=\"chars/space.gif\" align=bottom alt=\"space\"><p> "+"Substitute -V.4y V.7 for x in the first "+"equation:<br> V.2(-V.4y V.7) - V.3y = V.5<p><img "+"src=\"chars/space.gif\" align=bottom alt=\"space\"><p> "+"Simplify and solve this linear equation<br> "+"V.8y V.10 -V.3y = V.5 => V.8y -V.3y = V.5 V.12<p> "+"V.13y = V.14 => y = V.18 = V.1.<p><img src=\"chars/space.gif\""+" align=bottom alt=\"space\"><p> "+"Replace y with V.1<br> x = -V.4y V.7 = -V.4(V.1) "+"V.7 = V.19 V.7 = V.0.<p><img src=\"chars/space.gif\" "+"align=bottom alt=\"space\"><p> The solution "+"is (V.0, V.1).<p><img src=\"chars/space.gif\" "+"align=bottom alt=\"space\"><p> Checking solution:<br> "+"V.2x - V.3y = V.2(V.0) - V.3(V.1) = V.20 "+"- V.21 = V.5<br> x + V.4y = V.0 + V.4(V.1) = "+"V.0 + V.26 = V.6.<p><img src=\"chars/space.gif\" align=bottom alt=\"space\"><p> (<i>See pages 89-92 "+"of your text for more details.</i>)";
ts=new Array("(V.0,V.1)",NA);ta=new parent.Val("S",ts);tp[0]=new parent.Problem("M",31,tv,5,to,tq,ta,th,tw);tv=new Array();ts=new Array(-5,5);tv[0]=new parent.Val("I",ts);ts=new Array(1,5);tv[1]=new parent.Val("I",ts);ts=new Array(NA,NA);tv[2]=new parent.Val("S",ts);ts=new Array("V.0+V.1",NA);tv[3]=new parent.Val("I",ts);ts=new Array(2,6);tv[4]=new parent.Val("I",ts);ts=new Array("V.4+1",10);tv[5]=new parent.Val("I",ts);ts=new Array("3*V.4",NA);tv[6]=new parent.Val("I",ts);ts=new Array("-V.4*V.0+V.5*V.3",NA);tv[7]=new parent.Val("I",ts);ts=new Array("V.5*V.0-V.6*V.3",NA);tv[8]=new parent.Val("I",ts);ts=new Array("(V.7<0)?'-':'+'",NA);tv[9]=new parent.Val("SE",ts);ts=new Array(NA,NA);tv[10]=new parent.Val("S",ts);ts=new Array(NA,NA);tv[11]=new parent.Val("S",ts);ts=new Array("Math.abs(V.7)",NA);tv[12]=new parent.Val("I",ts);ts=new Array("V.9:V.12:V.5",NA);tv[13]=new parent.Val("M",ts);ts=new Array("0:V.4:V.5",NA);tv[14]=new parent.Val("M",ts);ts=new Array("V.6*V.4",NA);tv[15]=new parent.Val("I",ts);ts=new Array("V.6*V.7",NA);tv[16]=new parent.Val("I",ts);ts=new Array("0:V.15:V.5",NA);tv[17]=new parent.Val("M",ts);ts=new Array("(V.16<0)?'+':'-'",NA);tv[18]=new parent.Val("SE",ts);ts=new Array("Math.abs(V.16)",NA);tv[19]=new parent.Val("I",ts);ts=new Array("V.18:V.19:V.5",NA);tv[20]=new parent.Val("M",ts);ts=new Array("(V.16<0)?'-':'+'",NA);tv[21]=new parent.Val("SE",ts);ts=new Array("V.21:V.19:V.5",NA);tv[22]=new parent.Val("M",ts);ts=new Array("V.5*V.5",NA);tv[23]=new parent.Val("I",ts);ts=new Array("0:V.23-V.15:V.5",NA);tv[24]=new parent.Val("M",ts);ts=new Array("V.8*V.5",NA);tv[25]=new parent.Val("I",ts);ts=new Array("(V.16<0)?'-V.19':'+V.19'",NA);tv[26]=new parent.Val("SE",ts);ts=new Array("V.5*V.5-V.15",NA);tv[27]=new parent.Val("I",ts);ts=new Array("V.8*V.5+V.16",NA);tv[28]=new parent.Val("I",ts);ts=new Array("Math.abs(V.27)",NA);tv[29]=new parent.Val("I",ts);ts=new Array("Math.abs(V.28)",NA);tv[30]=new parent.Val("I",ts);ts=new Array("(V.27<0)?'-':'0'",NA);tv[31]=new parent.Val("SE",ts);
ts=new Array("(V.28<0)?'-':'0'",NA);tv[32]=new parent.Val("SE",ts);ts=new Array("V.31:V.29:V.5",NA);tv[33]=new parent.Val("M",ts);ts=new Array("V.32:V.30:V.5",NA);tv[34]=new parent.Val("M",ts);ts=new Array("0:V.25V.26:V.5",NA);tv[35]=new parent.Val("M",ts);ts=new Array("-V.4*V.0",NA);tv[36]=new parent.Val("I",ts);ts=new Array("(V.4*V.0<0)?'-':'0'",NA);tv[37]=new parent.Val("SE",ts);ts=new Array("Math.abs(V.4*V.0)",NA);tv[38]=new parent.Val("I",ts);ts=new Array("V.37:V.38:V.5",NA);tv[39]=new parent.Val("M",ts);ts=new Array("-V.36+V.7",NA);tv[40]=new parent.Val("I",ts);ts=new Array("(V.40<0)?'-':'0'",NA);tv[41]=new parent.Val("SE",ts);ts=new Array("Math.abs(V.40)",NA);tv[42]=new parent.Val("I",ts);ts=new Array("V.41:V.42:V.5",NA);tv[43]=new parent.Val("M",ts);ts=new Array("V.5*V.3",NA);tv[44]=new parent.Val("I",ts);ts=new Array("parent.term('V.44','')",NA);tv[45]=new parent.Val("SE",ts);ts=new Array("V.5*V.0",NA);tv[46]=new parent.Val("I",ts);ts=new Array("Math.abs(V.6*V.3)",NA);tv[47]=new parent.Val("I",ts);ts=new Array("(V.6*V.3<0)?'+V.47':'-V.47'",NA);tv[48]=new parent.Val("SE",ts);ts=new Array("-V.0",NA);tv[49]=new parent.Val("I",ts);ts=new Array("-V.3",NA);tv[50]=new parent.Val("I",ts);ts=new Array("V.0+2",NA);tv[51]=new parent.Val("I",ts);ts=new Array("V.3-1",NA);tv[52]=new parent.Val("I",ts);ts=new Array("0:V.34:V.33",NA);tv[53]=new parent.Val("M",ts);
tq="Solve the system of equations by the substitution "+"method.<br> -V.4x + V.5y = V.7<br> V.5x - V.6y "+"= V.8";to=new Array();ts=new Array("(V.49,V.50)",NA);to[0]=new parent.Val("S",ts);ts=new Array("(V.0,V.50)",NA);to[1]=new parent.Val("S",ts);ts=new Array("(V.51,V.3)",NA);to[2]=new parent.Val("S",ts);ts=new Array("(V.49,V.52)",NA);to[3]=new parent.Val("S",ts);ts=new Array("(V.51,V.52)",NA);to[4]=new parent.Val("S",ts);
th="chap1/sect2/prob2/hint.gif";tw="Solve one of the equations for one variables in<br> "+"terms of the other.<p><img src=\"chars/space.gif\" "+"align=bottom alt=\"space\"><p> Let\'s solve "+"the first equation for y:<br> -V.4x + V.5y = "+"V.7, V.5y = V.7 + V.4x<br> y = V.14x V.13.<p><img "+"src=\"chars/space.gif\" align=bottom alt=\"space\"><p> "+"Now, substitute V.14x V.13 for y in the "+"second equation:<br> V.5x - V.6 (V.14x V.13) = "+"V.8<br> V.5x - V.17x V.20 = V.8<br> (V.5 - V.17)x "+"= V.8 V.22<br> V.24x = V.35<br> V.33x = V.34<br> "+"x = V.53 = V.0.<p><img src=\"chars/space.gif\" "+"align=bottom alt=\"space\"><p> Now replace x with "+"V.0:<br> y = V.14x V.13 = V.14(V.0) V.13 =<br> "+"V.39 V.13 = V.43 = V.3.<br> The solution is (V.0,"+" V.3).<br> Checking the solution:<br> -V.4x "+"+ V.5y = -V.4 (V.0) + V.5 (V.3) = V.36 V.45 = V.7<br> "+"V.5x - V.6y = V.5 (V.0) - V.6 (V.3) = V.46 "+"V.48 = V.8.<p><img src=\"chars/space.gif\" align=bottom "+"alt=\"space\"><p> (<i>See pages 89-91 of "+"your text for more details.</i>)";
ts=new Array("(V.0,V.3)",NA);ta=new parent.Val("S",ts);tp[1]=new parent.Problem("M",54,tv,5,to,tq,ta,th,tw);tv=new Array();ts=new Array(1,10);tv[0]=new parent.Val("I",ts);ts=new Array(5,10);tv[1]=new parent.Val("I",ts);ts=new Array(1,2);tv[2]=new parent.Val("I",ts);ts=new Array(2,"V.1-1");tv[3]=new parent.Val("I",ts);ts=new Array("2*V.0*V.1*V.3*100",NA);tv[4]=new parent.Val("I",ts);ts=new Array(1,2);tv[5]=new parent.Val("I",ts);ts=new Array("V.5: airspeed of the plane, the wind speed",NA);tv[6]=new parent.Val("L.2",ts);ts=new Array("V.4/V.1",NA);tv[7]=new parent.Val("R.2",ts);ts=new Array("V.2:miles, kilometers",NA);tv[8]=new parent.Val("L.2",ts);ts=new Array("V.2:mph, kph",NA);tv[9]=new parent.Val("L.2",ts);ts=new Array("V.4/V.3",NA);tv[10]=new parent.Val("R.2",ts);ts=new Array("V.10-V.7",NA);tv[11]=new parent.Val("R.2",ts);ts=new Array("V.11/2",NA);tv[12]=new parent.Val("R.2",ts);ts=new Array("V.7+V.12",NA);tv[13]=new parent.Val("R.2",ts);ts=new Array("V.5: V.13,V.12",NA);tv[14]=new parent.Val("L.2",ts);
tq="Flying at a constant airspeed, a plane flies directly "+"into the wind for a distance of V.4 V.8 in "+"V.1 hours, and then returns at the same airspeed "+"in V.3 hours. Assuming that the wind speed was "+"the same and constant for both flights, what was "+"the V.6 (in V.9) during this round trip?";
th="chap1/sect2/prob3/hint.gif";tw="Let p = the airspeed of the plane<br> and w = the "+"wind speed.<p> We then have the system of equations<br> "+"V.1(p - w) = V.4 <br> V.3(p + w) = V.4.<p> "+"Let\'s take the first equation and solve for "+"p in terms of w.<br> V.1(p - w) = V.4<br> p - "+"w = V.4/V.1<br> p - w = V.7<br> p = w + V.7.<p> "+"Substituting this in for p in the second equation<br> "+"and solving for p we get:<br> V.3(p + w) = "+"V.4<br> V.3( w + V.7 + w) = V.4<br> 2w + V.7 = "+"V.4/V.3<br> 2w + V.7 = V.10<br> 2w = V.10 - V.7<br> "+"2w = V.11<br> w = V.11/2<br> w = V.12 V.9.<p> "+"We can now determine p by plugging this value "+"for w (in V.9)<br> into either or our original equations; "+"let\'s use the first.<br> V.1(p - w) = "+"V.4<br> V.1(p - V.12) = V.4<br> p - V.12 = V.4/V.1<br> "+"p - V.12 = V.7<br> p = V.7 + V.12.<br> p "+"= V.13 V.9.<p> Since we are asked for the V.6,<br> "+"the correct answer is V.14 V.9.<p> Don\'t forget "+"to check your work by plugging these values<br> "+"into the two original equations and making "+"sure that they<br> hold.<p> (<i>See pages 93-94 "+"of your text for more details.</i>)";
ts=new Array("V.14",NA);ta=new parent.Val("R.2",ts);tp[2]=new parent.Problem("S",15,tv,0,NA,tq,ta,th,tw);tv=new Array();ts=new Array("-.9","-.1");tv[0]=new parent.Val("R.1",ts);ts=new Array(".01",".09");tv[1]=new parent.Val("R.2",ts);ts=new Array(5,12);tv[2]=new parent.Val("I",ts);ts=new Array(2,"V.2-1");tv[3]=new parent.Val("I",ts);ts=new Array("Math.abs(V.0)",NA);tv[4]=new parent.Val("R.2",ts);ts=new Array("V.4+V.1",NA);tv[5]=new parent.Val("R.2",ts);ts=new Array("V.5*V.2",NA);tv[6]=new parent.Val("R.2",ts);ts=new Array("V.5*V.3",NA);tv[7]=new parent.Val("R.2",ts);ts=new Array(1,2);tv[8]=new parent.Val("I",ts);ts=new Array("V.8:price (in hundreds of dollars),quantity ",NA);tv[9]=new parent.Val("L.2",ts);ts=new Array("V.6-V.7",NA);tv[10]=new parent.Val("R.2",ts);ts=new Array("V.10/V.5",NA);tv[11]=new parent.Val("R.2",ts);ts=new Array("V.0*V.11+V.6",NA);tv[12]=new parent.Val("R.2",ts);ts=new Array("widgets,wagons,washing machines,wrecking balls,wine,"+"watches,weather vanes,welders,wheelchairs,whistles,"+"works of art",NA);tv[13]=new parent.Val("L.11",ts);ts=new Array("V.8: V.12,V.11",NA);tv[14]=new parent.Val("L.2",ts);
tq="A company that produces V.13 has the following price "+"demand and price supply equations (p=price in "+"hundreds of dollars, w=number of V.13).<br> p "+"= V.0w + V.6 <img src=\"chars/space.gif\" align=bottom "+"alt=\"space\"> (demand equation)<br> p = "+"V.1w + V.7 <img src=\"chars/space.gif\" align=bottom "+"alt=\"space\"> (supply equation)<br> What is "+"the equilibrium V.9?";
th="chap1/sect2/prob4/hint.gif";tw="We\'re given <br> p = V.0w + V.6 <img src=\"chars/space.gif\" "+"align=bottom alt=\"space\"> (demand "+"equation)<br> p = V.1w + V.7 <img src=\"chars/space.gif\" "+"align=bottom alt=\"space\"> (supply "+"equation).<p> Substituting the first equation into "+"the second for p and solving for w we get:<br> "+"p = V.1w + V.7<br> V.0w + V.6 = V.1w + V.7<br> "+"V.6 - V.7 = V.1w + V.4w<br> V.10 = V.5w<br> V.10/V.5 "+"= w<br> V.11 V.13 = w.<p> We can now determine "+"p by plugging this value for w <br> into either "+"or our original equations; let\'s use the first.<br> "+"p = V.0w + V.6<br> p = (V.0)(V.11) + V.6<br> "+"p = V.12 (hundreds of dollars).<p> Since "+"we are asked for the equilibrium V.9,<br> the correct "+"answer is V.14.<p> Don\'t forget to check "+"your work by plugging these values<br> into the "+"two original equations and making sure that they<br> "+"hold.<p> (<i>See pages 94-95 of your text for "+"more details.</i>)";
ts=new Array("V.14",NA);ta=new parent.Val("R.2",ts);tp[3]=new parent.Problem("S",15,tv,0,NA,tq,ta,th,tw);tv=new Array();ts=new Array(50,"99.99");tv[0]=new parent.Val("R.2*",ts);ts=new Array(10,"V.0-5");tv[1]=new parent.Val("R.2*",ts);ts=new Array(10,100);tv[2]=new parent.Val("I",ts);ts=new Array("(V.0-V.1)*V.2*100",NA);tv[3]=new parent.Val("R.2",ts);ts=new Array(NA,NA);tv[4]=new parent.Val("S",ts);ts=new Array("V.0-V.1",NA);tv[5]=new parent.Val("R.2",ts);ts=new Array("V.3/V.5",NA);tv[6]=new parent.Val("R.2",ts);ts=new Array("bicycles,pairs of skates,suits,bottles of perfume,"+"china sets,tables,couches,air conditioners",NA);tv[7]=new parent.Val("L.8",ts);
tq="A company that produces V.7 has the following cost "+"and revenue equations (n=number of V.7, d=dollars).<br> "+"d = V.0n <img src=\"chars/space.gif\" align=bottom alt=\"space\"> (revenue equation)<br> "+"d = V.1n + V.3 <img src=\"chars/space.gif\" "+"align=bottom alt=\"space\"> (cost equation)<br> "+"What is the number of V.7 the company must produce "+"to break even?";
th="chap1/sect2/prob5/hint.gif";tw="We\'re given <br> d = V.0n <img src=\"chars/space.gif\" "+"align=bottom alt=\"space\"> (demand equation)<br> "+"d = V.1n + V.3 <img src=\"chars/space.gif\" "+"align=bottom alt=\"space\"> (supply equation).<p> "+"Substituting the first equation into the "+"second for d and solving for n we get:<br> d = "+"V.1n + V.3<br> V.0n = V.1n + V.3<br> V.0n - V.1n "+"= V.3<br> V.5n = V.3<br> n = V.3/V.5<br> n = V.6.<p> "+"So the company will break even if it sells "+"V.6 V.7.<p> Don\'t forget to check your work by "+"plugging these values<br> into the two original "+"equations and making sure that they<br> hold.<p> "+"(<i>See pages 95-96 of your text for more details.</i>)";
ts=new Array("V.6",NA);ta=new parent.Val("R.2",ts);tp[4]=new parent.Problem("S",8,tv,0,NA,tq,ta,th,tw);np=5;st="Section 2.2 &nbsp; Systems of Linear Equations and "+"Applications";tl="help/none.html";ss[1]=new parent.Section(st,np,tp,tl,"sounds/sec2_2.wav","avi/sec2_2.avi");parent.hist[ch][1].max_questions=np;parent.hist[ch][1].title=st;
