48:@0.036727:0.974518:0.057230:0.974518:0.057230:0.956333:0.036727:0.956333:0.000000:0.000000
Números reales y funciones:@0.073089:0.043661:0.318030:0.043661:0.318030:0.024916:0.073089:0.024916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5.1 Modelización con funciones reales:@0.293660:0.231541:0.591259:0.231541:0.591259:0.214594:0.293660:0.214594:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ejercicio resuelto:@0.317369:0.265338:0.445951:0.265338:0.445951:0.248668:0.317369:0.248668:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Supongamos que, por simplicidad, la trayectoria de la ciudad AAA a la ciudad BBB es :@0.317369:0.299134:0.931448:0.299134:0.931448:0.283422:0.317369:0.283422:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
considerada una recta horizontal. Una ciclista parte de la ciudad AAA a las 9:00 h hacia :@0.317369:0.315776:0.931116:0.315776:0.931116:0.300064:0.317369:0.300064:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la ciudad BBB. Recorre 30 km en cada hora. Es decir, su velocidad media es :@0.317369:0.332418:0.931280:0.332418:0.931280:0.316705:0.317369:0.316705:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.926906:0.332418:0.930938:0.332418:0.930938:0.316705:0.926906:0.316705:0.000000
v:@0.317369:0.350419:0.325100:0.350419:0.325100:0.334984:0.317369:0.334984:0.000000
   30 :@0.325026:0.350419:0.370032:0.350419:0.370032:0.334706:0.325026:0.334706:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.328984:0.349864:0.344317:0.349864:0.344317:0.336149:0.328984:0.336149:0.000000
km:@0.370412:0.343070:0.388680:0.343070:0.388680:0.330441:0.370412:0.330441:0.000000:0.000000
h:@0.375653:0.359455:0.383424:0.359455:0.383424:0.346826:0.375653:0.346826:0.000000
.:@0.389073:0.350411:0.392276:0.350411:0.392276:0.334699:0.389073:0.334699:0.000000
La función de desplazamiento de la ciclista es  ( )   30 ,     9:00 h. Dos horas más :@0.317377:0.384208:0.930926:0.384208:0.930926:0.368496:0.317377:0.368496:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
s t:@0.659051:0.384208:0.675711:0.384208:0.675711:0.368773:0.659051:0.368773:0.000000:0.000000:0.000000
5:@0.685154:0.383654:0.700487:0.383654:0.700487:0.369938:0.685154:0.369938:0.000000
t t:@0.723036:0.384208:0.741554:0.384208:0.741554:0.368773:0.723036:0.368773:0.000000:0.000000:0.000000
$:@0.746100:0.383654:0.761434:0.383654:0.761434:0.369938:0.746100:0.369938:0.000000
tarde, parte un automóvil con una velocidad media de 70 :@0.317377:0.409421:0.784757:0.409421:0.784757:0.393708:0.317377:0.393708:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
km:@0.788173:0.400750:0.806441:0.400750:0.806441:0.388122:0.788173:0.388122:0.000000:0.000000
h:@0.793414:0.417135:0.801185:0.417135:0.801185:0.404506:0.793414:0.404506:0.000000
. La función de :@0.807306:0.409422:0.930911:0.409422:0.930911:0.393709:0.807306:0.393709:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
desplazamiento del automóvil es  ( )   70 ,     11:00 h. Durante las dos primeras :@0.317379:0.434634:0.930895:0.434637:0.930895:0.418924:0.317379:0.418922:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
s t:@0.567349:0.434634:0.589060:0.434637:0.589060:0.419201:0.567349:0.419199:0.000000:0.000000:0.000000
2:@0.573748:0.437508:0.578747:0.437508:0.578747:0.428764:0.573748:0.428764:0.000000
5:@0.598705:0.434082:0.614038:0.434082:0.614038:0.420366:0.598705:0.420366:0.000000
t t:@0.636817:0.434637:0.655547:0.434637:0.655547:0.419201:0.636817:0.419201:0.000000:0.000000:0.000000
$:@0.660259:0.434082:0.675592:0.434082:0.675592:0.420366:0.660259:0.420366:0.000000
horas, la ciclista recorre  (2)   30   2 km   60 km, lo que nos permite definir una :@0.317405:0.451279:0.931078:0.451279:0.931078:0.435566:0.317405:0.435566:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
