Algebra 2
Algebra 2
1st Edition
ISBN: 9780078884825
Author: McGraw-Hill/Glencoe
Publisher: Glencoe/McGraw-Hill School Pub Co
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Chapter 6.8, Problem 3BCYP
To determine

To calculate: The simplified form of the equation k(x)=2x45x3+20x245x+18 ,

Find all the possible zeros of rational function.

Expert Solution & Answer
Check Mark

Answer to Problem 3BCYP

The simplified form of the equation h(x)=x3+11x2+24 has no real roots.

Explanation of Solution

Given information:

The given equation:

  k(x)=2x45x3+20x245x+18

Calculation:

Consider the expression as:

  k(x)=2x45x3+20x245x+18

Now take f(x)=0 ,

Here,

  f(x)=02x45x3+20x245x+18=0

The leading coefficient is 2 and the trilling coefficient is 18 .

Now factor of leading coefficient is: 1,2

Now to find the list of positive rational solutions for the expression look at the factors of the constants.

That are:

  1,2,3,6,9,18

Here the last two terms subtracting values from the cube of the first and want to get zero,

So as have to take the positive number, and mostly take the less than mid-way.

So take a startup with 1,1 and check the result, then again tried to get zero.

  2x45x3+20x245x+18=02(1)45(1)3+20(1)245(1)+18=025+2045+18=010=0

So the value is not zero its too grater than zero.

So check with the value 2 .

  2x45x3+20x245x+18=02(2)45(2)3+20(2)245(2)+18=02(16)5(8)+20(4)90+18=03240+8090+18=0

To get zero:

  3240+8090+18=00=0

Here got the real root, it means (x2) is a factor.

Now divide the expression 2x45x3+20x245x+18=0 to the factor (x2) , to check for the other possible solutions.

  x22x3x2+18x92x45x3+20x245x+18         2x44x3                         x320x2                           x32x2                                             18x245x                                             18x236x                                                               9x+18                                                               9x+18                                                                             0

So the other factor is:

  2x3x2+18x9

Now find the factors of the expression 2x3x2+18x9:

The leading coefficient is 2 and the trilling coefficient is 9 .

Now factor of leading coefficient is: 1,2

Now to find the list of positive rational solutions for the expression look at the factors of the constants.

That are:

  1,3,9

Here the last two terms subtracting values from the cube of the first and want to get zero,

So as have to take the positive number, and mostly take the less than mid-way.

So take a startup with 1,1 and check the result, then again tried to get zero.

  2x3x2+18x9=02(1)3(1)2+18(1)9=021+189=010=0

So the value is not zero its too grater than zero.

So check with the value 1,2 that means p/q=0.5 .

  2x3x2+18x9=02(0.5)3(0.5)2+18(0.5)9=02(0.125)(0.25)+99=00.250.25+99=0

To get zero:

  0.250.25+99=00=0

As for the factor 1,2 its become zero.

Here got the real root, it means (2x1) is a factor.

Now divide the expression 2x3x2+18x9=0 to the factor (2x1) , to check for the other possible solutions.

  2x1x2+92x3x2+18x9          2x3x2                                         18x9                                         18x9                                                         0

So the other factor is:

  x2+9

Now find the roots of x2+9 .

  x2+9=0

The leading coefficient is: 1

The trilling coefficient is: 1,3,9

Here the last two terms subtracting values from the cube of the first and want to get zero,

So as have to take the positive number, and mostly take the less than mid-way.

So take a startup with 1 and check the result, then again tried to get zero.

  x2+9=0(1)2+9=010=0

So the value is not zero its too grater than zero.

So check with the value 3 .

  x2+9=0(3)2+9=0(9)+9=018=0

Here no polynomial rational roots are found.

Thus, the simplified form of the equation k(x)=2x45x3+20x245x+18 has no rational roots.