tp=new Array();tv=new Array();ts=new Array(1,5);tv[0]=new parent.Val("I",ts);ts=new Array(2,10);tv[1]=new parent.Val("I",ts);ts=new Array(-10,-2);tv[2]=new parent.Val("I",ts);ts=new Array("V.0:V.1,V.1,V.1,V.2,V.2",NA);tv[3]=new parent.Val("L.5",ts);ts=new Array("V.3*V.1",NA);tv[4]=new parent.Val("I",ts);ts=new Array(1,4);tv[5]=new parent.Val("I",ts);ts=new Array("<",NA);tv[6]=new parent.Val("S",ts);ts=new Array(">",NA);tv[7]=new parent.Val("S",ts);ts=new Array("<img src=\"chars/leq.gif\" align=bottom alt=\"leq\">",NA);tv[8]=new parent.Val("S",ts);ts=new Array("<img src=\"chars/geq.gif\" align=bottom alt=\"geq\">",NA);tv[9]=new parent.Val("S",ts);ts=new Array("V.5:V.6,V.7,V.8,V.9",NA);tv[10]=new parent.Val("L.4",ts);ts=new Array("0:1:V.3",NA);tv[11]=new parent.Val("M",ts);ts=new Array("V.5:V.7,V.6,V.9,V.8",NA);tv[12]=new parent.Val("L.4",ts);ts=new Array("V.0:V.10,V.10,V.10,V.12,V.12",NA);tv[13]=new parent.Val("L.5",ts);ts=new Array("V.4-V.5",NA);tv[14]=new parent.Val("I",ts);ts=new Array("V.4/V.3",NA);tv[15]=new parent.Val("R.2",ts);ts=new Array("V.0:V.12,V.12,V.12,V.10,V.10",NA);tv[16]=new parent.Val("L.5",ts);ts=new Array("V.5:V.8,V.9,V.6,V.7",NA);tv[17]=new parent.Val("L.4",ts);ts=new Array("V.5:V.9,V.8,V.7,V.6",NA);tv[18]=new parent.Val("L.4",ts);ts=new Array("-V.15",NA);tv[19]=new parent.Val("R.2",ts);ts=new Array("V.3/V.4",NA);tv[20]=new parent.Val("R.2",ts);ts=new Array("-V.20",NA);tv[21]=new parent.Val("R.2",ts);ts=new Array("(Remember to reverse the inequality when dividing "+"by a negative number.)",NA);tv[22]=new parent.Val("S",ts);ts=new Array("V.0: , , ,V.22,V.22",NA);tv[23]=new parent.Val("L.5",ts);tq="Solve the inequality: <img src=\"chars/space.gif\" "+"align=bottom alt=\"space\"> <nobr>V.3r V.10 V.4.</nobr>";
to=new Array();ts=new Array("r V.16 V.15",NA);to[0]=new parent.Val("S",ts);ts=new Array("r V.17 V.15",NA);to[1]=new parent.Val("S",ts);ts=new Array("r V.13 V.19",NA);to[2]=new parent.Val("S",ts);ts=new Array("r V.18 V.15",NA);to[3]=new parent.Val("S",ts);ts=new Array("r V.16 V.19",NA);to[4]=new parent.Val("S",ts);ts=new Array("r V.13 V.20",NA);to[5]=new parent.Val("S",ts);ts=new Array("r V.16 V.21",NA);to[6]=new parent.Val("S",ts);
th="chap1/sect3/prob1/hint.gif";tw="V.3r V.10 V.4 <p> Divide both sides by V.3. V.23<br> "+"V.3r/V.3 V.13 V.4/V.3 <br> r V.13 V.15.<p> "+"(<i>See pages 103-104 of your text for more details.</i>)";ts=new Array("r V.13 V.15",NA);ta=new parent.Val("S",ts);tp[0]=new parent.Problem("M",24,tv,7,to,tq,ta,th,tw);
tv=new Array();ts=new Array(1,2);tv[0]=new parent.Val("I",ts);ts=new Array(5,10);tv[1]=new parent.Val("I",ts);ts=new Array(-10,-1);tv[2]=new parent.Val("I",ts);ts=new Array(1,35);tv[3]=new parent.Val("I",ts);ts=new Array("V.0:V.1,V.2",NA);tv[4]=new parent.Val("L.2",ts);ts=new Array(11,25);tv[5]=new parent.Val("I",ts);ts=new Array("<",NA);tv[6]=new parent.Val("S",ts);ts=new Array(">",NA);tv[7]=new parent.Val("S",ts);ts=new Array("<img src=\"chars/leq.gif\" align=bottom alt=\"leq\">",NA);tv[8]=new parent.Val("S",ts);ts=new Array("<img src=\"chars/geq.gif\" align=bottom alt=\"geq\">",NA);tv[9]=new parent.Val("S",ts);ts=new Array(1,4);tv[10]=new parent.Val("I",ts);ts=new Array("V.4-V.5<0?', reversing the inequality since it is negative':'4'",NA);tv[11]=new parent.Val("SE",ts);ts=new Array("V.10:V.6,V.7,V.8,V.9",NA);tv[12]=new parent.Val("L.4",ts);ts=new Array("V.4-V.5",NA);tv[13]=new parent.Val("I",ts);ts=new Array("V.10:V.7,V.6,V.9,V.8",NA);tv[14]=new parent.Val("L.4",ts);ts=new Array("V.4-V.5<0?'V.14':'V.12'",NA);tv[15]=new parent.Val("SE",ts);ts=new Array("0:1:V.13",NA);tv[16]=new parent.Val("M",ts);ts=new Array("V.13<0?-1:1",NA);tv[17]=new parent.Val("I",ts);ts=new Array("V.4-V.5<0?'V.12':'V.14'",NA);tv[18]=new parent.Val("SE",ts);ts=new Array("V.10:V.8,V.9,V.6,V.7",NA);tv[19]=new parent.Val("L.4",ts);ts=new Array("V.10:V.9,V.8,V.7,V.6",NA);tv[20]=new parent.Val("L.4",ts);ts=new Array("V.3*V.17/parent.gcd(V.3,V.13)",NA);tv[21]=new parent.Val("I",ts);ts=new Array("V.13*V.17/parent.gcd(V.3,V.13)",NA);tv[22]=new parent.Val("I",ts);ts=new Array("V.21*(-1)",NA);tv[23]=new parent.Val("I",ts);ts=new Array("0:V.21:V.22",NA);tv[24]=new parent.Val("M",ts);ts=new Array("0:V.23:V.22",NA);tv[25]=new parent.Val("M",ts);ts=new Array("Math.abs(V.22)==1?V.22*V.21:'V.24'",NA);tv[26]=new parent.Val("SE",ts);ts=new Array("Math.abs(V.22)==1?V.22*V.23:'V.25'",NA);tv[27]=new parent.Val("SE",ts);
tq="Solve the inequality: <img src=\"chars/space.gif\" "+"align=bottom alt=\"space\"> <nobr>V.4r V.12 V.5r "+"+ V.3.</nobr>";to=new Array();ts=new Array("r V.18 V.26",NA);to[0]=new parent.Val("S",ts);ts=new Array("r V.19 V.26",NA);to[1]=new parent.Val("S",ts);ts=new Array("r V.14 V.27",NA);to[2]=new parent.Val("S",ts);ts=new Array("r V.20 V.26",NA);to[3]=new parent.Val("S",ts);ts=new Array("r V.18 V.27",NA);to[4]=new parent.Val("S",ts);ts=new Array("r V.19 V.27",NA);to[5]=new parent.Val("S",ts);
th="chap1/sect3/prob2/hint.gif";tw="V.4r V.12 V.5r + V.3 <br><img src=\"chars/space.gif\" "+"align=bottom alt=\"space\"><br> Subtract V.5r "+"from both sides to get <br> V.4r - V.5r V.12 "+"V.5r - V.5r + V.3 <br> (V.4 - V.5)r V.12 V.3 <br> "+"V.13r V.12 V.3 <br><img src=\"chars/space.gif\" "+"align=bottom alt=\"space\"><br> Multiplying both "+"sides by V.16 V.11.<br> V.16 <img src=\"chars/times.gif\" "+"align=bottom alt=\"times\"> V.13r "+"V.15 V.3 <img src=\"chars/times.gif\" align=bottom "+"alt=\"times\"> V.16<br> r V.15 V.26.<br><img "+"src=\"chars/space.gif\" align=bottom alt=\"space\"><br> "+"(<i>See pages 102-105 of your text for more "+"details.</i>)";
ts=new Array("r V.15 V.26",NA);ta=new parent.Val("S",ts);tp[1]=new parent.Problem("M",28,tv,6,to,tq,ta,th,tw);tv=new Array();ts=new Array(1,2);tv[0]=new parent.Val("I",ts);ts=new Array(4,15);tv[1]=new parent.Val("I",ts);ts=new Array(-15,-4);tv[2]=new parent.Val("I",ts);ts=new Array(1,10);tv[3]=new parent.Val("I",ts);ts=new Array("V.0:V.1,V.2",NA);tv[4]=new parent.Val("L.2",ts);ts=new Array("(V.1-3)*V.4 + V.3 -2",NA);tv[5]=new parent.Val("I",ts);ts=new Array("<",NA);tv[6]=new parent.Val("S",ts);ts=new Array("Math.abs((V.2-2)*V.4 + V.3 -1)",NA);tv[7]=new parent.Val("I",ts);ts=new Array("<img src=\"chars/leq.gif\" align=bottom alt=\"leq\">",NA);tv[8]=new parent.Val("S",ts);ts=new Array(1,7);tv[9]=new parent.Val("I",ts);ts=new Array("V.0: ,(remembering to reverse the inequality)",NA);tv[10]=new parent.Val("L.2",ts);ts=new Array("V.9:V.8,V.6,V.8,V.6,V.8,V.6,V.8",NA);tv[11]=new parent.Val("L.7",ts);ts=new Array("V.9:V.6,V.8,V.6,V.8,V.6,V.8,V.6",NA);tv[12]=new parent.Val("L.7",ts);ts=new Array("V.5-V.3",NA);tv[13]=new parent.Val("I",ts);ts=new Array("V.7-V.3",NA);tv[14]=new parent.Val("I",ts);ts=new Array(">",NA);tv[15]=new parent.Val("S",ts);ts=new Array("0:1:V.4",NA);tv[16]=new parent.Val("M",ts);ts=new Array("<img src=\"chars/geq.gif\" align=bottom alt=\"geq\">",NA);tv[17]=new parent.Val("S",ts);ts=new Array("V.9:V.17,V.15,V.17,V.15,V.17,V.15,V.17",NA);tv[18]=new parent.Val("L.7",ts);ts=new Array("V.9:V.15,V.17,V.15,V.17,V.15,V.17,V.15",NA);tv[19]=new parent.Val("L.7",ts);ts=new Array("V.0:V.12,V.19",NA);tv[20]=new parent.Val("L.2",ts);ts=new Array("V.0:V.11,V.18",NA);tv[21]=new parent.Val("L.2",ts);ts=new Array("V.4<0?-1:1",NA);tv[22]=new parent.Val("I",ts);ts=new Array("V.4*V.22/parent.gcd(V.4,V.13)",NA);tv[23]=new parent.Val("I",ts);ts=new Array("V.13*V.22/parent.gcd(V.4,V.13)",NA);tv[24]=new parent.Val("I",ts);ts=new Array("V.4*V.22/parent.gcd(V.4,V.14)",NA);tv[25]=new parent.Val("I",ts);ts=new Array("V.14*V.22/parent.gcd(V.4,V.14)",NA);tv[26]=new parent.Val("I",ts);ts=new Array("0:V.24:V.23",NA);
tv[27]=new parent.Val("M",ts);ts=new Array("0:V.26:V.25",NA);tv[28]=new parent.Val("M",ts);ts=new Array("V.0:V.18,V.11",NA);tv[29]=new parent.Val("L.2",ts);ts=new Array("V.0:V.19,V.12",NA);tv[30]=new parent.Val("L.2",ts);tq="Solve the inequality: <img src=\"chars/space.gif\" "+"align=bottom alt=\"space\"> <nobr>V.5 V.11 V.4r "+"+ V.3 V.12 V.7.</nobr>";
to=new Array();ts=new Array("V.27 V.20 r V.21 V.28",NA);to[0]=new parent.Val("S",ts);ts=new Array("V.22 V.29 r V.30 V.28",NA);to[1]=new parent.Val("S",ts);ts=new Array("V.27 V.17 r V.29 V.28",NA);to[2]=new parent.Val("S",ts);ts=new Array("r = V.27 or r = V.28",NA);to[3]=new parent.Val("S",ts);
th="chap1/sect3/prob3/hint.gif";tw="V.5 V.12 V.4r + V.3 V.11 V.7 <br><img src=\"chars/space.gif\" "+"align=bottom alt=\"space\"><br> Subtract "+"V.3 from each part of the inequality <br> "+"V.5 - V.3 V.12 V.4r + V.3 - V.3 V.11 V.7 - V.3 "+"<br> V.13 V.12 V.4r V.11 V.14. <br> Multiply through "+"by V.16 V.10 to get <br> V.16 <img src=\"chars/times.gif\" "+"align=bottom alt=\"times\"> V.13 "+"V.21 V.16 <img src=\"chars/times.gif\" align=bottom "+"alt=\"times\"> V.4r V.20 V.14 <img src=\"chars/times.gif\" "+"align=bottom alt=\"times\"> V.16 "+"<br> V.27 V.21 r V.20 V.28.<br><img src=\"chars/space.gif\" "+"align=bottom alt=\"space\"><br> (<i>See "+"page 105 of your text for more details.</i>)";
ts=new Array("V.27 V.21 r V.20 V.28",NA);ta=new parent.Val("S",ts);tp[2]=new parent.Problem("M",31,tv,4,to,tq,ta,th,tw);tv=new Array();ts=new Array(-30,20);tv[0]=new parent.Val("I",ts);ts=new Array("V.0+1",30);tv[1]=new parent.Val("I",ts);ts=new Array("5*V.0",NA);tv[2]=new parent.Val("I",ts);ts=new Array("5*V.1",NA);tv[3]=new parent.Val("I",ts);ts=new Array("9/5*V.2",NA);tv[4]=new parent.Val("R.1",ts);ts=new Array("9/5*V.3",NA);tv[5]=new parent.Val("R.1",ts);ts=new Array("V.4 + 32",NA);tv[6]=new parent.Val("R.1",ts);ts=new Array("V.5 + 32",NA);tv[7]=new parent.Val("R.1",ts);ts=new Array("V.6-1",NA);tv[8]=new parent.Val("R.1",ts);ts=new Array("V.7-1",NA);tv[9]=new parent.Val("R.1",ts);ts=new Array("-1*V.6",NA);tv[10]=new parent.Val("R.1",ts);ts=new Array("-1*V.8",NA);tv[11]=new parent.Val("R.1",ts);
tq="The relationship between degrees Celsius and degrees "+"Fahrenheit is given by the equation <br><img "+"src=\"chars/space.gif\" align=bottom alt=\"space\"><br> "+"<center> C = 5/9(F - 32).</center> <img "+"src=\"chars/space.gif\" align=bottom alt=\"space\"><br> "+"If the range of temperature is strictly "+"between V.2<sup>o</sup> Celsius and V.3<sup>o</sup> "+"Celsius (not including V.2<sup>o</sup> and "+"V.3<sup>o</sup>), what is the range in temperature "+"on the Fahrenheit Scale? (Answers are given "+"in interval notation, <nobr> i.e. (4.3, 54.1)</nobr>.)";to=new Array();ts=new Array("(V.6, V.9)",NA);to[0]=new parent.Val("S",ts);ts=new Array("(V.8, V.7)",NA);to[1]=new parent.Val("S",ts);ts=new Array("(V.8, V.9)",NA);to[2]=new parent.Val("S",ts);ts=new Array("(V.10, V.7)",NA);to[3]=new parent.Val("S",ts);ts=new Array("(V.10, V.9)",NA);to[4]=new parent.Val("S",ts);ts=new Array("(V.11, V.7)",NA);to[5]=new parent.Val("S",ts);ts=new Array("(V.11, V.9)",NA);to[6]=new parent.Val("S",ts);
th="chap1/sect3/prob4/hint.gif";tw="V.2 < C < V.3 <br> V.2 < 5/9(F - 32) < V.3 <br> "+"9/5<img src=\"chars/times.gif\" align=bottom alt=\"times\">V.2 "+"< F - 32 < 9/5<img src=\"chars/times.gif\" "+"align=bottom alt=\"times\">V.3 <br> V.4 "+"< F - 32 < V.5 <br> V.4 + 32 < F < V.5 + 32 <br> "+"V.6 < F < V.7. <p> In interval notation, <p> "+"(<i>See pages 105-106 of your text for more details.</i>) "+"(V.6, V.7) <br>";
ts=new Array("(V.6, V.7)",NA);ta=new parent.Val("S",ts);tp[3]=new parent.Problem("M",12,tv,7,to,tq,ta,th,tw);tv=new Array();ts=new Array(2,10);tv[0]=new parent.Val("R.1",ts);ts=new Array(2,10);tv[1]=new parent.Val("R.1",ts);ts=new Array("V.0+1",20);tv[2]=new parent.Val("R.1",ts);ts=new Array("V.2+5",40);tv[3]=new parent.Val("R.1",ts);ts=new Array("2*(V.0*V.1+V.0*V.2+V.1*V.2)",NA);tv[4]=new parent.Val("R.2",ts);ts=new Array("2*(V.0*V.1+V.0*V.3+V.1*V.3)",NA);tv[5]=new parent.Val("R.2",ts);ts=new Array("2*V.0*V.1",NA);tv[6]=new parent.Val("R.2",ts);ts=new Array("2*V.1 + 2*V.0",NA);tv[7]=new parent.Val("R.2",ts);ts=new Array("V.4 - V.6",NA);tv[8]=new parent.Val("R.2",ts);ts=new Array("V.5 - V.6",NA);tv[9]=new parent.Val("R.2",ts);ts=new Array("V.2-.01",NA);tv[10]=new parent.Val("R.2",ts);ts=new Array("V.2+.01",NA);tv[11]=new parent.Val("R.2",ts);ts=new Array("V.3-.01",NA);tv[12]=new parent.Val("R.2",ts);ts=new Array("V.3+.01",NA);tv[13]=new parent.Val("R.2",ts);
tq="The relationship between kilograms and the total "+"surface area (S) of a box of a specified width "+"(w), height (h), and length (l), is determined by "+"the following formula: <center> S = 2wh + 2hl "+"+ 2wl</center> If we know that a box has w=V.0, "+"h=V.1, and<br> V.4 < S <img src=\"chars/leq.gif\" "+"align=bottom alt=\"leq\"> V.5, what can we conclude "+"about the length (l) of the box?";
to=new Array();ts=new Array("V.10 < l <img src=\"chars/leq.gif\" align=bottom "+"alt=\"leq\"> V.12",NA);to[0]=new parent.Val("S",ts);ts=new Array("V.11 < l <img src=\"chars/leq.gif\" align=bottom "+"alt=\"leq\"> V.3",NA);to[1]=new parent.Val("S",ts);ts=new Array("V.10 < l <img src=\"chars/leq.gif\" align=bottom "+"alt=\"leq\"> V.13",NA);to[2]=new parent.Val("S",ts);ts=new Array("V.11 < l <img src=\"chars/leq.gif\" align=bottom "+"alt=\"leq\"> V.12",NA);to[3]=new parent.Val("S",ts);ts=new Array("V.10 < l <img src=\"chars/leq.gif\" align=bottom "+"alt=\"leq\"> V.3",NA);to[4]=new parent.Val("S",ts);