s:@0.493121:0.451279:0.499490:0.451279:0.499490:0.435843:0.493121:0.435843:0.000000
5:@0.523015:0.450724:0.538348:0.450724:0.538348:0.437008:0.523015:0.437008:0.000000
3:@0.565701:0.450724:0.581034:0.450724:0.581034:0.437008:0.565701:0.437008:0.000000
5:@0.627343:0.450724:0.642676:0.450724:0.642676:0.437008:0.627343:0.437008:0.000000
nueva función  ( )   60   30 ,    11:00 h. En la Figura 5.1 en el sistema de :@0.317442:0.467920:0.931028:0.467920:0.931028:0.452208:0.317442:0.452208:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
s t:@0.436003:0.467920:0.458382:0.467920:0.458382:0.452485:0.436003:0.452485:0.000000:0.000000:0.000000
1:@0.442590:0.470792:0.447589:0.470792:0.447589:0.462048:0.442590:0.462048:0.000000
5:@0.470365:0.467366:0.485698:0.467366:0.485698:0.453650:0.470365:0.453650:0.000000
1:@0.517699:0.467366:0.533032:0.467366:0.533032:0.453650:0.517699:0.453650:0.000000
t t:@0.558563:0.467920:0.579630:0.467920:0.579630:0.452485:0.558563:0.452485:0.000000:0.000000:0.000000
$:@0.586386:0.467366:0.601719:0.467366:0.601719:0.453650:0.586386:0.453650:0.000000
coordenadas rectangulares, representamos gráficamente estas dos funciones.:@0.317382:0.484562:0.879608:0.484562:0.879608:0.468850:0.317382:0.468850:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A cada instante, las distancias recorridas por la ciclista y el automóvil siempre aumentan, :@0.293674:0.518359:0.931428:0.518359:0.931428:0.502646:0.293674:0.502646:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
es decir que las funciones   y   son estrictamente crecientes. En las gráficas de estas :@0.293674:0.535001:0.930857:0.535001:0.930857:0.519288:0.293674:0.519288:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
s:@0.490778:0.535001:0.497147:0.535001:0.497147:0.519566:0.490778:0.519566:0.000000
1:@0.497171:0.537871:0.502170:0.537871:0.502170:0.529127:0.497171:0.529127:0.000000
s:@0.519909:0.535001:0.526278:0.535001:0.526278:0.519566:0.519909:0.519566:0.000000
2:@0.526316:0.537871:0.531315:0.537871:0.531315:0.529127:0.526316:0.529127:0.000000
funciones observamos que la de la ciclista es más inclinada que la del automóvil o que :@0.293653:0.551643:0.931211:0.551643:0.931211:0.535930:0.293653:0.535930:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la gráfica de la función de desplazamiento del automóvil es más empinada que la de la :@0.293653:0.568285:0.931474:0.568285:0.931474:0.552572:0.293653:0.552572:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ciclista. Esta observación se traduce en el hecho de que la gráfica que corresponde al :@0.293653:0.584926:0.930773:0.584926:0.930773:0.569214:0.293653:0.569214:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
automóvil tiene una pendiente mayor que la que le corresponde a la ciclista. Además, :@0.293653:0.601568:0.931146:0.601568:0.931146:0.585856:0.293653:0.585856:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
observamos que las dos gráficas se cortan en un punto  . Así, una estimación visual de :@0.293653:0.618210:0.931108:0.618210:0.931108:0.602497:0.293653:0.602497:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
t:@0.700859:0.618210:0.706234:0.618210:0.706234:0.602775:0.700859:0.602775:0.000000
1:@0.706172:0.621080:0.711171:0.621080:0.711171:0.612336:0.706172:0.612336:0.000000
t:@0.293668:0.634852:0.299043:0.634852:0.299043:0.619417:0.293668:0.619417:0.000000
1:@0.299095:0.637722:0.304094:0.637722:0.304094:0.628978:0.299095:0.628978:0.000000
 basada en las gráficas no resulta muy apropiada. Ahora, calculemos analíticamente :@0.304136:0.634852:0.930831:0.634852:0.930831:0.619139:0.304136:0.619139:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
este punto. Tenemos  ( )   60   30 y  ( )   70 , luego, :@0.293662:0.651494:0.728685:0.651494:0.728685:0.635781:0.293662:0.635781:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
