Ejercicios Rstudio

Ejercicio 1

x = 10; y = 3
x+y #a

## [1] 13

x*y #b

## [1] 30

x/y #c

## [1] 3.333333

sin(x) #d

## [1] -0.5440211

8*sin(y) #e

## [1] 1.12896

5*sin(2*y) #f

## [1] -1.397077

Ejercicio 2

x = 2; y = 5
(y*x^3)/(x-y) #a

## [1] -13.33333

(3*x)/(2*y) #b

## [1] 0.6

(3/2)*x*y #c

## [1] 15

x^5/(x^5-1) #d

## [1] 1.032258

Ejercicio 3

x = 3; y = 4
1/(1-(1/x^5)) #a

## [1] 1.004132

3*pi*x^2 #b

## [1] 84.823

(3*y)/(4*x-8) #c

## [1] 3

(4*(y-5))/(3*x-6) #d

## [1] -1.333333

Ejercicio 4

x = 2; y = 6*x^3+(4/x) #a
x = 8; y = 3*x/4 #b
x = 10; (4*x)^2/25 #c

## [1] 64

x = 2; 2*sin(x)/5 #d

## [1] 0.363719

x = 20; y = 7*(x^(1/3))+4*x^(0.58) #e

Ejercicio 5

a = 1.12; b = 2.34; c = 0.72; d = 0.81; f = 19.83
x = 1+a/b+c/f^2; x

## [1] 1.480463

s = (b-a)/(d-c); s

## [1] 13.55556

r = 1/(1/a+1/b+1/c+1/d); r

## [1] 0.2535713

y = (a*b*f^2)/(2*c)

Ejercicio 6

((3*6*7^2)/4)+((4^5)/(7^3-145))

## [1] 225.6717

(48.2*55-9^3)/(53+14^2)

## [1] 7.718876

(27^2/4)+(319^(4/5)/5)+(60*14^(-3))

## [1] 202.412

Ejercicio 7

fun.v <- function(r1){
  V1 = round(4*pi*r1^3/3,2)
  r2 = round(((3*(V1*1.3))/(4*pi))^(1/3),2)
  cat(paste0("Radio 1 = ",r1," y su Volumen = ", V1, "\n",
             "Volumen 2 (+30%) = ", 1.3*V1, "Su radio es = ", r2))
}
fun.v(5)

## Radio 1 = 5 y su Volumen = 523.6
## Volumen 2 (+30%) = 680.68Su radio es = 5.46

Ejercicio 8

x = -7-5i; y = 4+3i
x+y

## [1] -3-2i

x*y

## [1] -13-41i

x/y

## [1] -1.72+0.04i

Ejercicio 9

n = 1; R = 0.08206; Tm = 273.2; V = 22.41
a = 6.49; b = 0.0562 #gas Cl
gas.id <- function(n,R,Tm,V, a = 0, b = 0){
  (n*R*Tm/(V-n*b))-(a*n^2/V^2)
}
gas.id(n,R,Tm,V)

## [1] 1.000392

gas.id(n,R,Tm,V,a,b)

## [1] 0.9899845

Ejercicio 10

E.richter <- function(M){10^4.4*10^(1.5*M)}
E.richter(7.3)-E.richter(5.5)

## [1] 2.234254e+15

Ejercicio 11

curve(expr = (((6*log(t))-7*exp(0.2*t))), from = 1, to = 3, xname = "t",
      main = 'Temperatura ~ tiempo', xlab = 'tiempo (minutos)', ylab = 'Temperatura (°C)')

#### Ejercicio 12

curve(2*log10(60*x+1), 0, 2, col = 'blue',
      xlab = "Distancia (millas)", ylab = "Velocidad (millas/hora)")
curve(3*cos(6*x), 0, 2, col = 'red',
      add = T)
legend('topleft', legend = c("u","v"), fill = c('blue','red'))

#### Ejercicio 13

cerca <- function(W = 0, A = 0){
  D = W^2/4
  L = (A-(D^2/2))/W
  cat("        _____",round(L,2),"_____","\n",
      "      |                \\ D = ",round(D,2),"\n",
      "W =",round(W,2),"|    A =",round(A,2),"      \\","\n",
      "      |                 /","\n",
      "      |________________/","\n",
      "              Fig 1.    ","\n")
}
cerca(W = 6, A = 80)

##         _____ 6.58 _____ 
##        |                \ D =  9 
##  W = 6 |    A = 80       \ 
##        |                 / 
##        |________________/ 
##                Fig 1.