Chapter 6 Solutions

Algebra 2

Ch. 6.1 - Prob. 5CYPCh. 6.1 - Prob. 6ACYPCh. 6.1 - Prob. 6BCYPCh. 6.1 - Prob. 1CYUCh. 6.1 - Prob. 2CYUCh. 6.1 - Prob. 3CYUCh. 6.1 - Prob. 4CYUCh. 6.1 - Prob. 5CYUCh. 6.1 - Prob. 6CYUCh. 6.1 - Prob. 7CYUCh. 6.1 - Prob. 8CYUCh. 6.1 - Prob. 9CYUCh. 6.1 - Prob. 10CYUCh. 6.1 - Prob. 11CYUCh. 6.1 - Prob. 12CYUCh. 6.1 - Prob. 13CYUCh. 6.1 - Prob. 14CYUCh. 6.1 - Prob. 15CYUCh. 6.1 - Prob. 16PPSCh. 6.1 - Prob. 17PPSCh. 6.1 - Prob. 18PPSCh. 6.1 - Prob. 19PPSCh. 6.1 - Prob. 20PPSCh. 6.1 - Prob. 21PPSCh. 6.1 - Prob. 22PPSCh. 6.1 - Prob. 23PPSCh. 6.1 - Prob. 24PPSCh. 6.1 - Prob. 25PPSCh. 6.1 - Prob. 26PPSCh. 6.1 - Prob. 27PPSCh. 6.1 - Prob. 28PPSCh. 6.1 - Prob. 29PPSCh. 6.1 - Prob. 30PPSCh. 6.1 - Prob. 31PPSCh. 6.1 - Prob. 32PPSCh. 6.1 - Prob. 33PPSCh. 6.1 - Prob. 34PPSCh. 6.1 - Prob. 35PPSCh. 6.1 - Prob. 36PPSCh. 6.1 - Prob. 37PPSCh. 6.1 - Prob. 38PPSCh. 6.1 - Prob. 39PPSCh. 6.1 - Prob. 40PPSCh. 6.1 - Prob. 41PPSCh. 6.1 - Prob. 42PPSCh. 6.1 - Prob. 43PPSCh. 6.1 - Prob. 44PPSCh. 6.1 - Prob. 45PPSCh. 6.1 - Prob. 46PPSCh. 6.1 - Prob. 47PPSCh. 6.1 - Prob. 48PPSCh. 6.1 - Prob. 49PPSCh. 6.1 - Prob. 50PPSCh. 6.1 - Prob. 51PPSCh. 6.1 - Prob. 52PPSCh. 6.1 - Prob. 53PPSCh. 6.1 - Prob. 54PPSCh. 6.1 - Prob. 55PPSCh. 6.1 - Prob. 56PPSCh. 6.1 - Prob. 57PPSCh. 6.1 - Prob. 58PPSCh. 6.1 - Prob. 59PPSCh. 6.1 - Prob. 60PPSCh. 6.1 - Prob. 61PPSCh. 6.1 - Prob. 62PPSCh. 6.1 - Prob. 63PPSCh. 6.1 - Prob. 64PPSCh. 6.1 - Prob. 65HPCh. 6.1 - Prob. 66HPCh. 6.1 - Prob. 67HPCh. 6.1 - Prob. 68HPCh. 6.1 - Prob. 69HPCh. 6.1 - Prob. 70HPCh. 6.1 - Prob. 71HPCh. 6.1 - Prob. 72HPCh. 6.1 - Prob. 73HPCh. 6.1 - Prob. 74STPCh. 6.1 - Prob. 75STPCh. 6.1 - Prob. 76STPCh. 6.1 - Prob. 77STPCh. 6.1 - Prob. 78STPCh. 6.1 - Prob. 79STPCh. 6.1 - Prob. 80STPCh. 6.1 - Prob. 81STPCh. 6.1 - Prob. 82STPCh. 6.1 - Prob. 83STPCh. 6.1 - Prob. 84STPCh. 6.1 - Prob. 85STPCh. 6.1 - Prob. 86STPCh. 6.1 - Prob. 87STPCh. 6.1 - Prob. 88STPCh. 6.1 - Prob. 89STPCh. 6.1 - Prob. 90STPCh. 6.1 - Prob. 91SCh. 6.1 - Prob. 92SCh. 6.1 - Prob. 93SCh. 6.1 - Prob. 94SCh. 6.1 - Prob. 95SCh. 6.1 - Prob. 96SCh. 6.1 - Prob. 1ECh. 6.1 - Prob. 2ECh. 6.1 - Prob. 3ECh. 6.1 - Prob. 4ECh. 6.1 - Prob. 5ECh. 6.2 - Prob. 1ACYPCh. 6.2 - Prob. 1BCYPCh. 6.2 - Prob. 2ACYPCh. 