s t:@0.448504:0.651494:0.469941:0.651494:0.469941:0.636058:0.448504:0.636058:0.000000:0.000000:0.000000
1 1:@0.454809:0.654364:0.474867:0.654364:0.474867:0.645620:0.454809:0.645620:0.000000:0.000000:0.000000
5:@0.483566:0.650939:0.498899:0.650939:0.498899:0.637223:0.483566:0.637223:0.000000
1:@0.524504:0.650939:0.539837:0.650939:0.539837:0.637223:0.524504:0.637223:0.000000
t:@0.561502:0.651494:0.566877:0.651494:0.566877:0.636058:0.561502:0.636058:0.000000
1  :@0.566820:0.654364:0.576224:0.654364:0.576224:0.645620:0.566820:0.645620:0.000000:0.000000:0.000000
s t:@0.588136:0.651494:0.609575:0.651494:0.609575:0.636058:0.588136:0.636058:0.000000:0.000000:0.000000
2 1:@0.594441:0.654364:0.614501:0.654364:0.614501:0.645620:0.594441:0.645620:0.000000:0.000000:0.000000
5:@0.623198:0.650939:0.638532:0.650939:0.638532:0.637223:0.623198:0.637223:0.000000
t:@0.660197:0.651494:0.665572:0.651494:0.665572:0.636058:0.660197:0.636058:0.000000
1 :@0.665507:0.654364:0.672708:0.654364:0.672708:0.645620:0.665507:0.645620:0.000000:0.000000
s t:@0.385894:0.686650:0.407325:0.686642:0.407325:0.671207:0.385894:0.671214:0.000000:0.000000:0.000000
1 1:@0.392192:0.689513:0.412252:0.689513:0.412252:0.680769:0.392192:0.680769:0.000000:0.000000:0.000000
( )    ( ):@0.397146:0.686642:0.471340:0.686642:0.471340:0.670929:0.397146:0.670929:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.420950:0.686087:0.436283:0.686087:0.436283:0.672372:0.420950:0.672372:0.000000
s t:@0.440148:0.686642:0.461581:0.686642:0.461581:0.671207:0.440148:0.671207:0.000000:0.000000:0.000000
2 1:@0.446449:0.689513:0.466508:0.689513:0.466508:0.680769:0.446449:0.680769:0.000000:0.000000:0.000000
   :@0.471260:0.686484:0.494229:0.686484:0.494229:0.671751:0.471260:0.671751:0.000000:0.000000:0.000000
60   30    70  :@0.493816:0.686642:0.618070:0.686642:0.618070:0.670929:0.493816:0.670929:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.515573:0.686087:0.530906:0.686087:0.530906:0.672372:0.515573:0.672372:0.000000
t:@0.552572:0.686642:0.557946:0.686642:0.557946:0.671207:0.552572:0.671207:0.000000
1:@0.557874:0.689513:0.562873:0.689513:0.562873:0.680769:0.557874:0.680769:0.000000
5:@0.566785:0.686087:0.582119:0.686087:0.582119:0.672372:0.566785:0.672372:0.000000
t:@0.603784:0.686642:0.609159:0.686642:0.609159:0.671207:0.603784:0.671207:0.000000
1:@0.609083:0.689513:0.614082:0.689513:0.614082:0.680769:0.609083:0.680769:0.000000
   :@0.617988:0.686484:0.640958:0.686484:0.640958:0.671751:0.617988:0.671751:0.000000:0.000000:0.000000
60   40:@0.640543:0.686642:0.699391:0.686642:0.699391:0.670929:0.640543:0.670929:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.662301:0.686087:0.677634:0.686087:0.677634:0.672372:0.662301:0.672372:0.000000
t:@0.699299:0.686642:0.704674:0.686642:0.704674:0.671207:0.699299:0.671207:0.000000
1:@0.704602:0.689513:0.709601:0.689513:0.709601:0.680769:0.704602:0.680769:0.000000
   :@0.709557:0.686484:0.732526:0.686484:0.732526:0.671751:0.709557:0.671751:0.000000:0.000000:0.000000
  1:@0.732111:0.689513:0.744617:0.689513:0.744617:0.680769:0.732111:0.680769:0.000000:0.000000:0.000000
t:@0.734310:0.686642:0.739685:0.686642:0.739685:0.671207:0.734310:0.671207:0.000000
 :@0.744573:0.686642:0.748604:0.686642:0.748604:0.670929:0.744573:0.670929:0.000000
5 :@0.748530:0.686087:0.768373:0.686087:0.768373:0.672372:0.748530:0.672372:0.000000:0.000000
 :@0.768281:0.686642:0.772312:0.686642:0.772312:0.670929:0.768281:0.670929:0.000000
3:@0.778157:0.679301:0.785507:0.679301:0.785507:0.666445:0.778157:0.666445:0.000000
2:@0.778157:0.695685:0.785507:0.695685:0.785507:0.682830:0.778157:0.682830:0.000000
5:@0.791360:0.686087:0.806694:0.686087:0.806694:0.672372:0.791360:0.672372:0.000000
