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Page 1: Agenda Ver 5
Page 2: Agenda Ver 5

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mayoL M M J V S D

1 2 34 5 6 7 8 9 1011 12 13 14 15 16 1718 19 20 21 22 23 2425 26 27 28 29 30 31

marzoL M M J V S D

12 3 4 5 6 7 89 10 11 12 13 14 1516 17 18 19 20 21 2223 24 25 26 27 28 2930 31

abril 2015

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Lunes Martes Miércoles Jueves Viernes Sábado Domingo30 31 1 2 3 4 5

6 7 8 9 10 11 12

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27 28 29 30 1 2 3

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julioL M M J V S D

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mayoL M M J V S D

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Lunes Martes Miércoles Jueves Viernes Sábado Domingo1 2 3 4 5 6 7

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agostoL M M J V S D

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junioL M M J V S D1 2 3 4 5 6 78 9 10 11 12 13 1415 16 17 18 19 20 2122 23 24 25 26 27 2829 30

julio 2015

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Lunes Martes Miércoles Jueves Viernes Sábado Domingo29 30 1 2 3 4 5

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Área, perímetro y volumen de figuras del plano y del espacio www.vaxasoftware.com

A = Área, P = Perímetro, V = Volumen Figuras del plano

Cuadrado

2aA = °= 90 interno Ángulo α

aP 4= °= 90 externo Ángulo β 2 diagonales Núm. =ND

Rectángulo

hbA ·=

hbP 22 +=

Paralelogramo

hbA ·=

abP 22 +=

Rombo

2·DdA =

aP 4=

2224 Dda +=

Trapecio

hBbA2+

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Trapecio recto

hBbA2+

=

hBbaP +++=

222 )( hbBa +−=

Triángulo equilátero

2

43

2· ahaA == °= 60 interno Ángulo α

aP 3= °=120 externo Ángulo β

ah23

= 0 diagonales Núm. =ND

Triángulo isósceles

2sen ··

2· AbahbA ==

baP += 2 , Aah sen · =

222 44 bha +=

Triángulo escaleno

2·hbA =

))()(( csbsassA −−−= 2

cbas ++=

cbaP ++= CaAch sen · sen · ==

Triángulo rectángulo

2·abA = BcAca cos · sen · ==

cbaP ++= AcBcb cos · sen · ==

222 bac +=

Pentágono regular

°=+== 72sen ·255210

85

2·5 22 rrbaA

bP 5= 222 44 bar += °=108 interno Ángulo α

°=−= 36sen ·252102

rrb °= 72 externo Ángulo β

°=+= 36 cos·5264

rra 5 diagonales Núm. =ND

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Page 203: Agenda Ver 5

Hexágono regular

°== 06sen ·32

33 22 bbA °=120 interno Ángulo α

bP 6= °= 60 externo Ángulo β

°== 30·cos23 bba 9 diagonales Núm. =ND

Octágono regular

( )12

25,22tan

2 8282,52 ·tan·8··422

22

−=

°=−=°==

bbaabaA

°== 5,22·tan·16·8 abP °=135 interno Ángulo α

°= 5,22·cosra °= 45 externo Ángulo β

°= 2,52sen·2rb 20 diagonales Núm. =ND

Polígono regular de n lados

nanbanA °

==180 ·tan·

2·· 2

nn °−

=180)·2(

:interno Ángulo

α

nanbnP °

==180·tan·2·

αβ −°=180:externo Ángulo

nra °

=180·cos

nrb °

