Problem 1

#a.

x = 1.1
a = 2.2 
b = 3.3
z=x ^ (a^b)
print(z)
## [1] 3.61714
# result of z was 3.61714012551594

#b

x = 1.1
a = 2.2 
b = 3.3
z=(x^a) ^ b
print(z)
## [1] 1.997611

#c.

x = 1.1
a = 2.2 
b = 3.3
z= 3*(x^3) + 2*(x^2) + 1
print(z)
## [1] 7.413

Problem 2 #a

vector_a<-c(1:8,7:1)
print(vector_a)
##  [1] 1 2 3 4 5 6 7 8 7 6 5 4 3 2 1

#b

vector_b <- rep(x=1:5,times=1:5)
print(vector_b)
##  [1] 1 2 2 3 3 3 4 4 4 4 5 5 5 5 5
vector_c <- rep(x=5:1,times=1:5)
print(vector_c)
##  [1] 5 4 4 3 3 3 2 2 2 2 1 1 1 1 1

Problem 3

library(ggplot2) 
set.seed(2)
z <- runif(2) 
qplot(x=z)
## Warning: `qplot()` was deprecated in ggplot2 3.4.0.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

x=0.185
y=0.701
r= sqrt(x^2+y^2)
print(r)
## [1] 0.7250007
theta=atan(y/x)
print(theta)
## [1] 1.312771

#observation that tan^1=atan function

Problem 4

General set up of the queue

queue <- c("sheep", "fox", "owl", "ant")
z2 <- c("sheep"=1, "fox"=2, "owl"=3, "ant"=4)

print(z2)
## sheep   fox   owl   ant 
##     1     2     3     4

#a

queue <- c("sheep", "fox", "owl", "ant", "serpent")
z2 <- c("sheep"=1, "fox"=2, "owl"=3, "ant"=4, "serpent"=5 )
print(z2)
##   sheep     fox     owl     ant serpent 
##       1       2       3       4       5

#b

z2 <- c("fox"=1, "owl"=2,  "ant"=3, "serpent"=4 )
print(z2)
##     fox     owl     ant serpent 
##       1       2       3       4

#c

z2 <- c("donkey"=1, "fox"=2, "owl"=3, "ant"=4, "serpent"=5 )
print(z2)
##  donkey     fox     owl     ant serpent 
##       1       2       3       4       5

#d

z2 <- c("donkey"=1, "fox"=2, "ant"=3)
print(z2)
## donkey    fox    ant 
##      1      2      3

#e

z2 <- c("sheep"=1, "fox"=2, "ant"=3, "serpent"=4 )
print(z2)
##   sheep     fox     ant serpent 
##       1       2       3       4

#f

z2 <- c("sheep"=1, "fox"=2, "aphid"=3, "ant"=4, "serpent"=5 )
print(z2)
##   sheep     fox   aphid     ant serpent 
##       1       2       3       4       5

#g

# Third position

Problem 5.

x<-1:100
which(x%%2!=0 & x%%3!=0 & x%%7!=0)
##  [1]  1  5 11 13 17 19 23 25 29 31 37 41 43 47 53 55 59 61 65 67 71 73 79 83 85
## [26] 89 95 97