th="chap1/sect3/prob5/hint.gif";tw="V.4 < S <img src=\"chars/leq.gif\" align=bottom "+"alt=\"leq\"> V.5 <br> V.4 < 2wh + 2hl + 2wl <img "+"src=\"chars/leq.gif\" align=bottom alt=\"leq\"> "+"V.5. <br> Substituting values in for h and w and "+"simplifying:<br> V.4 < 2(V.0)(V.1) + 2(V.1)l + "+"2(V.0)l <img src=\"chars/leq.gif\" align=bottom "+"alt=\"leq\"> V.5<br> V.4 < V.6 + V.7l <img src=\"chars/leq.gif\" "+"align=bottom alt=\"leq\"> V.5.<br><img "+"src=\"chars/space.gif\" align=bottom alt=\"space\"><br> "+"Now subtracting V.6 from all parts "+"of the inequality<br> V.4 - V.6 < V.6 + V.7l "+"- V.6 <img src=\"chars/leq.gif\" align=bottom alt=\"leq\"> "+"V.5 - V.6<br> V.8 < V.7l <img src=\"chars/leq.gif\" align=bottom alt=\"leq\"> V.9<br><img "+"src=\"chars/space.gif\" align=bottom alt=\"space\"><br> "+"Now divide through by V.7<br> V.8/V.7 "+"< V.7l/V.7 <img src=\"chars/leq.gif\" align=bottom "+"alt=\"leq\"> V.9/V.7<br> V.2 < l <img src=\"chars/leq.gif\" "+"align=bottom alt=\"leq\"> V.3.<p> "+"(<i>See pages 105-106 of your text for more "+"details.</i>)";ts=new Array("V.2 < l <img src=\"chars/leq.gif\" align=bottom "+"alt=\"leq\"> V.3",NA);ta=new parent.Val("S",ts);
tp[4]=new parent.Problem("M",14,tv,5,to,tq,ta,th,tw);np=5;st="Section 2.3 &nbsp; Linear Inequalities";tl="help/sec2_3.html";ss[2]=new parent.Section(st,np,tp,tl,"sounds/sec2_3.wav","avi/sec2_3.avi");parent.hist[ch][2].max_questions=np;parent.hist[ch][2].title=st;
tp=new Array();tv=new Array();ts=new Array(2,9);tv[0]=new parent.Val("I",ts);ts=new Array("-12,-10,-8,-6,-4,-2,2,4,6,8,10,12",NA);tv[1]=new parent.Val("L.12",ts);ts=new Array("1,3,5,7,9,11,13,15,17,19,21,23",NA);tv[2]=new parent.Val("L.12",ts);ts=new Array("(V.1<0)?'':'+'",NA);tv[3]=new parent.Val("SE",ts);ts=new Array("V.2-V.1",NA);tv[4]=new parent.Val("I",ts);ts=new Array("-V.2-V.1",NA);tv[5]=new parent.Val("I",ts);ts=new Array("V.4/parent.gcd(V.4,V.0)",NA);tv[6]=new parent.Val("I",ts);ts=new Array("V.5/parent.gcd(V.5,V.0)",NA);tv[7]=new parent.Val("I",ts);ts=new Array("V.0/parent.gcd(V.4,V.0)",NA);tv[8]=new parent.Val("I",ts);ts=new Array("V.0/parent.gcd(V.5,V.0)",NA);tv[9]=new parent.Val("I",ts);ts=new Array("0:V.6:V.8",NA);tv[10]=new parent.Val("M",ts);ts=new Array("0:V.7:V.9",NA);tv[11]=new parent.Val("M",ts);ts=new Array("(V.8==1)?1:2",NA);tv[12]=new parent.Val("I",ts);ts=new Array("(V.9==1)?1:2",NA);tv[13]=new parent.Val("I",ts);ts=new Array("V.12:V.6,V.10",NA);tv[14]=new parent.Val("L.2",ts);ts=new Array("V.13:V.7,V.11",NA);tv[15]=new parent.Val("L.2",ts);ts=new Array("0:V.2:V.0",NA);tv[16]=new parent.Val("M",ts);ts=new Array("-:V.2:V.0",NA);tv[17]=new parent.Val("M",ts);ts=new Array("0:V.0:V.2",NA);tv[18]=new parent.Val("M",ts);ts=new Array("-:V.0:V.2",NA);tv[19]=new parent.Val("M",ts);ts=new Array("0:V.4:V.0",NA);tv[20]=new parent.Val("M",ts);ts=new Array("0:V.5:V.0",NA);tv[21]=new parent.Val("M",ts);
tq="Solve the equation : | V.0x V.3 V.1 | = V.2.<br>";to=new Array();ts=new Array("x = V.16 or x= V.17",NA);to[0]=new parent.Val("S",ts);ts=new Array("x = V.14 or x= V.17",NA);to[1]=new parent.Val("S",ts);ts=new Array("x = V.16 or x= V.15",NA);to[2]=new parent.Val("S",ts);ts=new Array("x = V.14 or x= V.18",NA);to[3]=new parent.Val("S",ts);ts=new Array("x = V.18 or x =V.19",NA);to[4]=new parent.Val("S",ts);
th="chap1/sect4/prob1/hint.gif";tw="There are two cases to consider :<br> Case 1 : <br> "+"V.0x V.3 V.1 =V.2 <br>V.0x = V.4<br> x = V.20.<br><p> "+"Case 2:<br> V.0x V.3 V.1 = -V.2 <br> V.0x "+"= V.5<br> x = V.21.<br> So the answer is x = "+"V.14 or x = V.15.<p> (<i>See pages 114-115 of your "+"text for more details.</i>)";
ts=new Array("x = V.14 or x = V.15",NA);ta=new parent.Val("S",ts);tp[0]=new parent.Problem("M",22,tv,5,to,tq,ta,th,tw);tv=new Array();ts=new Array(2,9);tv[0]=new parent.Val("I",ts);ts=new Array("-12,-10,-8,-6,-4,-2,2,4,6,8,10,12",NA);tv[1]=new parent.Val("L.12",ts);ts=new Array("1,3,5,7,9,11,13,15,17,19,21,23",NA);tv[2]=new parent.Val("L.12",ts);ts=new Array("(V.1<0)?'':'+'",NA);tv[3]=new parent.Val("SE",ts);ts=new Array("V.2-V.1",NA);tv[4]=new parent.Val("I",ts);ts=new Array("-V.2-V.1",NA);tv[5]=new parent.Val("I",ts);ts=new Array("V.4/parent.gcd(V.4,V.0)",NA);tv[6]=new parent.Val("I",ts);ts=new Array("V.5/parent.gcd(V.5,V.0)",NA);tv[7]=new parent.Val("I",ts);ts=new Array("V.0/parent.gcd(V.4,V.0)",NA);tv[8]=new parent.Val("I",ts);ts=new Array("V.0/parent.gcd(V.5,V.0)",NA);tv[9]=new parent.Val("I",ts);ts=new Array("0:V.6:V.8",NA);tv[10]=new parent.Val("M",ts);ts=new Array("0:V.7:V.9",NA);tv[11]=new parent.Val("M",ts);ts=new Array("(V.8==1)?1:2",NA);tv[12]=new parent.Val("I",ts);ts=new Array("(V.9==1)?1:2",NA);tv[13]=new parent.Val("I",ts);ts=new Array("V.12:V.6,V.10",NA);tv[14]=new parent.Val("L.2",ts);ts=new Array("V.13:V.7,V.11",NA);tv[15]=new parent.Val("L.2",ts);ts=new Array("0:V.2:V.0",NA);tv[16]=new parent.Val("M",ts);ts=new Array("-:V.2:V.0",NA);tv[17]=new parent.Val("M",ts);ts=new Array("0:V.0:V.2",NA);tv[18]=new parent.Val("M",ts);ts=new Array("-:V.0:V.2",NA);tv[19]=new parent.Val("M",ts);ts=new Array("0:V.4:V.0",NA);tv[20]=new parent.Val("M",ts);ts=new Array("0:V.5:V.0",NA);tv[21]=new parent.Val("M",ts);
tq="Solve the inequality : <img src=\"chars/space.gif\" "+"align=bottom alt=\"space\"> <nobr>|V.0xV.3V.1| "+"< V.2.</nobr>";to=new Array();ts=new Array("V.17 < x < V.21 ",NA);to[0]=new parent.Val("S",ts);ts=new Array("x < V.17 or x > V.21 ",NA);to[1]=new parent.Val("S",ts);ts=new Array("x < V.15 or x >V.14",NA);to[2]=new parent.Val("S",ts);ts=new Array("V.17 < x < V.15",NA);to[3]=new parent.Val("S",ts);ts=new Array(" x= V.18 or x =V.19",NA);to[4]=new parent.Val("S",ts);
th="chap1/sect4/prob2/hint.gif";tw="Write equivalent compound inequality :<br> -V.2 "+"< V.0xV.3V.1 < V.2 <br> V.5 < V.0x < V.4<br> V.21 "+"< x < V.20.<br> So the answer is V.15 < x < V.14.<br><img "+"src=\"chars/space.gif\" align=bottom "+"alt=\"space\"><p> (<i>See pages 115-116 of your "+"text for more details.</i>)";
ts=new Array(" V.15 < x < V.14",NA);ta=new parent.Val("S",ts);tp[1]=new parent.Problem("M",22,tv,5,to,tq,ta,th,tw);tv=new Array();ts=new Array(2,9);tv[0]=new parent.Val("I",ts);ts=new Array("-12,-10,-8,-6,-4,-2,2,4,6,8,10,12",NA);tv[1]=new parent.Val("L.12",ts);ts=new Array("1,3,5,7,9,11,13,15,17,19,21,23",NA);tv[2]=new parent.Val("L.12",ts);ts=new Array("(V.1<0)?'':'+'",NA);tv[3]=new parent.Val("SE",ts);ts=new Array("V.2-V.1",NA);tv[4]=new parent.Val("I",ts);ts=new Array("-V.2-V.1",NA);tv[5]=new parent.Val("I",ts);ts=new Array("V.4/parent.gcd(V.4,V.0)",NA);tv[6]=new parent.Val("I",ts);ts=new Array("V.5/parent.gcd(V.5,V.0)",NA);tv[7]=new parent.Val("I",ts);ts=new Array("V.0/parent.gcd(V.4,V.0)",NA);tv[8]=new parent.Val("I",ts);ts=new Array("V.0/parent.gcd(V.5,V.0)",NA);tv[9]=new parent.Val("I",ts);ts=new Array("0:V.6:V.8",NA);tv[10]=new parent.Val("M",ts);ts=new Array("0:V.7:V.9",NA);tv[11]=new parent.Val("M",ts);ts=new Array("(V.8==1)?1:2",NA);tv[12]=new parent.Val("I",ts);ts=new Array("(V.9==1)?1:2",NA);tv[13]=new parent.Val("I",ts);ts=new Array("V.12:V.6,V.10",NA);tv[14]=new parent.Val("L.2",ts);ts=new Array("V.13:V.7,V.11",NA);tv[15]=new parent.Val("L.2",ts);ts=new Array("0:V.2:V.0",NA);tv[16]=new parent.Val("M",ts);ts=new Array("-:V.2:V.0",NA);tv[17]=new parent.Val("M",ts);ts=new Array("0:V.0:V.2",NA);tv[18]=new parent.Val("M",ts);ts=new Array("-:V.0:V.2",NA);tv[19]=new parent.Val("M",ts);ts=new Array("0:V.4:V.0",NA);tv[20]=new parent.Val("M",ts);ts=new Array("0:V.5:V.0",NA);tv[21]=new parent.Val("M",ts);
tq="Solve the inequality : <img src=\"chars/space.gif\" "+"align=bottom alt=\"space\"> <nobr>| V.0xV.3V.1 "+"| <img src=\"chars/geq.gif\" align=bottom alt=\"geq\"> "+"V.2.</nobr>";to=new Array();ts=new Array("V.17 < x < V.15 ",NA);to[0]=new parent.Val("S",ts);ts=new Array("x < V.17 or x > V.21 ",NA);to[1]=new parent.Val("S",ts);ts=new Array("x < V.15 or x >V.14",NA);to[2]=new parent.Val("S",ts);ts=new Array("x<img src=\"chars/leq.gif\" align=bottom alt=\"leq\">V.17 "+"or x<img src=\"chars/geq.gif\" align=bottom "+"alt=\"geq\"> V.15",NA);to[3]=new parent.Val("S",ts);ts=new Array(" x= V.18 or x =V.19",NA);to[4]=new parent.Val("S",ts);
th="chap1/sect4/prob3/hint.gif";tw="Write equivalent compound inequality :<br> V.0xV.3V.1 "+"<img src=\"chars/leq.gif\" align=bottom alt=\"leq\"> "+"-V.2 or V.0xV.3V.1 <img src=\"chars/geq.gif\" "+"align=bottom alt=\"geq\"> V.2 <br> V.0x "+"<img src=\"chars/leq.gif\" align=bottom alt=\"leq\"> "+"V.5 or V.0x <img src=\"chars/geq.gif\" align=bottom "+"alt=\"geq\"> V.4<br> x <img src=\"chars/leq.gif\" "+"align=bottom alt=\"leq\"> V.21 or x "+"<img src=\"chars/geq.gif\" align=bottom alt=\"geq\"> "+"V.20.<br><img src=\"chars/space.gif\" align=bottom "+"alt=\"space\"><p> So the answer is x <img "+"src=\"chars/leq.gif\" align=bottom alt=\"leq\"> V.15 or x <img src=\"chars/geq.gif\" align=bottom "+"alt=\"geq\"> V.14.<br><img src=\"chars/space.gif\" "+"align=bottom alt=\"space\"><p> (<i>See pages "+"115-116 of your text for more details.</i>)";ts=new Array(" x <img src=\"chars/leq.gif\" align=bottom alt=\"leq\"> "+"V.15 or x <img src=\"chars/geq.gif\" align=bottom "+"alt=\"geq\"> V.14",NA);ta=new parent.Val("S",ts);
tp[2]=new parent.Problem("M",22,tv,5,to,tq,ta,th,tw);tv=new Array();ts=new Array(2,9);tv[0]=new parent.Val("I",ts);ts=new Array("-12,-10,-8,-6,-4,-2,2,4,6,8,10,12",NA);tv[1]=new parent.Val("L.12",ts);ts=new Array("1,3,5,7,9,11,13,15,17,19,21,23",NA);tv[2]=new parent.Val("L.12",ts);ts=new Array("(V.1<0)?'':'+'",NA);tv[3]=new parent.Val("SE",ts);ts=new Array("V.2-V.1",NA);tv[4]=new parent.Val("I",ts);ts=new Array("-V.2-V.1",NA);tv[5]=new parent.Val("I",ts);ts=new Array("V.4/parent.gcd(V.4,V.0)",NA);tv[6]=new parent.Val("I",ts);ts=new Array("V.5/parent.gcd(V.5,V.0)",NA);tv[7]=new parent.Val("I",ts);ts=new Array("V.0/parent.gcd(V.4,V.0)",NA);tv[8]=new parent.Val("I",ts);ts=new Array("V.0/parent.gcd(V.5,V.0)",NA);tv[9]=new parent.Val("I",ts);ts=new Array("0:V.6:V.8",NA);tv[10]=new parent.Val("M",ts);ts=new Array("0:V.7:V.9",NA);tv[11]=new parent.Val("M",ts);ts=new Array("(V.8==1)?1:2",NA);tv[12]=new parent.Val("I",ts);ts=new Array("(V.9==1)?1:2",NA);tv[13]=new parent.Val("I",ts);ts=new Array("V.12:V.6,V.10",NA);tv[14]=new parent.Val("L.2",ts);ts=new Array("V.13:V.7,V.11",NA);tv[15]=new parent.Val("L.2",ts);ts=new Array("0:V.2:V.0",NA);tv[16]=new parent.Val("M",ts);ts=new Array("-:V.2:V.0",NA);tv[17]=new parent.Val("M",ts);ts=new Array("0:V.0:V.2",NA);tv[18]=new parent.Val("M",ts);ts=new Array("-:V.0:V.2",NA);tv[19]=new parent.Val("M",ts);ts=new Array("0:V.4:V.0",NA);tv[20]=new parent.Val("M",ts);ts=new Array("0:V.5:V.0",NA);tv[21]=new parent.Val("M",ts);
tq="Solve the inequality : <img src=\"chars/space.gif\" "+"align=bottom alt=\"space\"> <nobr>|V.0xV.3V.1| "+"<img src=\"chars/leq.gif\" align=bottom alt=\"leq\"> "+"V.2.</nobr>";to=new Array();ts=new Array("V.17 <img src=\"chars/leq.gif\" align=bottom alt=\"leq\"> "+"x <img src=\"chars/leq.gif\" align=bottom "+"alt=\"leq\"> V.21 ",NA);to[0]=new parent.Val("S",ts);ts=new Array("x <img src=\"chars/leq.gif\" align=bottom alt=\"leq\"> V.17 or x <img src=\"chars/geq.gif\" align=bottom "+"alt=\"geq\"> V.21 ",NA);to[1]=new parent.Val("S",ts);ts=new Array("x <img src=\"chars/leq.gif\" align=bottom alt=\"leq\"> V.15 or x <img src=\"chars/geq.gif\" align=bottom "+"alt=\"geq\">V.14",NA);to[2]=new parent.Val("S",ts);ts=new Array("V.17 <img src=\"chars/leq.gif\" align=bottom alt=\"leq\"> "+"x <img src=\"chars/leq.gif\" align=bottom "+"alt=\"leq\"> V.15",NA);to[3]=new parent.Val("S",ts);ts=new Array(" x <img src=\"chars/leq.gif\" align=bottom alt=\"leq\"> V.18 ",NA);to[4]=new parent.Val("S",ts);
th="chap1/sect4/prob4/hint.gif";tw="Write equivalent compound inequality :<br> -V.2 "+"<img src=\"chars/leq.gif\" align=bottom alt=\"leq\"> "+"V.0xV.3V.1 <img src=\"chars/leq.gif\" align=bottom "+"alt=\"leq\"> V.2 <br> V.5<img src=\"chars/leq.gif\" "+"align=bottom alt=\"leq\"> V.0x <img "+"src=\"chars/leq.gif\" align=bottom alt=\"leq\"> "+"V.4<br> V.21 <img src=\"chars/leq.gif\" align=bottom "+"alt=\"leq\"> x <img src=\"chars/leq.gif\" align=bottom "+"alt=\"leq\"> V.20.<br><img src=\"chars/space.gif\" "+"align=bottom alt=\"space\"><p> So "+"the answer is V.15 <img src=\"chars/leq.gif\" align=bottom "+"alt=\"leq\"> x <img src=\"chars/leq.gif\" "+"align=bottom alt=\"leq\"> V.14.<br><img src=\"chars/space.gif\""+" align=bottom alt=\"space\"><p> (<i>See pages 115-116 of your text for more "+"details.</i>)";ts=new Array(" V.15 <img src=\"chars/leq.gif\" align=bottom alt=\"leq\"> "+"x <img src=\"chars/leq.gif\" align=bottom "+"alt=\"leq\"> V.14",NA);ta=new parent.Val("S",ts);
