142:@0.026565:0.967627:0.050760:0.967627:0.050760:0.951847:0.026565:0.951847:0.000000:0.000000:0.000000
Modelos matemáticos con funciones :@0.404235:0.119706:0.850820:0.119706:0.850820:0.075047:0.404235:0.075047:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cuadráticas:@0.404235:0.157425:0.545156:0.157425:0.545156:0.112766:0.404235:0.112766:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
M.5.1.31. Resolver (con o sin el uso de la tecnología) problemas o situaciones, reales o hipotéticas, que pueden ser modelizados con funciones cuadráticas, identificando las :@0.143371:0.958650:0.894722:0.958650:0.894722:0.948608:0.143371:0.948608:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
variables significativas presentes y las relaciones entre ellas; juzgar la pertinencia y validez de los resultados obtenidos.:@0.143371:0.967451:0.645734:0.967451:0.645734:0.957409:0.143371:0.957409:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Crecimiento del área urbana de una ciudad:@0.404236:0.182033:0.749598:0.182033:0.749598:0.164351:0.404236:0.164351:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Para planificar de las ciudades, es muy importante encontrar o cons-:@0.404236:0.205869:0.891763:0.205869:0.891763:0.189371:0.404236:0.189371:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
truir funciones a partir de datos históricos que permitan calcular, en :@0.404236:0.223219:0.895963:0.223219:0.895963:0.206722:0.404236:0.206722:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
forma aproximada, su crecimiento. En este ejemplo, se plantea el cre-:@0.404236:0.240570:0.891840:0.240570:0.891840:0.224072:0.404236:0.224072:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cimiento que experimenta el área urbana de una pequeña ciudad del :@0.404236:0.257921:0.895899:0.257921:0.895899:0.241423:0.404236:0.241423:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ecuador. En la siguiente tabla se muestran los resultados::@0.404236:0.275272:0.803347:0.275272:0.803347:0.258774:0.404236:0.258774:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Año:@0.436446:0.304827:0.468677:0.304827:0.468677:0.287881:0.436446:0.287881:0.000000:0.000000:0.000000
t:@0.544505:0.305058:0.550554:0.305058:0.550554:0.287896:0.544505:0.287896:0.000000
Área urbana aproximada (km²):@0.623319:0.304827:0.862630:0.304827:0.862630:0.287881:0.623319:0.287881:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1950:@0.435560:0.325706:0.469544:0.325706:0.469544:0.309208:0.435560:0.309208:0.000000:0.000000:0.000000:0.000000
0:@0.543272:0.325706:0.551768:0.325706:0.551768:0.309208:0.543272:0.309208:0.000000
15,0:@0.728835:0.325706:0.757078:0.325706:0.757078:0.309208:0.728835:0.309208:0.000000:0.000000:0.000000:0.000000
1970:@0.435541:0.347047:0.469524:0.347047:0.469524:0.330549:0.435541:0.330549:0.000000:0.000000:0.000000:0.000000
20:@0.539014:0.347047:0.556006:0.347047:0.556006:0.330549:0.539014:0.330549:0.000000:0.000000
23,0:@0.728835:0.347047:0.757078:0.347047:0.757078:0.330549:0.728835:0.330549:0.000000:0.000000:0.000000:0.000000
1990:@0.435541:0.368389:0.469524:0.368389:0.469524:0.351891:0.435541:0.351891:0.000000:0.000000:0.000000:0.000000
40:@0.539014:0.368389:0.556006:0.368389:0.556006:0.351891:0.539014:0.351891:0.000000:0.000000
39,8:@0.728835:0.368389:0.757078:0.368389:0.757078:0.351891:0.728835:0.351891:0.000000:0.000000:0.000000:0.000000
2007:@0.435541:0.389730:0.469524:0.389730:0.469524:0.373232:0.435541:0.373232:0.000000:0.000000:0.000000:0.000000