Ejercicio 14

seq(5,28, length.out = 100) == rep(5,100)+(0:99*(sum((28-5)/100^(1:100))))

##   [1] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
##  [15] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
##  [29] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
##  [43] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
##  [57] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
##  [71] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
##  [85] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
##  [99] TRUE TRUE

seq(2,14,0.2) == (0:(((14-2)/0.2)))*0.2+2

##  [1] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [15] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [29] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [43] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [57] TRUE TRUE TRUE TRUE TRUE

round(seq(-2,5, length.out = 50),5) == round(rep(1,50)+(0:49*(sum((8-1)/50^(1:100))))-3,5)

##  [1] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [15] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [29] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [43] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE

Ejercicio 15

10^seq(log10(10), log10(1000), length.out = 50)

##  [1]   10.00000   10.98541   12.06793   13.25711   14.56348   15.99859
##  [7]   17.57511   19.30698   21.20951   23.29952   25.59548   28.11769
## [13]   30.88844   33.93222   37.27594   40.94915   44.98433   49.41713
## [19]   54.28675   59.63623   65.51286   71.96857   79.06043   86.85114
## [25]   95.40955  104.81131  115.13954  126.48552  138.94955  152.64180
## [31]  167.68329  184.20700  202.35896  222.29965  244.20531  268.26958
## [37]  294.70517  323.74575  355.64803  390.69399  429.19343  471.48664
## [43]  517.94747  568.98660  625.05519  686.64885  754.31201  828.64277
## [49]  910.29818 1000.00000

10^seq(log10(10), log10(1000), length.out = 20)

##  [1]   10.00000   12.74275   16.23777   20.69138   26.36651   33.59818
##  [7]   42.81332   54.55595   69.51928   88.58668  112.88379  143.84499
## [13]  183.29807  233.57215  297.63514  379.26902  483.29302  615.84821
## [19]  784.75997 1000.00000

Ejercicio 16

a = matrix(c(3,7,-4,12,
             -5,9,10,2,
             6,13,8,11,
             15,5,4,1), 
           4, byrow = T)
(v = a[,2])

## [1]  7  9 13  5

(w = a[2,])

## [1] -5  9 10  2

Ejercicio 17

(a = a) #16

##      [,1] [,2] [,3] [,4]
## [1,]    3    7   -4   12
## [2,]   -5    9   10    2
## [3,]    6   13    8   11
## [4,]   15    5    4    1

(b = a[,2:4])

##      [,1] [,2] [,3]
## [1,]    7   -4   12
## [2,]    9   10    2
## [3,]   13    8   11
## [4,]    5    4    1

(c = a[2:4,])

##      [,1] [,2] [,3] [,4]
## [1,]   -5    9   10    2
## [2,]    6   13    8   11
## [3,]   15    5    4    1

(d = a[1:2,2:4])

##      [,1] [,2] [,3]
## [1,]    7   -4   12
## [2,]    9   10    2

Ejercicio 18

sqrt(sum(c(2,4,7)^2))

## [1] 8.306624

sqrt(sum(c(2,-4,7)^2))

## [1] 8.306624

Ejercicio 19

(a = a) #16

##      [,1] [,2] [,3] [,4]
## [1,]    3    7   -4   12
## [2,]   -5    9   10    2
## [3,]    6   13    8   11
## [4,]   15    5    4    1

apply(a, 2, max)

## [1] 15 13 10 12

apply(a, 1, max)

## [1] 12 10 13 15

Ejercicio 20

(a = a) #16

##      [,1] [,2] [,3] [,4]
## [1,]    3    7   -4   12
## [2,]   -5    9   10    2
## [3,]    6   13    8   11
## [4,]   15    5    4    1