 1,5,:@0.806602:0.686642:0.834710:0.686642:0.834710:0.670929:0.806602:0.670929:0.000000:0.000000:0.000000:0.000000:0.000000
es decir que después de hora y media de recorrido, el automóvil alcanza a la ciclista.:@0.293665:0.720439:0.900096:0.720439:0.900096:0.704726:0.293665:0.704726:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ejercicio resuelto:@0.293665:0.754236:0.422247:0.754236:0.422247:0.737566:0.293665:0.737566:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Uso de escalas:@0.293665:0.788032:0.403442:0.788032:0.403442:0.771363:0.293665:0.771363:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La unidad de medida de longitud en el Sistema Internacional es el metro (m) con sus :@0.293665:0.821829:0.930589:0.821829:0.930589:0.806117:0.293665:0.806117:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
múltiplos y submúltiplos. Sin embargo, en algunos países se utiliza la pulgada (in), el pie :@0.293665:0.838471:0.931375:0.838471:0.931375:0.822758:0.293665:0.822758:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(ft), la yarda (yd) y la milla (mi). Dada una medida     0 en un sistema, nos interesa el :@0.293665:0.855113:0.931158:0.855113:0.931158:0.839400:0.293665:0.839400:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
m:@0.657558:0.855113:0.672174:0.855113:0.672174:0.839678:0.657558:0.839678:0.000000
.:@0.676683:0.854558:0.692017:0.854558:0.692017:0.840843:0.676683:0.840843:0.000000
valor de esta medida en otro sistema.:@0.293665:0.871755:0.564018:0.871755:0.564018:0.856042:0.293665:0.856042:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Muchas magnitudes físicas (como la masa, temperatura, presión y otras) o de origen :@0.293665:0.905552:0.930981:0.905552:0.930981:0.889839:0.293665:0.889839:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
económico (como la cotización de una moneda frente a otra) se expresan en dos o más :@0.293665:0.922193:0.931320:0.922193:0.931320:0.906481:0.293665:0.906481:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
sistemas de medida y tienen un comportamiento lineal.:@0.293665:0.938835:0.698319:0.938835:0.698319:0.923123:0.293665:0.923123:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Tema 5. Modelos matemáticos con funciones reales simples:@0.073089:0.096388:0.925140:0.096388:0.925140:0.066058:0.073089:0.066058:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Cuál es la representación gráfica de la función área de un terreno de forma :@0.307891:0.165069:0.917066:0.165069:0.917066:0.149357:0.307891:0.149357:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
rectangular de largo 3  y ancho  ?:@0.307891:0.181711:0.554769:0.181711:0.554769:0.165999:0.307891:0.165999:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.467426:0.181711:0.474881:0.181711:0.474881:0.166276:0.467426:0.166276:0.000000
x:@0.540374:0.181711:0.547829:0.181711:0.547829:0.166276:0.540374:0.166276:0.000000
Reto matemático:@0.302768:0.139600:0.437491:0.139600:0.437491:0.122653:0.302768:0.122653:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
50:@0.089893:0.205111:0.100702:0.205111:0.100702:0.195658:0.089893:0.195658:0.000000:0.000000
0:@0.097081:0.215399:0.102485:0.215399:0.102485:0.205946:0.097081:0.205946:0.000000
2:@0.129694:0.215974:0.135099:0.215974:0.135099:0.206521:0.129694:0.206521:0.000000
Representación gráfica del área :@0.123210:0.131205:0.240253:0.131205:0.240253:0.123312:0.123210:0.123312:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de un terreno rectangular:@0.134387:0.139565:0.229074:0.139565:0.229074:0.131672:0.134387:0.131672:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A( ) :@0.108469:0.149049:0.124548:0.149049:0.124548:0.141157:0.108469:0.141157:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.116328:0.149049:0.120073:0.149049:0.120073:0.141296:0.116328:0.141296:0.000000
