kr_set = new Array();
kr_set[0] = new Array('kr0_0','kr0_1','kr0_2','kr0_3','kr0_4','kr0_5','kr0_6','kr0_7','kr0_8','kr0_9','kr0_10','kr0_11','kr0_12');
kr_set[1] = new Array('kr1_0','kr1_1','kr1_2','kr1_3','kr1_4','kr1_5','kr1_6','kr1_7','kr1_8','kr1_9','kr1_10');
kr_set[2] = new Array('kr2_0','kr2_1','kr2_2','kr2_3','kr2_4','kr2_5','kr2_6','kr2_7','kr2_8','kr2_9');
kr_set[3] = new Array('kr3_0','kr3_1','kr3_2','kr3_3','kr3_4','kr3_5','kr3_6','kr3_7','kr3_8','kr3_9');
kr_set[4] = new Array('kr4_0','kr4_1','kr4_2','kr4_3','kr4_4','kr4_5','kr4_6','kr4_7','kr4_8','kr4_9','kr4_10','kr4_11');
kr_set[5] = new Array('kr5_0','kr5_1','kr5_2','kr5_3','kr5_4','kr5_5','kr5_6','kr5_7','kr5_8','kr5_9','kr5_10','kr5_11','kr5_12','kr5_13','kr5_14');
kr_set[6] = new Array('kr6_0','kr6_1','kr6_2','kr6_3','kr6_4','kr6_5','kr6_6','kr6_7','kr6_8','kr6_9','kr6_10');
kr_set[7] = new Array('kr7_0','kr7_1','kr7_2','kr7_3','kr7_4','kr7_5','kr7_6','kr7_7');
ans_set = new Array();
ans_set[0] = new Array('1','2','2','6','4', '3','1','1','1','2', '3','5','6');
ans_set[1] = new Array('0','1', '3','2','5', '1','2', '3','9','8', '1');
ans_set[2] = new Array('4','2','2','6','2','3','5','6','4','3');
ans_set[3] = new Array('0','1','2','2','4','1','1','3','0','1');
ans_set[4] = new Array('0','3','1','3','1', '3','1','5','3','1', '5','2');
ans_set[5] = new Array('3','1','3','6','2', '1','3','1','5','4', '3','1','3','1','6');
ans_set[6] = new Array('1','3','4','1','2','1','3','7','2','2','8');
ans_set[7] = new Array('6','6','2','3','5','-','3','4');
h_button_set = new Array();
h_button_set[0] = new Array('h_button0_0','h_button0_1','h_button0_2','h_button0_3','h_button0_4','h_button0_5','h_button0_6','h_button0_7','h_button0_8','h_button0_9','h_button0_10','h_button0_11','h_button0_12');
h_button_set[1] = new Array('h_button1_0','h_button1_1','h_button1_2','h_button1_3','h_button1_4','h_button1_5','h_button1_6','h_button1_7','h_button1_8','h_button1_9','h_button1_10');
h_button_set[2] = new Array('h_button2_0','h_button2_1','h_button2_2','h_button2_3','h_button2_4','h_button2_5','h_button2_6','h_button2_7','h_button2_8','h_button2_9');
h_button_set[3] = new Array('h_button3_0','h_button3_1','h_button3_2','h_button3_3','h_button3_4','h_button3_5','h_button3_6','h_button3_7','h_button3_8','h_button3_9');
h_button_set[4] = new Array('h_button4_0','h_button4_1','h_button4_2','h_button4_3','h_button4_4','h_button4_5','h_button4_6','h_button4_7','h_button4_8','h_button4_9','h_button4_10','h_button4_11');
h_button_set[5] = new Array('h_button5_0','h_button5_1','h_button5_2','h_button5_3','h_button5_4','h_button5_5','h_button5_6','h_button5_7','h_button5_8','h_button5_9','h_button5_10','h_button5_11','h_button5_12','h_button5_13','h_button5_14');