(b = apply(a, 2, sort))

##      [,1] [,2] [,3] [,4]
## [1,]   -5    5   -4    1
## [2,]    3    7    4    2
## [3,]    6    9    8   11
## [4,]   15   13   10   12

(c = apply(a, 1, sort))

##      [,1] [,2] [,3] [,4]
## [1,]   -4   -5    6    1
## [2,]    3    2    8    4
## [3,]    7    9   11    5
## [4,]   12   10   13   15

(d = apply(a, 2, sum))

## [1] 19 34 18 26

(e = apply(a, 1, sum))

## [1] 18 16 38 25

Ejercicio 21

A = matrix(c(1,2,7,3,
             4,4,9,pi,
             2,100,7,42), 4)
B = log(A)
B[2,]

## [1] 0.6931472 1.3862944 4.6051702

sum(B[2,])

## [1] 6.684612

B[,2]*A[,1]

## [1]  1.386294  2.772589 15.380572  3.434190

max(B[,2]*A[,1])

## [1] 15.38057

sum(A[1,]/B[1:3,3])

## [1] 3.339081

Ejercicio 22

D = array(c(3,6,7,-2,8,9,1,-5,10,
            6,7,-8,9,5,2,-4,3,1,
            -7,10,3,-5,6,-9,2,1,8),
          dim = c(3,3,3))
dim(D)

## [1] 3 3 3

D[,,1]+D[,,2]+D[,,3]

##      [,1] [,2] [,3]
## [1,]    2    2   -1
## [2,]   23   19   -1
## [3,]    2    2   19

D[,,1]-D[,,2]+D[,,3]

##      [,1] [,2] [,3]
## [1,]  -10  -16    7
## [2,]    9    9   -7
## [3,]   18   -2   17

(D[,,1]+D[,,2])+D[,,3] == D[,,1]+(D[,,2]+D[,,3])

##      [,1] [,2] [,3]
## [1,] TRUE TRUE TRUE
## [2,] TRUE TRUE TRUE
## [3,] TRUE TRUE TRUE

Ejercicio 23

A = matrix(c(-7,4,16,9),2)
B = matrix(c(6,12,-5,-2),2)
C = matrix(c(-3,6,-9,8),2)
A+B+C

##      [,1] [,2]
## [1,]   -4    2
## [2,]   22   15

A-B+C

##      [,1] [,2]
## [1,]  -16   12
## [2,]   -2   19

(A+B)+C == A+(B+C)

##      [,1] [,2]
## [1,] TRUE TRUE
## [2,] TRUE TRUE

Ejercicio 24

fuerza = c(400,550,700,500,600)
distan = c(2,0.5,0.75,1.5,3)
(trabajo = fuerza*distan)

## [1]  800  275  525  750 1800

Ejercicio 25

salario_hora = c(5,5.5,6.5,6,6.25)
Hora_trabajada = c(40,43,37,50,45)
salida = c(1000,1100,100,1200,1100)
Hora_trabajada*salario_hora

## [1] 200.00 236.50 240.50 300.00 281.25

sum(Hora_trabajada*salario_hora)

## [1] 1258.25

sum(salida)

## [1] 4500

Ejercicio 26

d1 = c(-60,-25,-30)
d2 = c(-30,-55,-20)
sqrt(sum(d1^2)) # a

## [1] 71.58911

d1-d2 # b

## [1] -30  30 -10

sqrt(sum((d1-d2)^2)) # c

## [1] 43.58899

Ejercicio 27

fuerza = c(11,7,8,10,9)
k.resorte = c(1000,800,900,1200,700)
(x = fuerza/k.resorte) #f = k*x

## [1] 0.011000000 0.008750000 0.008888889 0.008333333 0.012857143

(ener.pot = (k.resorte*x^2)/2)