5 :@0.124548:0.148771:0.134561:0.148771:0.134561:0.141882:0.124548:0.141882:0.000000:0.000000
3 :@0.134561:0.149049:0.145462:0.149049:0.145462:0.141157:0.134561:0.141157:0.000000:0.000000:0.000000
x:@0.139073:0.149049:0.142818:0.149049:0.142818:0.141296:0.139073:0.141296:0.000000
Área (A):@0.084532:0.187424:0.084532:0.165579:0.074056:0.165579:0.074056:0.187424:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Área (B):@0.170484:0.222682:0.198793:0.222682:0.198793:0.214790:0.170484:0.214790:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
4:@0.159413:0.215978:0.164817:0.215978:0.164817:0.206524:0.159413:0.206524:0.000000
6:@0.190332:0.215978:0.195736:0.215978:0.195736:0.206524:0.190332:0.206524:0.000000
8:@0.220731:0.215978:0.226135:0.215978:0.226135:0.206524:0.220731:0.206524:0.000000
10:@0.245183:0.215978:0.255992:0.215978:0.255992:0.206524:0.245183:0.206524:0.000000:0.000000
100:@0.084495:0.193283:0.100708:0.193283:0.100708:0.183830:0.084495:0.183830:0.000000:0.000000:0.000000
150:@0.084495:0.181444:0.100708:0.181444:0.100708:0.171991:0.084495:0.171991:0.000000:0.000000:0.000000
200:@0.084495:0.169287:0.100708:0.169287:0.100708:0.159834:0.084495:0.159834:0.000000:0.000000:0.000000
250:@0.084495:0.157131:0.100708:0.157131:0.100708:0.147678:0.084495:0.147678:0.000000:0.000000:0.000000
300:@0.084495:0.144749:0.100708:0.144749:0.100708:0.135296:0.084495:0.135296:0.000000:0.000000:0.000000
Cátedra de :@0.080204:0.541010:0.169525:0.541010:0.169525:0.524063:0.080204:0.524063:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
emprendimiento:@0.080204:0.553617:0.213204:0.553617:0.213204:0.536670:0.080204:0.536670:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Al integrar funciones :@0.082576:0.577774:0.209026:0.577774:0.209026:0.564918:0.082576:0.564918:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
reales simples en un :@0.082576:0.591390:0.206126:0.591390:0.206126:0.578534:0.082576:0.578534:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
emprendimiento, puedes :@0.082576:0.605006:0.237351:0.605006:0.237351:0.592151:0.082576:0.592151:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
desarrollar modelos :@0.082576:0.618622:0.203200:0.618622:0.203200:0.605767:0.082576:0.605767:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemáticos que te ayudan :@0.082576:0.632238:0.252470:0.632238:0.252470:0.619383:0.082576:0.619383:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a comprender mejores :@0.082576:0.645854:0.221195:0.645854:0.221195:0.632999:0.082576:0.632999:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
conceptos empresariales. :@0.082576:0.659471:0.236185:0.659471:0.236185:0.646615:0.082576:0.646615:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Por ejemplo, un modelo de :@0.082576:0.673087:0.247881:0.673087:0.247881:0.660231:0.082576:0.660231:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
costos y beneficios.:@0.082576:0.686703:0.197219:0.686703:0.197219:0.673847:0.082576:0.673847:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Función de costos: :@0.082576:0.700319:0.196481:0.700319:0.196481:0.687463:0.082576:0.687463:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
C x:@0.082576:0.713935:0.100648:0.713935:0.100648:0.701306:0.082576:0.701306:0.000000:0.000000:0.000000
( )         * :@0.090618:0.713935:0.176712:0.713935:0.176712:0.701079:0.090618:0.701079:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.107742:0.713481:0.120287:0.713481:0.120287:0.702259:0.107742:0.702259:0.000000
C:@0.123450:0.713935:0.131552:0.713935:0.131552:0.701306:0.123450:0.701306:0.000000
f:@0.131502:0.716530:0.133741:0.716530:0.133741:0.709168:0.131502:0.709168:0.000000
1:@0.136947:0.713481:0.149493:0.713481:0.149493:0.702259:0.136947:0.702259:0.000000
