ed.sm - 4º eso - matemáticas - unidad 3 - ecuaciones y sistemas
DESCRIPTION
Editorial SM - Matemáticvas 4º ESOResolución de problemasTRANSCRIPT
Pg
4 ESO - MATEMTICAS - UNIDAD 3 (Ecuaciones y sistemas)
Pg.49 1a) ( (
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( (
EMBED Equation.3 minutos
Pg.49 5
( (
EMBED Equation.3
EMBED Equation.3
EMBED Equation.3
EMBED Equation.3 Pg.49 6
LibrosVivos.Net
Pg.50 7
( (
( ( (
( Slo vale esta ltimaPg.50 8a) ( (
b) ( ( Slo vale
c) ( (
d) ( (
Pg.50 9a) ( ( (no vale)
b) ( ( (no vale)
c) ( ( (
( ( (no vale)
d) ( (
( (
Pg.50 10
( ( (
(no vale)
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( (
(no vale)
Pg.51 12a)
EMBED Equation.3 b)
EMBED Equation.3
c)
EMBED Equation.3
d)
e)
EMBED Equation.3 f)
Pg.51 13a) ( ( (no vale)
b) ( (
c) ( ( (no vale)
Pg.51 14a) ( ( (no vale)
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Pg.51 15
(
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(
Pg.52 17
( (
EMBED Equation.3
EMBED Equation.3 Pg.52 18a) ( (
b) ( ( (
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Pg.52 19a) (
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Pg.52 20a) (
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(no vale)
Pg.53 21
(I)
(II)
Reduccin ( (II) 2((I) (I)
Igualacin ( (
Sustitucin ( (
Pg.53 22a) Reduccin ( 4((I) (ii) (
b) Sustitucin ( (
c) Igualacin ( (
Pg.53 23
yo t
ahora
futuro 1futuro 2
Monedasyo
X
X+70 X(70
Monedast
Y
Y(70
Y+70
Futuro 1 (
Futuro 2 (
Sistema (
(
Pg.53 24
LibrosVivos.Net
Pg.54 25 La pendiente de ambas rectas es , es decir, son paralelas
Las ordenadas al origen son y , es decir, no son coincidentes
Las rectas no se cortan. El sistema no tiene ninguna solucinPg.54 26a) (
Cortes con ejes
Recta en color (rojo)
(
Cortes con ejes
Recta en color (verde)
Solucin = Punto de corte
b) (
Cortes con ejes
Recta en color (rojo)
(
Cortes con ejes
Recta en color (verde)
Solucin = Punto de corte
c) (
Cortes con ejes
Recta en color (negro)
(
Recta idntica (coincidente) a la anterior
Solucin = Puntos comunes =
d) (
Cortes con ejes
Recta en color (rojo)
(
Cortes con ejes
Recta en color (verde) paralela a la anterior
Solucin = Puntos comunes =
Pg.54 27Porque la representacin grfica cartesiana es lineal, o sea, una lnea recta
Pg.54 28
x y ( (I)
y x = 36 + x y ( (II)
(I) + (II) (
(I) (II) ( (
Pg.55 29
(I)(I) + (II) (
(II) (I) ( (II) (
Con (
Con (
Con (
Con (
Pg.55 30a) (
b) (
(
(
Pg.55 31a) (
EMBED Equation.3 ( (ambas con igual signo)
(no vale)
b) (
EMBED Equation.3
EMBED Equation.3 (
EMBED Equation.3 (ambas con signos opuestos)
( (ambas con signos opuestos)Pg.55 32a)
EMBED Equation.3 Recta (verde)
Coordenadas origen
EMBED Equation.3 Parbola (roja)
Eje Vrtice Abertura +OY
Puntos