## [1] 0.06050000 0.03062500 0.03555556 0.04166667 0.05785714

Ejercicio 28

tbl = rbind(c(1,300,5,4,6),
            c(2,550,3,2,4),
            c(3,400,6,5,3),
            c(4,250,3,5,4),
            c(5,500,2,4,3))
colnames(tbl) = c('meterial','precio','mayo','junio','julio')
(cant_gastada = tbl[,3:5]*tbl[,2])

##      mayo junio julio
## [1,] 1500  1200  1800
## [2,] 1650  1100  2200
## [3,] 2400  2000  1200
## [4,]  750  1250  1000
## [5,] 1000  2000  1500

apply(cant_gastada,2,sum)

##  mayo junio julio 
##  7300  7550  7700

apply(cant_gastada,2,sum)

##  mayo junio julio 
##  7300  7550  7700

sum(cant_gastada)

## [1] 22550

Ejercicio 29

A = matrix(c(11,-9,5,-4),2)
B = matrix(c(-7,6,-8,20),2)
A%*%B

##      [,1] [,2]
## [1,]  -47   12
## [2,]   39   -8

B%*%A

##      [,1] [,2]
## [1,]   -5   -3
## [2,] -114  -50

Ejercicio 30

(A = matrix(c(3,6,7,-2,8,9,1,-5,10),3))

##      [,1] [,2] [,3]
## [1,]    3   -2    1
## [2,]    6    8   -5
## [3,]    7    9   10

(B = matrix(c(6,7,-8,9,5,2,-4,3,1),3))

##      [,1] [,2] [,3]
## [1,]    6    9   -4
## [2,]    7    5    3
## [3,]   -8    2    1

(C = matrix(c(-7,10,3,-5,6,-9,2,1,8),3))

##      [,1] [,2] [,3]
## [1,]   -7   -5    2
## [2,]   10    6    1
## [3,]    3   -9    8

A%*%(B+C) == A%*%B + A%*%C

##      [,1] [,2] [,3]
## [1,] TRUE TRUE TRUE
## [2,] TRUE TRUE TRUE
## [3,] TRUE TRUE TRUE

Ejercicio 31

(a = matrix(c(2,3,1,-9), 2))

##      [,1] [,2]
## [1,]    2    1
## [2,]    3   -9

(s = matrix(c(5,2),2))

##      [,1]
## [1,]    5
## [2,]    2

solve(a)%*%s

##           [,1]
## [1,] 2.2380952
## [2,] 0.5238095

(a = matrix(c(-8,-2,-5,7), 2))

##      [,1] [,2]
## [1,]   -8   -5
## [2,]   -2    7

(s = matrix(c(4,-10),2))

##      [,1]
## [1,]    4
## [2,]  -10

solve(a)%*%s

##            [,1]
## [1,]  0.3333333
## [2,] -1.3333333

(a = matrix(c(12,-3,6,-5,4,2,0,7,3), 3))

##      [,1] [,2] [,3]
## [1,]   12   -5    0
## [2,]   -3    4    7
## [3,]    6    2    3

(s = matrix(c(11,-3,22), 3))

##      [,1]
## [1,]   11
## [2,]   -3
## [3,]   22

solve(a)%*%s

##      [,1]
## [1,]    3
## [2,]    5
## [3,]   -2

(a = matrix(c(6,12,-5,-3,5,2,4,-7,6), 3))

##      [,1] [,2] [,3]
## [1,]    6   -3    4
## [2,]   12    5   -7
## [3,]   -5    2    6

(s = matrix(c(41,-26,14), 3))

##      [,1]
## [1,]   41
## [2,]  -26
## [3,]   14

solve(a,s)

##      [,1]
## [1,]    2
## [2,]   -3
## [3,]    5

Ejercicio 32

# A (BC + A) = B
# C = ((B * A-1) - A ) * B-1
(a = matrix(c(3,-2,9,4),2))

##      [,1] [,2]
## [1,]    3    9
## [2,]   -2    4

(b = matrix(c(2,7,-3,6),2))

##      [,1] [,2]
## [1,]    2   -3
## [2,]    7    6

(c = solve(b) %*% ((solve(a)%*%b) - a))