6.2 - Prob. 2BCYPCh. 6.2 - Prob. 3CYPCh. 6.2 - Prob. 4ACYPCh. 6.2 - Prob. 4BCYPCh. 6.2 - Prob. 4CCYPCh. 6.2 - Prob. 4DCYPCh. 6.2 - Prob. 5ACYPCh. 6.2 - Prob. 5BCYPCh. 6.2 - Prob. 5CCYPCh. 6.2 - Prob. 5DCYPCh. 6.2 - Prob. 1CYUCh. 6.2 - Prob. 2CYUCh. 6.2 - Prob. 3CYUCh. 6.2 - Prob. 4CYUCh. 6.2 - Prob. 5CYUCh. 6.2 - Prob. 6CYUCh. 6.2 - Prob. 7CYUCh. 6.2 - Prob. 8CYUCh. 6.2 - Prob. 9CYUCh. 6.2 - Prob. 10CYUCh. 6.2 - Prob. 11CYUCh. 6.2 - Prob. 12PPSCh. 6.2 - Prob. 13PPSCh. 6.2 - Prob. 14PPSCh. 6.2 - Prob. 15PPSCh. 6.2 - Prob. 16PPSCh. 6.2 - Prob. 17PPSCh. 6.2 - Prob. 18PPSCh. 6.2 - Prob. 19PPSCh. 6.2 - Prob. 20PPSCh. 6.2 - Prob. 21PPSCh. 6.2 - Prob. 22PPSCh. 6.2 - Prob. 23PPSCh. 6.2 - Prob. 24PPSCh. 6.2 - Prob. 25PPSCh. 6.2 - Prob. 26PPSCh. 6.2 - Prob. 27PPSCh. 6.2 - Prob. 28PPSCh. 6.2 - Prob. 29PPSCh. 6.2 - 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Prob. 4ACYPCh. 6.3 - Prob. 4BCYPCh. 6.3 - Prob. 1CYUCh. 6.3 - Prob. 2CYUCh. 6.3 - Prob. 3CYUCh. 6.3 - Prob. 4CYUCh. 6.3 - Prob. 5CYUCh. 6.3 - Prob. 6CYUCh. 6.3 - Prob. 7CYUCh. 6.3 - Prob. 8CYUCh. 6.3 - Prob. 9CYUCh. 6.3 - Prob. 10CYUCh. 6.3 - Prob. 11CYUCh. 6.3 - Prob. 12CYUCh. 6.3 - Prob. 13PPSCh. 6.3 - Prob. 14PPSCh. 6.3 - Prob. 15PPSCh. 6.3 - Prob. 16PPSCh. 6.3 - Prob. 17PPSCh. 6.3 - Prob. 18PPSCh. 6.3 - Prob. 19PPSCh. 6.3 - Prob. 20PPSCh. 6.3 - Prob. 21PPSCh. 6.3 - Prob. 22PPSCh. 6.3 - Prob. 23PPSCh. 6.3 - Prob. 24PPSCh. 6.3 - Prob. 25PPSCh. 6.3 - Prob. 26PPSCh. 6.3 - Prob. 27PPSCh. 6.3 - Prob. 28PPSCh. 6.3 - Prob. 29PPSCh. 6.3 - Prob. 30PPSCh. 6.3 - Prob. 31PPSCh. 6.3 - Prob. 32PPSCh. 6.3 - Prob. 33PPSCh. 6.3 - Prob. 34PPSCh. 6.3 - Prob. 35PPSCh. 6.3 - Prob. 36PPSCh. 6.3 - Prob. 37PPSCh. 6.3 - Prob. 38PPSCh. 6.3 - Prob. 39PPSCh. 6.3 - Prob. 40PPSCh. 6.3 - Prob. 41PPSCh. 6.3 - Prob. 42PPSCh. 6.3 - Prob. 43PPSCh. 6.3 - Prob. 44PPSCh. 6.3 - Prob. 45PPSCh. 6.3 - Prob. 46PPSCh. 6.3 - Prob. 47PPSCh. 6.3 - Prob. 48PPSCh. 6.3 - Prob. 49PPSCh. 6.3 - Prob. 50PPSCh. 6.3 - Prob. 51PPSCh. 6.3 - Prob. 52PPSCh. 6.3 - Prob. 53PPSCh. 6.3 - Prob. 54PPSCh. 6.3 - Prob. 55PPSCh. 6.3 - Prob. 56PPSCh. 6.3 - Prob. 57PPSCh. 6.3 - Prob. 58PPSCh. 6.3 - Prob. 59PPSCh. 6.3 - Prob. 60PPSCh. 6.3 - Prob. 61PPSCh. 6.3 - Prob. 62PPSCh. 