57:@0.539014:0.389730:0.556006:0.389730:0.556006:0.373232:0.539014:0.373232:0.000000:0.000000
61,0:@0.728835:0.389730:0.757078:0.389730:0.757078:0.373232:0.728835:0.373232:0.000000:0.000000:0.000000:0.000000
Nótese que al año 1950 se lo asocia con 0; a 1970, con 20; a 1990, con :@0.404215:0.430765:0.895940:0.430765:0.895940:0.414267:0.404215:0.414267:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
40; y al año 2007, con 57. Estos datos se grafican en el sistema de coor-:@0.404215:0.448115:0.891742:0.448115:0.891742:0.431618:0.404215:0.431618:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
denadas rectangulares (figura 3.16.).:@0.404215:0.465466:0.656317:0.465466:0.656317:0.448968:0.404215:0.448968:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Saberes previos:@0.199646:0.100622:0.307805:0.100622:0.307805:0.085150:0.199646:0.085150:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Qué es un modelo :@0.199884:0.129250:0.330630:0.129250:0.330630:0.114187:0.199884:0.114187:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemático?:@0.153341:0.145092:0.236946:0.145092:0.236946:0.130029:0.153341:0.130029:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Desequilibrio cognitivo:@0.199644:0.188680:0.363492:0.188680:0.363492:0.173208:0.199644:0.173208:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Qué factores intervie-:@0.199880:0.217308:0.346405:0.217308:0.346405:0.202244:0.199880:0.202244:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
nen en el crecimiento urbano :@0.153337:0.233149:0.348673:0.233149:0.348673:0.218086:0.153337:0.218086:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de la ciudad?:@0.153337:0.248991:0.237416:0.248991:0.237416:0.233928:0.153337:0.233928:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Se asume que el crecimiento es continuo, lo que permite trazar una :@0.404235:0.739507:0.895818:0.739507:0.895818:0.723010:0.404235:0.723010:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
curva continua que pasa por dichos puntos. El crecimiento que expe-:@0.404235:0.756858:0.891769:0.756858:0.891769:0.740360:0.404235:0.740360:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
rimenta la ciudad se modela con una función cuadrática de la forma :@0.404235:0.774209:0.895976:0.774209:0.895976:0.757711:0.404235:0.757711:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.443288:0.793446:0.454096:0.793446:0.454096:0.776948:0.443288:0.776948:0.000000
,:@0.531234:0.793446:0.533989:0.793446:0.533989:0.776948:0.531234:0.776948:0.000000
0, donde  ,  ,       son constantes. Para esa :@0.569559:0.793446:0.895903:0.793446:0.895903:0.776948:0.569559:0.776948:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.523019:0.785410:0.527937:0.785410:0.527937:0.775861:0.523019:0.775861:0.000000
At:@0.407950:0.793561:0.432822:0.793561:0.432822:0.777092:0.407950:0.777092:0.000000:0.000000
abtct:@0.457154:0.793561:0.521962:0.793561:0.521962:0.777092:0.457154:0.777092:0.000000:0.000000:0.000000:0.000000:0.000000
t:@0.546236:0.793561:0.551900:0.793561:0.551900:0.777092:0.546236:0.777092:0.000000
():@0.420463:0.797115:0.440286:0.797115:0.440286:0.775624:0.420463:0.775624:0.000000:0.000000
++:@0.467421:0.794082:0.507377:0.794082:0.507377:0.777801:0.467421:0.777801:0.000000:0.000000
≥:@0.555695:0.794082:0.566271:0.794082:0.566271:0.777801:0.555695:0.777801:0.000000