h_button_set[6] = new Array('h_button6_0','h_button6_1','h_button6_2','h_button6_3','h_button6_4','h_button6_5','h_button6_6','h_button6_7','h_button6_8','h_button6_9','h_button6_10');
h_button_set[7] = new Array('h_button7_0','h_button7_1','h_button7_2','h_button7_3','h_button7_4','h_button7_5','h_button7_6','h_button7_7');
msg_pos = new Array('msg0','msg1','msg2','msg3','msg4','msg5','msg6','msg7');
msg_set = new Array();
// **************************q1********************
msg_set[0] = new Array();
msg_set[0][0] = 'cos2θ=cos2θ−sin2θ=1−2sin2θだから
';
msg_set[0][0] += 'cos2θ=1−2t2
';
msg_set[0][1] = msg_set[0][0];
msg_set[0][2] = msg_set[0][0];
msg_set[0][3] = 'y=3(1−2t2)+4t=−6t2+4t+3';
msg_set[0][4] = msg_set[0][3];
msg_set[0][5] = msg_set[0][3];
msg_set[0][6] = 'y=−6t2+4t+3
';
msg_set[0][6] += '
=−6(t2−'+cFrac_102('2','3')+'t)+3';
msg_set[0][6] += '=−6{ (t−'+cFrac_102('1','3')+')2−'+cFrac_102('1','9')+'}+3
';
msg_set[0][6] += '=−6(t−'+cFrac_102('1','3')+')2+'+cFrac_102('2','3')+'+3';
msg_set[0][6] += '=−6(t−'+cFrac_102('1','3')+')2+'+cFrac_102('11','3')+'
';
msg_set[0][6] += 'ここで0°≦θ<180°により0≦t≦1
';
msg_set[0][6] += '右図のようなグラフになるから
';
msg_set[0][6] += 't='+cFrac_102('1','3')+'→M='+cFrac_102('11','3')+'';
msg_set[0][6] += 't=1→m=1
';
msg_set[0][7] = msg_set[0][6];
msg_set[0][8] = msg_set[0][6];
msg_set[0][9] = '0°<α<90°のとき0<sinα, cosα<1で
';
msg_set[0][9] += 'f(α)=−6t2+4t+3=3より
';
msg_set[0][9] += 't(3t−2)=0→t=sinα='+cFrac_102('2','3')+' (>0)
';
msg_set[0][9] += 'このときcosα='+cFrac_102(cRoot_102('5'),'3','',2,2,1)+' (>0)だから
';
msg_set[0][9] += 'sin(α+30°)=sinαcos30°+cosαsin30°
='+cFrac_102('2','3')+''+cFrac_102(cRoot_102('3'),'2','',2,2,1)+'+'+cFrac_102(cRoot_102('5'),'3','',2,2,1)+''+cFrac_102('1','2')+'='+cFrac_102('2'+cRoot_102('3')+'+'+cRoot_102('5'),'6','',7,7,1)+'
';
msg_set[0][10] = msg_set[0][9];
msg_set[0][11] = msg_set[0][9];
msg_set[0][12] = msg_set[0][9];
// ********************q2************************
msg_set[1] = new Array();
msg_set[1][0] = '対数の底xは,x>0かつx≠1を満たさなければならない';
msg_set[1][1] = msg_set[1][0];
msg_set[1][2] = '底の変換公式
';
msg_set[1][2] += 'logab='+cFrac_102('logcb','logca','',4,4,4)+'
';
msg_set[1][2] += 'により
';
msg_set[1][2] += 'logx27='+cFrac_102('log327','log3x','',5,5,4)+'='+cFrac_102('3','log3x','',4,1,4)+'
';
msg_set[1][3] = '0<x<1のとき,log3x<0だから
';
msg_set[1][3] += '2log3x−4'+cFrac_102('3','log3x','',4,1,4)+'≦5より';
msg_set[1][3] += '2(log3x)2−12≧5(log3x)
';
msg_set[1][3] += '2(log3x)2−5(log3x)−12≧0
';
msg_set[1][4] = msg_set[1][3];
msg_set[1][5] = msg_set[1][3];
msg_set[1][6] = msg_set[1][3];
msg_set[1][7] = '0<x<1→log3x<0のとき
';
msg_set[1][7] += '(2log3x+3)(log3x−4)≧0より
';
msg_set[1][7] += 'log3x≦−'+cFrac_102('3','2')+', 4≦log3x
';
msg_set[1][7] += 'log3x<0だから
';
msg_set[1][7] += 'log3x≦−'+cFrac_102('3','2')+'