6.3 - Prob. 63HPCh. 6.3 - Prob. 64HPCh. 6.3 - Prob. 65HPCh. 6.3 - Prob. 66HPCh. 6.3 - Prob. 67HPCh. 6.3 - Prob. 68HPCh. 6.3 - Prob. 69HPCh. 6.3 - Prob. 70HPCh. 6.3 - Prob. 71HPCh. 6.3 - Prob. 72HPCh. 6.3 - Prob. 73STPCh. 6.3 - Prob. 74STPCh. 6.3 - Prob. 75STPCh. 6.3 - Prob. 76STPCh. 6.3 - Prob. 77STPCh. 6.3 - Prob. 78STPCh. 6.3 - Prob. 79STPCh. 6.3 - Prob. 80STPCh. 6.3 - Prob. 81STPCh. 6.3 - Prob. 82STPCh. 6.3 - Prob. 83SCh. 6.3 - Prob. 84SCh. 6.3 - Prob. 85SCh. 6.3 - Prob. 1ECh. 6.3 - Prob. 2ECh. 6.3 - Prob. 3ECh. 6.3 - Prob. 4ECh. 6.4 - Prob. 1CYPCh. 6.4 - Prob. 2CYPCh. 6.4 - Prob. 3CYPCh. 6.4 - Prob. 4ACYPCh. 6.4 - Prob. 4BCYPCh. 6.4 - Prob. 4CCYPCh. 6.4 - Prob. 4DCYPCh. 6.4 - Prob. 1CYUCh. 6.4 - Prob. 2CYUCh. 6.4 - Prob. 3CYUCh. 6.4 - Prob. 4CYUCh. 6.4 - Prob. 5CYUCh. 6.4 - Prob. 6CYUCh. 6.4 - Prob. 7CYUCh. 6.4 - Prob. 8CYUCh. 6.4 - Prob. 9CYUCh. 6.4 - Prob. 10CYUCh. 6.4 - Prob. 11CYUCh. 6.4 - Prob. 12CYUCh. 6.4 - Prob. 13CYUCh. 6.4 - Prob. 14PPSCh. 6.4 - Prob. 15PPSCh. 6.4 - Prob. 16PPSCh. 6.4 - Prob. 17PPSCh. 6.4 - Prob. 18PPSCh. 6.4 - Prob. 19PPSCh. 6.4 - Prob. 20PPSCh. 6.4 - Prob. 21PPSCh. 6.4 - Prob. 22PPSCh. 6.4 - Prob. 23PPSCh. 6.4 - Prob. 24PPSCh. 6.4 - Prob. 25PPSCh. 6.4 - Prob. 26PPSCh. 6.4 - Prob. 27PPSCh. 6.4 - Prob. 28PPSCh. 6.4 - Prob. 29PPSCh. 6.4 - Prob. 30PPSCh. 6.4 - Prob. 31PPSCh. 6.4 - Prob. 32PPSCh. 6.4 - Prob. 33PPSCh. 6.4 - Prob. 34PPSCh. 6.4 - Prob. 35PPSCh. 6.4 - Prob. 36PPSCh. 6.4 - Prob. 37PPSCh. 6.4 - Prob. 38PPSCh. 6.4 - Prob. 39PPSCh. 6.4 - Prob. 40PPSCh. 6.4 - Prob. 41PPSCh. 6.4 - Prob. 42PPSCh. 6.4 - Prob. 43PPSCh. 6.4 - Prob. 44PPSCh. 6.4 - Prob. 45PPSCh. 6.4 - Prob. 46PPSCh. 6.4 - Prob. 47HPCh. 6.4 - Prob. 48HPCh. 6.4 - Prob. 49HPCh. 6.4 - Prob. 50HPCh. 6.4 - Prob. 51HPCh. 6.4 - Prob. 52HPCh. 6.4 - Prob. 53HPCh. 6.4 - Prob. 54HPCh. 6.4 - Prob. 55HPCh. 6.4 - Prob. 56HPCh. 6.4 - Prob. 57HPCh. 6.4 - Prob. 58STPCh. 6.4 - Prob. 59STPCh. 6.4 - Prob. 60STPCh. 6.4 - Prob. 61STPCh. 6.4 - Prob. 62STPCh. 6.4 - Prob. 63STPCh. 6.4 - Prob. 64STPCh. 6.4 - Prob. 65SCh. 6.4 - Prob. 66SCh. 6.4 - Prob. 67SCh. 6.4 - Prob. 68SCh. 6.4 - Prob. 69SCh. 6.4 - Prob. 70SCh. 6.4 - Prob. 1ECh. 6.4 - Prob. 2ECh. 6.4 - Prob. 3ECh. 6.4 - Prob. 4ECh. 6.4 - Prob. 5ECh. 6.4 - Prob. 6ECh. 6.4 - Prob. 7ECh. 6.4 - Prob. 8ECh. 6.4 - Prob. 9ECh. 6.4 - Prob. 10ECh. 6.4 - Prob. 11ECh. 6.4 - Prob. 12ECh. 6.4 - Prob. 13ECh. 6.5 - Prob. 1ACYPCh. 