Soluciones = puntos de corte
b)
EMBED Equation.3 Hiprbola (verde)
Asntotas
Puntos
EMBED Equation.3 Parbola (rojo)
Eje Vrtice Abertura OX
Puntos
Soluciones = puntos de corte
Pg.55 33
( (
EMBED Equation.3 ( ( (
Pg.55 34
(
( ( ( (
Pg.55 35
( (
( ( ( (
Pg.55 36 LibrosVivos.Net
Pg.56 37a) (
b) (I) (II)
(I) + 2(II) (
EMBED Equation.3
(II) ( ( (
Pg.56 38a) ( ( (
b)
EMBED Equation.3
( ( (
( ( (no vale)
Pg.56 39a) (I) (II)
(I) + (II) (
(I) (II) (
b)
EMBED Equation.3 ( Sistema incompatible
c) (I) (II)
Pg.58 40a) ( (
b) ( (
c) (
d) ( ( (
e) ( (
Pg.58 41a) ( (
b) ( (
c) ( (
d) ( (
e) ( (
Pg.58 42a) ( ( I . Sin solucin
b) ( (III. Dos soluciones
c) (
III. Dos soluciones
d) ( (
III. Dos solucionesPg.58 43a) (
b) (
c) ( (
d) (
e) ( Sin solucin
f) ( (
Pg.58 44a) (
b) (
c) (
d) (
e) ( (
f) (
Pg.58 45a) ( (
b) ( (
( (
c) (
( (
d) ( (
(
EMBED Equation.3 Sin solucin
e) ( (
(
Pg.58 46a) ( ( (
(
b) ( ( (
(
c) ( ( ( (
(
EMBED Equation.3 (no valen)
(
EMBED Equation.3 (no valen)
d) ( ( (
EMBED Equation.3 (
(
EMBED Equation.3
EMBED Equation.3
EMBED Equation.3 (no valen)
e) ( ( (
( ( (
EMBED Equation.3
EMBED Equation.3
( ( (
EMBED Equation.3
EMBED Equation.3
f) ( ( (
( (
El segundo parntesis es una ecuacin recproca tipo
Se descompone en dos de segundo grado
El valor de es el de las respectivas races de la ecuacin
( (
( Races Imaginarias ( no valen
Pg.58 47a) (
b) (
EMBED Equation.3
c) (
d)
(
Pg.58 48a) ( (
( (
b) (
( Imaginarias ( Sin solucin
c) ( (
d) ( (
( (
Pg.58 49a) ( ( ( ( (no)
b) ( ( ( (no)
c)
EMBED Equation.3
EMBED Equation.3
EMBED Equation.3 ( (no)
d) ( ( ( (no)
e) ( (
f) ( (
( ( (
( ( ( (no)
g) ( ( (
( ( (no)
h) (
( ( (
( y la cbica facilita y otras dos imaginariasPg.58 50a) ( ( ( (
b) ( (
Pg.59 51a) ( ( (
b) ( ( (
c) ( ( ( (no)
d) ( (no valen) ( Sin solucin
e) ( (
f) ( ( ( (no)Pg.59 52a) ( (
EMBED Equation.3
EMBED Equation.3
b) ( ( (
c) ( ( (
d) ( (
Pg.59 53a) ( (
b) ( (
c) ( (
(
EMBED Equation.3
EMBED Equation.3
d) ( (
e) ( (
f) ( ( (
Pg.59 54a) ( ( (
b) ( ( (
EMBED Equation.3
Pg.59 55a)
EMBED Equation.3 Recta (roja)
Coordenadas en origen
EMBED Equation.3 Recta (verde)
Coordenadas en origen
Solucin = P. Corte =
b)
EMBED Equation.3 Recta (roja)
Coordenadas en origen
EMBED Equation.3 Recta (verde)
Solucin = P. Corte =
Pg.59 56a) (I) (II) ( (i) + (II) (
b) ( ( (
c)
EMBED Equation.3 (I)
EMBED Equation.3 (II) (
( 3(I) + 2(II)
EMBED Equation.3 (
d) (I) (II) ( (II) (I)
EMBED Equation.3 (
Pg.59 57a) Cualquiera que sea incompatible. Por ejemplo:
b) Cualquiera que sea equivalente. Por ejemplo:
c) Cualquiera que sea secante. Por ejemplo:
P. Corte =
No, pues no satisfacen la ecuacin dada
S, pues s satisfacen la ecuacin dada
Pg.59 58( Un sistema LINEAL, al estar representado por dos rectas.