a b c:@0.638814:0.793561:0.678192:0.793561:0.678192:0.777092:0.638814:0.777092:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.682411:0.793229:0.698459:0.793229:0.698459:0.778582:0.682411:0.778582:0.000000
R:@0.702678:0.792477:0.716587:0.792477:0.716587:0.779030:0.702678:0.779030:0.000000
información, se ha encontrado que   = 15,   = 0,18,   = 0,001, con lo :@0.404240:0.810796:0.895945:0.810796:0.895945:0.794299:0.404240:0.794299:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.658424:0.810912:0.667401:0.810912:0.667401:0.794443:0.658424:0.794443:0.000000
b:@0.711422:0.810912:0.720689:0.810912:0.720689:0.794443:0.711422:0.794443:0.000000
c:@0.775961:0.810912:0.783147:0.810912:0.783147:0.794443:0.775961:0.794443:0.000000
que la función   se escribe como sigue::@0.404240:0.828147:0.683024:0.828147:0.683024:0.811649:0.404240:0.811649:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.510312:0.828263:0.521583:0.828263:0.521583:0.811794:0.510312:0.811794:0.000000
() =150,18:@0.419164:0.854598:0.513811:0.854598:0.513811:0.838030:0.419164:0.838030:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0,011 =15:@0.534725:0.854598:0.619543:0.854598:0.619543:0.838030:0.534725:0.838030:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(0,18 0,011 ),:@0.639606:0.854598:0.744003:0.854598:0.744003:0.838030:0.639606:0.838030:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0.:@0.784342:0.854598:0.795563:0.854598:0.795563:0.838030:0.784342:0.838030:0.000000:0.000000
2:@0.579620:0.846526:0.584559:0.846526:0.584559:0.836937:0.579620:0.836937:0.000000
At:@0.407967:0.854714:0.430429:0.854714:0.430429:0.838175:0.407967:0.838175:0.000000:0.000000
t:@0.514067:0.854714:0.519755:0.854714:0.519755:0.838175:0.514067:0.838175:0.000000
t:@0.572902:0.854714:0.578590:0.854714:0.578590:0.838175:0.572902:0.838175:0.000000
t:@0.633246:0.854714:0.638935:0.854714:0.638935:0.838175:0.633246:0.838175:0.000000
t:@0.728202:0.854714:0.733891:0.854714:0.733891:0.838175:0.728202:0.838175:0.000000
t:@0.760948:0.854714:0.766636:0.854714:0.766636:0.838175:0.760948:0.838175:0.000000
+:@0.470799:0.855236:0.481420:0.855236:0.481420:0.838886:0.470799:0.838886:0.000000
+:@0.521953:0.855236:0.532574:0.855236:0.532574:0.838886:0.521953:0.838886:0.000000
+:@0.620894:0.855236:0.631516:0.855236:0.631516:0.838886:0.620894:0.838886:0.000000
+:@0.677253:0.855236:0.687874:0.855236:0.687874:0.838886:0.677253:0.838886:0.000000
≥:@0.770409:0.855236:0.781031:0.855236:0.781031:0.838886:0.770409:0.838886:0.000000
Nótese que :@0.404235:0.885905:0.494278:0.885905:0.494278:0.869407:0.404235:0.869407:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.501804:0.886021:0.513074:0.886021:0.513074:0.869552:0.501804:0.869552:0.000000
A:@0.584317:0.886021:0.595587:0.886021:0.595587:0.869552:0.584317:0.869552:0.000000
A:@0.675615:0.886021:0.686885:0.886021:0.686885:0.869552:0.675615:0.869552:0.000000
A:@0.780996:0.886021:0.792266:0.886021:0.792266:0.869552:0.780996:0.869552:0.000000
0=15,:@0.521127:0.885905:0.571506:0.885905:0.571506:0.869407:0.521127:0.869407:0.000000:0.000000:0.000000:0.000000:0.000000
20 =23,:@0.603216:0.885905:0.662804:0.885905:0.662804:0.869407:0.603216:0.869407:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
40 =39,8,:@0.694938:0.885905:0.768204:0.885905:0.768204:0.869407:0.694938:0.869407:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
57 =60,999  :@0.799491:0.885905:0.895910:0.885905:0.895910:0.869407:0.799491:0.869407:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
():@0.513582:0.888840:0.537067:0.888840:0.537067:0.866861:0.513582:0.866861:0.000000:0.000000
