randFromArray([ [ "A", "B", "C" ], [ "J", "K", "L" ], [ "C", "J", "T" ] ])
POINTS[ 0 ] + POINTS[ 1 ]
POINTS[ 1 ] + POINTS[ 2 ]
POINTS[ 0 ] + POINTS[ 2 ]
randRangeNonZero( 2, 9 )
randRangeNonZero( 2, 9 )
randRangeNonZero( 2, 9 )
randRangeNonZero( 2, 9 )
randRange( 1, 9 )
( COEF_1 * X + CONST_1 ) + ( COEF_2 * X + CONST_2 )
shuffle([[BLUE,SEG_1+" = "+COEF_1+"x + "+CONST_1],[GREEN,SEG_2+" = "+COEF_2+"x + "+CONST_2],["purple",SEG_TOTAL+" = "+TOTAL]])
init({range:[[-1,11],[-1,1]]}),line([0,0],[10,0]),style({stroke:"#000",fill:"#000"}),graph.points=raphael.set(),graph.points.push(circle([0,0],.1)),graph.points.push(circle([10*(COEF_1*X+CONST_1)/TOTAL,0],.1)),graph.points.push(circle([10,0],.1)),label([0,0],POINTS[0],"below"),label([10*(COEF_1*X+CONST_1)/TOTAL,0],POINTS[1],"below"),label([10,0],POINTS[2],"below")
Si:
\qquad GIVEN[ 0 ][ 1 ],
\qquad GIVEN[ 1 ][ 1 ], y
\qquad GIVEN[ 2 ][ 1 ],
Encuentra SEG_2.
COEF_2 * X + CONST_2
style({stroke:BLUE,strokeWidth:3}),line([0,0],[10*(COEF_1*X+CONST_1)/TOTAL,0]),style({stroke:GREEN,strokeWidth:3}),line([10*(COEF_1*X+CONST_1)/TOTAL,0],[10,0]),graph.points.toFront(),$("#given0").css({color:GIVEN[0][0]}),$("#given1").css({color:GIVEN[1][0]}),$("#given2").css({color:GIVEN[2][0]})
A partir del diagrama, podemos ver que la longitud total de \purple{SEG_TOTAL} es la suma de \blue{SEG_1} y \green{SEG_2}:
\qquad \blue{SEG_1} + \green{SEG_2} = \purple{SEG_TOTAL}
Sustituye en las expresiones que fueron dadas para cada longitud:
\qquad \blue{COEF_1x + CONST_1} + \green{COEF_2x + CONST_2} = \purple{TOTAL}
Combina términos semejantes:
\qquadCOEF_1 + COEF_2x + CONST_1 + CONST_2 = \purple{TOTAL}
Resta CONST_1 + CONST_2 de ambos lados:
\qquadCOEF_1 + COEF_2x = TOTAL - CONST_1 - CONST_2
Divide ambos lados entre COEF_1 + COEF_2 para encontrar x:
\qquad x = X
Sustituye X por x en la expresión dada para SEG_2:
\qquad SEG_2 = COEF_2(\pink{X}) + CONST_2
Simplifica:
\qquad \green{SEG_2 = COEF_2 * X + CONST_2}
Simplifica para encontrar \green{SEG_2}:
\qquad \green{SEG_2 = COEF_2 * X + CONST_2}