Recta roja(
Coordenadas en origen
Recta verde (
Coordenadas en origen
( Solucin = Coordenadas P. Corte = (
Pg.59 59a) (
EMBED Equation.3
EMBED Equation.3
(
EMBED Equation.3
EMBED Equation.3
b) La combinacin de signos da :
: : :
c) (I) + (II)
EMBED Equation.3 (
d) (II)2 (I) (II) ( (
( (
e) ( ( (
( (no vale)
f) (II) ( (I) ( (
( Sin Solucin
(
Pg.59 60a) (I) (II) ( (
( (no vale)
b) (II) (I) ( ( (
( ( Y otras dos races imaginarias
( ( Y otras dos races imaginaria
c) (I) (II) ( ( (
(
EMBED Equation.3
EMBED Equation.3 (
(
EMBED Equation.3
EMBED Equation.3 ( (no valen)
d) (I) (II)
EMBED Equation.3 (
( ( ( no valen
( ( no valen (
Pg.59 61( El siguiente:(I) ( (II) (
( (II) (II) ( (
( (
Pg.59 62 1) 2) ( 3)(
4)
(
(
(
(
5) Quedan tabulados en el punto precedente
Pg.60 63a) (I) ( (II) (
(II) 4(I) (
(I) (
b) (I) ( (II) (
(I) 4(II) ( ( Sin SolucinPg.60 64a) ( ( (
b) ( ( (
( (
EMBED Equation.3 (no vale)Pg.60 65
( (
Pg.60 66
(I) (II)
(I) 2(II) ( ( (
( ( ( (no vale)Pg.60 67rea rombo = 4 ( rea Tringulo Rectngulo Catetos Semi diagonales
EMBED Equation.3
EMBED Equation.3
EMBED Equation.3
EMBED Equation.3 (
( (
(
EMBED Equation.3 Pg.60 68
( ( ( (no vale)Pg.60 69
(
( ( (
EMBED Equation.3
EMBED Equation.3 Pg.60 70
( (
Pg.60 71
( ( ( (
( (no vale)Pg.60 72
( (
Pg.60 - 73
( (
( ( ( (
EMBED Equation.3
EMBED Equation.3 (no vale)Pg.60 74
( (
( (I) (II) ( (II) 5(I)
( 8(I) (II)
Pg.60 75
( ( ( (no vale)
Pg.60 76
( ( ( (
(
EMBED Equation.3 Nmeros = 3, 4 y 5
(no vale)Pg.60 77
( (
( ( ( (
(
Superficie =
EMBED Equation.3
Pg.60 78
(
( ( (
( Lado Base = Altura =
(no vale)Pg.61 79
( ( (
Pg.61 80
( ( (
( (
EMBED Equation.3
EMBED Equation.3
EMBED Equation.3 Pg.61 81
(
EMBED Equation.3 (
( ( Opcin d)Pg.61 82
( (
( Coeficiente de x = 0 ( ( Opcin a)Pg.61 83
( ( ( (no vale)
EMBED Equation.3 Opcin c)Pg.61 84Suma de soluciones =
EMBED Equation.3 Producto de soluciones =
EMBED Equation.3
La ecuacin correcta es = ( Opcin a)Pg.61 85Producto races (
EMBED Equation.3 Opcin d)Pg.61 86
EMBED Equation.3
EMBED Equation.3
( ( Opcin d)Pg.61 1
( (
( (
Pg.61 2
( ( (
Pg.61 3
( (
( (
Pg.61 4a) ( (
EMBED Equation.3
b) ( (
Pg.61 5
( ( (
( ( (
Pg.61 6
(
Pg.61 7
( (
EMBED Equation.3
EMBED Equation.3 Pg.61 8Parbola Recta Solucin = P. Corte
Pg.61 9
( ( (
EMBED Equation.3
EMBED Equation.3 (no)Pg.61 10
( (
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