31:@0.922460:0.966765:0.939432:0.966765:0.939432:0.950778:0.922460:0.950778:0.000000:0.000000 2.:@0.108233:0.102698:0.120505:0.102698:0.120505:0.085983:0.108233:0.085983:0.000000:0.000000 Si < 0, < 0, entonces > 0. Por lo tanto, :@0.120505:0.102481:0.437993:0.102481:0.437993:0.085983:0.120505:0.085983:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.147438:0.102596:0.156415:0.102596:0.156415:0.086128:0.147438:0.086128:0.000000 b:@0.189455:0.102596:0.198722:0.102596:0.198722:0.086128:0.189455:0.086128:0.000000 a:@0.303223:0.094999:0.311420:0.094999:0.311420:0.079962:0.303223:0.079962:0.000000 b:@0.303082:0.111342:0.311543:0.111342:0.311543:0.096305:0.303082:0.096305:0.000000 a:@0.449391:0.094999:0.457588:0.094999:0.457588:0.079962:0.449391:0.079962:0.000000 b:@0.449250:0.111342:0.457711:0.111342:0.457711:0.096305:0.449250:0.096305:0.000000 está bien definida. :@0.464146:0.102481:0.599887:0.102481:0.599887:0.085983:0.464146:0.085983:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.108239:0.138759:0.112381:0.138759:0.112381:0.122261:0.108239:0.122261:0.000000 La igualdad:@0.131975:0.138759:0.209113:0.138759:0.209113:0.122261:0.131975:0.122261:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.208721:0.138438:0.212502:0.138438:0.212502:0.123375:0.208721:0.123375:0.000000 =:@0.242356:0.137290:0.252294:0.137290:0.252294:0.122254:0.242356:0.122254:0.000000 a:@0.224089:0.130291:0.232286:0.130291:0.232286:0.115254:0.224089:0.115254:0.000000 b:@0.223949:0.146635:0.232409:0.146635:0.232409:0.131598:0.223949:0.131598:0.000000 a:@0.268895:0.129572:0.277092:0.129572:0.277092:0.114535:0.268895:0.114535:0.000000 b:@0.268895:0.148431:0.277356:0.148431:0.277356:0.133395:0.268895:0.133395:0.000000 es absurda, ya que :@0.280922:0.138759:0.411076:0.138759:0.411076:0.122261:0.280922:0.122261:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.420717:0.138544:0.428914:0.138544:0.428914:0.123507:0.420717:0.123507:0.000000 y :@0.431794:0.138759:0.447245:0.138759:0.447245:0.122261:0.431794:0.122261:0.000000:0.000000:0.000000 b:@0.456906:0.138544:0.465367:0.138544:0.465367:0.123507:0.456906:0.123507:0.000000 no están definidas :@0.467982:0.138759:0.599930:0.138759:0.599930:0.122261:0.467982:0.122261:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 en .:@0.131977:0.156110:0.169179:0.156110:0.169179:0.139612:0.131977:0.139612:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.152515:0.155141:0.166424:0.155141:0.166424:0.141694:0.152515:0.141694:0.000000 :@0.108243:0.161141:0.112385:0.161141:0.112385:0.144644:0.108243:0.144644:0.000000 Ejercicios resueltos:@0.108243:0.178868:0.238898:0.178868:0.238898:0.162081:0.108243:0.162081:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1. :@0.108243:0.196060:0.124599:0.196060:0.124599:0.179345:0.108243:0.179345:0.000000:0.000000:0.000000 Sean = (2 – 3)(3 – 3) –4 3. Simplifica la escritura de . :@0.124598:0.195843:0.599899:0.195836:0.599899:0.179338:0.124598:0.179345:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.172454:0.195959:0.179929:0.195959:0.179929:0.179490:0.172454:0.179490:0.000000 x:@0.585489:0.195952:0.592964:0.195952:0.592964:0.179483:0.585489:0.179483:0.000000 Aplicando la propiedad distributiva, se tiene::@0.131965:0.213187:0.447854:0.213187:0.447854:0.196689:0.131965:0.196689:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.131964:0.241974:0.139439:0.241974:0.139439:0.225506:0.131964:0.225506:0.000000 = (2 – 3)(3 – 3) – 4 3 = 6 – 2 3 – 3 3 + ( 3) – 4 3 :@0.143639:0.241859:0.599900:0.241853:0.599900:0.225355:0.143639:0.225361:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.534439:0.234249:0.541392:0.234249:0.541392:0.224630:0.534439:0.224630:0.000000:0.000000 = 6 – 5 3 + 3 – 4 3 = 9 – 9 3 = 9(1 – 3).:@0.131966:0.261966:0.467349:0.261970:0.467349:0.245472:0.131966:0.245468:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2.:@0.108226:0.296859:0.120497:0.296859:0.120497:0.280145:0.108226:0.280145:0.000000:0.000000 Calcula: = :@0.120497:0.296643:0.215784:0.296643:0.215784:0.280146:0.120497:0.280145:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 t:@0.191028:0.296759:0.196692:0.296759:0.196692:0.280290:0.191028:0.280290:0.000000 1 + 2:@0.215894:0.288273:0.264018:0.286203:0.264018:0.269705:0.215894:0.271776:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2 – 2:@0.215932:0.306879:0.263981:0.308583:0.263981:0.292085:0.215932:0.290381:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 – :@0.266774:0.296654:0.289700:0.296654:0.289700:0.280156:0.266774:0.280156:0.000000:0.000000:0.000000:0.000000 1 – 2:@0.289841:0.288273:0.337887:0.286203:0.337887:0.269705:0.289841:0.271776:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2 + 2:@0.289801:0.306879:0.337926:0.308583:0.337926:0.292085:0.289801:0.290381:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 .:@0.340681:0.296654:0.347578:0.296654:0.347578:0.280156:0.340681:0.280156:0.000000:0.000000 :@0.108227:0.314005:0.112369:0.314005:0.112369:0.297508:0.108227:0.297508:0.000000 :@0.108227:0.335448:0.112369:0.335448:0.112369:0.318950:0.108227:0.318950:0.000000 Aplicando la propiedad – = :@0.131961:0.335447:0.382703:0.335446:0.382703:0.318948:0.131961:0.318950:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.309506:0.328564:0.316981:0.328564:0.316981:0.312095:0.309506:0.312095:0.000000 y:@0.309391:0.345914:0.317078:0.345914:0.317078:0.329446:0.309391:0.329446:0.000000 u:@0.345685:0.328564:0.354894:0.328564:0.354894:0.312095:0.345685:0.312095:0.000000 v:@0.346398:0.345914:0.354181:0.345914:0.354181:0.329446:0.346398:0.329446:0.000000 xv – yu:@0.382862:0.328289:0.433624:0.328289:0.433624:0.311821:0.382862:0.311821:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.433624:0.328174:0.437766:0.328174:0.437766:0.311676:0.433624:0.311676:0.000000 yu:@0.399738:0.345886:0.416730:0.345886:0.416730:0.329417:0.399738:0.329417:0.000000:0.000000 para :@0.433722:0.335447:0.473293:0.335447:0.473293:0.318949:0.433722:0.318949:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x, y, u, v:@0.473351:0.335562:0.526299:0.335562:0.526299:0.319094:0.473351:0.319094:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 con :@0.526299:0.335447:0.599904:0.335447:0.599904:0.318949:0.526299:0.318949:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.530453:0.335230:0.546501:0.335230:0.546501:0.320583:0.530453:0.320583:0.000000 R:@0.550701:0.334478:0.564610:0.334478:0.564610:0.321031:0.550701:0.321031:0.000000 y:@0.131970:0.352913:0.139657:0.352913:0.139657:0.336444:0.131970:0.336444:0.000000 ≠ 0, ≠ 0, resulta::@0.139657:0.352797:0.266577:0.352797:0.266577:0.336300:0.139657:0.336300:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 v :@0.174142:0.352913:0.186067:0.352913:0.186067:0.336444:0.174142:0.336444:0.000000:0.000000 t:@0.131971:0.387585:0.137635:0.387585:0.137635:0.371116:0.131971:0.371116:0.000000 = :@0.137635:0.387469:0.160869:0.387469:0.160869:0.370972:0.137635:0.370972:0.000000:0.000000:0.000000:0.000000 