';
msg_set[1][7] += '0<x≦3−'+cFrac_102('3','2','','','','','','10')+'='+cFrac_102('1',''+cRoot_102('33',2)+'','',3,1,3)+'='+cFrac_102('1','3'+cRoot_102('3',1)+'','',3,1,3)+'='+cFrac_102(cRoot_102('3'),'9','',2,2,1)+'
';
msg_set[1][8] = msg_set[1][7];
msg_set[1][9] = 'x>1→log3x>0のとき
';
msg_set[1][9] += '(2log3x+3)(log3x−4)≦0より
';
msg_set[1][9] += '−'+cFrac_102('3','2')+'≦log3x≦4
';
msg_set[1][9] += 'log3x>0だから
';
msg_set[1][9] += '0<log3x≦4
';
msg_set[1][9] += '1<x≦81
';
msg_set[1][10] = msg_set[1][9];
// ********************q2************************
msg_set[2] = new Array();
msg_set[2][0] = 'sin2x=2sinxcosx
';
msg_set[2][0] += 'cos(x+'+cFrac_102('π','4')+')=cosxcos'+cFrac_102('π','4')+'−sinxsin'+cFrac_102('π','4')+'='+cFrac_102('1',''+cRoot_102('2')+'','',2,1,2)+'(cosx−sinx)';
msg_set[2][0] += 'だから
';
msg_set[2][0] += '2sin x cos x>cos x−sin x+'+cFrac_102('1','2')+'';
msg_set[2][0] += '4 sinx cos x+2a−2b−1>0
';
msg_set[2][1] = msg_set[2][0];
msg_set[2][2] = msg_set[2][0];
msg_set[2][3] = '(2a−1)(2b+1)>0より
';
msg_set[2][3] += '(ア)a>'+cFrac_102('1','2')+', b>−'+cFrac_102('1','2')+'または(イ)a<'+cFrac_102('1','2')+', b<−'+cFrac_102('1','2')+'
';
msg_set[2][3] += '';
msg_set[2][3] += '(ア)のとき,右図の共通部分から
';
msg_set[2][3] += ''+cFrac_102('π','6')+'<x<'+cFrac_102('2','3')+'π
';
msg_set[2][3] += '';
msg_set[2][3] += '(イ)のとき,右図の共通部分から
';
msg_set[2][3] += ''+cFrac_102('5','6')+'π<x<'+cFrac_102('4','3')+'π
';
msg_set[2][4] = msg_set[2][3];
msg_set[2][5] = msg_set[2][3];
msg_set[2][6] = msg_set[2][3];
msg_set[2][7] = msg_set[2][3];
msg_set[2][8] = msg_set[2][3];
msg_set[2][9] = msg_set[2][3];
// ********************q3************************
msg_set[3] = new Array();
msg_set[3][0] = 'y>0, y≠1
';
msg_set[3][1] = msg_set[3][0];
msg_set[3][2] = '1−'+cFrac_102('1','2')+'>0よりx<2
';
msg_set[3][3] = '底の変換公式logab='+cFrac_102('logcb','logca','',4,4,4)+'
';
msg_set[3][3] += 'を使うと
';
msg_set[3][3] += 'log'+cRoot_102('y',1,'','','12')+'3='+cFrac_102('log33','log3'+cRoot_102('y')+'','',6,5,6)+'='+cFrac_102('log33',''+cFrac_102('1','2')+'log3y','',5,5,5)+'='+cFrac_102('2','log3y','',5,1,5)+'
';
msg_set[3][4] = '底の変換公式logab='+cFrac_102('logcb','logca','',4,4,4)+'
';
msg_set[3][4] += 'を使うと
';
msg_set[3][4] += 'logy81='+cFrac_102('log381','log3y','',5,5,4)+'='+cFrac_102('4','log3y','',4,1,4)+'
';
msg_set[3][5] = '2+'+cFrac_102('2','log3y','',4,1,4)+'<'+cFrac_102('4','log3y','',4,1,4)+'+'+cFrac_102('2log3(1−'+cFrac_102('x','2')+')','log3y','',10,10,4)+'
';
msg_set[3][5] += '1+'+cFrac_102('1','log3y','',4,1,4)+'<'+cFrac_102('2','log3y','',4,1,4)+'+'+cFrac_102('log3(1−'+cFrac_102('x','2')+')','log3y','',9,9,4)+'
';
msg_set[3][5] += '1<'+cFrac_102('1','log3y','',4,1,4)+'+'+cFrac_102('log3(1−'+cFrac_102('x','2')+')','log3y','',9,9,4)+'
';