=180sen·2

2)3·(

:diagonales Núm.−

=nnND

Círculo

2 π rA =

rP π2=

Sector circular

°=

360 π 2 αrA

°=

180 π αrL

LrP += 2 α en grados sexagesimales

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Page 204: Agenda Ver 5

Segmento circular

⎟⎠⎞

⎜⎝⎛ −

°=

2sen

360·π2 ααrA

⎟⎠⎞

⎜⎝⎛ −=

2cos1 αrh

2sen·2 αrc =

°=

180 π αrL

cLP += h

chr82

2

+= α en grados sexagesimales

Triángulo circular

2sen 2 αrA =

2sen·2 αrc =

crP += 2 α en grados sexagesimales

Trapecio circular

( )°

−=360

π 22 αrRA

)(2360

)( π2 rRrRP −+°

+=α

α en grados sexagesimales

Corona circular

( )22 π rRA −=

)( π2 rRP +=

Elipse

baA · π=

)( π baP +≅

∫ +=2/π

0

2222 cossen4 dttbtaP

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Page 205: Agenda Ver 5

Figuras del espacio

Cubo (hexaedro)

2 6 aA =

3aV =

Prisma recto

cbcabaA ·2·2·2 ++=

cbaV ··=

Esfera

2π·4 rA =

3·π4 3rV =

Cilindro

)( π2 rhrATOTAL +=

2 π2 rABASES = hrALATERAL · π2=

hrV ·π· 2=

Cono

2 π· π rgrATOTAL +=

2 π rABASE = grALATERAL · π=

3· π 2 hrV = 222 rhg +=

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Page 206: Agenda Ver 5

se clasifican

propiedades propiedades relaciones

aplicaciones de

am/n = n√am orden

tipos utilidad aplicaciones

ej. tipos

Nº REALES

IRRACIONALES √aRACIONALES (a/b)

• (a/b)m . (a/b)n = (a/b)m+n

• (a/b)m : (a/b)n = (a/b)m-n

• [(a/b)m ]n = (a/b)m.n

• (a/b . c/d )m = (a/b)m. (c/d)m

• n√ an = a

• n√ a . n√b = n√ab

• n

n

b

a = n

b

a

• (n√a)m = n√am

• n√m√an= nm√a

• n√an= nm√an

• Productos ycocientes

• Suma• Racionalización

INTERVALOS

• Abiertos ( )• Cerrados [ ]• Semiabiertos ( ]

VALOR | |ABSOLUTO

DISTANCIA

ERRORES• Error Absoluto ∆x = | x- x |• Redondeo• Notación científica• Error Relativo δx= ∆x/x CIFRAS

SIGNIFICATIVAS

Page 207: Agenda Ver 5

operaciones combinación

se relaciona con operaciones

ejemplo

factorización

de

polinomios

P(x) = (x- α1) . (x- α2) ….. (x- αk) C´(x)

POLINOMIOSP(x)= an x

n + an-1 xn-1 + …..+ a1 x0 + a0

• Suma : an xn + bn x

n = ( an + bn) xn • Resta: (- P(x) )

• Producto : (amxm) . (bn xn )= am bn x

m+n

• Cociente : P(x) = Q(X) . C(x) + R(x) ⇒ gr R(x) < gr Q(x)

• Regla de Ruffini ⇒ P(x) : (x-a)• Teorema del Resto ⇒ R = P(a)• Raíces de un polinomio

RAZONES ALGEBRAICASP(X) / Q (X)

• Reducir a comúndenominadorm.c.m

SUMA

• Producto

• Cociente

Page 208: Agenda Ver 5

igualdades desigualdades

resolución gráfica

Tipos clasificación solución tipos

tipos

tipos

IGUALDADES Y DESIGUALDADES

ECUACIONES (=)

• Primer grado, ax + b = 0 ⇒ a ≠0 ⇒ x= - b/a

• Segundo grado, ax2 + bx + c = 0 X= ( -b ± √b2 - 4ac ) / 2a

• Bicuadradas, ax4 + bx2 + c =0 ⇒ x2=z

• Ecuaciones con radicales

SISTEMAS DEECUACIONES

LINEALES

COMPATIBLES

INCOMPATIBLES

DETERMINADOS

INDETERMINADOS

MÉTODO DEGAUSS

INECUACIONES

• Primer grado, ax + b ≤ 0

• Segundo grado, ax2 + bx + c = a(x-x1 ) . (x-x2 )

