133:@0.938423:0.974518:0.967620:0.974518:0.967620:0.956590:0.938423:0.956590:0.000000:0.000000:0.000000
Pensamiento numérico y variacional:@0.603717:0.043661:0.926913:0.043661:0.926913:0.024916:0.603717:0.024916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
29.  Halla los números cuya suma S y producto P se dan :@0.073089:0.137730:0.489855:0.137730:0.489855:0.121061:0.073089:0.121061:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a continuación. Observa el ejemplo.:@0.103214:0.154372:0.373799:0.154372:0.373799:0.137702:0.103214:0.137702:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ejemplo:  = 4,   = –60.:@0.101546:0.179233:0.268845:0.179233:0.268845:0.162799:0.101546:0.162799:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
S:@0.168434:0.179233:0.176496:0.179233:0.176496:0.162826:0.168434:0.162826:0.000000
P:@0.211194:0.179233:0.219956:0.179233:0.219956:0.162826:0.211194:0.162826:0.000000
Formamos la ecuación de segundo grado: :@0.101546:0.199449:0.411439:0.199449:0.411439:0.183015:0.101546:0.183015:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.073089:0.219665:0.077120:0.219665:0.077120:0.203231:0.073089:0.203231:0.000000
x:@0.101549:0.219665:0.109004:0.219665:0.109004:0.203259:0.101549:0.203259:0.000000
² – 4  – 60 = 0:@0.108931:0.219665:0.210079:0.219665:0.210079:0.203231:0.108931:0.203231:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.140039:0.219665:0.147494:0.219665:0.147494:0.203259:0.140039:0.203259:0.000000
Buscamos la solución::@0.101546:0.239879:0.259826:0.239879:0.259826:0.223446:0.101546:0.223446:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(  – 10)(  + 6) = 0 :@0.101546:0.260095:0.229896:0.260095:0.229896:0.243662:0.101546:0.243662:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.106347:0.260095:0.113802:0.260095:0.113802:0.243689:0.106347:0.243689:0.000000
x:@0.158163:0.260095:0.165618:0.260095:0.165618:0.243689:0.158163:0.243689:0.000000
 :@0.073089:0.280312:0.077120:0.280312:0.077120:0.263878:0.073089:0.263878:0.000000
x:@0.101549:0.280312:0.109004:0.280312:0.109004:0.263905:0.101549:0.263905:0.000000
1:@0.108938:0.283484:0.114175:0.283484:0.114175:0.273903:0.108938:0.273903:0.000000
= 10;   = –6; estos son los números buscados.:@0.114128:0.280312:0.447856:0.280312:0.447856:0.263878:0.114128:0.263878:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.153833:0.280312:0.161288:0.280312:0.161288:0.263905:0.153833:0.263905:0.000000
2:@0.161235:0.283484:0.166472:0.283484:0.166472:0.273903:0.161235:0.273903:0.000000
La suma es 4 y el producto –60.:@0.101546:0.300526:0.329020:0.300526:0.329020:0.284092:0.101546:0.284092:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a.  S = 18,   = 72:@0.104633:0.327890:0.232362:0.327890:0.232362:0.311456:0.104633:0.311456:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
P:@0.186152:0.327890:0.194914:0.327890:0.198753:0.311483:0.189991:0.311483:0.000000
b.  S = 20,   = –18:@0.104633:0.358827:0.241492:0.358827:0.241492:0.342393:0.104633:0.342393:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
P:@0.186152:0.358827:0.194914:0.358827:0.198753:0.342421:0.189991:0.342421:0.000000
30.  Resuelve las siguientes situaciones.:@0.073089:0.383689:0.368881:0.383689:0.368881:0.367019:0.073089:0.367019:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a.  La ecuación 3 ² – 2  +   = 0 tiene como primera :@0.104633:0.408549:0.489866:0.408549:0.489866:0.392116:0.104633:0.392116:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.235025:0.408549:0.242480:0.408549:0.242480:0.392143:0.235025:0.392143:0.000000
x:@0.274122:0.408549:0.281577:0.408549:0.281577:0.392143:0.274122:0.392143:0.000000
k:@0.300904:0.408549:0.308470:0.408549:0.308470:0.392143:0.300904:0.392143:0.000000
raíz –4. Halla la otra raíz y determina el valor de k.:@0.134724:0.425191:0.486041:0.425191:0.486041:0.408757:0.134724:0.408757:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b.  Determina el valor de   en la ecuación :@0.104633:0.459702:0.489836:0.459702:0.489836:0.443268:0.104633:0.443268:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