6.5 - Prob. 1BCYPCh. 6.5 - Prob. 2ACYPCh. 6.5 - Prob. 2BCYPCh. 6.5 - Prob. 3ACYPCh. 6.5 - Prob. 3BCYPCh. 6.5 - Prob. 4CYPCh. 6.5 - Prob. 5ACYPCh. 6.5 - Prob. 5BCYPCh. 6.5 - Prob. 6ACYPCh. 6.5 - Prob. 6BCYPCh. 6.5 - Prob. 1CYUCh. 6.5 - Prob. 2CYUCh. 6.5 - Prob. 3CYUCh. 6.5 - Prob. 4CYUCh. 6.5 - Prob. 5CYUCh. 6.5 - Prob. 6CYUCh. 6.5 - Prob. 7CYUCh. 6.5 - Prob. 8CYUCh. 6.5 - Prob. 9CYUCh. 6.5 - Prob. 10CYUCh. 6.5 - Prob. 11CYUCh. 6.5 - Prob. 12CYUCh. 6.5 - Prob. 13CYUCh. 6.5 - Prob. 14CYUCh. 6.5 - Prob. 15CYUCh. 6.5 - Prob. 16CYUCh. 6.5 - Prob. 17CYUCh. 6.5 - Prob. 18CYUCh. 6.5 - Prob. 19CYUCh. 6.5 - Prob. 20PPSCh. 6.5 - Prob. 21PPSCh. 6.5 - Prob. 22PPSCh. 6.5 - Prob. 23PPSCh. 6.5 - Prob. 24PPSCh. 6.5 - Prob. 25PPSCh. 6.5 - Prob. 26PPSCh. 6.5 - Prob. 27PPSCh. 6.5 - Prob. 28PPSCh. 6.5 - Prob. 29PPSCh. 6.5 - Prob. 30PPSCh. 6.5 - Prob. 31PPSCh. 6.5 - Prob. 32PPSCh. 6.5 - Prob. 33PPSCh. 6.5 - Prob. 34PPSCh. 6.5 - Prob. 35PPSCh. 6.5 - Prob. 36PPSCh. 6.5 - Prob. 37PPSCh. 6.5 - Prob. 38PPSCh. 6.5 - Prob. 39PPSCh. 6.5 - Prob. 40PPSCh. 6.5 - Prob. 41PPSCh. 6.5 - Prob. 42PPSCh. 6.5 - Prob. 43PPSCh. 6.5 - Prob. 44PPSCh. 6.5 - Prob. 45PPSCh. 6.5 - Prob. 46PPSCh. 6.5 - Prob. 47PPSCh. 6.5 - Prob. 48PPSCh. 6.5 - Prob. 49PPSCh. 6.5 - Prob. 50PPSCh. 6.5 - Prob. 51PPSCh. 6.5 - Prob. 52PPSCh. 6.5 - Prob. 53PPSCh. 6.5 - Prob. 54PPSCh. 6.5 - Prob. 55PPSCh. 6.5 - 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Prob. 7ECh. 6.5 - Prob. 8ECh. 6.5 - Prob. 9ECh. 6.6 - Prob. 1ACYPCh. 6.6 - Prob. 1BCYPCh. 6.6 - Prob. 2CYPCh. 6.6 - Prob. 3CYPCh. 6.6 - Prob. 1CYUCh. 6.6 - Prob. 2CYUCh. 6.6 - Prob. 3CYUCh. 6.6 - Prob. 4CYUCh. 6.6 - Prob. 5CYUCh. 6.6 - Prob. 6CYUCh. 6.6 - Prob. 7CYUCh. 6.6 - Prob. 8PPSCh. 6.6 - Prob. 9PPSCh. 6.6 - Prob. 10PPSCh. 6.6 - Prob. 11PPSCh. 6.6 - Prob. 12PPSCh. 6.6 - Prob. 13PPSCh. 6.6 - Prob. 14PPSCh. 6.6 - Prob. 15PPSCh. 6.6 - Prob. 16PPSCh. 6.6 - Prob. 17PPSCh. 6.6 - Prob. 18PPSCh. 6.6 - Prob. 19PPSCh. 6.6 - Prob. 20PPSCh. 6.6 - Prob. 21PPSCh. 6.6 - Prob. 22PPSCh. 6.6 - Prob. 23PPSCh. 6.6 - Prob. 24PPSCh. 6.6 - Prob. 25PPSCh. 6.6 - Prob. 26PPSCh. 6.6 - Prob. 27PPSCh. 6.6 - Prob. 28PPSCh. 