C:@0.152655:0.713935:0.160758:0.713935:0.160758:0.701306:0.152655:0.701306:0.000000
v:@0.160691:0.716530:0.164379:0.716530:0.164379:0.709168:0.160691:0.709168:0.000000
x:@0.176637:0.713935:0.182736:0.713935:0.182736:0.701306:0.176637:0.701306:0.000000
C:@0.082584:0.727551:0.090687:0.727551:0.090687:0.714922:0.082584:0.714922:0.000000
f:@0.090624:0.730146:0.092863:0.730146:0.092863:0.722784:0.090624:0.722784:0.000000
 costos fijos (alquiler, :@0.092831:0.727551:0.217327:0.727551:0.217327:0.714695:0.092831:0.714695:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
sueldos).:@0.082575:0.741167:0.134639:0.741167:0.134639:0.728311:0.082575:0.728311:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
C:@0.082575:0.754783:0.090677:0.754783:0.090677:0.742154:0.082575:0.742154:0.000000
v:@0.090624:0.757378:0.094312:0.757378:0.094312:0.750016:0.090624:0.750016:0.000000
 costos variables :@0.094280:0.754783:0.194345:0.754783:0.194345:0.741927:0.094280:0.741927:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
por unidad producida :@0.082578:0.768399:0.216220:0.768399:0.216220:0.755543:0.082578:0.755543:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(materiales, mano de obra).:@0.082578:0.782015:0.243993:0.782015:0.243993:0.769159:0.082578:0.769159:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.082578:0.795631:0.089897:0.795631:0.089897:0.783002:0.082578:0.783002:0.000000
: cantidad de productos :@0.089837:0.795631:0.234323:0.795631:0.234323:0.782775:0.089837:0.782775:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
vendidos.:@0.082578:0.809247:0.139781:0.809247:0.139781:0.796391:0.082578:0.796391:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Función de ingresos::@0.082578:0.822863:0.204640:0.822863:0.204640:0.810007:0.082578:0.810007:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R x:@0.082578:0.836479:0.099867:0.836479:0.099867:0.823850:0.082578:0.823850:0.000000:0.000000:0.000000
( )     *   :@0.089837:0.836479:0.151465:0.836479:0.151465:0.823623:0.089837:0.823623:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.106961:0.836025:0.119506:0.836025:0.119506:0.824803:0.106961:0.824803:0.000000
P x:@0.122669:0.836479:0.148166:0.836479:0.148166:0.823850:0.122669:0.823850:0.000000:0.000000:0.000000
P:@0.082563:0.850095:0.089732:0.850095:0.089732:0.837466:0.082563:0.837466:0.000000
: precio de venta por :@0.089671:0.850095:0.215176:0.850095:0.215176:0.837239:0.089671:0.837239:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
unidad.:@0.082563:0.863711:0.127091:0.863711:0.127091:0.850855:0.082563:0.850855:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Función de beneficio: :@0.082563:0.877327:0.213719:0.877327:0.213719:0.864471:0.082563:0.864471:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
B x:@0.082563:0.890943:0.099762:0.890943:0.099762:0.878314:0.082563:0.878314:0.000000:0.000000:0.000000
( ) :@0.089732:0.890943:0.106931:0.890943:0.106931:0.878087:0.089732:0.878087:0.000000:0.000000:0.000000:0.000000
5 :@0.106855:0.890489:0.123091:0.890489:0.123091:0.879268:0.106855:0.879268:0.000000:0.000000
R x:@0.123015:0.890943:0.140305:0.890943:0.140305:0.878314:0.123015:0.878314:0.000000:0.000000:0.000000
( ) :@0.130274:0.890943:0.147474:0.890943:0.147474:0.878087:0.130274:0.878087:0.000000:0.000000:0.000000:0.000000
2 :@0.147398:0.890489:0.163633:0.890489:0.163633:0.879268:0.147398:0.879268:0.000000:0.000000
C x:@0.163558:0.890943:0.181631:0.890943:0.181631:0.878314:0.163558:0.878314:0.000000:0.000000:0.000000
( ). :@0.171600:0.890943:0.191420:0.890943:0.191420:0.878087:0.171600:0.878087:0.000000:0.000000:0.000000:0.000000:0.000000