tp[3]=new parent.Problem("M",22,tv,5,to,tq,ta,th,tw);tv=new Array();ts=new Array(2,9);tv[0]=new parent.Val("I",ts);ts=new Array("-12,-10,-8,-6,-4,-2,2,4,6,8,10,12",NA);tv[1]=new parent.Val("L.12",ts);ts=new Array("1,3,5,7,9,11,13,15,17,19,21,23",NA);tv[2]=new parent.Val("L.12",ts);ts=new Array("(V.1<0)?'':'+'",NA);tv[3]=new parent.Val("SE",ts);ts=new Array("V.2-V.1",NA);tv[4]=new parent.Val("I",ts);ts=new Array("-V.2-V.1",NA);tv[5]=new parent.Val("I",ts);ts=new Array("V.4/parent.gcd(V.4,V.0)",NA);tv[6]=new parent.Val("I",ts);ts=new Array("V.5/parent.gcd(V.5,V.0)",NA);tv[7]=new parent.Val("I",ts);ts=new Array("V.0/parent.gcd(V.4,V.0)",NA);tv[8]=new parent.Val("I",ts);ts=new Array("V.0/parent.gcd(V.5,V.0)",NA);tv[9]=new parent.Val("I",ts);ts=new Array("0:V.6:V.8",NA);tv[10]=new parent.Val("M",ts);ts=new Array("0:V.7:V.9",NA);tv[11]=new parent.Val("M",ts);ts=new Array("(V.8==1)?1:2",NA);tv[12]=new parent.Val("I",ts);ts=new Array("(V.9==1)?1:2",NA);tv[13]=new parent.Val("I",ts);ts=new Array("V.12:V.6,V.10",NA);tv[14]=new parent.Val("L.2",ts);ts=new Array("V.13:V.7,V.11",NA);tv[15]=new parent.Val("L.2",ts);ts=new Array("0:V.2:V.0",NA);tv[16]=new parent.Val("M",ts);ts=new Array("-:V.2:V.0",NA);tv[17]=new parent.Val("M",ts);ts=new Array("0:V.0:V.2",NA);tv[18]=new parent.Val("M",ts);ts=new Array("-:V.0:V.2",NA);tv[19]=new parent.Val("M",ts);ts=new Array("0:V.4:V.0",NA);tv[20]=new parent.Val("M",ts);ts=new Array("0:V.5:V.0",NA);tv[21]=new parent.Val("M",ts);ts=new Array(2,7);tv[22]=new parent.Val("I",ts);ts=new Array(3,12);tv[23]=new parent.Val("I",ts);ts=new Array("V.23-V.22*V.2",NA);tv[24]=new parent.Val("I",ts);ts=new Array("-V.1",NA);tv[25]=new parent.Val("I",ts);ts=new Array("0:V.24-V.23:-V.22",NA);tv[26]=new parent.Val("M",ts);ts=new Array("V.23-V.24",NA);tv[27]=new parent.Val("I",ts);ts=new Array("0:V.27:V.22",NA);tv[28]=new parent.Val("M",ts);
tq="Solve the equation: <img src=\"chars/space.gif\" align=bottom alt=\"space\"> <nobr>V.23 - (V.22)| "+"V.25 - V.0x | = V.24.</nobr>";to=new Array();ts=new Array("x = V.16 or x= V.17",NA);to[0]=new parent.Val("S",ts);ts=new Array("x = V.14 or x= V.17",NA);to[1]=new parent.Val("S",ts);ts=new Array("x = V.16 or x= V.15",NA);to[2]=new parent.Val("S",ts);ts=new Array("x = V.14 or x= V.18",NA);to[3]=new parent.Val("S",ts);ts=new Array("x = V.18 or x =V.19",NA);to[4]=new parent.Val("S",ts);
th="chap1/sect4/prob5/hint.gif";tw="V.23 - (V.22)|V.25 - V.0x | = V.24<br> - (V.22)|V.25 "+"- V.0x |=V.24 - V.23<br> |V.25 - V.0x | = V.26 "+"= V.28 = V.2<br> |V.0x V.3 V.1| = V.2 > 0. <br><img "+"src=\"chars/space.gif\" align=bottom alt=\"space\"><p> "+"There are two cases to consider :<br> "+"Case 1 :<br> V.0x V.3 V.1 =V.2 <br> V.0x = "+"V.4<br> x = V.20.<br><img src=\"chars/space.gif\" "+"align=bottom alt=\"space\"><p> Case 2:<br> V.0x "+"V.3 V.1 = -V.2 <br> V.0x = V.5<br> x = V.21.<br><img "+"src=\"chars/space.gif\" align=bottom alt=\"space\"><p> "+"So the answer is x = V.14 or x = V.15. "+"<br><img src=\"chars/space.gif\" align=bottom "+"alt=\"space\"><p> (<i>See pages 114-115 of your "+"text for more details.</i>)";
ts=new Array("x = V.14 or x = V.15",NA);ta=new parent.Val("S",ts);tp[4]=new parent.Problem("M",29,tv,5,to,tq,ta,th,tw);np=5;st="Section 2.4 &nbsp; Absolute Value in Equations and "+"Inequalities";tl="help/none.html";ss[3]=new parent.Section(st,np,tp,tl,"sounds/sec2_4.wav","avi/sec2_4.avi");parent.hist[ch][3].max_questions=np;parent.hist[ch][3].title=st;
tp=new Array();tv=new Array();ts=new Array(2,7);tv[0]=new parent.Val("R.1",ts);ts=new Array("-V.0,V.0",NA);tv[1]=new parent.Val("L.2",ts);ts=new Array(2,7);tv[2]=new parent.Val("R.1",ts);ts=new Array("-V.2,V.2",NA);tv[3]=new parent.Val("L.2",ts);ts=new Array(2,7);tv[4]=new parent.Val("R.1",ts);ts=new Array("-V.4,V.4",NA);tv[5]=new parent.Val("L.2",ts);ts=new Array(2,7);tv[6]=new parent.Val("R.1",ts);ts=new Array("-V.6,V.6",NA);tv[7]=new parent.Val("L.2",ts);ts=new Array("V.1+V.5",NA);tv[8]=new parent.Val("R.1",ts);ts=new Array("V.3+V.7",NA);tv[9]=new parent.Val("R.1",ts);ts=new Array("V.1-V.5",NA);tv[10]=new parent.Val("R.1",ts);ts=new Array("V.3-V.7",NA);tv[11]=new parent.Val("R.1",ts);ts=new Array("V.1+V.3",NA);tv[12]=new parent.Val("R.1",ts);ts=new Array("V.5+V.7",NA);tv[13]=new parent.Val("R.1",ts);ts=new Array("parent.term(V.9,'i')",NA);tv[14]=new parent.Val("SE",ts);ts=new Array("parent.term(V.11,'i')",NA);tv[15]=new parent.Val("SE",ts);ts=new Array("parent.term(V.13,'i')",NA);tv[16]=new parent.Val("SE",ts);ts=new Array("parent.term(V.3,'i')",NA);tv[17]=new parent.Val("SE",ts);ts=new Array("parent.term(V.7,'i')",NA);tv[18]=new parent.Val("SE",ts);ts=new Array(1,2);tv[19]=new parent.Val("I",ts);ts=new Array("V.19:+,-",NA);tv[20]=new parent.Val("L.2",ts);ts=new Array("V.19:-,+",NA);tv[21]=new parent.Val("L.2",ts);ts=new Array("V.8 V.14",NA);tv[22]=new parent.Val("S",ts);ts=new Array("V.10 V.15",NA);tv[23]=new parent.Val("S",ts);ts=new Array("V.19:V.22,V.23",NA);tv[24]=new parent.Val("L.2",ts);ts=new Array("V.19:V.23,V.22",NA);tv[25]=new parent.Val("L.2",ts);
tq="Add or subtract as indicated:<br> (V.1 V.17) V.20 (V.5 V.18)";to=new Array();ts=new Array("V.25",NA);to[0]=new parent.Val("S",ts);ts=new Array("V.10 V.14",NA);to[1]=new parent.Val("S",ts);ts=new Array("V.8 V.15",NA);to[2]=new parent.Val("S",ts);ts=new Array("V.12 V.17",NA);to[3]=new parent.Val("S",ts);ts=new Array("V.12 V.15",NA);to[4]=new parent.Val("S",ts);ts=new Array("V.10 V.17",NA);to[5]=new parent.Val("S",ts);
th="chap1/sect5/prob1/hint.gif";tw="(V.1 V.17) V.20 (V.5 V.18)<br> =(V.1 V.20 V.5)+(V.3 "+"V.20 V.7)i<br> =V.24.<p> (<i>See pages 122-123 "+"of your text for more details.</i>)";ts=new Array("V.24",NA);ta=new parent.Val("S",ts);tp[0]=new parent.Problem("M",26,tv,6,to,tq,ta,th,tw);
tv=new Array();ts=new Array(1,9);tv[0]=new parent.Val("R.1",ts);ts=new Array("-V.0,V.0",NA);tv[1]=new parent.Val("L.2",ts);ts=new Array(1,9);tv[2]=new parent.Val("R.1",ts);ts=new Array("-V.2,V.2",NA);tv[3]=new parent.Val("L.2",ts);ts=new Array(1,9);tv[4]=new parent.Val("R.1",ts);ts=new Array("-V.4,V.4",NA);tv[5]=new parent.Val("L.2",ts);ts=new Array(1,9);tv[6]=new parent.Val("R.1",ts);ts=new Array("-V.6,V.6",NA);tv[7]=new parent.Val("L.2",ts);ts=new Array("parent.term('V.3','i')",NA);tv[8]=new parent.Val("SE",ts);ts=new Array("parent.term('V.7','i')",NA);tv[9]=new parent.Val("SE",ts);ts=new Array("parent.term1('V.3','i')",NA);tv[10]=new parent.Val("SE",ts);ts=new Array("parent.term1('V.7','i')",NA);tv[11]=new parent.Val("SE",ts);ts=new Array("V.1*V.5",NA);tv[12]=new parent.Val("R.2",ts);ts=new Array("V.1*V.7",NA);tv[13]=new parent.Val("R.2",ts);ts=new Array("V.3*V.5",NA);tv[14]=new parent.Val("R.2",ts);ts=new Array("V.3*V.7",NA);tv[15]=new parent.Val("R.2",ts);ts=new Array("V.13+V.14",NA);tv[16]=new parent.Val("R.2",ts);ts=new Array("V.12-V.15",NA);tv[17]=new parent.Val("R.2",ts);ts=new Array("parent.term('V.13','i')",NA);tv[18]=new parent.Val("SE",ts);ts=new Array("parent.term('V.14','i')",NA);tv[19]=new parent.Val("SE",ts);ts=new Array("parent.term('V.16','i')",NA);tv[20]=new parent.Val("SE",ts);ts=new Array("parent.term('-V.16','i')",NA);tv[21]=new parent.Val("SE",ts);ts=new Array("V.13-V.14",NA);tv[22]=new parent.Val("R.2",ts);ts=new Array("V.14-V.13",NA);tv[23]=new parent.Val("R.2",ts);ts=new Array("V.12+V.15",NA);tv[24]=new parent.Val("R.2",ts);ts=new Array("parent.term('V.15','i')",NA);tv[25]=new parent.Val("SE",ts);ts=new Array("parent.term('V.22','i')",NA);tv[26]=new parent.Val("SE",ts);ts=new Array("parent.term('V.23','i')",NA);tv[27]=new parent.Val("SE",ts);
tq="Multiply: (V.1 V.8)(V.5 V.9)";to=new Array();ts=new Array("V.17 V.21",NA);to[0]=new parent.Val("S",ts);ts=new Array("V.24 V.27",NA);to[1]=new parent.Val("S",ts);ts=new Array("V.17 V.26",NA);to[2]=new parent.Val("S",ts);ts=new Array("V.24 V.20",NA);to[3]=new parent.Val("S",ts);ts=new Array("V.24 V.26",NA);to[4]=new parent.Val("S",ts);ts=new Array("V.12 V.25",NA);to[5]=new parent.Val("S",ts);
th="chap1/sect5/prob2/hint.gif";tw="We will use FOIL method:<br> (V.1 V.8)(V.5 V.9)= "+"(V.1)(V.5)+(V.1)(V.11)+(V.10)(V.5)+(V.10)(V.11)<br> "+"= V.12 V.18 V.19 +(V.15)(i<sup>2</sup>)= V.12 "+"V.20 +(V.15)(-1)<br> = V.17 V.20. <p> (<i>See "+"pages 124-125 of your text for more details.</i>)";ts=new Array("V.17 V.20",NA);ta=new parent.Val("S",ts);
tp[1]=new parent.Problem("M",28,tv,6,to,tq,ta,th,tw);tv=new Array();ts=new Array(1,11);tv[0]=new parent.Val("I",ts);ts=new Array("-V.0,V.0",NA);tv[1]=new parent.Val("L.2",ts);ts=new Array(1,11);tv[2]=new parent.Val("I",ts);ts=new Array("-V.2,V.2",NA);tv[3]=new parent.Val("L.2",ts);ts=new Array("(V.3!=V.1)?V.3:-12",NA);tv[4]=new parent.Val("I",ts);ts=new Array("parent.term('V.4','i')",NA);tv[5]=new parent.Val("SE",ts);ts=new Array("parent.term('-V.4','i')",NA);tv[6]=new parent.Val("SE",ts);ts=new Array("parent.term('V.1','i')",NA);tv[7]=new parent.Val("SE",ts);ts=new Array("parent.term('-V.1','i')",NA);tv[8]=new parent.Val("SE",ts);ts=new Array("-V.1",NA);tv[9]=new parent.Val("I",ts);ts=new Array("-V.4",NA);tv[10]=new parent.Val("I",ts);
tq="Find the conjugate of the complex number V.1 V.5.";to=new Array();ts=new Array("V.1 V.5",NA);to[0]=new parent.Val("S",ts);ts=new Array("V.9 V.6",NA);to[1]=new parent.Val("S",ts);ts=new Array("V.9 V.5",NA);to[2]=new parent.Val("S",ts);ts=new Array("V.4 V.7",NA);to[3]=new parent.Val("S",ts);ts=new Array("V.4 V.8",NA);to[4]=new parent.Val("S",ts);ts=new Array("V.10 V.7",NA);to[5]=new parent.Val("S",ts);ts=new Array("V.10 V.8",NA);to[6]=new parent.Val("S",ts);
th="chap1/sect5/prob3/hint.gif";tw="The conjugate of a complex number a+bi is a-bi, "+"<br> therefore the answer is V.1 V.6.<p> (<i>See "+"page 125 of your text for more details.</i>)";ts=new Array("V.1 V.6.",NA);ta=new parent.Val("S",ts);tp[2]=new parent.Problem("M",11,tv,7,to,tq,ta,th,tw);
tv=new Array();ts=new Array(1,9);tv[0]=new parent.Val("I",ts);ts=new Array("-V.0,V.0",NA);tv[1]=new parent.Val("L.2",ts);ts=new Array(1,9);tv[2]=new parent.Val("I",ts);ts=new Array("-V.2,V.2",NA);tv[3]=new parent.Val("L.2",ts);ts=new Array(1,9);tv[4]=new parent.Val("I",ts);ts=new Array("-V.4,V.4",NA);tv[5]=new parent.Val("L.2",ts);ts=new Array(1,9);tv[6]=new parent.Val("I",ts);ts=new Array("-V.6,V.6",NA);tv[7]=new parent.Val("L.2",ts);ts=new Array("parent.term('V.3','i')",NA);tv[8]=new parent.Val("SE",ts);ts=new Array("parent.term('V.7','i')",NA);tv[9]=new parent.Val("SE",ts);ts=new Array("parent.term('-V.7','i')",NA);tv[10]=new parent.Val("SE",ts);ts=new Array("0:V.1 V.8:V.5 V.9",NA);tv[11]=new parent.Val("M",ts);ts=new Array("0:V.5 V.10:V.5 V.10",NA);tv[12]=new parent.Val("M",ts);ts=new Array("(V.1 V.8)(V.5 V.10)",NA);tv[13]=new parent.Val("S",ts);ts=new Array("(V.5 V.9)(V.5 V.10)",NA);tv[14]=new parent.Val("S",ts);ts=new Array("0:V.13:V.14",NA);tv[15]=new parent.Val("M",ts);ts=new Array("(V.1)(V.5) V.10(V.1) V.8(V.5) V.8(V.10)",NA);tv[16]=new parent.Val("S",ts);ts=new Array("(V.5)(V.5) V.10(V.5) V.9(V.5) V.9(V.10)",NA);tv[17]=new parent.Val("S",ts);ts=new Array("0:V.16:V.17",NA);tv[18]=new parent.Val("M",ts);ts=new Array("V.1*V.5+V.3*V.7",NA);tv[19]=new parent.Val("I",ts);ts=new Array("-V.1*V.7+V.3*V.5",NA);tv[20]=new parent.Val("I",ts);ts=new Array("parent.term('V.20','i')",NA);tv[21]=new parent.Val("SE",ts);ts=new Array("V.5*V.5+V.7*V.7",NA);tv[22]=new parent.Val("I",ts);ts=new Array("0:V.19 V.21:V.22",NA);tv[23]=new parent.Val("M",ts);ts=new Array("0:V.19:V.22",NA);tv[24]=new parent.Val("M",ts);ts=new Array("0:V.20:V.22",NA);tv[25]=new parent.Val("M",ts);ts=new Array("(V.19<0)?'-':''",NA);tv[26]=new parent.Val("SE",ts);ts=new Array("Math.abs(V.19)",NA);tv[27]=new parent.Val("I",ts);ts=new Array("V.27/parent.gcd(V.27,V.22)",NA);tv[28]=new parent.Val("I",ts);ts=new Array("V.22/parent.gcd(V.27,V.22)",NA);tv[29]=new parent.Val("I",ts);ts=new Array("0:V.28:V.29",NA);tv[30]=new parent.Val("M",ts);
ts=new Array("(V.29==1)?'V.28':'V.30'",NA);tv[31]=new parent.Val("SE",ts);ts=new Array("(V.20<0)?'-':'+'",NA);tv[32]=new parent.Val("SE",ts);ts=new Array("Math.abs(V.20)",NA);tv[33]=new parent.Val("I",ts);ts=new Array("V.33/parent.gcd(V.33,V.22)",NA);tv[34]=new parent.Val("I",ts);ts=new Array("V.22/parent.gcd(V.33,V.22)",NA);tv[35]=new parent.Val("I",ts);ts=new Array("0:V.34:V.35",NA);tv[36]=new parent.Val("M",ts);ts=new Array("(V.34==1)?'':'V.34'",NA);tv[37]=new parent.Val("SE",ts);ts=new Array("(V.35==1)?'V.37':'V.36'",NA);tv[38]=new parent.Val("SE",ts);ts=new Array("(V.20==0)?'':'V.38 i'",NA);tv[39]=new parent.Val("SE",ts);ts=new Array("(V.19==0)?'':'V.31'",NA);tv[40]=new parent.Val("SE",ts);ts=new Array("((V.19==0)&&(V.20>0))?'':'V.32'",NA);tv[41]=new parent.Val("SE",ts);ts=new Array("(V.19>0)?'-':(V.19==0)?1:''",NA);tv[42]=new parent.Val("SE",ts);ts=new Array("(V.20>0)?'-':''",NA);tv[43]=new parent.Val("SE",ts);ts=new Array("(V.19<0)?'-':'+'",NA);tv[44]=new parent.Val("SE",ts);ts=new Array("(V.19<0)?'+':'-'",NA);tv[45]=new parent.Val("SE",ts);ts=new Array("(V.20<0)?'-':''",NA);tv[46]=new parent.Val("SE",ts);ts=new Array("(V.35==1)?'V.34':'V.36'",NA);tv[47]=new parent.Val("SE",ts);ts=new Array("parent.term('V.26V.28','i')",NA);tv[48]=new parent.Val("SE",ts);ts=new Array("(V.29==1)?'V.48':'V.30 i'",NA);tv[49]=new parent.Val("SE",ts);ts=new Array("(V.20>0)?'-':'+'",NA);tv[50]=new parent.Val("SE",ts);ts=new Array(NA,NA);tv[51]=new parent.Val("S",ts);ts=new Array(NA,NA);tv[52]=new parent.Val("S",ts);ts=new Array("V.26 V.40 V.41 V.39",NA);tv[53]=new parent.Val("S",ts);tq="Divide V.1V.8 by V.5V.9.";
to=new Array();ts=new Array("V.42 V.40 V.32 V.39",NA);to[0]=new parent.Val("S",ts);ts=new Array("V.26 V.40 V.50 V.39",NA);to[1]=new parent.Val("S",ts);ts=new Array("V.42 V.40 V.50 V.39",NA);to[2]=new parent.Val("S",ts);ts=new Array("V.46 V.47 V.44 V.49",NA);to[3]=new parent.Val("S",ts);ts=new Array("V.46 V.47 V.45 V.49",NA);to[4]=new parent.Val("S",ts);
th="chap1/sect5/prob4/hint.gif";tw="V.11 <br> = V.11<img src=\"chars/times.gif\" align=bottom "+"alt=\"times\">V.12 <br> = V.15 <br> = "+"V.18<br> = V.23 <br> = V.53.<p> (<i>See pages 125-126 "+"of your text for more details.</i>).<p>";ts=new Array("V.53",NA);ta=new parent.Val("S",ts);