##            [,1]      [,2]
## [1,] -0.6212121 -2.363636
## [2,]  1.1969697  2.157576

a %*% ((b%*%c) + a)

##      [,1] [,2]
## [1,]    2   -3
## [2,]    7    6

Ejercicio 33

(a = matrix(c(-2,-2,1,1),2))

##      [,1] [,2]
## [1,]   -2    1
## [2,]   -2    1

(s = matrix(c(-5,3),2))

##      [,1]
## [1,]   -5
## [2,]    3

(b = matrix(c(-2,-8,1,4),2))

##      [,1] [,2]
## [1,]   -2    1
## [2,]   -8    4

(s = matrix(c(3,12),2))

##      [,1]
## [1,]    3
## [2,]   12

(c = matrix(c(-2,-2,1,1),2))

##      [,1] [,2]
## [1,]   -2    1
## [2,]   -2    1

(s = matrix(c(-5,-5.00001)))

##          [,1]
## [1,] -5.00000
## [2,] -5.00001

Ejercicio 34

function(dato = 0, unidades = 'gramos' , conver = 'masa'){
  if(conver == 'masa'){
    cat('SI (gramo): ',dato ,'\n')
  }
  if(conver == 'distancia'){
    
  }
  if(conver == 'fuerza'){}
}

## function(dato = 0, unidades = 'gramos' , conver = 'masa'){
##   if(conver == 'masa'){
##     cat('SI (gramo): ',dato ,'\n')
##   }
##   if(conver == 'distancia'){
##     
##   }
##   if(conver == 'fuerza'){}
## }

Ejercicio 35

a = c(5,8)
(ang = (a[1]/sqrt(sum(a^2)))*180/pi)

## [1] 30.3667

a = c(-5,8)
(ang = (a[1]/sqrt(sum(a^2)))*180/pi)

## [1] -30.3667

a = c(5,-8)
(ang = (a[1]/sqrt(sum(a^2)))*180/pi)

## [1] 30.3667

a = c(-5,-8)
(ang = (a[1]/sqrt(sum(a^2)))*180/pi)

## [1] -30.3667

Ejercicio 36

centi <- function(far)(5/9)*(far-32)
centi(140)

## [1] 60

Ejercicio 37

caida <- function(h,v0,g = 9.81){
  vf = sqrt(2*g*h+v0^2)
  t = (vf-v0)/g
  return(t)
}
caida(h = 100,v0 = 50,g = 9.81)

## [1] 1.712355

Ejercicio 38

x = c(-2,0,2,4)
y = c(-20,4,68,508)
poli3 <- function(x, y){
  ecu = cbind(x^3,x^2,x,rep(1,length(x)))
  inv = solve(ecu)
  res = inv %*% y
  rownames(res) = LETTERS[1:4]
  colnames(res) = 'Coef'
  print(res)
}
poli3(x,y)

##   Coef
## A    7
## B    5
## C   -6
## D    4

Ejercicio 39

gg <- function(x)10*exp(-2*x)
curve(gg,0,2)

#### Ejercicio 40

gg <- function(x)20*x^2-200*x+3
curve(gg,-100,100)

#### Ejercicio 41

(x = 6)

## [1] 6

(z = (x<10))

## [1] TRUE

(z = (x==10))

## [1] FALSE

(z = (x>4))

## [1] TRUE

(z = (x!=7))

## [1] TRUE

Ejercicio 42

x = c(-3,0,0,2,6,8)
y = c(-5,-2,0,3,4,10)
x[x>y]

## [1] -3  0  6

Ejercicio 43

precio = c(19,18,22,21,25,19,17,21,27,29)
sum(precio>20)

## [1] 6

sum(precio>=20)

## [1] 6

Ejercicio 44

precio_a = c(19,18,22,21,25,19,17,21,27,29)
precio_b = c(22,17,20,19,24,18,16,25,28,27)
sum(precio_a>precio_b)