6.6 - Prob. 29PPSCh. 6.6 - Prob. 30PPSCh. 6.6 - Prob. 31PPSCh. 6.6 - Prob. 32PPSCh. 6.6 - Prob. 33PPSCh. 6.6 - Prob. 34PPSCh. 6.6 - Prob. 35PPSCh. 6.6 - Prob. 36HPCh. 6.6 - Prob. 37HPCh. 6.6 - Prob. 38HPCh. 6.6 - Prob. 39HPCh. 6.6 - Prob. 40HPCh. 6.6 - Prob. 41HPCh. 6.6 - Prob. 42HPCh. 6.6 - Prob. 43HPCh. 6.6 - Prob. 44HPCh. 6.6 - Prob. 45HPCh. 6.6 - Prob. 46HPCh. 6.6 - Prob. 47HPCh. 6.6 - Prob. 48STPCh. 6.6 - Prob. 49STPCh. 6.6 - Prob. 50STPCh. 6.6 - Prob. 51STPCh. 6.6 - Prob. 52STPCh. 6.6 - Prob. 53STPCh. 6.6 - Prob. 54STPCh. 6.6 - Prob. 55STPCh. 6.6 - Prob. 56STPCh. 6.6 - Prob. 57STPCh. 6.6 - Prob. 58SCh. 6.6 - Prob. 59SCh. 6.6 - Prob. 60SCh. 6.6 - Prob. 61SCh. 6.6 - Prob. 62SCh. 6.6 - Prob. 63SCh. 6.7 - Prob. 1ACYPCh. 6.7 - Prob. 1BCYPCh. 6.7 - Prob. 1CCYPCh. 6.7 - Prob. 1DCYPCh. 6.7 - Prob. 2CYPCh. 6.7 - Prob. 3CYPCh. 6.7 - Prob. 4CYPCh. 6.7 - Prob. 1CYUCh. 6.7 - Prob. 2CYUCh. 6.7 - Prob. 3CYUCh. 6.7 - Prob. 4CYUCh. 6.7 - Prob. 5CYUCh. 6.7 - Prob. 6CYUCh. 6.7 - Prob. 7CYUCh. 6.7 - Prob. 8CYUCh. 6.7 - Prob. 9CYUCh. 6.7 - Prob. 10CYUCh. 6.7 - Prob. 11CYUCh. 6.7 - Prob. 12CYUCh. 6.7 - Prob. 13CYUCh. 6.7 - Prob. 14CYUCh. 6.7 - Prob. 15CYUCh. 6.7 - Prob. 16CYUCh. 6.7 - Prob. 17PPSCh. 6.7 - Prob. 18PPSCh. 6.7 - Prob. 19PPSCh. 6.7 - Prob. 20PPSCh. 6.7 - Prob. 21PPSCh. 6.7 - Prob. 22PPSCh. 6.7 - Prob. 23PPSCh. 6.7 - Prob. 24PPSCh. 6.7 - Prob. 25PPSCh. 6.7 - Prob. 26PPSCh. 6.7 - Prob. 27PPSCh. 6.7 - Prob. 28PPSCh. 6.7 - Prob. 29PPSCh. 6.7 - Prob. 30PPSCh. 6.7 - Prob. 31PPSCh. 6.7 - Prob. 32PPSCh. 6.7 - Prob. 33PPSCh. 6.7 - Prob. 34PPSCh. 6.7 - Prob. 35PPSCh. 6.7 - Prob. 36PPSCh. 6.7 - Prob. 37PPSCh. 6.7 - Prob. 38PPSCh. 6.7 - Prob. 39PPSCh. 6.7 - Prob. 40PPSCh. 6.7 - Prob. 41PPSCh. 6.7 - Prob. 42PPSCh. 6.7 - Prob. 43PPSCh. 6.7 - Prob. 44PPSCh. 6.7 - Prob. 45PPSCh. 6.7 - Prob. 46PPSCh. 6.7 - Prob. 47PPSCh. 6.7 - Prob. 48PPSCh. 6.7 - Prob. 49PPSCh. 6.7 - Prob. 50PPSCh. 6.7 - Prob. 51PPSCh. 6.7 - Prob. 52PPSCh. 6.7 - Prob. 53PPSCh. 6.7 - Prob. 54PPSCh. 6.7 - Prob. 55PPSCh. 6.7 - Prob. 56HPCh. 6.7 - Prob. 57HPCh. 6.7 - Prob. 58HPCh. 6.7 - Prob. 59HPCh. 6.7 - Prob. 60HPCh. 6.7 - Prob. 61HPCh. 6.7 - Prob. 62HPCh. 6.7 - Prob. 63HPCh. 6.7 - Prob. 64HPCh. 6.7 - Prob. 65STPCh. 6.7 - Prob. 66STPCh. 