msg_set[3][6] = 'y>1のとき,log3y>0だから
';
msg_set[3][6] += '分母を払うと
';
msg_set[3][6] += 'log3y<1+log3{3(1−'+cFrac_102('x','2')+')}
';
msg_set[3][7] = msg_set[3][6];
msg_set[3][8] = '0<y<1のとき,log3y<0だから
';
msg_set[3][8] += '分母を払って符号を変えると
';
msg_set[3][8] += 'log3y>1+log3{3(1−'+cFrac_102('x','2')+')}
';
msg_set[3][9] = 'y>1, y<3(1−'+cFrac_102('x','2')+')
';
msg_set[3][9] += '0<y<1, y>3(1−'+cFrac_102('x','2')+'), x<2→1
';
// ********************q4************************
msg_set[4] = new Array();
msg_set[4][0] = '真数だからx>0
';
msg_set[4][1] = '(*)を変形すると
';
msg_set[4][1] += '5y=31+log10x−1=3·3log10x−1';
msg_set[4][2] = '5y=3z−1>0より
';
msg_set[4][2] += 'z>'+cFrac_102('1','3')+'
';
msg_set[4][3] = msg_set[4][2];
msg_set[4][4] = 'K='+cFrac_102('5y','3','',1,1,1)+'+3−log10x='+cFrac_102('3z−1','3','',4,4,1)+'+'+cFrac_102('1','z')+'
';
msg_set[4][4] += '=z+'+cFrac_102('1','z')+'−'+cFrac_102('1','3')+'
';
msg_set[4][5] = msg_set[4][4];
msg_set[4][6] = 'z>'+cFrac_102('1','3')+'>0だから,(相加平均)≧(相乗平均)の関係より
';
msg_set[4][6] += 'z+'+cFrac_102('1','z')+'≧2'+cRoot_102('z·'+cFrac_102('1','z'),3,'')+'=2
';
msg_set[4][6] += '(等号はz=1のとき)
';
msg_set[4][6] += 'Kはz=1のとき最小値2−'+cFrac_102('1','3')+'='+cFrac_102('5','3')+'をとる
';
msg_set[4][7] = msg_set[4][6];
msg_set[4][8] = msg_set[4][6];
msg_set[4][9] = '3log10x=1=30より
';
msg_set[4][9] += 'x=1
';
msg_set[4][10] = '5y=3×30−1=2
';
msg_set[4][10] += 'y=log52
';
msg_set[4][11] = msg_set[4][10];
// ********************q5************************
msg_set[5] = new Array();
msg_set[5][0] = 'θ=πのとき'+cFrac_102('π','2')+'−'+cFrac_102('θ','3')+'='+cFrac_102('π','6')+'だから
';
msg_set[5][0] += 'Qの座標は(2cos'+cFrac_102('π','6')+', 2sin'+cFrac_102('π','6')+')=('+cRoot_102('3')+', 1)';
msg_set[5][1] = msg_set[5][0];
msg_set[5][2] = 'aθ='+cFrac_102('π','2')+'−'+cFrac_102('θ','3')+'より';
msg_set[5][2] += '(a+'+cFrac_102('1','3')+')θ='+cFrac_102('π','2')+'';
msg_set[5][2] += ''+cFrac_102('3a+1','3')+'θ='+cFrac_102('π','2')+'';
msg_set[5][2] += 'θ='+cFrac_102('3','3a+1','')+''+cFrac_102('π','2')+'='+cFrac_102('3','6a+2','')+'π';
msg_set[5][3] = msg_set[5][2];
msg_set[5][4] = msg_set[5][2];
msg_set[5][5] = '0≦θ≦'+cFrac_102('3','6a+2','')+'πのとき';
msg_set[5][5] += ''+cFrac_102('π','2','')+'−'+cFrac_102('π','6a+2','')+'≦'+cFrac_102('π','2')+'−'+cFrac_102('θ','3')+'≦'+cFrac_102('π','2','')+'になり';
msg_set[5][5] += '扇形の中心角はα='+cFrac_102('π','6a+2','')+'';
msg_set[5][5] += '';
msg_set[5][5] += '【扇形の面積の公式】
半径
r,中心角
αの扇形の面積は
';
msg_set[5][5] += '
S='+cFrac_102('1','2','')+'r2α ';
msg_set[5][5] += '面積は';
msg_set[5][5] += 'S='+cFrac_102('1','2','')+'22'+cFrac_102('π','6a+2','')+'='+cFrac_102('1','3a+1','')+'π';
msg_set[5][6] = msg_set[5][5];
msg_set[5][7] = msg_set[5][5];
msg_set[5][8] = 'OPの偏角aθとOQの偏角'+cFrac_102('π','2')+'−'+cFrac_102('θ','3')+'のなす角は