tp[3]=new parent.Problem("M",54,tv,5,to,tq,ta,th,tw);tv=new Array();ts=new Array(0,3);tv[0]=new parent.Val("I",ts);ts=new Array(3,10);tv[1]=new parent.Val("I",ts);ts=new Array("2*V.1+(V.0-0.5)/2",NA);tv[2]=new parent.Val("I",ts);ts=new Array("4*V.1+V.0",NA);tv[3]=new parent.Val("I",ts);ts=new Array(NA,NA);tv[4]=new parent.Val("S",ts);ts=new Array("4*V.1",NA);tv[5]=new parent.Val("I",ts);ts=new Array("i<sup>V.3</sup>=i(i)<sup>V.3-1</sup>=i(i<sup>2</sup>)<sup>V.2</su"+"p>=i(-1)<sup>V.2</sup>=i(1)=i",NA);tv[6]=new parent.Val("S",ts);ts=new Array("i<sup>V.3</sup>=i(i)<sup>V.3-1</sup>=i(i<sup>2</sup>)<sup>V.2</su"+"p>=i(-1)<sup>V.2</sup>=i(-1)=-i",NA);tv[7]=new parent.Val("S",ts);ts=new Array("V.0==0?'':'i<sup>V.0</sup>'",NA);tv[8]=new parent.Val("SE",ts);ts=new Array("V.0+1:1,i,-1,-i",NA);tv[9]=new parent.Val("L.4",ts);ts=new Array("V.0+1:i,-1,-i,1",NA);tv[10]=new parent.Val("L.4",ts);ts=new Array("V.0+1:-1,-i,1,i",NA);tv[11]=new parent.Val("L.4",ts);ts=new Array("V.0+1:-i,1,i,-1",NA);tv[12]=new parent.Val("L.4",ts);ts=new Array("(-1)<sup>V.3</sup>",NA);tv[13]=new parent.Val("S",ts);
tq="Simplify: i<sup>V.3</sup>";to=new Array();ts=new Array("V.10",NA);to[0]=new parent.Val("S",ts);ts=new Array("V.11",NA);to[1]=new parent.Val("S",ts);ts=new Array("V.12",NA);to[2]=new parent.Val("S",ts);ts=new Array("V.13",NA);to[3]=new parent.Val("S",ts);ts=new Array("V.3 i",NA);to[4]=new parent.Val("S",ts);ts=new Array("-V.3",NA);to[5]=new parent.Val("S",ts);
th="chap1/sect5/prob5/hint.gif";tw="i<sup>V.3</sup> = V.8i<sup>V.5</sup> = V.8i<sup>(4)(V.1)</sup> "+"= V.8(1) = V.9.<p> (<i>See pages "+"126-127 of your text for more details.</i>)";ts=new Array("V.9",NA);ta=new parent.Val("S",ts);tp[4]=new parent.Problem("M",14,tv,6,to,tq,ta,th,tw);
np=5;st="Section 2.5 &nbsp; Complex Numbers";tl="help/none.html";ss[4]=new parent.Section(st,np,tp,tl,"sounds/sec2_5.wav","avi/sec2_5.avi");parent.hist[ch][4].max_questions=np;parent.hist[ch][4].title=st;tp=new Array();tv=new Array();ts=new Array("1,3,5",NA);tv[0]=new parent.Val("L.3",ts);ts=new Array("2,4,6",NA);tv[1]=new parent.Val("L.3",ts);ts=new Array("2*V.0",NA);tv[2]=new parent.Val("I",ts);ts=new Array("2*V.1",NA);tv[3]=new parent.Val("I",ts);ts=new Array("V.2+V.3",NA);tv[4]=new parent.Val("I",ts);ts=new Array("V.2*V.3",NA);tv[5]=new parent.Val("I",ts);ts=new Array("V.4/2",NA);tv[6]=new parent.Val("I",ts);ts=new Array("Math.pow(V.6,2)",NA);tv[7]=new parent.Val("I",ts);ts=new Array("V.7-V.5",NA);tv[8]=new parent.Val("I",ts);ts=new Array("Math.sqrt(V.8)",NA);tv[9]=new parent.Val("I",ts);ts=new Array("V.9-V.6",NA);tv[10]=new parent.Val("I",ts);ts=new Array("(-1*V.9)-V.6",NA);tv[11]=new parent.Val("I",ts);ts=new Array(1,2);tv[12]=new parent.Val("I",ts);ts=new Array("V.12:-V.2,-V.3",NA);tv[13]=new parent.Val("L.2",ts);ts=new Array("V.12:-V.3,-V.2",NA);tv[14]=new parent.Val("L.2",ts);ts=new Array(2,5);tv[15]=new parent.Val("I",ts);ts=new Array("V.4*V.15",NA);tv[16]=new parent.Val("I",ts);ts=new Array("V.5*V.15",NA);tv[17]=new parent.Val("I",ts);ts=new Array("Math.max(V.10,V.11)",NA);tv[18]=new parent.Val("I",ts);
tq="Solve the quadratic equation below for x by completing "+"the square. What is the maximum solution?<br> "+"<center>V.15x<sup>2</sup> + V.16x = -V.17</center>";th="chap1/sect6/prob1/hint.gif";tw="V.15x<sup>2</sup> + V.16x = -V.17.<p> First, divide "+"through by V.15.<br> x<sup>2</sup> + V.4x = "+"-V.5.<p> Complete the square on the left-hand<br> "+"side by adding V.7 to both sides.<br> x<sup>2</sup> "+"+ V.4x + V.7 = -V.5 + V.7<br> (x + V.6)<sup>2</sup> "+"= V.8.<p> Take the square root of both "+"sides.<br> x + V.6 = <img src=\"chars/pm.gif\" "+"align=bottom alt=\"pm\">V.9<p> <u>Case I:</u><br> "+"x + V.6 = V.9<br> x = V.10<p> <u>Case II:</u><br> "+"x + V.6 = -V.9<br> x = V.11.<p> The maximum "+"solution is thus: V.18.<p> (<i>See pages 134-136 "+"of your text for more details.</i>)";
ts=new Array("V.18",NA);ta=new parent.Val("I",ts);tp[0]=new parent.Problem("S",19,tv,0,NA,tq,ta,th,tw);tv=new Array();ts=new Array(1,12);tv[0]=new parent.Val("I",ts);ts=new Array("V.0*2",NA);tv[1]=new parent.Val("I",ts);ts=new Array("Math.pow(V.0,2)",NA);tv[2]=new parent.Val("I",ts);ts=new Array("'-b <img src=\"chars/pm.gif\" align=bottom alt=\"pm\">'+parent.dsqr"+"t('b<sup>2</sup> - 4ac')",NA);tv[3]=new parent.Val("SE",ts);ts=new Array("<img src=\"chars/space.gif\" align=bottom alt=\"space\"><img src=\"chars/space.gif\" align=bottom "+"alt=\"space\"><img src=\"chars/space.gif\" align=bottom "+"alt=\"space\"><img src=\"chars/space.gif\" "+"align=bottom alt=\"space\">2a",NA);tv[4]=new parent.Val("S",ts);ts=new Array("0:V.3:V.4",NA);tv[5]=new parent.Val("M",ts);ts=new Array("'-V.1 <img src=\"chars/pm.gif\" align=bottom alt=\"pm\">'+parent.ds"+"qrt('V.1<sup>2</sup> - 4(1)(V.2)')",NA);tv[6]=new parent.Val("SE",ts);ts=new Array("<img src=\"chars/space.gif\" align=bottom alt=\"space\"><img src=\"chars/space.gif\" align=bottom "+"alt=\"space\"><img src=\"chars/space.gif\" align=bottom "+"alt=\"space\"><img src=\"chars/space.gif\" "+"align=bottom alt=\"space\">2(1)",NA);tv[7]=new parent.Val("S",ts);ts=new Array("0:V.6:V.7",NA);tv[8]=new parent.Val("M",ts);ts=new Array("Math.pow(V.1,2)",NA);tv[9]=new parent.Val("I",ts);ts=new Array("4*V.2",NA);tv[10]=new parent.Val("I",ts);ts=new Array("'-V.1 <img src=\"chars/pm.gif\" align=bottom alt=\"pm\">'+parent.ds"+"qrt('V.9 - V.10')",NA);tv[11]=new parent.Val("SE",ts);ts=new Array("<img src=\"chars/space.gif\" align=bottom alt=\"space\"><img src=\"chars/space.gif\" align=bottom "+"alt=\"space\"><img src=\"chars/space.gif\" align=bottom "+"alt=\"space\"><img src=\"chars/space.gif\" "+"align=bottom alt=\"space\">2",NA);tv[12]=new parent.Val("S",ts);ts=new Array("0:V.11:V.12",NA);tv[13]=new parent.Val("M",ts);ts=new Array("'-V.1 <img src=\"chars/pm.gif\" align=bottom alt=\"pm\">'+parent.ds"+"qrt('0')",NA);tv[14]=new parent.Val("SE",ts);ts=new Array("0:V.14:V.12",NA);
tv[15]=new parent.Val("M",ts);ts=new Array("0:-V.1:2",NA);tv[16]=new parent.Val("M",ts);ts=new Array("-1*V.0",NA);tv[17]=new parent.Val("I",ts);tq="Find x using the Quadratic Formula.<br> <center>x<sup>2</sup> "+"+ V.1x + V.2 = 0</center>";th="chap1/sect6/prob2/hint.gif";
tw="x<sup>2</sup> + V.1x + V.2 = 0<br> a = 1, b = V.1,"+" c = V.2<br> x = V.5<br> x = V.8<br> x = V.13<br> "+"x = V.15<br> x = V.16 = V.17.<p> (<i>See pages "+"135-138 of your text for more details.</i>)";ts=new Array("V.17",NA);ta=new parent.Val("I",ts);
tp[1]=new parent.Problem("S",18,tv,0,NA,tq,ta,th,tw);tv=new Array();ts=new Array(1,5);tv[0]=new parent.Val("I",ts);ts=new Array(" ",NA);tv[1]=new parent.Val("S",ts);ts=new Array(NA,NA);tv[2]=new parent.Val("S",ts);ts=new Array("V.0:4,6,V.1 V.1, ,2",NA);tv[3]=new parent.Val("L.5",ts);ts=new Array("V.0:4,6,1,1,2",NA);tv[4]=new parent.Val("L.5",ts);ts=new Array("V.0:-4,5,2,-6,8",NA);tv[5]=new parent.Val("L.5",ts);ts=new Array("V.0:-3,-4,-2,-9,1",NA);tv[6]=new parent.Val("L.5",ts);ts=new Array("V.5*V.5-4*V.4*V.6",NA);tv[7]=new parent.Val("I",ts);ts=new Array("Math.sqrt(V.7)",NA);tv[8]=new parent.Val("R.3",ts);ts=new Array("-V.5+V.8",NA);tv[9]=new parent.Val("R.3",ts);ts=new Array("-V.5-V.8",NA);tv[10]=new parent.Val("R.3",ts);ts=new Array("2*V.4",NA);tv[11]=new parent.Val("I",ts);ts=new Array("V.9/V.11",NA);tv[12]=new parent.Val("R.2",ts);ts=new Array("V.10/V.11",NA);tv[13]=new parent.Val("R.2",ts);ts=new Array("V.0:-,+,+,-,+",NA);tv[14]=new parent.Val("L.5",ts);ts=new Array("V.0:4,5,2,6,8",NA);tv[15]=new parent.Val("L.5",ts);ts=new Array("V.0:-,-,-,-,+",NA);tv[16]=new parent.Val("L.5",ts);ts=new Array("V.0:3,4,2,9,1",NA);tv[17]=new parent.Val("L.5",ts);ts=new Array("<img src=\"chars/space.gif\" align=bottom alt=\"space\"><img src=\"chars/space.gif\" align=bottom "+"alt=\"space\"><img src=\"chars/space.gif\" align=bottom "+"alt=\"space\">2a",NA);tv[18]=new parent.Val("S",ts);ts=new Array("-V.5",NA);tv[19]=new parent.Val("I",ts);ts=new Array("V.19 <img src=\"chars/plusminus.gif\" align=bottom "+"alt=\"plusminus\"> V.8",NA);tv[20]=new parent.Val("S",ts);ts=new Array("0:V.20:V.11",NA);tv[21]=new parent.Val("M",ts);ts=new Array("-V.12",NA);tv[22]=new parent.Val("R.2",ts);ts=new Array("-V.13",NA);tv[23]=new parent.Val("R.2",ts);ts=new Array("V.9/V.4",NA);tv[24]=new parent.Val("R.2",ts);ts=new Array("V.10/V.4",NA);tv[25]=new parent.Val("R.2",ts);ts=new Array("'-b <img src=\"chars/pm.gif\" align=bottom alt=\"pm\">'+parent.dsqr"+"t('b<sup>2</sup>-4ac')",NA);tv[26]=new parent.Val("SE",ts);ts=new Array("V.0: ,-,-, ,-",NA);
tv[27]=new parent.Val("L.5",ts);ts=new Array("0:V.26:V.18",NA);tv[28]=new parent.Val("M",ts);tq="Given V.3x<sup>2</sup> V.16 V.17 = V.27V.15x <br> "+"Use the quadratic formula to find the solution "+"or solutions (rounded to two decimal places).";to=new Array();ts=new Array("V.9 and V.10",NA);to[0]=new parent.Val("S",ts);ts=new Array("V.12",NA);to[1]=new parent.Val("S",ts);ts=new Array("V.25",NA);to[2]=new parent.Val("S",ts);ts=new Array("V.22 and V.23",NA);to[3]=new parent.Val("S",ts);ts=new Array("V.24 and V.25",NA);to[4]=new parent.Val("S",ts);
th="chap1/sect6/prob3/hint.gif";tw="First bring V.27V.15x to the other side to get V.3x<sup>2</sup> "+"V.14 V.15x V.16 V.17 = 0<br> Using "+"the quadratic formula, with a = V.4, b = V.5,"+" c = V.6 we get <p> x = V.28 <p> x = V.21 <br> x "+"= V.12 and x = V.13.<p> (<i>See pages 135-138 of "+"your text for more details.</i>)";
ts=new Array("V.13 and V.12",NA);ta=new parent.Val("S",ts);tp[2]=new parent.Problem("M",29,tv,5,to,tq,ta,th,tw);tv=new Array();ts=new Array(2,10);tv[0]=new parent.Val("I",ts);ts=new Array(2,20);tv[1]=new parent.Val("I",ts);ts=new Array(1,15);tv[2]=new parent.Val("I",ts);ts=new Array("V.1*V.1",NA);tv[3]=new parent.Val("I",ts);ts=new Array("4*V.0*V.2",NA);tv[4]=new parent.Val("I",ts);ts=new Array("V.3-V.4",NA);tv[5]=new parent.Val("I",ts);ts=new Array("V.5>0?3:2",NA);tv[6]=new parent.Val("I",ts);ts=new Array("V.5<0?1:V.6",NA);tv[7]=new parent.Val("I",ts);ts=new Array("V.7:two imaginary/complex solutions, one repeated "+"real solution, two distinct real solutions",NA);tv[8]=new parent.Val("L.3",ts);ts=new Array("V.7:one repeated real solution, two distinct real "+"solutions, two imaginary/complex solutions",NA);tv[9]=new parent.Val("L.3",ts);ts=new Array("V.7:two distinct real solutions, two imaginary/complex "+"solutions, one repeated real solution",NA);tv[10]=new parent.Val("L.3",ts);ts=new Array("V.7:<,=,>",NA);tv[11]=new parent.Val("L.3",ts);ts=new Array(" one real and one imaginary solution",NA);tv[12]=new parent.Val("S",ts);ts=new Array("one repeated imaginary solution",NA);tv[13]=new parent.Val("S",ts);tq="Check the discriminant to see what types of solutions "+"the following quadratic equation has.<br> "+"V.0x<sup>2</sup> + V.1x + V.2 = 0.";
to=new Array();ts=new Array("V.9",NA);to[0]=new parent.Val("S",ts);ts=new Array("V.12",NA);to[1]=new parent.Val("S",ts);ts=new Array("V.10",NA);to[2]=new parent.Val("S",ts);ts=new Array("V.13",NA);to[3]=new parent.Val("S",ts);th="chap1/sect6/prob4/hint.gif";
tw="The discriminant is b<sup>2</sup> - 4ac. <br> In "+"our case, a = V.0, b = V.1, and c = V.2.<br> So,"+" we get (V.1)<sup>2</sup> - 4(V.0)(V.2) = V.3 - "+"V.4 = V.5 V.11 0.<br> Since, V.5 V.11 0, we have "+"V.8.<p> (<i>See page 138 of your text for more "+"details.</i>)";
ts=new Array("V.8",NA);ta=new parent.Val("S",ts);tp[3]=new parent.Problem("M",14,tv,4,to,tq,ta,th,tw);tv=new Array();ts=new Array("chap1/sect6/prob5/V0.gif",NA);tv[0]=new parent.Val("G.175.135",ts);ts=new Array(1,4);tv[1]=new parent.Val("I",ts);ts=new Array("V.1:Sara,Jessica,Christian,Matt",NA);tv[2]=new parent.Val("L.4",ts);ts=new Array("V.1:She,She,He,He",NA);tv[3]=new parent.Val("L.4",ts);ts=new Array("V.1:her,her,his,his",NA);tv[4]=new parent.Val("L.4",ts);ts=new Array("V.1:she,she,he,he",NA);tv[5]=new parent.Val("L.4",ts);ts=new Array(10,18);tv[6]=new parent.Val("I",ts);ts=new Array(19,25);tv[7]=new parent.Val("I",ts);ts=new Array(10,20);tv[8]=new parent.Val("I",ts);ts=new Array("Math.pow(V.8,2)",NA);tv[9]=new parent.Val("I",ts);ts=new Array("V.8+V.7",NA);tv[10]=new parent.Val("I",ts);ts=new Array("V.8+V.6",NA);tv[11]=new parent.Val("I",ts);ts=new Array("V.10*V.11",NA);tv[12]=new parent.Val("I",ts);ts=new Array("V.6*V.7",NA);tv[13]=new parent.Val("I",ts);ts=new Array("V.6+V.7",NA);tv[14]=new parent.Val("I",ts);ts=new Array("V.12-V.13",NA);tv[15]=new parent.Val("I",ts);ts=new Array("parent.dsqrt('V.14<sup>2</sup> - 4(1)(-V.15)')",NA);tv[16]=new parent.Val("SE",ts);ts=new Array("0:-V.14 <img src=\"chars/pm.gif\" align=bottom alt=\"pm\"> "+"V.16 : 2(1)",NA);tv[17]=new parent.Val("M",ts);ts=new Array("(-1*V.14 - Math.sqrt(V.14*V.14+4*V.15))/2",NA);tv[18]=new parent.Val("I",ts);
tq="V.2 lives in a square blue house in the corner of "+"a lot. V.3 wants to know the area of V.4 house,"+" but all V.5 knows is that the lot extends V.6 "+"feet beyond the house in one direction and V.7 feet "+"beyond the house in the other direction. If "+"the area of the lot is V.12 square feet, what is "+"the area of the house?";