Esto te permite analizar :@0.082533:0.904559:0.224350:0.904559:0.224350:0.891704:0.082533:0.891704:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cuándo un emprendimiento :@0.082533:0.918175:0.255313:0.918175:0.255313:0.905320:0.082533:0.905320:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
se vuelve rentable.:@0.082533:0.931791:0.192684:0.931791:0.192684:0.918936:0.082533:0.918936:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
11h:@0.086845:0.458505:0.107086:0.458505:0.107086:0.447078:0.086845:0.447078:0.000000:0.000000:0.000000
12h:@0.130272:0.458505:0.150514:0.458505:0.150514:0.447078:0.130272:0.447078:0.000000:0.000000:0.000000
13h:@0.182147:0.458505:0.202389:0.458505:0.202389:0.447078:0.182147:0.447078:0.000000:0.000000:0.000000
14h:@0.230676:0.458505:0.250917:0.458505:0.250917:0.447078:0.230676:0.447078:0.000000:0.000000:0.000000
1:@0.139971:0.446906:0.146504:0.446906:0.146504:0.435479:0.139971:0.435479:0.000000
t   2 :@0.163854:0.446906:0.198048:0.446906:0.198048:0.435479:0.163854:0.435479:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.167989:0.450723:0.172988:0.450723:0.172988:0.441979:0.167989:0.441979:0.000000
3:@0.237111:0.446906:0.243644:0.446906:0.243644:0.435479:0.237111:0.435479:0.000000
s:@0.075961:0.257302:0.080593:0.257302:0.080593:0.246076:0.075961:0.246076:0.000000
(km):@0.080593:0.257302:0.104610:0.257302:0.104610:0.245874:0.080593:0.245874:0.000000:0.000000:0.000000:0.000000
S S (t):@0.195966:0.355854:0.236012:0.355854:0.236012:0.343927:0.195966:0.343927:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.202196:0.355425:0.214045:0.355425:0.214045:0.344827:0.202196:0.344827:0.000000
1:@0.220274:0.358305:0.224321:0.358305:0.224321:0.351226:0.220274:0.351226:0.000000
S S (t):@0.180952:0.301179:0.220995:0.301174:0.220995:0.289247:0.180952:0.289252:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.187182:0.300751:0.199030:0.300751:0.199030:0.290152:0.187182:0.290152:0.000000
2:@0.205257:0.303626:0.209304:0.303626:0.209304:0.296548:0.205257:0.296548:0.000000
0:@0.080468:0.447164:0.088226:0.447164:0.088226:0.433594:0.080468:0.433594:0.000000
150:@0.071764:0.329492:0.091363:0.329492:0.091363:0.318065:0.071764:0.318065:0.000000:0.000000:0.000000
140:@0.071764:0.338317:0.091363:0.338317:0.091363:0.326890:0.071764:0.326890:0.000000:0.000000:0.000000
120:@0.071764:0.353446:0.091363:0.353446:0.091363:0.342019:0.071764:0.342019:0.000000:0.000000:0.000000
100:@0.071764:0.366054:0.091363:0.366054:0.091363:0.354626:0.071764:0.354626:0.000000:0.000000:0.000000
70:@0.078297:0.386225:0.091363:0.386225:0.091363:0.374798:0.078297:0.374798:0.000000:0.000000
60:@0.078297:0.395051:0.091363:0.395051:0.091363:0.383623:0.078297:0.383623:0.000000:0.000000
50:@0.078297:0.403876:0.091363:0.403876:0.091363:0.392448:0.078297:0.392448:0.000000:0.000000
t(horas):@0.252197:0.447164:0.300349:0.447164:0.300349:0.433594:0.252197:0.433594:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Figura 5.1:@0.072614:0.483566:0.123940:0.483566:0.123940:0.472139:0.072614:0.472139:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A( )   3:@0.618264:0.185846:0.656673:0.185846:0.656673:0.175847:0.618264:0.175847:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.628220:0.185846:0.632964:0.185846:0.632964:0.176024:0.628220:0.176024:0.000000
5:@0.638634:0.185493:0.648391:0.185493:0.648391:0.176765:0.638634:0.176765:0.000000
x:@0.656673:0.185846:0.661417:0.185846:0.661417:0.176024:0.656673:0.176024:0.000000
2:@0.661417:0.181988:0.664750:0.181988:0.664750:0.176158:0.661417:0.176158:0.000000
MUESTRA EDITORIAL:@0.248902:0.947499:0.888171:0.113285:0.743922:0.050540:0.104653:0.884754:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 Muestra editorial solo para fines didácticos – Prohibida su venta:@0.095585:0.659700:0.095585:0.341447:0.077558:0.341447:0.077558:0.659700:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000