6.7 - Prob. 67STPCh. 6.7 - Prob. 68STPCh. 6.7 - Prob. 69STPCh. 6.7 - Prob. 70STPCh. 6.7 - Prob. 71STPCh. 6.7 - Prob. 72STPCh. 6.7 - Prob. 73STPCh. 6.7 - Prob. 74SCh. 6.7 - Prob. 75SCh. 6.7 - Prob. 76SCh. 6.8 - Prob. 1ACYPCh. 6.8 - Prob. 1BCYPCh. 6.8 - Prob. 2CYPCh. 6.8 - Prob. 3ACYPCh. 6.8 - Prob. 3BCYPCh. 6.8 - Prob. 1CYUCh. 6.8 - Prob. 2CYUCh. 6.8 - Prob. 3CYUCh. 6.8 - Prob. 4CYUCh. 6.8 - Prob. 5CYUCh. 6.8 - Prob. 6CYUCh. 6.8 - Prob. 7CYUCh. 6.8 - Prob. 8CYUCh. 6.8 - Prob. 9CYUCh. 6.8 - Prob. 10PPSCh. 6.8 - Prob. 11PPSCh. 6.8 - Prob. 12PPSCh. 6.8 - Prob. 13PPSCh. 6.8 - Prob. 14PPSCh. 6.8 - Prob. 15PPSCh. 6.8 - Prob. 16PPSCh. 6.8 - Prob. 17PPSCh. 6.8 - Prob. 18PPSCh. 6.8 - Prob. 19PPSCh. 6.8 - Prob. 20PPSCh. 6.8 - Prob. 21PPSCh. 6.8 - Prob. 22PPSCh. 6.8 - Prob. 23PPSCh. 6.8 - Prob. 24PPSCh. 6.8 - Prob. 25PPSCh. 6.8 - Prob. 26PPSCh. 6.8 - Prob. 27PPSCh. 6.8 - Prob. 28PPSCh. 6.8 - Prob. 29PPSCh. 6.8 - Prob. 30PPSCh. 6.8 - Prob. 31PPSCh. 6.8 - Prob. 32PPSCh. 6.8 - Prob. 33PPSCh. 6.8 - Prob. 34PPSCh. 6.8 - Prob. 35PPSCh. 6.8 - Prob. 36PPSCh. 6.8 - Prob. 37PPSCh. 6.8 - Prob. 38PPSCh. 6.8 - Prob. 39PPSCh. 6.8 - Prob. 40PPSCh. 6.8 - Prob. 41PPSCh. 6.8 - Prob. 42PPSCh. 6.8 - Prob. 43PPSCh. 6.8 - Prob. 44PPSCh. 6.8 - Prob. 45PPSCh. 6.8 - Prob. 46HPCh. 6.8 - Prob. 47HPCh. 6.8 - Prob. 48HPCh. 6.8 - Prob. 49HPCh. 6.8 - Prob. 50HPCh. 6.8 - Prob. 51HPCh. 6.8 - Prob. 52HPCh. 6.8 - Prob. 53HPCh. 6.8 - Prob. 54HPCh. 6.8 - Prob. 55HPCh. 6.8 - Prob. 56STPCh. 6.8 - Prob. 57STPCh. 6.8 - Prob. 58STPCh. 6.8 - Prob. 59STPCh. 6.8 - Prob. 60STPCh. 6.8 - Prob. 61STPCh. 6.8 - Prob. 62STPCh. 6.8 - Prob. 63STPCh. 6.8 - Prob. 64SCh. 6.8 - Prob. 65SCh. 6.8 - Prob. 66SCh. 6.8 - Prob. 67SCh. 6.8 - Prob. 68SCh. 6.8 - Prob. 69SCh. 6.8 - Prob. 1SGRCh. 6.8 - Prob. 2SGRCh. 6.8 - Prob. 3SGRCh. 6.8 - Prob. 4SGRCh. 6.8 - Prob. 5SGRCh. 6.8 - Prob. 6SGRCh. 6.8 - Prob. 7SGRCh. 6.8 - Prob. 8SGRCh. 6.8 - Prob. 9SGRCh. 6.8 - Prob. 10SGRCh. 6.8 - Prob. 11SGRCh. 6.8 - Prob. 12SGRCh. 6.8 - Prob. 13SGRCh. 6.8 - Prob. 14SGRCh. 6.8 - Prob. 15SGRCh. 6.8 - Prob. 16SGRCh. 6.8 - Prob. 17SGRCh. 6.8 - Prob. 18SGRCh. 6.8 - Prob. 19SGRCh. 6.8 - Prob. 20SGRCh. 6.8 - Prob. 21SGRCh. 6.8 - Prob. 22SGRCh. 6.8 - Prob. 23SGRCh. 6.8 - Prob. 24SGRCh. 6.8 - Prob. 25SGRCh. 