1 + 2:@0.160970:0.380353:0.209093:0.379540:0.209093:0.363042:0.160970:0.363855:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2 – 2:@0.161007:0.398958:0.209057:0.400662:0.209057:0.384165:0.161007:0.382460:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 – :@0.211850:0.387476:0.230634:0.387476:0.230634:0.370978:0.211850:0.370978:0.000000:0.000000:0.000000 1 – 2:@0.230775:0.380353:0.278822:0.379540:0.278822:0.363042:0.230775:0.363855:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2 + 2:@0.230736:0.398958:0.278860:0.400662:0.278860:0.384165:0.230736:0.382460:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 = :@0.281615:0.387476:0.300707:0.387476:0.300707:0.370978:0.281615:0.370978:0.000000:0.000000:0.000000 (1 + 2 )(2 + 2 ) – (1 – 2 )(2 – 2 ):@0.308148:0.380353:0.579077:0.380349:0.579077:0.363852:0.308148:0.363855:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 (2 – 2)(2 + 2):@0.380587:0.401474:0.506623:0.401471:0.506623:0.384974:0.380587:0.384976:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.586419:0.387475:0.590561:0.387475:0.590561:0.370977:0.586419:0.370977:0.000000 = :@0.108236:0.438240:0.139080:0.438240:0.139080:0.421743:0.108236:0.421743:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2 + 3 2 + ( 2) – (2 – 3 2 + ( 2) ) 2 + 3 2 + 2 – 2 + 3 2 – 2:@0.137645:0.431124:0.592126:0.431120:0.592126:0.414623:0.137645:0.414626:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.245913:0.423515:0.250866:0.423515:0.250866:0.413897:0.245913:0.413897:0.000000 2:@0.381835:0.422258:0.386788:0.422258:0.386788:0.412640:0.381835:0.412640:0.000000 4 – ( 2):@0.231114:0.452249:0.294023:0.452242:0.294023:0.435745:0.231114:0.435751:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.294031:0.440866:0.298984:0.440866:0.298984:0.431248:0.294031:0.431248:0.000000 = :@0.393572:0.438247:0.409003:0.438247:0.409003:0.421749:0.393572:0.421749:0.000000:0.000000:0.000000 4 – 2:@0.482719:0.449729:0.518880:0.449729:0.518880:0.433231:0.482719:0.433231:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.595767:0.438249:0.599909:0.438249:0.599909:0.421751:0.595767:0.421751:0.000000 =:@0.131976:0.484243:0.142784:0.484243:0.142784:0.467745:0.131976:0.467745:0.000000 3 2 + 3 2 6 2 :@0.147177:0.477119:0.283806:0.477115:0.283806:0.460617:0.147177:0.460621:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.182865:0.495724:0.191361:0.495724:0.191361:0.479226:0.182865:0.479226:0.000000 = :@0.227291:0.484243:0.246383:0.484243:0.246383:0.467746:0.227291:0.467746:0.000000:0.000000:0.000000 2:@0.259686:0.495724:0.268182:0.495724:0.268182:0.479226:0.259686:0.479226:0.000000 = 3 2.:@0.281494:0.484243:0.333828:0.484236:0.333828:0.467739:0.281494:0.467746:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.108232:0.525415:0.112258:0.525415:0.112258:0.508469:0.108232:0.508469:0.000000 Conclusión: = :@0.131966:0.524953:0.244360:0.524953:0.244360:0.508455:0.131966:0.508455:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 t:@0.219604:0.525068:0.225268:0.525068:0.225268:0.508600:0.219604:0.508600:0.000000 1 + 2:@0.244465:0.517833:0.292589:0.517018:0.292589:0.500520:0.244465:0.501335:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2 – 2:@0.244503:0.536436:0.292550:0.538141:0.292550:0.521643:0.244503:0.519939:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 – :@0.295344:0.524954:0.314128:0.524954:0.314128:0.508456:0.295344:0.508456:0.000000:0.000000:0.000000 