():@0.596096:0.888840:0.627594:0.888840:0.627594:0.866861:0.596096:0.866861:0.000000:0.000000
():@0.687394:0.888840:0.719297:0.888840:0.719297:0.866861:0.687394:0.866861:0.000000:0.000000
():@0.792775:0.888840:0.823849:0.888840:0.823849:0.866861:0.792775:0.866861:0.000000:0.000000
y :@0.404241:0.905135:0.416205:0.905135:0.416205:0.888638:0.404241:0.888638:0.000000:0.000000
A:@0.421620:0.905257:0.432890:0.905257:0.432890:0.888789:0.421620:0.888789:0.000000
A:@0.472037:0.905257:0.483307:0.905257:0.483307:0.888789:0.472037:0.888789:0.000000
A:@0.530457:0.905257:0.541727:0.905257:0.541727:0.888789:0.530457:0.888789:0.000000
A:@0.589293:0.905257:0.600563:0.905257:0.600563:0.888789:0.589293:0.888789:0.000000
0<:@0.440937:0.905142:0.469277:0.905142:0.469277:0.888644:0.440937:0.888644:0.000000:0.000000
20 <:@0.490931:0.905142:0.527708:0.905142:0.527708:0.888644:0.490931:0.888644:0.000000:0.000000:0.000000:0.000000
40<:@0.549786:0.905142:0.586544:0.905142:0.586544:0.888644:0.549786:0.888644:0.000000:0.000000:0.000000
57 .  De manera general, si :@0.607774:0.905142:0.814057:0.905142:0.814057:0.888644:0.607774:0.888644:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
():@0.433399:0.908077:0.456883:0.908077:0.456883:0.886098:0.433399:0.886098:0.000000:0.000000
():@0.483816:0.908077:0.515315:0.908077:0.515315:0.886098:0.483816:0.886098:0.000000:0.000000
():@0.542247:0.908077:0.574151:0.908077:0.574151:0.886098:0.542247:0.886098:0.000000:0.000000
():@0.601084:0.908077:0.632158:0.908077:0.632158:0.886098:0.601084:0.886098:0.000000:0.000000
tt:@0.820624:0.905257:0.842837:0.905257:0.842837:0.888789:0.820624:0.888789:0.000000:0.000000
,:@0.833397:0.905142:0.836152:0.905142:0.836152:0.888644:0.833397:0.888644:0.000000
1:@0.826224:0.907361:0.831142:0.907361:0.831142:0.897812:0.826224:0.897812:0.000000
2:@0.843240:0.907361:0.848157:0.907361:0.848157:0.897812:0.843240:0.897812:0.000000
∈:@0.853291:0.905778:0.867027:0.905778:0.867027:0.889497:0.853291:0.889497:0.000000
+:@0.881874:0.897474:0.887996:0.897474:0.887996:0.888051:0.881874:0.888051:0.000000
 :@0.891768:0.905142:0.895910:0.905142:0.895910:0.888644:0.891768:0.888644:0.000000
con   <  ,  se tiene  ( ) <  ( ), es decir que la función   es estricta-:@0.404241:0.922492:0.891772:0.922493:0.891772:0.905995:0.404241:0.905995:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
t:@0.435316:0.922608:0.440980:0.922608:0.440980:0.906139:0.435316:0.906139:0.000000
1:@0.440974:0.925165:0.445497:0.925165:0.445497:0.916383:0.440974:0.916383:0.000000
t:@0.464551:0.922609:0.470215:0.922609:0.470215:0.906140:0.464551:0.906140:0.000000
2:@0.470219:0.925165:0.474741:0.925165:0.474741:0.916383:0.470219:0.916383:0.000000
A t:@0.544114:0.922609:0.567001:0.922609:0.567001:0.906140:0.544114:0.906140:0.000000:0.000000:0.000000
1:@0.567013:0.925226:0.571309:0.925226:0.571309:0.916460:0.567013:0.916460:0.000000
A t:@0.596314:0.922609:0.619201:0.922609:0.619201:0.906140:0.596314:0.906140:0.000000:0.000000:0.000000
2:@0.619206:0.925226:0.623503:0.925226:0.623503:0.916460:0.619206:0.916460:0.000000
A:@0.800397:0.922609:0.811667:0.922609:0.811667:0.906140:0.800397:0.906140:0.000000
mente creciente.:@0.404245:0.939844:0.522399:0.939844:0.522399:0.923346:0.404245:0.923346:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
10:@0.537475:0.678903:0.546014:0.678903:0.546014:0.671007:0.537475:0.671007:0.000000:0.000000
20:@0.580209:0.678903:0.588749:0.678903:0.588749:0.671007:0.580209:0.671007:0.000000:0.000000