';
msg_set[5][8] += 'aθ−('+cFrac_102('π','2')+'−'+cFrac_102('θ','3')+')='+cFrac_102('3a+1','3')+'θ−'+cFrac_102('π','2')+'
';
msg_set[5][8] += 'OP=1, OQ=2だから,余弦定理により
';
msg_set[5][8] += 'PQ2=12+22−2×1×2×cos('+cFrac_102('3a+1','3')+'θ−'+cFrac_102('π','2')+')
';
msg_set[5][8] += 'ここでcos(θ−'+cFrac_102('π','2')+')=cos('+cFrac_102('π','2')+'− θ)=sinθだから
';
msg_set[5][8] += 'PQ2=5−4sin('+cFrac_102('3a+1','3')+'θ)
';
msg_set[5][9] = msg_set[5][8];
msg_set[5][10] = msg_set[5][8];
msg_set[5][11] = msg_set[5][8];
msg_set[5][12] = msg_set[5][8];
msg_set[5][13] = 'sinkθの基本周期は'+cFrac_102('2π','k')+'だから';
msg_set[5][13] += ''+cFrac_102('3','3a+1')+'2π=4π';
msg_set[5][13] += '6a+2=3
';
msg_set[5][13] += 'a='+cFrac_102('1','6')+'
';
msg_set[5][14] = msg_set[5][13];
// ********************q6************************
msg_set[6] = new Array();
msg_set[6][0] = 'x≧2のとき,s=log2x≧log22=1';
msg_set[6][1] = '8≦xy≦16のとき,log2xy=log2x+log2y=s+tだから
';
msg_set[6][1] += '3=log28≦s+t≦log216=4
';
msg_set[6][2] = msg_set[6][1];
msg_set[6][3] = 'log2'+cRoot_102('x')+'=log2x'+cFrac_102('1','2','','','','','','10')+'='+cFrac_102('1','2')+'log2xだから';
msg_set[6][3] += 'z='+cFrac_102('1','2')+'s+t';
msg_set[6][4] = msg_set[6][3];
msg_set[6][5] = '';
msg_set[6][5] += 's≧1, t≧1, 3≦s+t≦4を満たす領域内における';
msg_set[6][5] += 'z='+cFrac_102('1','2')+'s+t → t=−'+cFrac_102('1','2')+'s+z';
msg_set[6][5] += 'zのとり得る値の範囲を考えると,s=1, t=3の点において最大値をとることがわかる.
';
msg_set[6][5] += '最大値はz='+cFrac_102('1','2')+'+3='+cFrac_102('7','2')+'
';
msg_set[6][6] = msg_set[6][5];
msg_set[6][7] = msg_set[6][5];
msg_set[6][8] = msg_set[6][5];
msg_set[6][9] = 's=log2x=1よりx=2';
msg_set[6][10] = 't=log2y=3よりy=8';
// ********************q7************************
msg_set[7] = new Array();
msg_set[7][0] = 'cos2θ=cos2θ−sin2θ=1−2sin2θ
だから
';
msg_set[7][0] += '5 sin θ−3(1−2sin2θ)=3
';
msg_set[7][0] += '6sin2θ+5 sinθ−6=0
';
msg_set[7][1] = msg_set[7][0];
msg_set[7][2] = '因数分解すると
';
msg_set[7][2] += '(3sin θ−2)(2sinθ+3)=0
';
msg_set[7][2] += 'sin θ='+cFrac_102('2','3')+' , −'+cFrac_102('3','2')+'
';
msg_set[7][2] += 'ここで−1≦sin θ≦1だから
';
msg_set[7][2] += 'sin θ='+cFrac_102('2','3')+'
';
msg_set[7][3] = msg_set[7][2];
msg_set[7][4] = 'cos2θ=1−sin2θ=1−('+cFrac_102('2','3')+')2='+cFrac_102('5','9')+'
';
msg_set[7][4] += 'cos θ=±'+cFrac_102(cRoot_102('5'),'3','',2,2,1)+'
';
msg_set[7][4] += '右図のようになるから
';
msg_set[7][4] += 'cos θ1='+cFrac_102(cRoot_102('5'),'3','',2,2,1)+' , cos θ2='+cFrac_102('−'+cRoot_102('5'),'3','',4,4,1)+'
';
msg_set[7][5] = msg_set[7][4];
msg_set[7][6] = 'cos'+cFrac_102('π','12')+'='+cFrac_102(cRoot_102('6')+'+'+cRoot_102('2'),'4','',5,5,1)+'≒0.95
';
msg_set[7][6] += 'cos'+cFrac_102('π','6')+'='+cFrac_102(cRoot_102('3'),'2','',2,2,1)+'≒0.86
';