k:@0.338400:0.459702:0.345965:0.459702:0.345965:0.443296:0.338400:0.443296:0.000000
 :@0.485787:0.459702:0.489818:0.459702:0.489818:0.443268:0.485787:0.443268:0.000000
9 ² +   + 1 = 0, para que las raíces sean iguales y :@0.134779:0.476344:0.490002:0.476344:0.490002:0.459910:0.134779:0.459910:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.143688:0.476344:0.151143:0.476344:0.151143:0.459937:0.143688:0.459937:0.000000
kx:@0.174483:0.476344:0.189430:0.476344:0.189430:0.459937:0.174483:0.459937:0.000000:0.000000
opuestas.:@0.134779:0.492985:0.203615:0.492985:0.203615:0.476552:0.134779:0.476552:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
31.  Indica, sin dibujarlas, en cuántos puntos cortan al :@0.073089:0.527497:0.489651:0.527497:0.489651:0.510827:0.073089:0.510827:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
eje de abscisas las siguientes parábolas::@0.103214:0.544139:0.402669:0.544139:0.402669:0.527469:0.103214:0.527469:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a.  y = 3  ² – 5  + 4:@0.104633:0.578649:0.248167:0.578649:0.248167:0.562215:0.104633:0.562215:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.170544:0.578649:0.177999:0.578649:0.177999:0.562243:0.170544:0.562243:0.000000
x:@0.212991:0.578649:0.220446:0.578649:0.220446:0.562243:0.212991:0.562243:0.000000
b.  y = –2  ² –   + 3:@0.104633:0.613160:0.248388:0.613160:0.248388:0.596726:0.104633:0.596726:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.179674:0.613160:0.187129:0.613160:0.187129:0.596753:0.179674:0.596753:0.000000
x:@0.213212:0.613160:0.220667:0.613160:0.220667:0.596753:0.213212:0.596753:0.000000
c.  y = – 3  ² + 5  – 6:@0.104633:0.647670:0.261237:0.647670:0.261237:0.631236:0.104633:0.631236:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.183613:0.647670:0.191068:0.647670:0.191068:0.631264:0.183613:0.631264:0.000000
x:@0.227827:0.647670:0.235282:0.647670:0.235282:0.631264:0.227827:0.631264:0.000000
32.  Analiza cada gráfica y determina el tipo de raíces :@0.073089:0.682182:0.489619:0.682182:0.489619:0.665512:0.073089:0.665512:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
que tiene la función cuadrática en cada caso.:@0.103214:0.698823:0.441472:0.698823:0.441472:0.682154:0.103214:0.682154:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a. :@0.104633:0.723684:0.120077:0.723684:0.120077:0.707250:0.104633:0.707250:0.000000:0.000000:0.000000
x:@0.275952:0.767940:0.282052:0.767940:0.282052:0.754517:0.275952:0.754517:0.000000
y:@0.195319:0.722020:0.201433:0.722020:0.201433:0.708597:0.195319:0.708597:0.000000
2:@0.193971:0.751432:0.199688:0.751432:0.199688:0.740974:0.193971:0.740974:0.000000
4:@0.193971:0.737135:0.199688:0.737135:0.199688:0.726677:0.193971:0.726677:0.000000
2:@0.223349:0.774201:0.229066:0.774201:0.229066:0.763743:0.223349:0.763743:0.000000
–2:@0.180407:0.774201:0.191980:0.774201:0.191980:0.763743:0.180407:0.763743:0.000000:0.000000
–2:@0.187213:0.780423:0.198786:0.780423:0.198786:0.769965:0.187213:0.769965:0.000000:0.000000
–4:@0.187213:0.795020:0.198786:0.795020:0.198786:0.784562:0.187213:0.784562:0.000000:0.000000
–4:@0.163621:0.774201:0.175194:0.774201:0.175194:0.763743:0.163621:0.763743:0.000000:0.000000
4:@0.242314:0.774201:0.248030:0.774201:0.248030:0.763743:0.242314:0.763743:0.000000
f(x):@0.160597:0.726038:0.178519:0.726038:0.178519:0.712615:0.160597:0.712615:0.000000:0.000000:0.000000:0.000000
b. :@0.104633:0.844930:0.121531:0.844930:0.121531:0.828496:0.104633:0.828496:0.000000:0.000000:0.000000
x:@0.276190:0.887373:0.282289:0.887373:0.282289:0.873950:0.276190:0.873950:0.000000
y:@0.195782:0.841986:0.201897:0.841986:0.201897:0.828563:0.195782:0.828563:0.000000
2:@0.194209:0.870865:0.199925:0.870865:0.199925:0.860407:0.194209:0.860407:0.000000
4:@0.194209:0.856568:0.199925:0.856568:0.199925:0.846110:0.194209:0.846110:0.000000
2:@0.223083:0.893634:0.228800:0.893634:0.228800:0.883176:0.223083:0.883176:0.000000
–2:@0.180539:0.893634:0.192112:0.893634:0.192112:0.883176:0.180539:0.883176:0.000000:0.000000
–2:@0.186970:0.899855:0.198543:0.899855:0.198543:0.889398:0.186970:0.889398:0.000000:0.000000
–4:@0.186970:0.914452:0.198543:0.914452:0.198543:0.903995:0.186970:0.903995:0.000000:0.000000