• Otros grados, (x-a) . (x+b) …..≥ 0

Page 209: Agenda Ver 5

clasificación combinación

nomenclatura operaciones

producto escalar

operaciones ejemplo

módulo

producto escalar

operaciones

representantes

VECTORESQ P

VECTOR FIJO• Q , origen• P , extremo• QP , desplazamiento• , módulo

Suma : a + b

Resta : a - b

Multiplicación : ra

VECTOR LIBRE

DIRECCIÓN SENTIDO MÓDULO

Suma; regladel polígono

Multiplicación

rPA

BASESMATRIZ DECOMPONENTES

BASESCARTESIANAS v= √[ ( v1)2 + (v2)2]

a.b = a1.b1 + a2. b2

a.b=1/2(a 2+b 2-b-a2)

Page 210: Agenda Ver 5

tipos

identificación relación con posición

punto

aplicación

asocia

forman

relación

aplicación

son

aplicación

GEOMETRÍA VECTORIAL DEL PLANO

VECTOR LIBRE

ORIGEN

VECTORPOSICIÓN

BASE

COORDENADAS(X,Y)SISTEMA DE

COORDENADAS

AB = OB - OA

COORDENADASDEL PUNTOMEDIO

RECTA

VECTORIALr = OA + t. v

PARAMÉTRICAX= a1 + t . v1Y= a2 + t . v2

CONTINUAx -a1/v1 = y-a2/v2

GENERALAx +By + C = 0

PUNTO - RECTA EXPLÍCITAy= mx + hPENDIENTE, m

PARALELAS

PERPENDICULARES

SECANTE COINCIDENTE NOCOINCIDENTE

DOSPUNTOS

DISTANCIA

Page 211: Agenda Ver 5

soporte estructura se identifican caracteriza

se

define consta

relación entre ellas operaciones formas de

Expresión

operaciones

operaciones

Nos COMPLEJOS

TRIGONOMETRIA

RAZONESTRIGONOMÉTRICAS

IDENTIDADES

REDUCCIÓN AL PRIMER CUADRANTE

AFIJO VECTOR DEPOSICIÓN (x ,y)

X, PARTEREAL

Y, PARTEIMAGINARIA

CUERPO

SUMA

PRODUCTOPOR Nº REAL

PRODUCTO

COCIENTE

POTENCIA

RAÍZ

BINÓMICAZ= x+yi

(a+bi) . (c+di) = (ac-bd)+(ad+bc)i

Multiplico conjugado

Multiplicaciones sucesivas

z . z´= ( r. r´ ) α+β

z : z´= (r / r´ ) α - β

zm = ( rm )mα

n√r α = { R= n√r , θ = α/n + k360º/n

POLAR r α

r = |z |x = r cos αy = r sen α

Page 212: Agenda Ver 5

son operaciones

relación

son nomenclatura

aplicación

Equivalencia

TRIGONOMETRÍA

Sen α = y

cos α = x

Tang α = y/x

Cosec α= 1/y

Sec α = 1/x

Cotangα = x/y

RAZONESTRIGONOMÉTRICAS

IDENTIDADES BÁSICAS

sen2 α + cos2 α = 1 1 + tang2α = sec2α 1 + cotang2α = cosec2α

Suma de ángulos• Sen(α+β)=senα .cos β+ cos α . senβ• Sen(α-β)=senα .cosβ - cos α . senβ• cos(α+β)=cos α.cosβ - sen α . senβ• cos(α+β)=cosα .cosβ +sen α . senβ

Ángulo doble• Sen2α = 2 senα . cosα• cos2α = cos2α - sen2α

Ángulo mitad

• Sen α/2= ± √ (1 - cos α) / 2

• Cos α/2= ± √ (1 + cos α) / 2

Suma de razones• SenA + senB = 2sen (A+B)/2 . cos (A - B)/2• SenA - senB = 2cos (A+B)/2 . sen (A - B)/2• cosA + cosB = 2cos (A+B)/2 . cos (A - B)/2• cosA + cosB = 2sen (A+B)/2 . sen (A - B)/2