30:@0.622944:0.678903:0.631484:0.678903:0.631484:0.671007:0.622944:0.671007:0.000000:0.000000
40:@0.665679:0.678903:0.674218:0.678903:0.674218:0.671007:0.665679:0.671007:0.000000:0.000000
50:@0.708413:0.678903:0.716953:0.678903:0.716953:0.671007:0.708413:0.671007:0.000000:0.000000
60:@0.751148:0.678903:0.759688:0.678903:0.759688:0.671007:0.751148:0.671007:0.000000:0.000000
10:@0.484686:0.650991:0.493226:0.650991:0.493226:0.643095:0.484686:0.643095:0.000000:0.000000
20:@0.484686:0.629605:0.493226:0.629605:0.493226:0.621708:0.484686:0.621708:0.000000:0.000000
30:@0.484686:0.608218:0.493226:0.608218:0.493226:0.600322:0.484686:0.600322:0.000000:0.000000
40:@0.484686:0.586831:0.493226:0.586831:0.493226:0.578935:0.484686:0.578935:0.000000:0.000000
50:@0.484686:0.565444:0.493226:0.565444:0.493226:0.557548:0.484686:0.557548:0.000000:0.000000
60:@0.484686:0.544058:0.493226:0.544058:0.493226:0.536162:0.484686:0.536162:0.000000:0.000000
70:@0.484686:0.522671:0.493226:0.522671:0.493226:0.514775:0.484686:0.514775:0.000000:0.000000
A(t):@0.477257:0.496343:0.492264:0.496343:0.492264:0.488447:0.477257:0.488447:0.000000:0.000000:0.000000:0.000000
km²:@0.477655:0.505020:0.491866:0.505020:0.491866:0.497124:0.477655:0.497124:0.000000:0.000000:0.000000
t(años):@0.787146:0.678904:0.812946:0.678904:0.812946:0.671008:0.787146:0.671008:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0:@0.491846:0.675286:0.496116:0.675286:0.496116:0.667390:0.491846:0.667390:0.000000
1950:@0.490471:0.689089:0.507551:0.689089:0.507551:0.681193:0.490471:0.681193:0.000000:0.000000:0.000000:0.000000
1960:@0.533206:0.689089:0.550285:0.689089:0.550285:0.681193:0.533206:0.681193:0.000000:0.000000:0.000000:0.000000
1970:@0.575941:0.689089:0.593020:0.689089:0.593020:0.681193:0.575941:0.681193:0.000000:0.000000:0.000000:0.000000
1980:@0.618675:0.689089:0.635755:0.689089:0.635755:0.681193:0.618675:0.681193:0.000000:0.000000:0.000000:0.000000
1990:@0.661410:0.689089:0.678489:0.689089:0.678489:0.681193:0.661410:0.681193:0.000000:0.000000:0.000000:0.000000
2000:@0.704145:0.689089:0.721224:0.689089:0.721224:0.681193:0.704145:0.681193:0.000000:0.000000:0.000000:0.000000
2010:@0.746879:0.689089:0.763959:0.689089:0.763959:0.681193:0.746879:0.681193:0.000000:0.000000:0.000000:0.000000
A(t) = 15+0,18t+0,01t²:@0.603378:0.618622:0.685057:0.618622:0.685057:0.610725:0.603378:0.610725:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.822929:0.712089:0.834409:0.712089:0.834409:0.702064:0.822929:0.702064:0.000000
 Figura 3.16.:@0.834409:0.712797:0.891769:0.712797:0.891769:0.701320:0.834409:0.701320:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
François Viète. www.biografiasyvidas.com:@0.385284:0.855304:0.385284:0.740042:0.373816:0.740042:0.373816:0.855304:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 H. Benalcázar,:@0.826728:0.403739:0.879306:0.403739:0.879306:0.395132:0.826728:0.395132:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Interdisciplinariedad:@0.199286:0.407212:0.346071:0.407212:0.346071:0.391739:0.199286:0.391739:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Matemática e Historia:@0.199522:0.436261:0.355190:0.436261:0.355190:0.420789:0.199522:0.420789:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