–4:@0.161575:0.893634:0.173148:0.893634:0.173148:0.883176:0.161575:0.883176:0.000000:0.000000
4:@0.241052:0.893634:0.246768:0.893634:0.246768:0.883176:0.241052:0.883176:0.000000
f(x):@0.161784:0.845469:0.179706:0.845469:0.179706:0.832046:0.161784:0.832046:0.000000:0.000000:0.000000:0.000000
33.  Resolver las siguientes ecuaciones cuadráticas en :@0.514231:0.137730:0.931014:0.137730:0.931014:0.121061:0.514231:0.121061:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
los números complejos.:@0.544355:0.154372:0.723611:0.154372:0.723611:0.137702:0.544355:0.137702:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a.   2  + 2 = 0:@0.545774:0.179233:0.656924:0.179233:0.656924:0.162799:0.545774:0.162799:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.588824:0.179233:0.596279:0.179233:0.596279:0.162826:0.588824:0.162826:0.000000
2:@0.596217:0.173169:0.601454:0.173169:0.601454:0.163588:0.596217:0.163588:0.000000
b.  3  + 12 = 0:@0.545774:0.210170:0.661882:0.210170:0.661882:0.193736:0.545774:0.193736:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.584885:0.210170:0.592340:0.210170:0.592340:0.193764:0.584885:0.193764:0.000000
2:@0.592268:0.204106:0.597504:0.204106:0.597504:0.194525:0.592268:0.194525:0.000000
c.  4  - 16  + 52 = 0:@0.545774:0.241107:0.700372:0.241107:0.700372:0.224674:0.545774:0.224674:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.584885:0.241107:0.592340:0.241107:0.592340:0.224701:0.584885:0.224701:0.000000
2:@0.592268:0.235044:0.597504:0.235044:0.597504:0.225463:0.592268:0.225463:0.000000
x:@0.628565:0.241107:0.636020:0.241107:0.636020:0.224701:0.628565:0.224701:0.000000
d.  5  + 30  + 125 = 0:@0.545774:0.272044:0.714766:0.272044:0.714766:0.255610:0.545774:0.255610:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.584885:0.272044:0.592340:0.272044:0.592340:0.255637:0.584885:0.255637:0.000000
2:@0.592268:0.265980:0.597504:0.265980:0.597504:0.256399:0.592268:0.256399:0.000000
x:@0.634050:0.272044:0.641505:0.272044:0.641505:0.255637:0.634050:0.255637:0.000000
e.  6  + 54 = 0:@0.545774:0.302981:0.661882:0.302981:0.661882:0.286547:0.545774:0.286547:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.584885:0.302981:0.592340:0.302981:0.592340:0.286575:0.584885:0.286575:0.000000
2:@0.592268:0.296917:0.597504:0.296917:0.597504:0.287336:0.592268:0.287336:0.000000
34.  Resuelve la siguiente situación:@0.514231:0.327842:0.775699:0.327842:0.775699:0.311172:0.514231:0.311172:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
.:@0.775513:0.327842:0.778716:0.327842:0.778716:0.311408:0.775513:0.311408:0.000000
El:@0.542689:0.352704:0.555040:0.352704:0.555040:0.336270:0.542689:0.336270:0.000000:0.000000
número de teléfonos celulares (en miles), vendidos :@0.558914:0.352704:0.931197:0.352704:0.931197:0.336270:0.558914:0.336270:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
por una empresa entre los años 2017 y 2021, se :@0.542697:0.369345:0.930979:0.369345:0.930979:0.352912:0.542697:0.352912:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
representa en la siguiente tabla::@0.542697:0.385987:0.772990:0.385987:0.772990:0.369553:0.542697:0.369553:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.514231:0.473269:0.518262:0.473269:0.518262:0.456835:0.514231:0.456835:0.000000
Núm.  :@0.585833:0.413981:0.631734:0.413981:0.631734:0.398574:0.585833:0.398574:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(en miles):@0.570254:0.429110:0.640386:0.429110:0.640386:0.413703:0.570254:0.413703:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
20:@0.683492:0.421545:0.699825:0.421545:0.699825:0.406605:0.683492:0.406605:0.000000:0.000000
35:@0.730933:0.421545:0.747265:0.421545:0.747265:0.406605:0.730933:0.406605:0.000000:0.000000
50:@0.778373:0.421545:0.794706:0.421545:0.794706:0.406605:0.778373:0.406605:0.000000:0.000000
70:@0.825898:0.421545:0.842062:0.421545:0.842062:0.406605:0.825898:0.406605:0.000000:0.000000
65:@0.873338:0.421545:0.889503:0.421545:0.889503:0.406605:0.873338:0.406605:0.000000:0.000000
años:@0.588076:0.458123:0.622564:0.458123:0.622564:0.442717:0.588076:0.442717:0.000000:0.000000:0.000000:0.000000