ECUACIONESTRIGONOMÉTRICAS

RADIAN180º = Π rad

Page 213: Agenda Ver 5

relación entre lados y ángulos resolución

utilizando aplicación

aplicación utilizando

TRIÁNGULOS C B a

 c B

TEOREMA DEL COSENOa2= b2 + c2 - 2abc cosA

TEOREMA DEL SENOa/senA = b/senB = c/senC

CIRCUNFERENCIACIRCUNSCRITAa/senA= 2R

TRIÁNGULOSRECTANGULOS

RAZONES TRIGONOMÉTRICASRELACIONES TRIGONOMÉTRICAS

CASOGENERAL

ÁNGULOS DEELEVACIÓN YDEPRESIÓN

CÁLCULO DEDISTANCIASINACCESIBLES

Page 214: Agenda Ver 5

asocia se define tipos

asigna clasificación

propiedades

operaciones

FUNCIONES

DOMINIO; Dx⇒y= f (x)

COJUNTO IMAGEN

Imf= {f(x) x∈D }

GRÁFICA( X, f(x) )

INYECTIVAf (x1 ) = f (x2 ) ⇒ x1=x2

SIMETRÍAS

PARf (-x) = f(x)

IMPARf (-x) = - f(x)

F . PLINÓMICAf(x)= an xn + an-1 xn-1 +….+a1 x + a0

F . CONSTANTEf (x)= c

F . IDENTIDADf(x) =x

F . PRIMER GRADOf(x) = ax + b

pendiente o.o

F. SEGUNDO GRADOf(x)=ax2 + bx + c

F. PROPORCIONALIDADINVERSAy = c ⁄ x

SUMAf (x) + g(x) = (f+g) (x)

RESTAf (x) - g(x) = (f-g) (x)

PRODUCTO POR cte(C. f)(x) = C . f(x)

PROCUCTO(f . g) (x) = f(x) . g(x)

COCIENTE(f/g) (x) = f(x)/g(x)

COMPOSICIÓN(g 0 f) = g(f(x))

Page 215: Agenda Ver 5

tipos indeterminaciones

clasificación propiedades

propiedades indeterminaciones

Tipos

LÍMITES

LÍMITES ENEL INFINITO

limx à ± ∞ =

VALORES MUYGRANDES

limx à + ∞ =

VALORES MUYPEQUEÑOS

limx à - ∞ =

• ∞/ ∞• ∞−∞• 0 . ∞• 0/0

• limxà+∞ =[f(x)+g(x)]= limxà+∞ f(x) +

limxà+∞ g(x) = l + m

• limxà+∞ =[f(x).g(x)]=[ limxà+∞ f(x) ].

[ limxà+∞ g(x) ]= l .m

• limxà+∞ =[f(x):g(x)]=[ limxà+∞ f(x) ]:

[ limxà+∞ g(x) ]= l/m

Cte + ∞ = ∞ (+∞)+(+∞)= +∞ (-∞)+(-∞)= -∞ Cte . ±∞ =± ∞ ±∞ .± ∞=± ∞

l/± ∞=0l ≠0

l/0 = ∞l ≠0

±∞ / l = ± ∞l ≠0

± ∞ / 0 = + ∞

LÍMITE EN UN PUNTOlimx à ± a =

0 /0

CONTINUA

limx àa f(x) = f(a)DISCONTINUA

1ª ESPECIE 2ª ESPECIEEVITABLE

• limx àa c =c

• limx àa x = a

• limx àaf(x)=l l>0 , entonces

limx àa√f(x) = √l

Page 216: Agenda Ver 5

aplicación

definición técnicas de derivación

conclusión

1º Criterio

estudia 2º Criterio

son

1º Criterio

2º Criterio

implica

DERIVADAf(x) derivada f´(x)

f ´(x0) = lim h→0 f (x0 +h ) - f (xo) h

f(x) = mx + b → f´(x)=m RECTA TANGENTEy- f(x0 )= f´(xo) . (x - xo)