th="chap1/sect6/prob5/hint.gif";tw="<table cellpadding=0 cellspacing=0 border=0> <tr><td><img "+"src=\"chars/space.gif\" align=bottom alt=\"space\"></td><"+"td align=right>V.7 <img src=\"chars/space.gif\" "+"align=bottom alt=\"space\"> <img "+"src=\"chars/space.gif\" align=bottom alt=\"space\"></td></tr> "+"<tr><td valign=bottom>V.6</td><td "+"rowspan=2 align=left>V.0</td></tr> <tr><td><img "+"src=\"chars/space.gif\" align=bottom alt=\"space\"><br><img "+"src=\"chars/space.gif\" align=bottom "+"alt=\"space\"></td></tr> </table> <p> Let x "+"denote the length of the sides of the house.<br> "+"Since the house is square, the area will be x<sup>2</sup>,"+"<br> so we begin by finding x. We\'re "+"given the length of<br> the lot as x + V.7 and "+"the width of the lot as x + V.6.<br> The area, "+"then, is (x + V.7)(x + V.6) which we\'re given<br> "+"as V.12. Hence, we have the following:<br> (x "+"+ V.7)(x + V.6) = V.12<br> x<sup>2</sup> + V.7x "+"+ V.6x + V.13 = V.12<br> x<sup>2</sup> + V.14x "+"- V.15 = 0<br> So, use the Quadratic Formula with "+"a = 1, b = V.14,<br> and c = -V.15 to solve for "+"x.<br> x = V.17.<BR> So x = V.8 or x = V.18.<p> "+"Since x is a distance, x must be V.8.<br> Thus "+"the area of V.2\'s house is (V.8)<sup>2</sup> = "+"V.9 square feet.<p> Check: (V.8 + V.7)(V.8 + V.6) "+"= (V.10)(V.11) = V.12.<p> (<i>See pages 138-142 "+"of your text for more details.</i>)";
ts=new Array("V.9",NA);ta=new parent.Val("I",ts);tp[4]=new parent.Problem("S",19,tv,0,NA,tq,ta,th,tw);np=5;st="Section 2.6 &nbsp; Quadratic Equations and Applications";tl="help/none.html";ss[5]=new parent.Section(st,np,tp,tl,"sounds/sec2_6.wav","avi/sec2_6.avi");parent.hist[ch][5].max_questions=np;parent.hist[ch][5].title=st;
tp=new Array();tv=new Array();ts=new Array(1,2);tv[0]=new parent.Val("I",ts);ts=new Array("V.0:largest,smallest",NA);tv[1]=new parent.Val("L.2",ts);ts=new Array("x,y,z,u,v,w,a,b,c,d",NA);tv[2]=new parent.Val("L.10",ts);ts=new Array(2,13);tv[3]=new parent.Val("I",ts);ts=new Array(2,13);tv[4]=new parent.Val("I",ts);ts=new Array("V.3+V.4",NA);tv[5]=new parent.Val("I",ts);ts=new Array("V.3*V.4",NA);tv[6]=new parent.Val("I",ts);ts=new Array("parent.dsqrt('V.5V.2 - V.6')",NA);tv[7]=new parent.Val("SE",ts);ts=new Array("V.3",NA);tv[8]=new parent.Val("I",ts);ts=new Array("V.4",NA);tv[9]=new parent.Val("I",ts);ts=new Array("Math.max(V.8,V.9)",NA);tv[10]=new parent.Val("I",ts);ts=new Array("Math.min(V.8,V.9)",NA);tv[11]=new parent.Val("I",ts);ts=new Array("V.0:V.10,V.11",NA);tv[12]=new parent.Val("L.2",ts);ts=new Array("parent.dsqrt('V.5(V.3) - V.6')",NA);tv[13]=new parent.Val("SE",ts);ts=new Array("V.5*V.3 - V.6",NA);tv[14]=new parent.Val("I",ts);ts=new Array("parent.dsqrt('V.14')",NA);tv[15]=new parent.Val("SE",ts);ts=new Array("Math.sqrt(V.14)",NA);tv[16]=new parent.Val("R.3",ts);ts=new Array("parent.dsqrt('V.5(V.4) - V.6')",NA);tv[17]=new parent.Val("SE",ts);ts=new Array("V.5*V.4 - V.6",NA);tv[18]=new parent.Val("I",ts);ts=new Array("parent.dsqrt('V.18')",NA);tv[19]=new parent.Val("SE",ts);
tq="What is the V.1 solution for:<br> V.2 = V.7.";th="chap1/sect7/prob1/hint.gif";tw="V.2 = V.7.<p> Square both sides so we have:<br> "+"V.2<sup>2</sup> = (V.7)<sup>2</sup><br> V.2<sup>2</sup> "+"= V.5V.2 - V.6.<p> Take all the terms to "+"one side:<br> V.2<sup>2</sup> - V.5V.2 + V.6 = "+"0.<p> Factor and solve:<br> (V.2 - V.3)(V.2 - V.4) "+"= 0<br> V.2 = V.3 or V.2 = V.4.<p> Now we need "+"to check and make sure these are indeed <p> solutions "+"to our original equation:<p> <u>Checking "+"if V.2 = V.3 is a solution.</u><p> V.7 <img src=\"chars/space.gif\""+" align=bottom alt=\"space\">=<img "+"src=\"chars/space.gif\" align=bottom alt=\"space\"> "+"V.13 <img src=\"chars/space.gif\" align=bottom "+"alt=\"space\">=<img src=\"chars/space.gif\" "+"align=bottom alt=\"space\"> V.15 <img src=\"chars/space.gif\" "+"align=bottom alt=\"space\">=<img "+"src=\"chars/space.gif\" align=bottom alt=\"space\"> "+"V.3 = V.2.<br> So V.3 is a solution.<p> "+"<u>Checking if V.2 = V.4 is a solution.</u><p> V.7 "+"<img src=\"chars/space.gif\" align=bottom alt=\"space\">=<img "+"src=\"chars/space.gif\" align=bottom "+"alt=\"space\"> V.17 <img src=\"chars/space.gif\" "+"align=bottom alt=\"space\">=<img src=\"chars/space.gif\" "+"align=bottom alt=\"space\"> V.19 "+"<img src=\"chars/space.gif\" align=bottom alt=\"space\">=<img "+"src=\"chars/space.gif\" align=bottom "+"alt=\"space\"> V.4 = V.2.<br> So V.4 is a solution.<p> "+"Thus the V.1 solution is V.12.<p> (<i>See "+"page 145 of your text for more details.</i>)";ts=new Array("V.12",NA);ta=new parent.Val("I",ts);
tp[0]=new parent.Problem("S",20,tv,0,NA,tq,ta,th,tw);tv=new Array();ts=new Array(1,2);tv[0]=new parent.Val("I",ts);ts=new Array("V.0:largest,smallest",NA);tv[1]=new parent.Val("L.2",ts);ts=new Array("x,y,z,u,v,w,a,b,c,d",NA);tv[2]=new parent.Val("L.10",ts);ts=new Array(5,15);tv[3]=new parent.Val("I",ts);ts=new Array(1,"V.3-1");tv[4]=new parent.Val("I",ts);ts=new Array("4,9,25,16,36",NA);tv[5]=new parent.Val("L.5",ts);ts=new Array("V.3-V.4",NA);tv[6]=new parent.Val("I",ts);ts=new Array("V.4*V.3",NA);tv[7]=new parent.Val("I",ts);ts=new Array("V.6*V.5",NA);tv[8]=new parent.Val("I",ts);ts=new Array("V.7*V.5",NA);tv[9]=new parent.Val("I",ts);ts=new Array("Math.sqrt(V.5)",NA);tv[10]=new parent.Val("I",ts);ts=new Array("parent.dsqrt('-V.8V.2 + V.9')",NA);tv[11]=new parent.Val("SE",ts);ts=new Array("V.7",NA);tv[12]=new parent.Val("I",ts);ts=new Array("V.8",NA);tv[13]=new parent.Val("I",ts);ts=new Array("Math.max(V.5,V.6)",NA);tv[14]=new parent.Val("I",ts);ts=new Array("Math.min(V.5,V.6)",NA);tv[15]=new parent.Val("I",ts);ts=new Array("V.0:V.14,V.15",NA);tv[16]=new parent.Val("L.2",ts);ts=new Array("parent.dsqrt('-V.8(V.4) + V.9')",NA);tv[17]=new parent.Val("SE",ts);ts=new Array("V.9 - V.8*V.4",NA);tv[18]=new parent.Val("I",ts);ts=new Array("parent.dsqrt(V.18)",NA);tv[19]=new parent.Val("SE",ts);ts=new Array("Math.sqrt(V.18)",NA);tv[20]=new parent.Val("I",ts);
tq="What is the V.1 solution for:<br> V.10V.2 = V.11?";th="chap1/sect7/prob2/hint.gif";tw="V.10V.2 = V.11.<p> Square both sides so we have:<br> "+"(V.10<sup>2</sup>)V.2<sup>2</sup> = (V.11)<sup>2</sup><br> "+"V.5V.2<sup>2</sup> = -V.8V.2 + V.9.<p> "+"Take all the terms to one side:<br> V.5V.2<sup>2</sup> "+"+ V.8V.2 - V.9 = 0.<p> Divide through "+"by V.5:<br> V.2<sup>2</sup> + V.6V.2 - V.7 = "+"0.<p> Factor and solve:<br> (V.2 - V.4)(V.2 + V.3) "+"= 0<br> V.2 = V.4 or V.2 = -V.3.<p> Now we need "+"to check if these are solutions to the original "+"equation.<p> <u>Checking if V.2 = V.4 is a solution.</u><p> "+"V.11 <img src=\"chars/space.gif\" "+"align=bottom alt=\"space\">=<img src=\"chars/space.gif\" "+"align=bottom alt=\"space\"> V.17 <img "+"src=\"chars/space.gif\" align=bottom alt=\"space\">=<img "+"src=\"chars/space.gif\" align=bottom alt=\"space\"> "+"V.19 <img src=\"chars/space.gif\" "+"align=bottom alt=\"space\">=<img src=\"chars/space.gif\" "+"align=bottom alt=\"space\"> V.20 = (V.10)(V.4) "+"= V.10V.2.<br> So V.4 is a solution to our "+"problem.<p> <u>Checking if V.2 = -V.3 is a solution.</u><p> "+"We note that V.10V.2 = (V.10)(-V.3) "+"< 0. There is no real<br> number whose square "+"root is a negative value so this cannot<br> be "+"a solution to our equation.<p> So the V.1 (and only) "+"solution is V.4.<p> <P>(<i>See page 145 of "+"your text for more details.</i>)";
ts=new Array("V.4",NA);ta=new parent.Val("I",ts);tp[1]=new parent.Problem("S",21,tv,0,NA,tq,ta,th,tw);tv=new Array();ts=new Array(2,25);tv[0]=new parent.Val("I",ts);ts=new Array(1,2);tv[1]=new parent.Val("I",ts);ts=new Array("x,u,v,w,z,a,b,c,d",NA);tv[2]=new parent.Val("L.9",ts);ts=new Array("V.0*V.0",NA);tv[3]=new parent.Val("I",ts);ts=new Array("parent.dsqrt('V.3')",NA);tv[4]=new parent.Val("SE",ts);ts=new Array("V.4 = V.3<sup><sup>1</sup>/ <sup>2</sup></sup>.,V.4 = V.0.",NA);tv[5]=new parent.Val("L.2",ts);ts=new Array("If V.2<sup>2</sup> = V.3 then V.2 = <img src=\"chars/pm.gif\" "+"align=bottom alt=\"pm\">V.3<sup><sup>1</sup>/<sub>2"+"</sub></sup>.,If V.2<sup>2</sup> "+"= V.3 then V.2 = <img src=\"chars/pm.gif\" align=bottom "+"alt=\"pm\">V.4., If V.2<sup>2</sup> = "+"V.3 then V.2 = <img src=\"chars/pm.gif\" align=bottom "+"alt=\"pm\">V.0.",NA);tv[6]=new parent.Val("L.3",ts);ts=new Array("V.1:V.5,V.6",NA);tv[7]=new parent.Val("L.2",ts);ts=new Array(NA,NA);tv[8]=new parent.Val("S",ts);ts=new Array("V.4 = V.3<sup><sup>1</sup>/ <sup>2</sup></sup> = V.0.",NA);tv[9]=new parent.Val("S",ts);ts=new Array("If V.2<sup>2</sup> = V.3 then V.2 = <img src=\"chars/pm.gif\" "+"align=bottom alt=\"pm\">V.3<sup><sup>1</sup>/ "+"<sup>2</sup></sup> = <img src=\"chars/pm.gif\" "+"align=bottom alt=\"pm\">V.0.",NA);tv[10]=new parent.Val("S",ts);ts=new Array("V.1:V.9,V.10",NA);tv[11]=new parent.Val("L.2",ts);
tq="Which of the following statements are true?";to=new Array();ts=new Array("V.1:V.4 = <img src=\"chars/pm.gif\" align=bottom "+"alt=\"pm\">V.0., If V.2<sup>2</sup> = V.3 then "+"V.2 = V.0.",NA);to[0]=new parent.Val("L.2",ts);ts=new Array("V.1:V.4 = <img src=\"chars/pm.gif\" align=bottom "+"alt=\"pm\">V.3<sup><sup>1</sup>/ <sup>2</sup></sup>.,"+"If V.2 = V.3 then V.2 = V.3<sup><sup>1</sup>/ "+"<sup>2</sup></sup>.",NA);to[1]=new parent.Val("L.2",ts);ts=new Array("V.1:V.4 = V.3<sup>-2</sup>.,If V.2 = V.3 then V.2 "+"= V.3<sup>-2</sup>.",NA);to[2]=new parent.Val("L.2",ts);ts=new Array("V.1:V.4 = <img src=\"chars/pm.gif\" align=bottom "+"alt=\"pm\">V.3<sup>-2</sup>.,If V.2 = V.3 then "+"V.2 = <img src=\"chars/pm.gif\" align=bottom alt=\"pm\">V.3<sup>-2<"+"/sup>.",NA);to[3]=new parent.Val("L.2",ts);
th="chap1/sect7/prob3/hint.gif";tw="V.11<p> (<i>See page 146 of your text for more details.</i>)";ts=new Array("V.7",NA);ta=new parent.Val("S",ts);tp[2]=new parent.Problem("M",12,tv,4,to,tq,ta,th,tw);tv=new Array();ts=new Array("x,y,z,a,b,c,z,v,w",NA);tv[0]=new parent.Val("L.9",ts);ts=new Array(1,NA);tv[1]=new parent.Val("I",ts);ts=new Array("V.1:V.0,V.0<sup><sup>2</sup>/ <sup>3</sup></sup>,"+"V.0<sup><sup>1</sup>/ <sup>2</sup></sup>",NA);tv[2]=new parent.Val("L.3",ts);ts=new Array("V.1:V.0<sup><sup>1</sup>/ <sup>3</sup></sup>,V.0<sup><sup>1</sup>"+"/ <sup>3</sup></sup>,V.0<sup><sup>1</sup>/ "+"<sup>3</sup></sup>",NA);tv[3]=new parent.Val("L.3",ts);ts=new Array("V.1:25,6,4",NA);tv[4]=new parent.Val("L.3",ts);ts=new Array(3,"V.4");tv[5]=new parent.Val("I",ts);ts=new Array(2,"V.5-1");tv[6]=new parent.Val("I",ts);ts=new Array("V.1:2,3,4",NA);tv[7]=new parent.Val("L.3",ts);ts=new Array("Math.pow(-V.5,V.7)",NA);tv[8]=new parent.Val("I",ts);ts=new Array("Math.pow(-V.6,V.7)",NA);tv[9]=new parent.Val("I",ts);ts=new Array("Math.max(V.8,V.9)",NA);tv[10]=new parent.Val("I",ts);ts=new Array("V.5+V.6",NA);tv[11]=new parent.Val("I",ts);ts=new Array("V.5*V.6",NA);tv[12]=new parent.Val("I",ts);
tq="What is the largest solution of:<br> V.2 + V.11V.3 + V.12 = 0?";th="chap1/sect7/prob4/hint.gif";tw="V.2 + V.11V.3 + V.12 = 0.<p> Let u = V.3. We can "+"rewrite the above as: u<sup>2</sup> + V.11u +V.12 "+"= 0.<p> Solving in terms of u:<br> (u + V.5)(u "+"+ V.6) = 0<br> so u = -V.5 or u = -V.6<p> Now "+"substituting V.3 back in for u and solving for V.0:<br> "+"V.3 = -V.5 or V.3 = -V.6<br> (V.3)<sup>V.7</sup> "+"= (-V.5)<sup>V.7</sup> or (V.3)<sup>V.7</sup> "+"= (-V.6)<sup>V.7</sup><br> V.0 = V.8 or V.0 "+"= V.9.<p> Don\'t forget to check your answers "+"by plugging them into<br> the original equation "+"and making sure it is still true.<br> If you do "+"this we see that both answers are solutions, <Br> "+"Thus the largest solution is: V.10.<p> (<i>See "+"pages 148-149 of your text for more details.</i>)";
ts=new Array("V.10",NA);ta=new parent.Val("I",ts);tp[3]=new parent.Problem("S",13,tv,0,NA,tq,ta,th,tw);tv=new Array();ts=new Array("x,y,z,a,b,c,z,v,w",NA);tv[0]=new parent.Val("L.9",ts);ts=new Array(1,3);tv[1]=new parent.Val("I",ts);ts=new Array("V.1:2,3,4",NA);tv[2]=new parent.Val("L.3",ts);ts=new Array("V.2*2",NA);tv[3]=new parent.Val("I",ts);ts=new Array("V.1:25,6,4",NA);tv[4]=new parent.Val("L.3",ts);ts=new Array(3,"V.4");tv[5]=new parent.Val("I",ts);ts=new Array(2,"V.5-1");tv[6]=new parent.Val("I",ts);ts=new Array("V.1:(V.0<sup>V.3</sup>)<sup><sup>1</sup>/ <sup>2</sup></sup>,"+"(V.0<sup>V.3</sup>)<sup><sup>1</sup>/ "+"<sup>3</sup></sup>,(V.0<sup>V.3</sup>)<sup><sup>1</sup>/ "+"<sup>4</sup></sup>",NA);tv[7]=new parent.Val("L.3",ts);ts=new Array("Math.pow(V.5,V.2)",NA);tv[8]=new parent.Val("I",ts);ts=new Array("Math.pow(V.6,V.2)",NA);tv[9]=new parent.Val("I",ts);ts=new Array("Math.max(V.5,V.6)",NA);tv[10]=new parent.Val("I",ts);ts=new Array("V.8+V.9",NA);tv[11]=new parent.Val("I",ts);ts=new Array("V.8*V.9",NA);tv[12]=new parent.Val("I",ts);ts=new Array("V.2==2||V.2==V.4?'<img src=\"chars/pm.gif\" align=bottom alt=\"pm\">'"+":''",NA);tv[13]=new parent.Val("SE",ts);