2017 2018 2019 2020 2021:@0.674642:0.458123:0.896566:0.458123:0.896566:0.443183:0.674642:0.443183:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a.  Haz una gráfica del problema con la información :@0.545774:0.500632:0.931169:0.500632:0.931169:0.484198:0.545774:0.484198:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de la tabla. :@0.575895:0.517274:0.657973:0.517274:0.657973:0.500840:0.575895:0.500840:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b.  Escribe el modelo matemático que determina el :@0.545774:0.542135:0.931193:0.542135:0.931193:0.525702:0.545774:0.525702:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
problema.:@0.575902:0.558777:0.650113:0.558777:0.650113:0.542344:0.575902:0.542344:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
c.  Establece conclusiones.:@0.545774:0.583638:0.746776:0.583638:0.746776:0.567204:0.545774:0.567204:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
35.  Resuelve los siguientes problemas::@0.514231:0.608500:0.807481:0.608500:0.807481:0.591830:0.514231:0.591830:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a.  El lado de un rectángulo mide el doble que el :@0.545774:0.633362:0.930981:0.633362:0.930981:0.616928:0.545774:0.616928:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
otro lado. Si al mayor se le aumenta en 2 unidades :@0.575902:0.650004:0.930959:0.650004:0.930959:0.633570:0.575902:0.633570:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y al menor se le disminuye en 2 unidades, el :@0.575902:0.666645:0.931134:0.666645:0.931134:0.650212:0.575902:0.650212:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
rectángulo obtenido tiene 4 m² de área más que :@0.575902:0.683287:0.931184:0.683287:0.931184:0.666853:0.575902:0.666853:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la mitad del primer rectángulo. ¿Cuáles son las :@0.575902:0.699929:0.930847:0.699929:0.930847:0.683495:0.575902:0.683495:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
dimensiones? :@0.575902:0.716571:0.680032:0.716571:0.680032:0.700137:0.575902:0.700137:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b.  Juan tiene un alambre de 17  . ¿Cómo debe :@0.545774:0.754655:0.930908:0.754655:0.930908:0.738222:0.545774:0.738222:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
m:@0.804833:0.754655:0.819448:0.754655:0.819448:0.738249:0.804833:0.738249:0.000000
doblarlo para que forme un ángulo recto de :@0.575902:0.771297:0.930919:0.771297:0.930919:0.754864:0.575902:0.754864:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
modo que sus extremos queden a 9  ? :@0.575902:0.787939:0.867362:0.787939:0.867362:0.771505:0.575902:0.771505:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
m:@0.841776:0.787939:0.856392:0.787939:0.856392:0.771533:0.841776:0.771533:0.000000
c.  Una región rectangular tiene un perímetro de :@0.545774:0.826022:0.930978:0.826022:0.930978:0.809589:0.545774:0.809589:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
300 :@0.575902:0.842664:0.607047:0.842664:0.607047:0.826231:0.575902:0.826231:0.000000:0.000000:0.000000:0.000000
cm:@0.607802:0.842664:0.630130:0.842664:0.630130:0.826258:0.607802:0.826258:0.000000:0.000000
. Expresa el área de la región en función :@0.630166:0.842664:0.930877:0.842664:0.930877:0.826231:0.630166:0.826231:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de la longitud de uno de sus lados. :@0.575883:0.859306:0.832319:0.859306:0.832319:0.842872:0.575883:0.842872:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d.  Una piscina rectangular fue construida con un :@0.545774:0.897391:0.931180:0.897391:0.931180:0.880957:0.545774:0.880957:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
área de 1000 m2 y un perímetro de 140 m. ¿Qué :@0.575902:0.914033:0.930877:0.914033:0.930877:0.897599:0.575902:0.897599:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
longitud tiene cada lado de la piscina?:@0.575902:0.930675:0.846665:0.930675:0.846665:0.914241:0.575902:0.914241:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
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