GRÁFICAS

ASÍNTOTAS ASINTOTA VERTICALLim x→ a f(x)= ∞

ASINTOTA HORIZONTALLim x→ ∞ f(x)

CRECIMIENTO

F . CRECIENTE X1 < X2

f(x1) < f(x2)

F . DECRECIENTE X1 < X2

f(x1) > f(x2 )

OPTIMIZACIÓNDE FUNCIONES

EXTREMOSRELATIVOSf ´(x)=0

MÁXIMO

Creciente→Decreciente

f ´(x0)=0 → f ´´(x0) < 0

MÍNIMO Decreciente→Creciente

f ´(x0)=0 → f ´´(x0) > 0

CONCAVIDAD YCONVEXIDAD

PUNTOS DE INFLEXIÓNf ´´ (x0 )=0

CONVEXA ; f ´´(x)<0 ⇒ f ´(x)decreciente

CONCAVA ; f ´´(x)>0 ⇒ f ´(x)creciente

f(x) ± g(x) = [f ´(x) ± g ´(x)]

f ´(x) . g(x) = [f ´(x) . g(x) +g ´(x) . f(x)]

f ´(x) : g(x) = [f ´(x) . g(x) +g ´(x) . f(x)] : g 2 (x)

[ x n ] ´ = n x n - 1 → n√pm = p m/n

h (x)= ( u(x) )n ; n∈Qh ´(x) = n ( u(x) )n-1 . u ´(x)

Page 217: Agenda Ver 5

definición teorema

fundamental

del

sabiendo cálculo propiedades

cálculo

integral

aplicaciones

ejemplo

INTEGRAL ; ∫b

a

∫b

af(x) dx = lim n→∞ =[f (ξ1 ) ∆x1 + f (ξ2) ∆x2 +

… + f (ξn ) ∆xn ]

Sn = f (ξ1) ∆x1 + f (ξ2) ∆x2 + … + f (ξn ) ∆xn

a , límite inferiorb , límite superior

∫b

af(t) dx es una primitiva

de f(x)

FUNCIÓN PRIMITIVA→H(x) primitiva f(x)

∫b

af(x) dx = G(b) - G(a)

G(x) primitiva

∫b

af(x) dx = - ∫

b

af(x) dx ; a<b

∫b

a

f(x) dx = 0

LINEALIDAD; ∫b

aC f(x) dx = C ∫

b

af(x) dx

∫b

a [f(x)+g(x)] dx = ∫

b

af(x) dx + ∫

b

ag(x) dx

ADITIVIDAD DE INTERVALOS

∫b

af(x) dx = ∫

b

af(x) dx + ∫

b

af(x) dx

a<c<b y f(x) ≥0

CÁLCULO DE ÁREAS

A=

∫b

a

f(x) dx , f(x) ≥0 , x ∈ (a,b)ENERGÍAPOTENCIAL

Page 218: Agenda Ver 5

datos método de cálculo ej.