François Viète  :@0.152979:0.458810:0.251129:0.458810:0.251129:0.443747:0.152979:0.443747:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(Francia, 1540-1603):@0.152979:0.474652:0.283725:0.474652:0.283725:0.459589:0.152979:0.459589:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Fue un matemático francés :@0.152979:0.497623:0.333151:0.497623:0.333151:0.482560:0.152979:0.482560:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
que consideró las ecuacio-:@0.152979:0.513465:0.323899:0.513465:0.323899:0.498402:0.152979:0.498402:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
nes cuadráticas de la manera :@0.152979:0.529307:0.343422:0.529307:0.343422:0.514244:0.152979:0.514244:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
general, :@0.152979:0.545149:0.205958:0.545149:0.205958:0.530086:0.152979:0.530086:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ax:@0.205958:0.545254:0.220997:0.545254:0.220997:0.530218:0.205958:0.530218:0.000000:0.000000
2:@0.221003:0.539347:0.225526:0.539347:0.225526:0.530565:0.221003:0.530565:0.000000
 +   +   = 0, donde :@0.225527:0.545147:0.360317:0.545147:0.360317:0.530084:0.225527:0.530084:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
bx c:@0.242958:0.545253:0.282237:0.545253:0.282237:0.530216:0.242958:0.530216:0.000000:0.000000:0.000000:0.000000
a, b, c :@0.152985:0.561095:0.192088:0.561095:0.192088:0.546058:0.152985:0.546058:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
son cantidades conoci-:@0.192088:0.560989:0.342694:0.560989:0.342694:0.545926:0.192088:0.545926:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
das. Gracias a esto, es posible :@0.152985:0.576831:0.344221:0.576831:0.344221:0.561768:0.152985:0.561768:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
escribir la fórmula de resolución :@0.152985:0.592673:0.364328:0.592673:0.364328:0.577610:0.152985:0.577610:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de la ecuación cuadrática para :@0.152985:0.608515:0.353772:0.608515:0.353772:0.593452:0.152985:0.593452:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
resolver ecuaciones de este tipo :@0.152985:0.624357:0.363005:0.624357:0.363005:0.609294:0.152985:0.609294:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y convertir otras reducibles a :@0.152985:0.640199:0.343394:0.640199:0.343394:0.625136:0.152985:0.625136:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cuadráticas.:@0.152985:0.656041:0.229254:0.656041:0.229254:0.640978:0.152985:0.640978:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.152985:0.867096:0.164466:0.867096:0.164466:0.857072:0.152985:0.857072:0.000000
 :@0.164466:0.867804:0.167347:0.867804:0.167347:0.856328:0.164466:0.856328:0.000000
François Viète:@0.167347:0.867804:0.236367:0.867804:0.236367:0.856328:0.167347:0.856328:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Indaga:@0.152985:0.894241:0.200617:0.894241:0.200617:0.878769:0.152985:0.878769:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 sobre François Viète, :@0.200617:0.893818:0.340931:0.893818:0.340931:0.878755:0.200617:0.878755:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
luego:@0.152985:0.909660:0.188904:0.909660:0.188904:0.894597:0.152985:0.894597:0.000000:0.000000:0.000000:0.000000:0.000000
 confecciona:@0.188904:0.910083:0.277030:0.910083:0.277030:0.894611:0.188904:0.894611:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 una ficha :@0.277030:0.909660:0.344259:0.909660:0.344259:0.894597:0.277030:0.894597:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
bibliográfica.:@0.152985:0.925502:0.235534:0.925502:0.235534:0.910439:0.152985:0.910439:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000