msg_set[7][6] += 'cos'+cFrac_102('π','5')+'='+cFrac_102('1+'+cRoot_102('2'),'4','',4,4,1)+'≒0.80
';
msg_set[7][6] += 'cos θ1='+cFrac_102(cRoot_102('5','','','','','r'),'3','',2,2,1,'','','r')+'≒0.74
';
msg_set[7][6] += 'cos'+cFrac_102('π','4')+'='+cFrac_102(cRoot_102('2'),'2','',2,2,1)+'≒0.70
';
msg_set[7][6] += 'cos'+cFrac_102('π','3')+'='+cFrac_102('1','2','',1,1,1)+'=0.5
';
msg_set[7][6] += 'cos'+cFrac_102('π','2')+'=0
';
msg_set[7][6] += 'だから'+cFrac_102('π','5')+'<θ1<'+cFrac_102('π','4')+'
';
msg_set[7][7] = ''+cFrac_102('π','5')+'<θ1<'+cFrac_102('π','4')+' , '+cFrac_102('3π','4')+'<θ2<'+cFrac_102('4π','5')+'
';
msg_set[7][7] += 'だから
';
msg_set[7][7] += '3θ1<'+cFrac_102('3π','4')+'<θ2
';
msg_set[7][7] += 'θ2<'+cFrac_102('4π','5')+'<4θ1<π
';
msg_set[7][7] += 'となるから
n=4が最小';
function saiten(qx_num, qnum, anum)
{if(anum == ans_set[qx_num][qnum])
{document.getElementById(kr_set[qx_num][qnum]).innerHTML = '○';
// ***************************
if(qx_num == 0)
{pg_ox_information[qnum] = 1;
}
else
{var count_q = 0;
for(var my_local_kk = 0; my_local_kk < qx_num; my_local_kk ++)
count_q += ans_set[my_local_kk].length;
pg_ox_information[qnum + count_q] = 1;
}
// ***************************
}
else
{document.getElementById(kr_set[qx_num][qnum]).innerHTML = '×';
document.getElementById(h_button_set[qx_num][qnum]).style.visibility = 'visible';
}
// ***************************
once_answer = 1;
// ***************************
}
function view_help(qx_num, qnum)
{document.getElementById(msg_pos[qx_num]).innerHTML = msg_set[qx_num][qnum];
}
msg_posx = new Array();
msg_posx[0] = new Array('msg_posx_00','msg_posx_01','msg_posx_02');
msg_posx[1] = new Array('msg_posx_10','msg_posx_11','msg_posx_12');
msg_posx[2] = new Array('msg_posx_20','msg_posx_21','msg_posx_22','msg_posx_23');
msg_posx[3] = new Array('msg_posx_30','msg_posx_31','msg_posx_32','msg_posx_33','msg_posx_34','msg_posx_35');
msg_posx[4] = new Array('msg_posx_40','msg_posx_41','msg_posx_42','msg_posx_43','msg_posx_44','msg_posx_45','msg_posx_46','msg_posx_47','msg_posx_48','msg_posx_49');
msg_posx[5] = new Array('msg_posx_50','msg_posx_51','msg_posx_52','msg_posx_53','msg_posx_54','msg_posx_55','msg_posx_56','msg_posx_57','msg_posx_58','msg_posx_59');
msg_posx[6] = new Array('msg_posx_60','msg_posx_61','msg_posx_62','msg_posx_63','msg_posx_64','msg_posx_65','msg_posx_66','msg_posx_67','msg_posx_68','msg_posx_69');
msg_posx[7] = new Array('msg_posx_70','msg_posx_71','msg_posx_72','msg_posx_73','msg_posx_74','msg_posx_75','msg_posx_76','msg_posx_77','msg_posx_78','msg_posx_79');
function view_helpx(qx_num, qnum)
{document.getElementById(msg_posx[qx_num][qnum]).style.visibility = 'visible';
}
function close_helpx(qx_num, qnum)
{document.getElementById(msg_posx[qx_num][qnum]).style.visibility = 'hidden';
}