subconjunto

Representación

características número de datos grande

clasificación

ordenación

de datos

tipos representación gráfica tipos

medidas medidas

de de

dispersión centralización

ejemplo

son

ESTADÍSTICAPOBLACIÓN

MUESTRA

VARIABLEESTADÍSTICA, X

INTERVALOS Xi= (Li-1 + Li ) / 2

HISTOGRAMAS

POLÍGONOS DEFRECUENCIA

CUANTITATIVA

CUALITATIVA

DISCRETA

CONTINUA

DISTRIBUCIÓN DEFRECUENCIAS

FRECUENCIAABSOLUTA, fi

FRECUENCIARELATIVAhi =fi /N

DIAGRAMAS

BARRAS

POLIGONAL

SECTORES

MEDIA

DIVISIÓN DEDATOS

CUARTILES MEDIANA

DECILES

PERCENTILES

RANGO

VARIANZA

DESVIACIÓN TÍPICA

DESVIACIÓN MEDIA

COEFICIENTE DE VARIACIÓN

SUMATORIO,

∑FRECUENCIASACUMULADASABSOLUTAS YRELATIVAS

Page 219: Agenda Ver 5

definición definición definición

relación

propiedades

propiedades

tipos

propiedades

propiedades

derivada

propiedades

derivada tipos relación

FUNCIONESTRASCENDENTES

FUNCIÓN EXPONENCIALf(x)= ax

FUNCIÓN LOGARÍTMICAy= loga x

FUNCIONESTRIGONOMÉTRICASsen x, cos x

ap/q = q√a p donde p,q ∈Z , q≠o

a >1 CRECIENTEINYECTIVA

limx→+∞ ax= +∞ limx→-∞ ax= 0ax>o ⇒x

o<a<1 DECRECIENTE

limx→∞ ax= 0 , limx→-∞ ax= +∞ax>o ⇒x

BASE e COMÚN a >1

(ex)´= ex ⇒ [e u/x] ´ = u ´ (x) eu (x)

(ax ) ´= ax ln a ⇒ [au(x)] ´= au(x) u´(x) Ln a

loga x =y ⇔ ay =x

loga 1 =0 →a0=1

loga a =1 →a1=a

loga (ax) =x si x ∈ R

aLogax =x si x ∈ R

loga (x.y) = loga x + loga y

loga (1/x) = - loga x

loga (y/x) = loga y - loga x

loga (xy) = y loga x

DECIMAL ; BASE 1O

NEPERIANO ; BASE e

CAMBIO BASELog b x =(1/ loga b). loga x

(Ln x)´= 1/x ⇒ [au(x)]´= au(x). u´(x) Ln a

Cos(t) =0 , Sen (t)=y

Tang (t)

-1 ≤cos t≤ 1- 1 ≤sen t≤ 1-

Cos(t+2Π)=costSen(t+2Π)=sentTang(t+2Π)=tan

• (senx)´=cosx[senu(x) ]´=u´(x).sen u(x)• (cosx)´=-senxcosu(x)]´=- u´(x). sen u(x)• (tangx)´=1/cos 2x[tangu(x)]´= u´(x)/ cos2 u(x)

Page 220: Agenda Ver 5

derivada

ejemplo caracteriza

representación relación

relación relación grado de medidaentre dependencia devariables medidas aritméticas aproximación

tipos medida

interpretación

relación clasificación

VARIABLES ESTADÍSTICAS BIDIMENSIONALES

VARIABLESBIDIMENSIONALES(X , Y)

DEPENDIENTES

FUNCIONALCORRELACIÓN

INDEPENDIENTES

Media X = ∑ xi /N

Media Y = ∑ yi /N

Media XY= ∑ xi. yi

/N

Covarianza σ xy = XY - mx .my

DIAGRAMA DE DISPERSIÓN

LINEAL

NO LINEAL

REGRESIÓN LINEAL

CORRELACIÓNLINEAL

COEFICIENTE DECORRELACIÓN, r

r = σxy /σxσy- 1 < r < 1 → Intervalo

r >0

r < 0

RECTACRECIENTE

RECTADECRECIENTE

CORRELACIÓNDIRECTA

CORRELACIÓNINVERSA

ERRORCUADRÁTICOMEDIO E2 = (y - a - bx2)

r =±1→ E2=0

Y sobre X : Y -m y = σxy / σ2

x ( X - mx )X sobre Y : X -m x = σxy / σ

2y ( Y - my )

Page 221: Agenda Ver 5

en general planteamiento de posibilidades posibilidades de combinación

característica

concepto asociado

fórmulas concepto asociado características

TÉCNICAS DE CONTAR

DIAGRAMADE ÁRBOL

DIAGRAMADE CAJAS

PRINCIPIO DEMULTIPLICACIÓN

VARIACIONESVm

k= m.(m-1)…(m-k1)

VARIACIONES CONREPETICIÓNVRm

k= mk

IMPORTA ORDEN

PERMUTACIONESPm= Vm

mPERMUTACIONESCON REPETICIÓNPRn

k1 k2 = n!