tq="What is the largest solution of:<br> V.0<sup>V.3</sup> "+"- V.11V.0<sup>V.2</sup> + V.12 = 0?";th="chap1/sect7/prob5/hint.gif";tw="V.0<sup>V.3</sup> - V.11V.0<sup>V.2</sup> + V.12 "+"= 0.<p> Let u = V.0<sup>V.2</sup>. We can rewrite "+"the above as:<br> u<sup>2</sup> + V.11u +V.12 "+"= 0.<p> Solving in terms of u:<br> (u - V.8)(u "+"- V.9) = 0<br> so u = V.8 or u = V.9<p> Now substituting "+"V.0<sup>V.2</sup> back in for u and solving "+"for V.0:<br> V.0<sup>V.2</sup> = V.8 or V.0<sup>V.2</sup> "+"= V.9<br> V.0 = V.13V.8<sup>1/V.2</sup> "+"or V.0 = V.13V.9<sup>1/V.2</sup><br> V.0 "+"= V.13V.5 or V.0 = V.13V.6.<p> If we plug each of "+"these four solutions into our original<br> equation,"+" we would see that they are all 4 solutions.<p> "+"Thus the largest solution is: V.10.<p> (<i>See "+"pages 149-150 of your text for more details.</i>)";
ts=new Array("V.10",NA);ta=new parent.Val("I",ts);tp[4]=new parent.Problem("S",14,tv,0,NA,tq,ta,th,tw);np=5;st="Section 2.7 &nbsp; Equations Reducible to Quadratic Form";tl="help/none.html";ss[6]=new parent.Section(st,np,tp,tl,"sounds/sec2_7.wav","avi/sec2_7.avi");parent.hist[ch][6].max_questions=np;parent.hist[ch][6].title=st;
tp=new Array();tv=new Array();ts=new Array(3,10);tv[0]=new parent.Val("I",ts);ts=new Array("-V.0,V.0",NA);tv[1]=new parent.Val("L.2",ts);ts=new Array(3,10);tv[2]=new parent.Val("I",ts);ts=new Array("-V.2,V.2",NA);tv[3]=new parent.Val("L.2",ts);ts=new Array("Math.min(V.1,V.3)-2",NA);tv[4]=new parent.Val("I",ts);ts=new Array("Math.max(V.1,V.3)",NA);tv[5]=new parent.Val("I",ts);ts=new Array("(V.4==0)?-2:V.4",NA);tv[6]=new parent.Val("I",ts);ts=new Array("(V.5*(V.6+V.5)==0)?Math.abs(V.4)+2:V.5",NA);tv[7]=new parent.Val("I",ts);ts=new Array(1,NA);tv[8]=new parent.Val("I",ts);ts=new Array("-V.8*(V.6+V.7)",NA);tv[9]=new parent.Val("I",ts);ts=new Array("V.8*V.6*V.7",NA);tv[10]=new parent.Val("I",ts);ts=new Array("parent.term1('V.8','x<sup>2</sup>')",NA);tv[11]=new parent.Val("SE",ts);ts=new Array("parent.term('V.9','x')",NA);tv[12]=new parent.Val("SE",ts);ts=new Array("parent.term('V.10','')",NA);tv[13]=new parent.Val("SE",ts);ts=new Array(1,4);tv[14]=new parent.Val("I",ts);ts=new Array("V.14:>,<img src=\"chars/geq.gif\" align=bottom alt=\"geq\">,"+"<,<img src=\"chars/leq.gif\" align=bottom "+"alt=\"leq\">",NA);tv[15]=new parent.Val("L.4",ts);ts=new Array("(-<img src=\"chars/infty.gif\" align=bottom alt=\"infty\">,"+"V.6)<img src=\"chars/union.gif\" align=bottom "+"alt=\"union\">(V.7,<img src=\"chars/infty.gif\" "+"align=bottom alt=\"infty\">)",NA);tv[16]=new parent.Val("S",ts);ts=new Array("(-<img src=\"chars/infty.gif\" align=bottom alt=\"infty\">,"+"V.6]<img src=\"chars/union.gif\" align=bottom "+"alt=\"union\">[V.7,<img src=\"chars/infty.gif\" "+"align=bottom alt=\"infty\">)",NA);tv[17]=new parent.Val("S",ts);ts=new Array("(V.6,V.7)",NA);tv[18]=new parent.Val("S",ts);ts=new Array("[V.6,V.7]",NA);tv[19]=new parent.Val("S",ts);ts=new Array("V.14:V.16,V.17,V.18,V.19",NA);tv[20]=new parent.Val("L.4",ts);ts=new Array(-6,6);tv[21]=new parent.Val("I",ts);ts=new Array(-6,6);tv[22]=new parent.Val("I",ts);ts=new Array("Math.min(V.21,V.22)",NA);tv[23]=new parent.Val("I",ts);ts=new Array("Math.max(V.21,V.22)+1",NA);
tv[24]=new parent.Val("I",ts);ts=new Array("parent.term(-V.6,'')",NA);tv[25]=new parent.Val("SE",ts);ts=new Array("parent.term(-V.7,'')",NA);tv[26]=new parent.Val("SE",ts);ts=new Array("(V.6>0)?0:V.6-1",NA);tv[27]=new parent.Val("I",ts);ts=new Array("(V.6*V.7<0)?0:(V.6+V.7)/2",NA);tv[28]=new parent.Val("I",ts);ts=new Array("(V.7<0)?0:(V.7+1)",NA);tv[29]=new parent.Val("I",ts);ts=new Array("V.8*V.27*V.27+V.9*V.27+V.10",NA);tv[30]=new parent.Val("I",ts);ts=new Array("V.8*V.28*V.28+V.9*V.28+V.10",NA);tv[31]=new parent.Val("I",ts);ts=new Array("V.8*V.29*V.29+V.9*V.29+V.10",NA);tv[32]=new parent.Val("I",ts);ts=new Array("(V.14<3)?'Yes':'No'",NA);tv[33]=new parent.Val("SE",ts);ts=new Array("(V.14<3)?'No':'Yes'",NA);tv[34]=new parent.Val("SE",ts);ts=new Array("included",NA);tv[35]=new parent.Val("S",ts);ts=new Array("not included",NA);tv[36]=new parent.Val("S",ts);ts=new Array("V.14:V.36,V.35,V.36,V.35",NA);tv[37]=new parent.Val("L.4",ts);
tq="Solve: V.11 V.12 V.13 V.15 0.";to=new Array();ts=new Array("V.14:V.19,V.16,V.17,V.18",NA);to[0]=new parent.Val("L.4",ts);ts=new Array("V.14:V.18,V.19,V.16,V.17",NA);to[1]=new parent.Val("L.4",ts);ts=new Array("V.14:V.17,V.18,V.19,V.16",NA);to[2]=new parent.Val("L.4",ts);ts=new Array("(-<img src=\"chars/infty.gif\" align=bottom alt=\"infty\">,"+"V.23)<img src=\"chars/union.gif\" align=bottom "+"alt=\"union\">(V.24,<img src=\"chars/infty.gif\" "+"align=bottom alt=\"infty\">)",NA);to[3]=new parent.Val("S",ts);ts=new Array("(V.23,V.24)",NA);to[4]=new parent.Val("S",ts);ts=new Array("[V.23,V.24]",NA);to[5]=new parent.Val("S",ts);ts=new Array("(-<img src=\"chars/infty.gif\" align=bottom alt=\"infty\">,"+"V.23]<img src=\"chars/union.gif\" align=bottom "+"alt=\"union\">[V.24,<img src=\"chars/infty.gif\" "+"align=bottom alt=\"infty\">)",NA);to[6]=new parent.Val("S",ts);th="chap1/sect8/prob1/hint.gif";
tw="The inequality is already in standard form.<p> To "+"find the real zeros, solve the equation: <br> "+"V.11 V.12 V.13=0.<br> V.11 V.12 V.13=<br> (x V.25)(x "+"V.26)=0<br> so x=V.6 and x=V.7 are the zeros.<p> "+"Thus, the intervals are (-<img src=\"chars/infty.gif\" "+"align=bottom alt=\"infty\">,V.6),(V.6,"+"V.7) and (V.7,<img src=\"chars/infty.gif\" align=bottom "+"alt=\"infty\">). <p><table cellpadding=3 "+"border=1> <tr align=center><td>Interval</td><td>Test "+"Point</td><td>Value</td><td>Conclusion</td></tr> "+"<tr align=center><td>(-<img src=\"chars/infty.gif\" "+"align=bottom alt=\"infty\">,V.6)</td><td>V.27</td><"+"td>V.30</td><td>V.33</td></tr> "+"<tr align=center><td>(V.6,V.7)</td><td>V.28</td><td>V.31</td><td>"+"V.34</td></tr> <tr align=center><td>(V.7,"+"<img src=\"chars/infty.gif\" align=bottom "+"alt=\"infty\">)</td><td>V.29</td><td>V.32</td><td>V.33</td></"+"tr> </table><p> Because the inequality "+"is V.15, the zeros<br> are V.37.<p> Therefore,"+" the solution is V.20.<p> (<i>See pages 155-157 "+"of your text for more details.</i>)";
ts=new Array("V.20",NA);ta=new parent.Val("S",ts);tp[0]=new parent.Problem("M",38,tv,7,to,tq,ta,th,tw);tv=new Array();ts=new Array(2,10);tv[0]=new parent.Val("I",ts);ts=new Array("-V.0,V.0",NA);tv[1]=new parent.Val("L.2",ts);ts=new Array(2,10);tv[2]=new parent.Val("I",ts);ts=new Array("-V.2,V.2",NA);tv[3]=new parent.Val("L.2",ts);ts=new Array("Math.min(V.1,V.3)-2",NA);tv[4]=new parent.Val("I",ts);ts=new Array("Math.max(V.1,V.3)",NA);tv[5]=new parent.Val("I",ts);ts=new Array("(V.4==0)?-2:V.4",NA);tv[6]=new parent.Val("I",ts);ts=new Array("(V.5*(V.6+V.5)==0)?Math.abs(V.4)+2:V.5",NA);tv[7]=new parent.Val("I",ts);ts=new Array(2,7);tv[8]=new parent.Val("I",ts);ts=new Array("-V.8*(V.6+V.7)",NA);tv[9]=new parent.Val("I",ts);ts=new Array("V.8*V.6*V.7",NA);tv[10]=new parent.Val("I",ts);ts=new Array("parent.term1('V.8','x<sup>2</sup>')",NA);tv[11]=new parent.Val("SE",ts);ts=new Array("parent.term('V.9','x')",NA);tv[12]=new parent.Val("SE",ts);ts=new Array("parent.term('V.10','')",NA);tv[13]=new parent.Val("SE",ts);ts=new Array(1,4);tv[14]=new parent.Val("I",ts);ts=new Array("V.14:>,<img src=\"chars/geq.gif\" align=bottom alt=\"geq\">,"+"<,<img src=\"chars/leq.gif\" align=bottom "+"alt=\"leq\">",NA);tv[15]=new parent.Val("L.4",ts);ts=new Array("(-<img src=\"chars/infty.gif\" align=bottom alt=\"infty\">,"+"V.6)<img src=\"chars/union.gif\" align=bottom "+"alt=\"union\">(V.7,<img src=\"chars/infty.gif\" "+"align=bottom alt=\"infty\">)",NA);tv[16]=new parent.Val("S",ts);ts=new Array("(-<img src=\"chars/infty.gif\" align=bottom alt=\"infty\">,"+"V.6]<img src=\"chars/union.gif\" align=bottom "+"alt=\"union\">[V.7,<img src=\"chars/infty.gif\" "+"align=bottom alt=\"infty\">)",NA);tv[17]=new parent.Val("S",ts);ts=new Array("(V.6,V.7)",NA);tv[18]=new parent.Val("S",ts);ts=new Array("[V.6,V.7]",NA);tv[19]=new parent.Val("S",ts);ts=new Array("V.14:V.16,V.17,V.18,V.19",NA);tv[20]=new parent.Val("L.4",ts);ts=new Array(-6,6);tv[21]=new parent.Val("I",ts);ts=new Array(-6,6);tv[22]=new parent.Val("I",ts);
ts=new Array("Math.min(V.21,V.22)",NA);tv[23]=new parent.Val("I",ts);ts=new Array("Math.max(V.21,V.22)+1",NA);tv[24]=new parent.Val("I",ts);ts=new Array("parent.term(-V.6,'')",NA);tv[25]=new parent.Val("SE",ts);ts=new Array("parent.term(-V.7,'')",NA);tv[26]=new parent.Val("SE",ts);ts=new Array("(V.6>0)?0:V.6-1",NA);tv[27]=new parent.Val("I",ts);ts=new Array("(V.6*V.7<0)?0:(V.6+V.7)/2",NA);tv[28]=new parent.Val("I",ts);ts=new Array("(V.7<0)?0:(V.7+1)",NA);tv[29]=new parent.Val("I",ts);ts=new Array("V.8*V.27*V.27+V.9*V.27+V.10",NA);tv[30]=new parent.Val("I",ts);ts=new Array("V.8*V.28*V.28+V.9*V.28+V.10",NA);tv[31]=new parent.Val("I",ts);ts=new Array("V.8*V.29*V.29+V.9*V.29+V.10",NA);tv[32]=new parent.Val("I",ts);ts=new Array("(V.14<3)?'Yes':'No'",NA);tv[33]=new parent.Val("SE",ts);ts=new Array("(V.14<3)?'No':'Yes'",NA);tv[34]=new parent.Val("SE",ts);ts=new Array("included",NA);tv[35]=new parent.Val("S",ts);ts=new Array("not included",NA);tv[36]=new parent.Val("S",ts);ts=new Array("V.14:V.36,V.35,V.36,V.35",NA);tv[37]=new parent.Val("L.4",ts);
tq="Solve: V.11 V.12 V.13 V.15 0.";to=new Array();ts=new Array("V.14:V.19,V.16,V.17,V.18",NA);to[0]=new parent.Val("L.4",ts);ts=new Array("V.14:V.18,V.19,V.16,V.17",NA);to[1]=new parent.Val("L.4",ts);ts=new Array("V.14:V.17,V.18,V.19,V.16",NA);to[2]=new parent.Val("L.4",ts);ts=new Array("(-<img src=\"chars/infty.gif\" align=bottom alt=\"infty\">,"+"V.23)<img src=\"chars/union.gif\" align=bottom "+"alt=\"union\">(V.24,<img src=\"chars/infty.gif\" "+"align=bottom alt=\"infty\">)",NA);to[3]=new parent.Val("S",ts);ts=new Array("(V.23,V.24)",NA);to[4]=new parent.Val("S",ts);ts=new Array("[V.23,V.24]",NA);to[5]=new parent.Val("S",ts);ts=new Array("(-<img src=\"chars/infty.gif\" align=bottom alt=\"infty\">,"+"V.23]<img src=\"chars/union.gif\" align=bottom "+"alt=\"union\">[V.24,<img src=\"chars/infty.gif\" "+"align=bottom alt=\"infty\">)",NA);to[6]=new parent.Val("S",ts);th="chap1/sect8/prob2/hint.gif";
tw="Note that the equation is already in standard form.<p> "+"First find the zeros of the equation:<br> "+"V.11 V.12 V.13=0.<br> V.11 V.12 V.13=V.8(x V.25)(x "+"V.26)=0<br> x=V.6 and x=V.7 are the zeros.<br> "+"The intervals are (-<img src=\"chars/infty.gif\" "+"align=bottom alt=\"infty\">,V.6),(V.6,V.7) and "+"(V.7,<img src=\"chars/infty.gif\" align=bottom "+"alt=\"infty\">). <p><table cellpadding=3 border=1> "+"<tr align=center><td>Interval</td><td>Test "+"Point</td><td>Value</td><td>Conclusion</td></tr> "+"<tr align=center><td>(-<img src=\"chars/infty.gif\" "+"align=bottom alt=\"infty\">,V.6)</td><td>V.27</td><td>V.30</"+"td><td>V.33</td></tr> <tr align=center><td>(V.6,"+"V.7)</td><td>V.28</td><td>V.31</td><td>V.34</td>"+"</tr> <tr align=center><td>(V.7,"+"<img src=\"chars/infty.gif\" align=bottom alt=\"infty\">)</td><td>"+"V.29</td><td>V.32</td><td>V.33</td></tr> "+"</table><p> Because the inequality is "+"V.15, the zeros<br> are V.37.<br> Therefore, the "+"solution is V.20.<p> (<i>See pages 154-157 of "+"your text for more details.</i>)";
ts=new Array("V.20",NA);ta=new parent.Val("S",ts);tp[1]=new parent.Problem("M",38,tv,7,to,tq,ta,th,tw);tv=new Array();ts=new Array(2,10);tv[0]=new parent.Val("I",ts);ts=new Array("-V.0,V.0",NA);tv[1]=new parent.Val("L.2",ts);ts=new Array(2,10);tv[2]=new parent.Val("I",ts);ts=new Array("-V.2,V.2",NA);tv[3]=new parent.Val("L.2",ts);ts=new Array("Math.min(V.1,V.3)-2",NA);tv[4]=new parent.Val("I",ts);ts=new Array("Math.max(V.1,V.3)",NA);tv[5]=new parent.Val("I",ts);ts=new Array("(V.4==0)?-2:V.4",NA);tv[6]=new parent.Val("I",ts);ts=new Array("(V.5*(V.6+V.5)==0)?Math.abs(V.4)+2:V.5",NA);tv[7]=new parent.Val("I",ts);ts=new Array(2,7);tv[8]=new parent.Val("I",ts);ts=new Array("-V.8*(V.6+V.7)",NA);tv[9]=new parent.Val("I",ts);ts=new Array("V.8*V.6*V.7",NA);tv[10]=new parent.Val("I",ts);ts=new Array("parent.term1('V.8','x<sup>2</sup>')",NA);tv[11]=new parent.Val("SE",ts);ts=new Array("parent.term('V.9','x')",NA);tv[12]=new parent.Val("SE",ts);ts=new Array("parent.term('V.10','')",NA);tv[13]=new parent.Val("SE",ts);ts=new Array(1,4);tv[14]=new parent.Val("I",ts);ts=new Array("V.14:>,<img src=\"chars/geq.gif\" align=bottom alt=\"geq\">,"+"<,<img src=\"chars/leq.gif\" align=bottom "+"alt=\"leq\">",NA);tv[15]=new parent.Val("L.4",ts);ts=new Array("(-<img src=\"chars/infty.gif\" align=bottom alt=\"infty\">,"+"V.6)<img src=\"chars/union.gif\" align=bottom "+"alt=\"union\">(V.7,<img src=\"chars/infty.gif\" "+"align=bottom alt=\"infty\">)",NA);tv[16]=new parent.Val("S",ts);ts=new Array("(-<img src=\"chars/infty.gif\" align=bottom alt=\"infty\">,"+"V.6]<img src=\"chars/union.gif\" align=bottom "+"alt=\"union\">[V.7,<img src=\"chars/infty.gif\" "+"align=bottom alt=\"infty\">)",NA);tv[17]=new parent.Val("S",ts);ts=new Array("(V.6,V.7)",NA);tv[18]=new parent.Val("S",ts);ts=new Array("[V.6,V.7]",NA);tv[19]=new parent.Val("S",ts);ts=new Array("V.14:V.16,V.17,V.18,V.19",NA);tv[20]=new parent.Val("L.4",ts);ts=new Array(-6,6);tv[21]=new parent.Val("I",ts);ts=new Array(-6,6);tv[22]=new parent.Val("I",ts);
