31:@0.942772:0.974518:0.963274:0.974518:0.963274:0.956333:0.942772:0.956333:0.000000:0.000000
Pensamiento numérico y variacional :@0.603816:0.043660:0.930949:0.043660:0.930949:0.024915:0.603816:0.024915:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Tema 5. Racionalización de expresiones numéricas y algebraicas:@0.073089:0.095370:0.902856:0.095370:0.902856:0.068034:0.073089:0.068034:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Reto matemático:@0.305481:0.139193:0.427956:0.139193:0.427956:0.123786:0.305481:0.123786:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.651214:0.163050:0.660473:0.163050:0.660473:0.146644:0.651214:0.146644:0.000000
c:@0.983649:0.163050:0.991307:0.163050:0.991307:0.146644:0.983649:0.146644:0.000000
)24 __________b) 48 ______________ )54 _________:@0.661467:0.163050:1.114267:0.163050:1.114267:0.146616:0.661467:0.146616:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3:@0.999383:0.156193:1.004588:0.156193:1.004588:0.146669:0.999383:0.146669:0.000000
a.   :@0.641119:0.163116:0.675219:0.163116:0.675219:0.146447:0.641119:0.146447:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.603797:0.160817:0.613056:0.160817:0.613056:0.144411:0.603797:0.144411:0.000000
c:@0.936232:0.160817:0.943890:0.160817:0.943890:0.144411:0.936232:0.144411:0.000000
)24 __________b) 48 ______________ )54 _________:@0.614050:0.160817:1.066840:0.160817:1.066840:0.144383:0.614050:0.144383:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3:@0.951965:0.153961:0.957171:0.153961:0.957171:0.144436:0.951965:0.144436:0.000000
b.   :@0.738401:0.160884:0.772503:0.160884:0.772503:0.144214:0.738401:0.144214:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.520817:0.160817:0.530076:0.160817:0.530076:0.144411:0.520817:0.144411:0.000000
c:@0.853252:0.160817:0.860910:0.160817:0.860910:0.144411:0.853252:0.144411:0.000000
)24 __________:@0.531070:0.160817:0.667081:0.160817:0.667081:0.144383:0.531070:0.144383:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b):@0.668554:0.160817:0.683372:0.160817:0.683372:0.144383:0.668554:0.144383:0.000000:0.000000
48:@0.700877:0.160817:0.718640:0.160817:0.718640:0.144383:0.700877:0.144383:0.000000:0.000000
______________:@0.722156:0.160817:0.851007:0.160817:0.851007:0.144383:0.722156:0.144383:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
)5:@0.862346:0.160817:0.888373:0.160817:0.888373:0.144383:0.862346:0.144383:0.000000:0.000000
4:@0.888178:0.160817:0.897160:0.160817:0.897160:0.144383:0.888178:0.144383:0.000000
_________:@0.901043:0.160817:0.983875:0.160817:0.983875:0.144383:0.901043:0.144383:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3:@0.868987:0.153961:0.874193:0.153961:0.874193:0.144436:0.868987:0.144436:0.000000
c.   :@0.836000:0.160884:0.870100:0.160884:0.870100:0.144214:0.836000:0.144214:0.000000:0.000000:0.000000:0.000000:0.000000
Extrae:@0.293658:0.163768:0.344168:0.163768:0.344168:0.146821:0.293658:0.146821:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 factores de los siguientes radicales::@0.344168:0.163768:0.603430:0.163768:0.603430:0.147334:0.344168:0.147334:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La racionalización de una expresión fraccionaria es el procedimiento mediante el cual :@0.072698:0.209630:0.709937:0.209630:0.709937:0.193197:0.072698:0.193197:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
se logra :@0.072698:0.226272:0.133900:0.226272:0.133900:0.209838:0.072698:0.209838:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
transformar:@0.133900:0.226272:0.228421:0.226272:0.228421:0.209325:0.133900:0.209325:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 el denominador en un número o expresión sin radicales.:@0.228421:0.226272:0.644401:0.226272:0.644401:0.209838:0.228421:0.209838:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5.1 Racionalización de monomios:@0.072698:0.260776:0.335679:0.260776:0.335679:0.243829:0.072698:0.243829:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a. Cuando el radical es de índice 2:@0.072698:0.284560:0.335712:0.284560:0.335712:0.267613:0.072698:0.267613:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ejemplo 1:@0.072698:0.308344:0.149069:0.308344:0.149069:0.291675:0.072698:0.291675:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Observemos diferentes ejemplos de racionalización.:@0.072698:0.328564:0.453524:0.328564:0.453524:0.312130:0.072698:0.312130:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1. :@0.101154:0.364969:0.117371:0.364969:0.117371:0.348535:0.101154:0.348535:0.000000:0.000000:0.000000
denominador:@0.132597:0.382557:0.189202:0.382557:0.189202:0.372949:0.132597:0.372949:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
irracional:@0.132597:0.390679:0.171513:0.390679:0.171513:0.381071:0.132597:0.381071:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
denominador:@0.325052:0.382557:0.381657:0.382557:0.381657:0.372949:0.325052:0.372949:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
racional:@0.325052:0.390679:0.358653:0.390679:0.358653:0.381071:0.325052:0.381071:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