FACTORIALn! = n . (n-1) . (n-2)…

COMBINACIONESCm

k= Vmk / Pk NO REPETICIÓN

NO IMPORTA ORDEN

NÚMERO COMBINATORIO(m

k) = m! / k! (m-k)!

BINOMIO DE NEWTON

TRIÁNGULO DE PASCAL

Page 222: Agenda Ver 5

TABLAS DE CONVERSION DE UNIDADES

LONGITUD

metro milímetro pulgada pie yarda milla (statute)

m mm in (¨) ft yd mi

1 1000 39,3700787 3,2808399 1,0936133 0,00062137

0,001 1 0,0393701 0,0032808 0,0010936 0,00000062137

0,0254 25,4 1 0,08333 0,02777 0,000015782

0,3048 304,8 12 1 0,333 0,00018939

0,9144 914,4 36 3 1 0,00056818

SUPERFICIE

metro cuadrado hectárea pulgada cuadrada pie cuadrado yarda cuadrada acre

ha

1 0,0001 1550,0031 10,76391 1,19599 0,00024711

10000 1 15500031 107639,1 0,0001196 2,4710538

0,0006,4516 0,00000006451 1 0,006944 0,0007716 0,00000015942

0,09290304 0,000009290351 144 1 0,111 0,000022957

0,8361274 0,000083613 1296 9 1 0,00020661

4046,856 0,4046856 6272640 43560 4840 1

m2 in2 ft2 yd2

VOLUMEN

metro cúbico litro pie cúbico galón (USA) galón imperial (GB) barril de petróleo

gal gal bbl (oil)

1 1000 35,3146667 264,17205 219,96923 6,2898108

0,001 1 0,0353147 0,2641721 0,2199692 0,0062898

0,0283168 28,3168466 1 7,4805195 6,2288349 0,1781076

0,0037854 3,7854118 0,1336806 1 0,8326741 0,0238095

0,0045461 4,5460904 0,1635437 1,20095 1 0,028594

1589873 158987295 56145833 42' 34,9723128 1

dm3m3 ft3

1 gal (USA) =3,78541dm3

1 ft3=0,0283 m3

UNIDADES DE PRESIONUNIDADES DE PRESION

kilopascal atmósfera técnica milímetro de c. Hg metros de c. agua bar

(0ºC) (4ºC) 100000 Pa

kPa atm mm Hg psi bar (hpz)

1 0,0101972 7,5006278 0,1019745 0,1450377 0,01

98,0665 1 735,560217 1000028 14,2233433 0,980665

0,1333222 0,0013595 1 0,0135955 193367 0,0013332

9,8063754 0,0999972 73,5539622 1 1,4222945 0,0980638

6,8947573 0,070307 51,7150013 0,7030893 1 0,0689476

100 1,0197162 750,062679 10,1974477 14,5037738 1

in H2O (60ºF=20ºC)=0,248641 kPain H2O (60ºF=20ºC)=0,248641 kPa

1 atmósfera física (Atm)= 101,325 kPa=760 mm Hg1 atmósfera física (Atm)= 101,325 kPa=760 mm Hg1 atmósfera física (Atm)= 101,325 kPa=760 mm Hg

in Hg (60ºF=20ºC)=3,37685 kPain Hg (60ºF=20ºC)=3,37685 kPa

1 Torr= (101,325/760) kPa1 Torr= (101,325/760) kPa

kN /m2 Kgf/cm2 lib/in2libras por pulgada2

m H2O

1 in H2O (60ºF = 15,55ºC) = 0,248843 kPa

Tablas.-431

Page 223: Agenda Ver 5

ENERGIA (Calor y Trabajo)ENERGIA (Calor y Trabajo)

Kilojulio kW/hora Hourse power/hora Caballo/hora Kilocaloría (IT) British

USA 550 ft.lbf/seg 75 m.Kgf/seg Kcal(IT) Thermal Unit

kJ kW h hp. h CV.h Kcal (IT) Btu (IT)