ts=new Array("Math.min(V.21,V.22)",NA);tv[23]=new parent.Val("I",ts);ts=new Array("Math.max(V.21,V.22)+1",NA);tv[24]=new parent.Val("I",ts);ts=new Array("parent.term(-V.6,'')",NA);tv[25]=new parent.Val("SE",ts);ts=new Array("parent.term(-V.7,'')",NA);tv[26]=new parent.Val("SE",ts);ts=new Array("(V.6>0)?0:V.6-1",NA);tv[27]=new parent.Val("I",ts);ts=new Array("(V.6*V.7<0)?0:(V.6+V.7)/2",NA);tv[28]=new parent.Val("I",ts);ts=new Array("(V.7<0)?0:(V.7+1)",NA);tv[29]=new parent.Val("I",ts);ts=new Array("V.8*V.27*V.27+V.9*V.27+V.10",NA);tv[30]=new parent.Val("I",ts);ts=new Array("V.8*V.28*V.28+V.9*V.28+V.10",NA);tv[31]=new parent.Val("I",ts);ts=new Array("V.8*V.29*V.29+V.9*V.29+V.10",NA);tv[32]=new parent.Val("I",ts);ts=new Array("(V.14<3)?'Yes':'No'",NA);tv[33]=new parent.Val("SE",ts);ts=new Array("(V.14<3)?'No':'Yes'",NA);tv[34]=new parent.Val("SE",ts);ts=new Array("V.14:<,<img src=\"chars/leq.gif\" align=bottom alt=\"leq\">,"+">,<img src=\"chars/geq.gif\" align=bottom "+"alt=\"geq\">",NA);tv[35]=new parent.Val("L.4",ts);ts=new Array("parent.term1('-V.9','x')",NA);tv[36]=new parent.Val("SE",ts);ts=new Array("parent.term('-V.10','')",NA);tv[37]=new parent.Val("SE",ts);ts=new Array("parent.term1('-V.8','x<sup>2</sup>')",NA);tv[38]=new parent.Val("SE",ts);ts=new Array("parent.term('-V.9','x')",NA);tv[39]=new parent.Val("SE",ts);ts=new Array("included",NA);tv[40]=new parent.Val("S",ts);ts=new Array("not included",NA);tv[41]=new parent.Val("S",ts);ts=new Array("V.14:V.41,V.40,V.41,V.40",NA);tv[42]=new parent.Val("L.4",ts);
tq="Solve V.36 V.37 V.35 V.11 for x.";to=new Array();ts=new Array("V.14:V.19,V.16,V.17,V.18",NA);to[0]=new parent.Val("L.4",ts);ts=new Array("V.14:V.18,V.19,V.16,V.17",NA);to[1]=new parent.Val("L.4",ts);ts=new Array("V.14:V.17,V.18,V.19,V.16",NA);to[2]=new parent.Val("L.4",ts);ts=new Array("(-<img src=\"chars/infty.gif\" align=bottom alt=\"infty\">,"+"V.23)<img src=\"chars/union.gif\" align=bottom "+"alt=\"union\">(V.24,<img src=\"chars/infty.gif\" "+"align=bottom alt=\"infty\">)",NA);to[3]=new parent.Val("S",ts);ts=new Array("(V.23,V.24)",NA);to[4]=new parent.Val("S",ts);ts=new Array("[V.23,V.24]",NA);to[5]=new parent.Val("S",ts);ts=new Array("(-<img src=\"chars/infty.gif\" align=bottom alt=\"infty\">,"+"V.23]<img src=\"chars/union.gif\" align=bottom "+"alt=\"union\">[V.24,<img src=\"chars/infty.gif\" "+"align=bottom alt=\"infty\">)",NA);to[6]=new parent.Val("S",ts);th="chap1/sect8/prob3/hint.gif";
tw="Let\'s first get it in standard form <br> by moving "+"all terms to the left side:<br> V.38 V.39 V.37 "+"V.35 0<p> We can multiply both sides by (-1),"+" so that the<br> coefficient before x<sup>2</sup> "+"is positive.<br> (Also, change the direction of "+"the inequality because<br> -1 is a negative number.)<br> "+"V.11 V.12 V.13 V.15 0.<p> Now find the "+"zeros for the equation:<br> V.11 V.12 V.13=0<br> "+"V.11 V.12 V.13=0<br> V.8(x V.25)(x V.26)=0<br> "+"x=V.6 and x=V.7 are the zeros.<p> The intervals "+"are (-<img src=\"chars/infty.gif\" align=bottom "+"alt=\"infty\">,V.6),(V.6,V.7) and (V.7,<img src=\"chars/infty.gif\""+" align=bottom alt=\"infty\">). <p><table cellpadding=3 border=1> <tr align=center><td>Interv"+"al</td><td>Test Point</td><td>Value</td><td>Conc"+"lusion</td></tr> <tr align=center><td>(-<img "+"src=\"chars/infty.gif\" align=bottom "+"alt=\"infty\">,V.6)</td><td>V.27</td><td>V.30</td><td>V.33</td"+"></tr> <tr align=center><td>(V.6,"+"V.7)</td><td>V.28</td><td>V.31</td><td>V.34</td></tr> "+"<tr align=center><td>(V.7,<img src=\"chars/infty.gif\" "+"align=bottom alt=\"infty\">)</td><td>V.29</td><td>"+"V.32</td><td>V.33</td></tr> </table><p> "+"Because the inequality is V.15, the x-intercepts "+"are<br> V.42.<p> Therefore, the solution "+"is V.20.<p> (<i>See pages 153-157 of your text "+"for more details.</i>)";ts=new Array("V.20",NA);ta=new parent.Val("S",ts);
tp[2]=new parent.Problem("M",43,tv,7,to,tq,ta,th,tw);tv=new Array();ts=new Array(2,12);tv[0]=new parent.Val("I",ts);ts=new Array("-V.0,V.0",NA);tv[1]=new parent.Val("L.2",ts);ts=new Array(2,12);tv[2]=new parent.Val("I",ts);ts=new Array("-V.2,V.2",NA);tv[3]=new parent.Val("L.2",ts);ts=new Array("Math.min(V.1,V.3)-2",NA);tv[4]=new parent.Val("I",ts);ts=new Array("Math.max(V.1,V.3)",NA);tv[5]=new parent.Val("I",ts);ts=new Array("(V.4==0)?-2:V.4",NA);tv[6]=new parent.Val("I",ts);ts=new Array("(V.5*(V.6+V.5)==0)?Math.abs(V.4)+2:V.5",NA);tv[7]=new parent.Val("I",ts);ts=new Array(2,7);tv[8]=new parent.Val("I",ts);ts=new Array("V.8*V.7",NA);tv[9]=new parent.Val("I",ts);ts=new Array("parent.term('-V.6','')",NA);tv[10]=new parent.Val("SE",ts);ts=new Array("parent.term('-V.8','x')",NA);tv[11]=new parent.Val("SE",ts);ts=new Array("0:V.9 V.11:x V.10",NA);tv[12]=new parent.Val("M",ts);ts=new Array("0:P(x):Q(x)",NA);tv[13]=new parent.Val("M",ts);ts=new Array(1,4);tv[14]=new parent.Val("I",ts);ts=new Array("V.14:<,<img src=\"chars/leq.gif\" align=bottom alt=\"leq\">,"+">,<img src=\"chars/geq.gif\" align=bottom "+"alt=\"geq\">",NA);tv[15]=new parent.Val("L.4",ts);ts=new Array("(-<img src=\"chars/infty.gif\" align=bottom alt=\"infty\">,"+"V.6)<img src=\"chars/union.gif\" align=bottom "+"alt=\"union\">(V.7,<img src=\"chars/infty.gif\" "+"align=bottom alt=\"infty\">)",NA);tv[16]=new parent.Val("S",ts);ts=new Array("(-<img src=\"chars/infty.gif\" align=bottom alt=\"infty\">,"+"V.6]<img src=\"chars/union.gif\" align=bottom "+"alt=\"union\">[V.7,<img src=\"chars/infty.gif\" "+"align=bottom alt=\"infty\">)",NA);tv[17]=new parent.Val("S",ts);ts=new Array("(V.6,V.7)",NA);tv[18]=new parent.Val("S",ts);ts=new Array("(V.6,V.7]",NA);tv[19]=new parent.Val("S",ts);ts=new Array("V.14:V.16,V.17,V.18,V.19",NA);tv[20]=new parent.Val("L.4",ts);ts=new Array(-6,6);tv[21]=new parent.Val("I",ts);ts=new Array(-6,6);tv[22]=new parent.Val("I",ts);ts=new Array("Math.min(V.21,V.22)",NA);tv[23]=new parent.Val("I",ts);ts=new Array("Math.max(V.21,V.22)+1",NA);
tv[24]=new parent.Val("I",ts);ts=new Array("parent.term(-V.6,'')",NA);tv[25]=new parent.Val("SE",ts);ts=new Array("parent.term(-V.7,'')",NA);tv[26]=new parent.Val("SE",ts);ts=new Array("(V.6>0)?0:V.6-1",NA);tv[27]=new parent.Val("I",ts);ts=new Array("(V.6*V.7<0)?0:(V.6+V.7)/2",NA);tv[28]=new parent.Val("I",ts);ts=new Array("(V.7<0)?0:(V.7+1)",NA);tv[29]=new parent.Val("I",ts);ts=new Array("V.8*(V.7-V.27)",NA);tv[30]=new parent.Val("I",ts);ts=new Array("V.8*(V.7-V.28)",NA);tv[31]=new parent.Val("I",ts);ts=new Array("V.8*(V.7-V.29)",NA);tv[32]=new parent.Val("I",ts);ts=new Array("(V.14<3)?'Yes':'No'",NA);tv[33]=new parent.Val("SE",ts);ts=new Array("(V.14<3)?'No':'Yes'",NA);tv[34]=new parent.Val("SE",ts);ts=new Array("(<sup>V.9</sup>/<sub>V.8</sub>",NA);tv[35]=new parent.Val("S",ts);ts=new Array("-V.9",NA);tv[36]=new parent.Val("I",ts);ts=new Array(" <sup>V.36</sup>/<sub>-V.8</sub>",NA);tv[37]=new parent.Val("S",ts);ts=new Array("V.27-V.6",NA);tv[38]=new parent.Val("I",ts);ts=new Array("V.30/V.38",NA);tv[39]=new parent.Val("I",ts);ts=new Array("V.30/parent.gcd(V.30,V.38)",NA);tv[40]=new parent.Val("I",ts);ts=new Array("V.38/parent.gcd(V.30,V.38)",NA);tv[41]=new parent.Val("I",ts);ts=new Array(" <sup>V.40</sup>/<sub>V.41</sub>",NA);tv[42]=new parent.Val("S",ts);ts=new Array("(V.30%V.38==0)?'V.39':'V.42'",NA);tv[43]=new parent.Val("SE",ts);ts=new Array("V.28-V.6",NA);tv[44]=new parent.Val("I",ts);ts=new Array("V.31/V.44",NA);tv[45]=new parent.Val("I",ts);ts=new Array("V.31/parent.gcd(V.31,V.44)",NA);tv[46]=new parent.Val("I",ts);ts=new Array("V.44/parent.gcd(V.31,V.44)",NA);tv[47]=new parent.Val("I",ts);ts=new Array(" <sup>V.46</sup>/<sub>V.47</sub>",NA);tv[48]=new parent.Val("S",ts);ts=new Array("(V.31%V.44==0)?'V.45':'V.48'",NA);tv[49]=new parent.Val("SE",ts);ts=new Array("V.29-V.6",NA);tv[50]=new parent.Val("I",ts);ts=new Array("V.32/V.50",NA);tv[51]=new parent.Val("I",ts);ts=new Array("V.32/parent.gcd(V.32,V.50)",NA);tv[52]=new parent.Val("I",ts);ts=new Array("V.50/parent.gcd(V.32,V.50)",NA);
tv[53]=new parent.Val("I",ts);ts=new Array("<sup>V.52</sup>/<sub>V.53</sub>",NA);tv[54]=new parent.Val("S",ts);ts=new Array("(V.32%V.50==0)?'V.51':'V.54'",NA);tv[55]=new parent.Val("SE",ts);ts=new Array("included",NA);tv[56]=new parent.Val("S",ts);ts=new Array("not included",NA);tv[57]=new parent.Val("S",ts);ts=new Array("V.14:V.57,V.56,V.57,V.56",NA);tv[58]=new parent.Val("L.4",ts);
tq="Solve V.12 V.15 0 for x.";to=new Array();ts=new Array("V.14:V.19,V.16,V.17,V.18",NA);to[0]=new parent.Val("L.4",ts);ts=new Array("V.14:V.18,V.19,V.16,V.17",NA);to[1]=new parent.Val("L.4",ts);ts=new Array("V.14:V.17,V.18,V.19,V.16",NA);to[2]=new parent.Val("L.4",ts);ts=new Array("(-<img src=\"chars/infty.gif\" align=bottom alt=\"infty\">,"+"V.23)<img src=\"chars/union.gif\" align=bottom "+"alt=\"union\">(V.24,<img src=\"chars/infty.gif\" "+"align=bottom alt=\"infty\">)",NA);to[3]=new parent.Val("S",ts);ts=new Array("(V.23,V.24)",NA);to[4]=new parent.Val("S",ts);ts=new Array("[V.23,V.24]",NA);to[5]=new parent.Val("S",ts);ts=new Array("(-<img src=\"chars/infty.gif\" align=bottom alt=\"infty\">,"+"V.23]<img src=\"chars/union.gif\" align=bottom "+"alt=\"union\">[V.24,<img src=\"chars/infty.gif\" "+"align=bottom alt=\"infty\">)",NA);to[6]=new parent.Val("S",ts);th="chap1/sect8/prob4/hint.gif";
tw="The inequality is already in the standard form<br> "+"of V.13 V.15 0, where P(x)=V.9 V.11 and Q(x)=x "+"V.10.<p> Find all real zeros of P(x)=0 and Q(x)=0:<br> "+"V.9 V.11=0<br> -V.8x=V.36<br> x=V.37<br> "+"x=V.7.<p> x V.10=0<br>x=V.6.<p> Thus the zeros "+"are x=V.6 and x=V.7.<p> The intervals are (-<img "+"src=\"chars/infty.gif\" align=bottom alt=\"infty\">,"+"V.6),(V.6,V.7) and (V.7,<img src=\"chars/infty.gif\" "+"align=bottom alt=\"infty\">). <p><table "+"cellspacing=3 border=1> <tr align=right><td>Interval</td><td>T"+"est Point</td><td>Value</td><td>Conclusion</td><"+"/tr> <tr align=right><td>(-<img "+"src=\"chars/infty.gif\" align=bottom alt=\"infty\">,"+"V.6)</td><td>V.27</td><td>V.43</td><td>V.33</td></tr> "+"<tr align=right><td>(V.6,V.7)</td><td>V.28</td><td>V.4"+"9</td><td>V.34</td></tr> <tr align=right><td>(V."+"7,<img src=\"chars/infty.gif\" "+"align=bottom alt=\"infty\">)</td><td>V.29</td><td>V.55</td><td>V."+"33</td></tr> </table><p> Since "+"the inequality is V.15, the zeros<br> are V.58.<p> "+"Therefore,the answer is V.20.<p> (<i>See pages "+"158-160 of your text for more details.</i>)";ts=new Array("V.20",NA);ta=new parent.Val("S",ts);
tp[3]=new parent.Problem("M",59,tv,7,to,tq,ta,th,tw);tv=new Array();ts=new Array(1,12);tv[0]=new parent.Val("I",ts);ts=new Array("V.0*V.0",NA);tv[1]=new parent.Val("I",ts);ts=new Array("2*V.0",NA);tv[2]=new parent.Val("I",ts);ts=new Array("-:V.1:x + V.2",NA);tv[3]=new parent.Val("M",ts);ts=new Array("0:V.1:x + V.2",NA);tv[4]=new parent.Val("M",ts);ts=new Array("0:x<sup>2</sup> + V.2x + V.1:x + V.2",NA);tv[5]=new parent.Val("M",ts);ts=new Array("0:(x + V.0)<sup>2</sup>:x + V.2",NA);tv[6]=new parent.Val("M",ts);ts=new Array("x <img src=\"chars/element.gif\" align=bottom alt=\"element\"> "+"(-<img src=\"chars/infty.gif\" align=bottom "+"alt=\"infty\">,-V.2)",NA);tv[7]=new parent.Val("S",ts);
tq="Solve: x <img src=\"chars/leq.gif\" align=bottom "+"alt=\"leq\"> V.3";to=new Array();ts=new Array("x <img src=\"chars/element.gif\" align=bottom alt=\"element\"> "+"(-<img src=\"chars/infty.gif\" align=bottom "+"alt=\"infty\">,-V.0]",NA);to[0]=new parent.Val("S",ts);ts=new Array("x <img src=\"chars/element.gif\" align=bottom alt=\"element\"> "+"(-V.2,-V.0]",NA);to[1]=new parent.Val("S",ts);ts=new Array("x <img src=\"chars/element.gif\" align=bottom alt=\"element\"> "+"(-V.2,-V.0] <img src=\"chars/union.gif\" "+"align=bottom alt=\"union\"> [V.0,+<img src=\"chars/infty.gif\""+" align=bottom alt=\"infty\">)",NA);to[2]=new parent.Val("S",ts);ts=new Array("x <img src=\"chars/element.gif\" align=bottom alt=\"element\"> "+"(-V.2,V.0]",NA);to[3]=new parent.Val("S",ts);
th="chap1/sect8/prob5/hint.gif";tw="First put the problem into standard form:<br> x "+"<img src=\"chars/leq.gif\" align=bottom alt=\"leq\"> "+"V.3 <br> x +V.4 <img src=\"chars/leq.gif\" "+"align=bottom alt=\"leq\"> 0 <br> V.5 <img src=\"chars/leq.gif\" align=bottom alt=\"leq\"> 0 <br> "+"V.6 <img src=\"chars/leq.gif\" align=bottom alt=\"leq\"> "+"0. <p> Note 1: We have a singularity at "+"x = -V.2.<br> Note 2: The numerator = 0 when x "+"= -V.0.<p> Thus the regions we must consider are:<br> "+"A = (-<img src=\"chars/infty.gif\" align=bottom "+"alt=\"infty\">,-V.2)<br> B = (-V.2,-V.0]<br> "+"C = [-V.0,+<img src=\"chars/infty.gif\" align=bottom "+"alt=\"infty\">).<p> By checking values "+"in these regions we find that<br> x<img src=\"chars/element.gif\" "+"align=bottom alt=\"element\">A "+"satisfies the inequality while<br> x<img src=\"chars/element.gif\" align=bottom alt=\"element\">B and x<img src=\"chars/element.gif\" align=bottom "+"alt=\"element\">C does not.<p> So our final "+"answer is: V.7.<p> (<i>See pages 158-160 of your "+"text for more details.</i>)";
ts=new Array("V.7",NA);ta=new parent.Val("S",ts);tp[4]=new parent.Problem("M",8,tv,4,to,tq,ta,th,tw);np=5;st="Section 2.8 &nbsp; Polynomial and Rational Inequalities";tl="help/sec2_8.html";ss[7]=new parent.Section(st,np,tp,tl,"sounds/sec2_8.wav","avi/sec2_8.avi");parent.hist[ch][7].max_questions=np;parent.hist[ch][7].title=st;
st="Chapter 2 &nbsp; Equations and Inequalities";tl="help/chap2.html";parent.chapter=new parent.Chapter(parent.CHAPTITLES[ch],parent.NSECTIONS[ch],ss,tl,"sounds/chap2.wav","avi/chap2.avi");parent.mkdb=true;}parent.chld=true;