# Khan/khan-exercises

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 d103285 Split measuring_segments into 4 exercises beneater authored Apr 3, 2012 1 2 3 4e4cb9b lint: tabs->spaces and jQuery->$for exercises beneater authored Apr 10, 2012 4 5 Segment addition 6 d103285 Split measuring_segments into 4 exercises beneater authored Apr 3, 2012 7 8 9 4e4cb9b lint: tabs->spaces and jQuery->$ for exercises beneater authored Apr 10, 2012 10
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13 randFromArray([ [ "A", "B", "C" ], [ "J", "K", "L" ], [ "C", "J", "T" ] ]) 14 POINTS[ 0 ] + POINTS[ 1 ] 15 POINTS[ 1 ] + POINTS[ 2 ] 16 POINTS[ 0 ] + POINTS[ 2 ] 17 randRangeNonZero( 2, 9 ) 18 randRangeNonZero( 2, 9 ) 19 randRangeNonZero( 2, 9 ) 20 randRangeNonZero( 2, 9 ) 21 randRange( 1, 9 ) 22 ( COEF_1 * X + CONST_1 ) + ( COEF_2 * X + CONST_2 ) 23 shuffle([ 24 [ BLUE, SEG_1 + " = " + COEF_1 + "x + " + CONST_1 ], 25 [ GREEN, SEG_2 + " = " + COEF_2 + "x + " + CONST_2 ], 26 [ "purple", SEG_TOTAL + " = " + TOTAL ] 27 ]) 28
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31 init({ 32 range: [ [ -1, 11 ], [ -1, 1 ] ] 33 }); 34 line( [ 0, 0 ], [ 10, 0 ] ); 35 style({ stroke: "#000", fill: "#000" }); 36 graph.points = raphael.set(); 37 graph.points.push( circle( [ 0, 0 ], 0.10 ) ); 38 graph.points.push( circle( [ 10 * ( COEF_1 * X + CONST_1 ) / TOTAL, 0 ], 0.10 ) ); 39 graph.points.push( circle( [ 10, 0 ], 0.10 ) ); 40 label( [ 0, 0 ], POINTS[ 0 ], "below" ); 41 label( [ 10 * ( COEF_1 * X + CONST_1 ) / TOTAL, 0 ], POINTS[ 1 ], "below" ); 42 label( [ 10, 0 ], POINTS[ 2 ], "below" ); 43
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45 If:
46 \qquad GIVEN[ 0 ][ 1 ],
47 \qquad GIVEN[ 1 ][ 1 ], and
48 \qquad GIVEN[ 2 ][ 1 ], 49

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Find SEG_2.

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COEF_2 * X + CONST_2
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56 style({ stroke: BLUE, strokeWidth: 3 }); 57 line( [ 0, 0 ], [ 10 * ( COEF_1 * X + CONST_1 ) / TOTAL, 0 ] ); 58 style({ stroke: GREEN, strokeWidth: 3 }); 59 line( [ 10 * ( COEF_1 * X + CONST_1 ) / TOTAL, 0 ], [ 10, 0 ] ); 60 graph.points.toFront(); 61 $( "#given0" ).css({ "color": GIVEN[ 0 ][ 0 ] }); 62$( "#given1" ).css({ "color": GIVEN[ 1 ][ 0 ] }); 63 \$( "#given2" ).css({ "color": GIVEN[ 2 ][ 0 ] }); 64
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From the diagram, we can see that the total length of \purple{SEG_TOTAL} is the sum of \blue{SEG_1} and \green{SEG_2}:

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\qquad \blue{SEG_1} + \green{SEG_2} = \purple{SEG_TOTAL}

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Substitute in the expressions that were given for each length:

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\qquad \blue{COEF_1x + CONST_1} + \green{COEF_2x + CONST_2} = \purple{TOTAL}

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Combine like terms:

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\qquadCOEF_1 + COEF_2x + CONST_1 + CONST_2 = \purple{TOTAL}

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Subtract CONST_1 + CONST_2 from both sides:

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\qquadCOEF_1 + COEF_2x = TOTAL - CONST_1 - CONST_2

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Divide both sides by COEF_1 + COEF_2 to find x:

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Substitute X for x in the expression that was given for SEG_2: 86

\qquad SEG_2 = COEF_2(\pink{X}) + CONST_2

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Simplify:

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\qquad \green{SEG_2 = COEF_2 * X + CONST_2}

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Simplify to find \green{SEG_2}:

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\qquad \green{SEG_2 = COEF_2 * X + CONST_2}

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d103285 Split measuring_segments into 4 exercises beneater authored Apr 3, 2012 99
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