1 0,0002777 0,000372506 0,000377673 0,2388459 0,9478171

3600 1 1,3410221 1,3596216 859,84523 3412,1416

2684,5195 0,7456999 1 1,0138697 641,18648 2544,4336

2647,7955 0,7354988 0,9863201 1 632,41509 2509,6259

4,1868 0,001163 0,00155961 0,00158124 1 3,9683207

1,0550559 0,000293071 0,00039301 0,000398466 0,2519958 1

1 termia = 1000 Kcal

1 therm = 100.000 Btu1 therm = 100.000 Btu

1 But (IT) = 1055,0558 J1 But (IT) = 1055,0558 J

1 kilogramo fuerza.metro (m.Kgf) = 0,00980665 kJ1 kilogramo fuerza.metro (m.Kgf) = 0,00980665 kJ1 kilogramo fuerza.metro (m.Kgf) = 0,00980665 kJ

IT se refiere a las unidades definidas en International Steam TableIT se refiere a las unidades definidas en International Steam TableIT se refiere a las unidades definidas en International Steam Table

MACROUNIDADES ENERGETICASMACROUNIDADES ENERGETICAS

Terajulio Gigavatio hora Teracaloría (IT) Ton. equivalente Ton. equivalente Barril de petróleo

de carbón de petróleo día-año

TJ GW h Tcal (IT) Tec Tep bd

1 0,2727 0,2388459 34,1208424 23,8845897 0,4955309

3,6 1 0,8598452 122,8350326 85,9845228 1,7839113

4,1868 1,163 1 142,8571429 100 2,0746888

0,0293076 0,008141 0,007 1 0,7 0,0145228

0,041868 0,01163 0,01 1,4285714 1 0,0207469

2,0180376 0,560568 0,482 68,8571429 48,2 1

POTENCIA

Kilowatio Kilocaloría/hora Btu (IT)/hora Horse power (USA) Caballo vapor Tonelada demétrico refrigeración

kW Kcal (IT)/h Btu (IT)/h hp CV

1 859,84523 3412,1416 1,3410221 1,3596216 0,2843494

0,001163 1 3,9683207 0,0015596 0,0015812 0,0003307

0,00029307 0,2519958 1 0,00039301 0,00039847 0,000083335

0,7456999 641,18648 2544,4336 1 1,0138697 0,2120393

0,7354988 632,41509 2509,6259 0,9863201 1 0,2091386

3,5168 3023,9037 11999,82 4,7161065 4,7815173 1

1 caballo vapor (métrico> = 75 m kgf/seg = 735,499 W1 caballo vapor (métrico> = 75 m kgf/seg = 735,499 W1 caballo vapor (métrico> = 75 m kgf/seg = 735,499 W

1 Horse power (USA) mecánico = 550 ft Ibf/seg1 Horse power (USA) mecánico = 550 ft Ibf/seg1 Horse power (USA) mecánico = 550 ft Ibf/seg

TEMPERATURA

Temperatura en ºC = (ºF -32)/1,8

Temperatura en ºF = 1,8 ºC + 32

Temperatura en ºK = ºC + 273,14

PREFIJOS DEL SISTEMA INTERNACIONAL DE UNIDADESPREFIJOS DEL SISTEMA INTERNACIONAL DE UNIDADESPREFIJOS DEL SISTEMA INTERNACIONAL DE UNIDADESPREFIJOS DEL SISTEMA INTERNACIONAL DE UNIDADESPREFIJOS DEL SISTEMA INTERNACIONAL DE UNIDADESPREFIJOS DEL SISTEMA INTERNACIONAL DE UNIDADESPREFIJOS DEL SISTEMA INTERNACIONAL DE UNIDADESPREFIJOS DEL SISTEMA INTERNACIONAL DE UNIDADES

Prefijo exa peta tera giga mega kilo hecto deca deci centi mili micro nano pico femto atto

Símbolo E P T G M k h da d c m m n p f a

Factor 1e +18 1e +15 1e +12 1e +9 1e +6 1000 100 10 0,1 0,01 0,001 1e-6 1e-9 1e -12 1e -15 1e -18

Tablas.-432