1 – 2:@0.314269:0.517833:0.362316:0.517018:0.362316:0.500520:0.314269:0.501335:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2 + 2:@0.314230:0.536436:0.362354:0.538141:0.362354:0.521643:0.314230:0.519939:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 = 3 2 .:@0.365109:0.524954:0.418887:0.524950:0.418887:0.508453:0.365109:0.508456:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 3. :@0.108235:0.566158:0.124591:0.566158:0.124591:0.549444:0.108235:0.549444:0.000000:0.000000:0.000000 Sea = 2 20 + 3 5 –2 45 . Simplifica la escritura :@0.124397:0.565941:0.485149:0.565938:0.485149:0.549441:0.124397:0.549443:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.159557:0.566056:0.167244:0.566056:0.167244:0.549588:0.159557:0.549588:0.000000 de . Puesto que:@0.131978:0.583289:0.244928:0.583289:0.244928:0.566791:0.131978:0.566791:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.153401:0.583405:0.161088:0.583405:0.161088:0.566936:0.153401:0.566936:0.000000 20 = 4 × 5 = 4 5 = 2 5, y, :@0.145996:0.606958:0.368114:0.607767:0.368114:0.591270:0.145996:0.590460:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.108225:0.632247:0.112367:0.632247:0.112367:0.615749:0.108225:0.615749:0.000000 45 = 9 × 5 = 9 5 = 3 5,:@0.142336:0.631436:0.343763:0.632246:0.343763:0.615748:0.142336:0.614938:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 entonces:@0.131959:0.660282:0.193974:0.660282:0.193974:0.643785:0.131959:0.643785:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.218210:0.660398:0.225897:0.660398:0.225897:0.643929:0.218210:0.643929:0.000000 =:@0.249940:0.660282:0.260266:0.660282:0.260266:0.643785:0.249940:0.643785:0.000000 2 20:@0.284791:0.660282:0.320173:0.659479:0.320173:0.642981:0.284791:0.643785:0.000000:0.000000:0.000000:0.000000 +:@0.347818:0.660289:0.358144:0.660289:0.358144:0.643791:0.347818:0.643791:0.000000 3 5:@0.382669:0.660289:0.411161:0.659479:0.411161:0.642981:0.382669:0.643791:0.000000:0.000000:0.000000 –:@0.437959:0.660289:0.447977:0.660289:0.447977:0.643791:0.437959:0.643791:0.000000 2:@0.472501:0.660289:0.480997:0.660289:0.480997:0.643791:0.472501:0.643791:0.000000 45 =:@0.142336:0.676830:0.172775:0.677639:0.172775:0.661142:0.142336:0.660332:0.000000:0.000000:0.000000:0.000000 2(2 5):@0.197242:0.677639:0.246969:0.677639:0.246969:0.661142:0.197242:0.661142:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 +:@0.271436:0.677639:0.281762:0.677639:0.281762:0.661142:0.271436:0.661142:0.000000 3 5:@0.306229:0.677639:0.334745:0.676830:0.334745:0.660332:0.306229:0.661142:0.000000:0.000000:0.000000 –:@0.361485:0.677639:0.371503:0.677639:0.371503:0.661142:0.361485:0.661142:0.000000 2(3 5):@0.395970:0.677639:0.445716:0.677639:0.445716:0.661142:0.395970:0.661142:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 =:@0.470183:0.677639:0.480991:0.677639:0.480991:0.661142:0.470183:0.661142:0.000000 :@0.480991:0.677639:0.485133:0.677639:0.485133:0.661142:0.480991:0.661142:0.000000 4 5 + 3 5 – 6 5 = 5.:@0.131962:0.700268:0.302440:0.700271:0.302440:0.683773:0.131962:0.683770:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 4. :@0.108227:0.740091:0.124583:0.740091:0.124583:0.723376:0.108227:0.723376:0.000000:0.000000:0.000000 Sea = :@0.124583:0.739874:0.191550:0.739874:0.191550:0.723377:0.124583:0.723377:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 z:@0.163018:0.739990:0.169665:0.739990:0.169665:0.723521:0.163018:0.723521:0.000000 