## [1] 7

Ejercicio 45

precio_a = c(19,18,22,21,25,19,17,21,27,29)
precio_b = c(22,17,20,19,24,18,16,25,28,27)
precio_c = c(17,13,22,23,19,17,20,21,24,28)
sum(precio_a>precio_b & precio_a>precio_c)

## [1] 4

sum(precio_a>precio_b | precio_a>precio_c)

## [1] 9

sum((precio_a>precio_b & !(precio_a>precio_c))|
      (!(precio_a>precio_b) & precio_a>precio_c))

## [1] 5

Ejercicio 46

a=1;b=2;c=3;d=4
T&(T|F)

## [1] TRUE

T|(T&F)

## [1] TRUE

Ejercicio 47

fun_partes <- function(x){
  if(x<(-1)) y = exp(x+1)
  if(x>=(-1) & x<(5)) y = 2+cos(pi*x)
  if(x >= (5)) y = 10*(x-5)
  return(y)
}
fun_partes(-5)

## [1] 0.01831564

fun_partes(3)

## [1] 1

fun_partes(15)

## [1] 100

Ejercicio 48

x = 1; y = 2; z = 1
if(x<y){
  if(z<10){
    w = x*y*z
  }
}
w

## [1] 2

Ejercicio 49

sal = 0
for(i in 1:10){
  print(sal)
  sal = sal + 5*i^3
}

## [1] 0
## [1] 5
## [1] 45
## [1] 180
## [1] 500
## [1] 1125
## [1] 2205
## [1] 3920
## [1] 6480
## [1] 10125

Ejercicio 50

t = seq(0,4,length.out = 100)
x=5*t-10
y = 25*t^2-120*t+144
dis = sqrt(x^2+y^2)
t[dis == min(dis)]

## [1] 2.222222

x[dis == min(dis)]

## [1] 1.111111

y[dis == min(dis)]

## [1] 0.7901235

plot(x,y,type='l')
abline(h=0,v=0, col ='blue')
points(x[dis == min(dis)],y[dis == min(dis)], pch = 16, col='red')

md = sqrt(max(x)^2+max(y)^2)
for (i in 1:length(t)) {
  if(sqrt(x[i]^2+y[i]^2)<md){
    md = sqrt(x[i]^2+y[i]^2)
    mt = t[i]
  }
}
md; mt

## [1] 1.363401

## [1] 2.222222

Ejercicio 51

(a = matrix(c(3,-8,-17,5,-1,6,-4,33,-9),3))

##      [,1] [,2] [,3]
## [1,]    3    5   -4
## [2,]   -8   -1   33
## [3,]  -17    6   -9

(b = matrix(NA,3,3))

##      [,1] [,2] [,3]
## [1,]   NA   NA   NA
## [2,]   NA   NA   NA
## [3,]   NA   NA   NA

for (i in 1:nrow(a)) {
  for (j in 1:ncol(a)) {
    if(a[i,j]<1) 
      b[i,j] = a[i,j]+20
    else 
      b[i,j] = log(a[i,j])
  }
}
b

##           [,1]      [,2]      [,3]
## [1,]  1.098612  1.609438 16.000000
## [2,] 12.000000 19.000000  3.496508
## [3,]  3.000000  1.791759 11.000000

# b = ifelse(a<1, a[a<1]+20, log(a[!(a<1)]))

Ejercicio 52

suma = 0
k = 1
while (suma<=2000) {
  suma = suma + 2^k
  k = k+1
}
suma; k

## [1] 2046

## [1] 11

sum(2^(1:11))

## [1] 4094

Ejercicio 53

tot = 1000
an = 1
while(tot<50000){
  tot = tot+tot*0.045+1000
  an = an+1
}
tot; an

## [1] 50711.32

## [1] 27

Ejercicio 54

v.res <- function(t) 10^9+10^8*(1-exp(-t/100))-10^7*t
curve(v.res,0,100,xname = 't')
abline(h = 10^9*0.5, col='blue')
abline(v = 54, col='darkgreen')