  2. :@0.407397:0.364969:0.431676:0.364969:0.431676:0.348535:0.407397:0.348535:0.000000:0.000000:0.000000:0.000000:0.000000
3. :@0.101154:0.428521:0.117371:0.428521:0.117371:0.412087:0.101154:0.412087:0.000000:0.000000:0.000000
4. :@0.101154:0.527373:0.117371:0.527373:0.117371:0.510940:0.101154:0.510940:0.000000:0.000000:0.000000
b. Cuando el radical no es índice 2:@0.072693:0.578526:0.337287:0.578526:0.337287:0.561579:0.072693:0.561579:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ejemplo 2:@0.072693:0.602315:0.149065:0.602315:0.149065:0.585645:0.072693:0.585645:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Observemos varios ejemplos de racionalización.:@0.072693:0.622534:0.423534:0.622534:0.423534:0.606101:0.072693:0.606101:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1. :@0.101154:0.661449:0.117371:0.661449:0.117371:0.645015:0.101154:0.645015:0.000000:0.000000:0.000000
2. :@0.101154:0.713984:0.117371:0.713984:0.117371:0.697550:0.101154:0.697550:0.000000:0.000000:0.000000
3.  :@0.101154:0.774926:0.133643:0.774926:0.133643:0.758492:0.101154:0.758492:0.000000:0.000000:0.000000:0.000000
4. :@0.101154:0.830826:0.117371:0.830826:0.117371:0.814392:0.101154:0.814392:0.000000:0.000000:0.000000
Competencia :@0.740294:0.221195:0.838985:0.221195:0.838985:0.205789:0.740294:0.205789:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática :@0.740294:0.236324:0.828908:0.236324:0.828908:0.220918:0.740294:0.220918:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Para racionalizar :@0.749032:0.262448:0.859676:0.262448:0.859676:0.247508:0.749032:0.247508:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
monomios, puedes :@0.749032:0.277577:0.881615:0.277577:0.881615:0.262637:0.749032:0.262637:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tener los siguientes :@0.749032:0.292706:0.881663:0.292706:0.881663:0.277766:0.749032:0.277766:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
casos: :@0.749032:0.307835:0.792055:0.307835:0.792055:0.292895:0.749032:0.292895:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a):@0.749032:0.333680:0.761850:0.333680:0.761850:0.318526:0.749032:0.318526:0.000000:0.000000
Radicales del tipo::@0.768005:0.333685:0.887669:0.333685:0.887669:0.318745:0.768005:0.318745:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.810174:0.356406:0.813839:0.356406:0.813839:0.341466:0.810174:0.341466:0.000000
multiplica       :@0.813839:0.356406:0.905641:0.356406:0.905641:0.341466:0.813839:0.341466:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 numerador y :@0.763691:0.378682:0.857849:0.378682:0.857849:0.363743:0.763691:0.363743:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
denominador por::@0.768005:0.393811:0.889759:0.393811:0.889759:0.378872:0.768005:0.378872:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
  :@0.889759:0.393811:0.897088:0.393811:0.897088:0.378872:0.889759:0.378872:0.000000:0.000000
.:@0.793608:0.408940:0.796520:0.408940:0.796520:0.394000:0.793608:0.394000:0.000000
b):@0.749032:0.431216:0.763256:0.431216:0.763256:0.416062:0.749032:0.416062:0.000000:0.000000
Radicales del tipo::@0.768005:0.431216:0.887669:0.431216:0.887669:0.416277:0.768005:0.416277:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
; multiplica :@0.814693:0.452541:0.891083:0.452541:0.891083:0.437601:0.814693:0.437601:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
el numerador y el :@0.768005:0.482799:0.888506:0.482799:0.888506:0.467859:0.768005:0.467859:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
denominador por::@0.768005:0.496667:0.889759:0.496667:0.889759:0.481727:0.768005:0.481727:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
.:@0.814693:0.525664:0.817604:0.525664:0.817604:0.510724:0.814693:0.510724:0.000000
Transformar. :@0.746150:0.595905:0.835237:0.594147:0.834711:0.578998:0.745623:0.580756:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Hacer :@0.835140:0.594150:0.877178:0.593321:0.876659:0.578386:0.834621:0.579216:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
que algo cambie o :@0.746672:0.611030:0.873957:0.608519:0.873438:0.593584:0.746153:0.596095:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
sea distinto, pero sin :@0.747198:0.626154:0.885118:0.623432:0.884599:0.608498:0.746679:0.611219:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
alterar totalmente :@0.747724:0.641278:0.869920:0.638867:0.869400:0.623932:0.747204:0.626343:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
todas sus características :@0.748249:0.656401:0.909031:0.653229:0.908511:0.638294:0.747730:0.641467:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
esenciales.:@0.748775:0.671525:0.818709:0.670145:0.818190:0.655211:0.748256:0.656590:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Glosario:@0.799205:0.572812:0.858825:0.572812:0.858825:0.557406:0.799205:0.557406:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
EBC Reconoce los números complejos como raíces no reales de una función cuadrática, y desarrolla y comprende sus propiedades.:@0.083509:0.971336:0.773434:0.971336:0.773434:0.959384:0.083509:0.959384:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
MUESTRA EDITORIAL:@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