2 + 5:@0.212989:0.731950:0.251828:0.731501:0.251828:0.715004:0.212989:0.715452:0.000000:0.000000:0.000000:0.000000:0.000000 2 2 – 3:@0.194841:0.750110:0.258088:0.750110:0.258088:0.733612:0.194841:0.733612:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 . Expresa de modo que el denominador no :@0.258454:0.739887:0.599871:0.739887:0.599871:0.723389:0.258454:0.723389:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 z:@0.329428:0.740003:0.336074:0.740003:0.336074:0.723534:0.329428:0.723534:0.000000 :@0.595729:0.739887:0.599871:0.739887:0.599871:0.723389:0.595729:0.723389:0.000000 :@0.595729:0.739887:0.599871:0.739887:0.599871:0.723389:0.595729:0.723389:0.000000 contenga raíces cuadradas. El número real 2 2 + 3 se denomina :@0.131978:0.763773:0.599911:0.763769:0.599911:0.747272:0.131978:0.747276:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 conjugado de 2 2 – 3. Se tiene: :@0.131977:0.787656:0.363021:0.787658:0.363021:0.771161:0.131977:0.771158:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.108221:0.798980:0.112363:0.798980:0.112363:0.782483:0.108221:0.782483:0.000000 (2 2 + 3)(2 2 – 3) = (2 2 ) – (3) = 4( 2 ) – 9 = 8 – 9 – = –1.:@0.131956:0.816331:0.595418:0.816328:0.595418:0.799831:0.131956:0.799833:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.341008:0.809977:0.345961:0.809977:0.345961:0.800359:0.341008:0.800359:0.000000 2:@0.385147:0.809977:0.390100:0.809977:0.390100:0.800359:0.385147:0.800359:0.000000 2:@0.452835:0.809977:0.457788:0.809977:0.457788:0.800359:0.452835:0.800359:0.000000 :@0.108239:0.833679:0.112381:0.833679:0.112381:0.817182:0.108239:0.817182:0.000000 Entonces,:@0.131973:0.851030:0.199977:0.851030:0.199977:0.834532:0.131973:0.834532:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.108239:0.885081:0.112381:0.885081:0.112381:0.868584:0.108239:0.868584:0.000000 z:@0.131973:0.885197:0.138619:0.885197:0.138619:0.868728:0.131973:0.868728:0.000000 = :@0.138619:0.885081:0.157711:0.885081:0.157711:0.868584:0.138619:0.868584:0.000000:0.000000:0.000000 2 + 5:@0.176328:0.877149:0.215167:0.876701:0.215167:0.860203:0.176328:0.860651:0.000000:0.000000:0.000000:0.000000:0.000000 2 2 – 3:@0.158180:0.895310:0.221427:0.895309:0.221427:0.878811:0.158180:0.878812:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 = :@0.221793:0.885086:0.240885:0.885086:0.240885:0.868589:0.221793:0.868589:0.000000:0.000000:0.000000 2 + 5:@0.259509:0.877149:0.298348:0.876701:0.298348:0.860203:0.259509:0.860651:0.000000:0.000000:0.000000:0.000000:0.000000 2 2 – 3 2 2 + 3:@0.241361:0.895310:0.387598:0.895309:0.387598:0.878811:0.241361:0.878812:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.304976:0.885086:0.323721:0.885086:0.323721:0.868589:0.304976:0.868589:0.000000:0.000000:0.000000:0.000000 .:@0.313260:0.885202:0.315437:0.885202:0.315437:0.868733:0.313260:0.868733:0.000000 2 2 + 3:@0.326113:0.876707:0.385432:0.876701:0.385432:0.860203:0.326113:0.860209:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 = :@0.387810:0.885086:0.406901:0.885086:0.406901:0.868589:0.387810:0.868589:0.000000:0.000000:0.000000 ( 2 + 5)(2 2 + 3):@0.413540:0.876707:0.547500:0.876701:0.547500:0.860203:0.413540:0.860209:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 (2 2 – 3)(2 2 + 3):@0.409253:0.895310:0.551883:0.895309:0.551883:0.878811:0.409253:0.878812:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.554137:0.885086:0.558279:0.885086:0.558279:0.868589:0.554137:0.868589:0.000000 :@0.108242:0.931081:0.112384:0.931081:0.112384:0.914583:0.108242:0.914583:0.000000 = :@0.131976:0.931081:0.146926:0.931081:0.146926:0.914583:0.131976:0.914583:0.000000:0.000000 4 + 13 2 + 15:@0.150392:0.922700:0.254290:0.922695:0.254290:0.906198:0.150392:0.906202:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 –1:@0.192833:0.941304:0.211829:0.941304:0.211829:0.924806:0.192833:0.924806:0.000000:0.000000 = –19 – 13 2 .:@0.257757:0.931082:0.366110:0.932332:0.366110:0.915835:0.257757:0.914584:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Competencia :@0.684804:0.094669:0.782426:0.094669:0.782426:0.079197:0.684804:0.079197:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 matemática:@0.684804:0.107237:0.768866:0.107237:0.768866:0.091765:0.684804:0.091765:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 La idea principal del :@0.685042:0.131712:0.818091:0.131712:0.818091:0.116649:0.685042:0.116649:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 término racionalización es la :@0.638498:0.147554:0.826657:0.147554:0.826657:0.132491:0.638498:0.132491:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 de expresar el número real de :@0.638498:0.163396:0.833552:0.163396:0.833552:0.148333:0.638498:0.148333:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 modo que en el denominador :@0.638498:0.179238:0.838652:0.179238:0.838652:0.164175:0.638498:0.164175:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 no figuren raíces cuadradas de :@0.638498:0.195080:0.839003:0.195080:0.839003:0.180017:0.638498:0.180017:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 números reales.:@0.638498:0.210922:0.738848:0.210922:0.738848:0.195859:0.638498:0.195859:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Sean :@0.638498:0.235398:0.673010:0.235398:0.673010:0.220334:0.638498:0.220334:0.000000:0.000000:0.000000:0.000000:0.000000 a, b, c :@0.673010:0.235503:0.712113:0.235503:0.712113:0.220466:0.673010:0.220466:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.712117:0.235504:0.728165:0.235504:0.728165:0.220857:0.712117:0.220857:0.000000 :@0.728165:0.235721:0.750358:0.235721:0.750358:0.219223:0.728165:0.219223:0.000000:0.000000:0.000000 R:@0.732307:0.234752:0.746216:0.234752:0.746216:0.221305:0.732307:0.221305:0.000000 con > 0,:@0.750357:0.235400:0.814913:0.235400:0.814913:0.220337:0.750357:0.220337:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 b :@0.778748:0.235506:0.790990:0.235506:0.790990:0.220469:0.778748:0.220469:0.000000:0.000000 a:@0.638503:0.259982:0.646699:0.259982:0.646699:0.244945:0.638503:0.244945:0.000000 ≠ 0, ≠ :@0.646699:0.259876:0.702178:0.259876:0.702178:0.244813:0.646699:0.244813:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 c a b:@0.678186:0.259982:0.728781:0.259984:0.728781:0.244947:0.678186:0.244945:0.000000:0.000000:0.000000:0.000000:0.000000 y :@0.731789:0.259878:0.746494:0.259878:0.746494:0.244815:0.731789:0.244815:0.000000:0.000000:0.000000 a b:@0.746494:0.259984:0.773091:0.259984:0.773091:0.244947:0.746494:0.244947:0.000000:0.000000:0.000000 + ≠ 0.:@0.776091:0.260199:0.832711:0.260199:0.832711:0.243701:0.776091:0.243701:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 c:@0.795183:0.260315:0.802369:0.260315:0.802369:0.243846:0.795183:0.243846:0.000000 Al número real :@0.638503:0.284358:0.739013:0.284358:0.739013:0.269295:0.638503:0.269295:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a