#### Ejercicio 55

curve((-1)^(x)/((2*(x))+1), from = 0,to = 200)

plot(0,pi/4, xlim = c(0,200), type ='n')
abline(h=pi/4)
for (i in 0:200) {
  y = sum((-1)^(0:i)/((2*(0:i))+1))
  points(i,y, cex = 0.5, pch = 16, col = 'blue')
}

#### Ejercicio 56

A = matrix(c(0,5,10,15,20,
             -8,-4,-1,1,2,
             6,3,1,0,-1),5)
A

##      [,1] [,2] [,3]
## [1,]    0   -8    6
## [2,]    5   -4    3
## [3,]   10   -1    1
## [4,]   15    1    0
## [5,]   20    2   -1

plot(A, type ='n', ylim=c(min(A[,2:3]),max(A[,2:3])),
     xlab = 'tiempo (s)', ylab = 'fuerza (N)')
lines(A[,1],A[,2], col ='blue')
lines(A[,1],A[,3], col ='darkgreen')

#### Ejercicio 57

x = seq(0,1,length.out = 100)
curve(sin(x), col = 'red')
points(x,x, type = 'l')

plot(x,sin(x)-x, type='l')

plot(x,(sin(x)-x)/sin(x), type='l')

#### Ejercicio 58

x = seq(0,2*pi, length.out = 100)
plot(x,tan(2*x), type='l', col = 'red')
points(x, (2*tan(x))/(1-(tan(x))^2), pch = 16, col = 'blue')

#### Ejercicio 59

b = seq(0,1, length.out = 10)[-1]
t = seq(0,100, length.out = 100)
plot(t,1-exp(-b[1]*t), type='l')
for (i in 2:length(b)) {
  text(-0.5,1-exp(-b[i]),i)
  points(t,1-exp(-b[i]*t), type='l', col = 'blue')
}

#### Ejercicio 60

v = seq(20,100)
p = function(v,m)m*286.7*293/v
y = c(p(v,1),p(v,3),p(v,7))
plot(v,p(v,1), type='l', col = 1, ylim=c(min(y),max(y)))
points(v,p(v,3), type='l', col = 2)
points(v,p(v,7), type='l', col = 3)

#### Ejercicio 61

t = c(1:8,10)
s = c(1210,1866,2301,2564,2724,
      2881,2879,2915,3010)
plot(t,s, pch = 16, col = 'red')
# points(t,2000*(1-exp(-0.2*t)), type = 'l', col = 1)
bb = seq(200,3000, length.out = 3)
cc = seq(-1,0, length.out = 3)
for (i in 1:length(bb)) {
  for (j in 1:length(cc)) {
    points(t,bb[i]*(1-exp(cc[j]*t)), type = 'l')
    text(2,bb[i]*(1-exp(cc[j]*2)), paste(bb[i],',',cc[j]))
  }
}
mc = log((1866/1210)-1)
mb = 1210/(2-(1866/1210))
points(t,mb*(1-exp(mc*t)), type = 'l', col = 'blue')

Ejercicios Rstudio

Carlos Rivera Moreno

Ejercicio 1

Ejercicio 2

Ejercicio 3

Ejercicio 4

Ejercicio 5

Ejercicio 6

Ejercicio 7

Ejercicio 8

Ejercicio 9

Ejercicio 10

Ejercicio 11

Ejercicio 14

Ejercicio 15

Ejercicio 16

Ejercicio 17

Ejercicio 18

Ejercicio 19

Ejercicio 20

Ejercicio 21

Ejercicio 22

Ejercicio 23

Ejercicio 24

Ejercicio 25

Ejercicio 26

Ejercicio 27

Ejercicio 28

Ejercicio 29

Ejercicio 30

Ejercicio 31

Ejercicio 32

Ejercicio 33

Ejercicio 34

Ejercicio 35

Ejercicio 36

Ejercicio 37

Ejercicio 38

Ejercicio 39

Ejercicio 42

Ejercicio 43

Ejercicio 44

Ejercicio 45

Ejercicio 46

Ejercicio 47

Ejercicio 48

Ejercicio 49

Ejercicio 50

Ejercicio 51

Ejercicio 52

Ejercicio 53

Ejercicio 54