6.8 - Prob. 26SGRCh. 6.8 - Prob. 27SGRCh. 6.8 - Prob. 28SGRCh. 6.8 - Prob. 29SGRCh. 6.8 - Prob. 30SGRCh. 6.8 - Prob. 31SGRCh. 6.8 - Prob. 32SGRCh. 6.8 - Prob. 33SGRCh. 6.8 - Prob. 34SGRCh. 6.8 - Prob. 35SGRCh. 6.8 - Prob. 36SGRCh. 6.8 - Prob. 37SGRCh. 6.8 - Prob. 38SGRCh. 6.8 - Prob. 39SGRCh. 6.8 - Prob. 40SGRCh. 6.8 - Prob. 41SGRCh. 6.8 - Prob. 42SGRCh. 6.8 - Prob. 43SGRCh. 6.8 - Prob. 44SGRCh. 6.8 - Prob. 45SGRCh. 6.8 - Prob. 46SGRCh. 6.8 - Prob. 47SGRCh. 6.8 - Prob. 48SGRCh. 6.8 - Prob. 49SGRCh. 6.8 - Prob. 50SGRCh. 6.8 - Prob. 51SGRCh. 6.8 - Prob. 52SGRCh. 6.8 - Prob. 53SGRCh. 6.8 - Prob. 54SGRCh. 6.8 - Prob. 55SGRCh. 6.8 - Prob. 56SGRCh. 6.8 - Prob. 1PTCh. 6.8 - Prob. 2PTCh. 6.8 - Prob. 3PTCh. 6.8 - Prob. 4PTCh. 6.8 - Prob. 5PTCh. 6.8 - Prob. 6PTCh. 6.8 - Prob. 7PTCh. 6.8 - Prob. 8PTCh. 6.8 - Prob. 9PTCh. 6.8 - Prob. 10PTCh. 6.8 - Prob. 11PTCh. 6.8 - Prob. 12PTCh. 6.8 - Prob. 13PTCh. 6.8 - Prob. 14PTCh. 6.8 - Prob. 15PTCh. 6.8 - Prob. 16PTCh. 6.8 - Prob. 17PTCh. 6.8 - Prob. 18PTCh. 6.8 - Prob. 19PTCh. 6.8 - Prob. 20PTCh. 6.8 - Prob. 21PTCh. 6.8 - Prob. 22PTCh. 6.8 - Prob. 23PTCh. 6.8 - Prob. 24PTCh. 6.8 - Prob. 25PTCh. 6.8 - Prob. 1ECh. 6.8 - Prob. 2ECh. 6.8 - Prob. 1STPCh. 6.8 - Prob. 2STPCh. 6.8 - Prob. 3STPCh. 6.8 - Prob. 4STPCh. 6.8 - Prob. 5STPCh. 6.8 - Prob. 6STPCh. 6.8 - Prob. 7STPCh. 6.8 - Prob. 8STPCh. 6.8 - Prob. 9STPCh. 6.8 - Prob. 10STPCh. 6.8 - Prob. 11STPCh. 6.8 - Prob. 12STPCh. 6.8 - Prob. 13STPCh. 6.8 - Prob. 14STPCh. 6.8 - Prob. 15STPCh. 6.8 - Prob. 16STPCh. 6.8 - Prob. 17STPCh. 6 - Prob. 1QCCh. 6 - Prob. 2QCCh. 6 - Prob. 3QCCh. 6 - Prob. 4QCCh. 6 - Prob. 5QCCh. 6 - Prob. 6QCCh. 6 - Prob. 7QCCh. 6 - Prob. 8QCCh. 6 - Prob. 9QCCh. 6 - Prob. 10QCCh. 6 - Prob. 11QCCh. 6 - Prob. 12QCCh. 6 - Prob. 13QCCh. 6 - Prob. 14QCCh. 6 - Prob. 15QCCh. 6 - Prob. 1MCQCh. 6 - Prob. 2MCQCh. 6 - Prob. 3MCQCh. 6 - Prob. 4MCQCh. 6 - Prob. 5MCQCh. 6 - Prob. 6MCQCh. 6 - Prob. 7MCQCh. 6 - Prob. 8MCQCh. 6 - Prob. 9MCQCh. 6 - Prob. 10MCQCh. 6 - Prob. 11MCQCh. 6 - Prob. 12MCQCh. 6 - Prob. 13MCQCh. 6 - Prob. 14MCQCh. 6 - Prob. 15MCQCh. 6 - Prob. 16MCQCh. 6 - Prob. 17MCQCh. 6 - Prob. 18MCQCh. 6 - Prob. 19MCQCh. 6 - Prob. 20MCQCh. 6 - Prob. 21MCQ
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