b:@0.739013:0.284464:0.765616:0.284464:0.765616:0.269427:0.739013:0.269427:0.000000:0.000000:0.000000 – :@0.768618:0.284679:0.787401:0.284679:0.787401:0.268181:0.768618:0.268181:0.000000:0.000000:0.000000 c:@0.787401:0.284794:0.794587:0.284794:0.794587:0.268326:0.787401:0.268326:0.000000 se lo :@0.794585:0.284358:0.831505:0.284358:0.831505:0.269295:0.794585:0.269295:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 llama conjugado de :@0.638509:0.301705:0.770310:0.301705:0.770310:0.286642:0.638509:0.286642:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a b:@0.770310:0.301811:0.796907:0.301814:0.796907:0.286778:0.770310:0.286774:0.000000:0.000000:0.000000 + :@0.799908:0.302029:0.819000:0.302029:0.819000:0.285532:0.799908:0.285532:0.000000:0.000000:0.000000 c :@0.819000:0.302145:0.834470:0.302145:0.834470:0.285676:0.819000:0.285676:0.000000:0.000000:0.000000 y viceversa.:@0.638503:0.319380:0.717470:0.319380:0.717470:0.302883:0.638503:0.302883:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Practica:@0.638503:0.343960:0.695845:0.343960:0.695845:0.328488:0.638503:0.328488:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 .:@0.695845:0.343859:0.698600:0.343859:0.698600:0.327361:0.695845:0.327361:0.000000 Escribe:@0.638503:0.359802:0.688879:0.359802:0.688879:0.344330:0.638503:0.344330:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 el conjugado de:@0.688879:0.359380:0.796653:0.359380:0.796653:0.344317:0.688879:0.344317:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 3:@0.638503:0.383856:0.646261:0.383856:0.646261:0.368793:0.638503:0.368793:0.000000 2 – 5.:@0.658244:0.384623:0.699530:0.384175:0.699530:0.367677:0.658244:0.368125:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 En la práctica, sin embargo, la raíz cuadrada :@0.638792:0.686205:0.854762:0.686205:0.854762:0.674728:0.638792:0.674728:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 sirve para hallar el lado de una figura geomé-:@0.629008:0.698275:0.851870:0.698275:0.851870:0.686798:0.629008:0.686798:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 trica cuadrada o para explicar y realizar el :@0.629008:0.710345:0.854751:0.710345:0.854751:0.698868:0.629008:0.698868:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Teorema de Pitágoras. Del mismo modo, :@0.629008:0.722415:0.854746:0.722415:0.854746:0.710938:0.629008:0.710938:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 permite resolver ecuaciones cuadráticas, des-:@0.629008:0.734485:0.851869:0.734485:0.851869:0.723008:0.629008:0.723008:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 pejar fórmulas físicas, químicas, estadísticas, :@0.629008:0.746555:0.854750:0.746555:0.854750:0.735079:0.629008:0.735079:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y muchas otras aplicaciones.:@0.629008:0.758625:0.769055:0.758625:0.769055:0.747149:0.629008:0.747149:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Pixabay.com:@0.866555:0.662559:0.866555:0.628190:0.855087:0.628190:0.855087:0.662559:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ©:@0.079553:0.731952:0.079553:0.720342:0.061505:0.720342:0.061505:0.731952:0.000000:0.000000 maya:@0.080774:0.720340:0.080774:0.684191:0.055786:0.684191:0.055786:0.720340:0.000000:0.000000:0.000000:0.000000 ®EDUCACIÓN – Libro resuelto solo para fines didácticos – Prohibida su reproducción :@0.079553:0.684191:0.079553:0.268044:0.061505:0.268044:0.061505:0.684191:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000