Homework 4

Question 1

x <- 1.1
a <- 2.2
b <- 3.3

#Part a 
z <- x^(a^b)
print (z)

## [1] 3.61714

#Part b 
z <- (x^a)^b
print(z)

## [1] 1.997611

#Part c
z <- 3*(x^3)+ 2*(x^2)+1
print(z)

## [1] 7.413

Question 2

#Part a
my_vec <- c(1:8,7:1)
print(my_vec) 

##  [1] 1 2 3 4 5 6 7 8 7 6 5 4 3 2 1

#Part b
my_vec <- c(1:5)
rep(x=my_vec,times=my_vec)

##  [1] 1 2 2 3 3 3 4 4 4 4 5 5 5 5 5

#Part c
my_vec <- c(5:1)
my_vec1 <- c(1:5)
rep(x=my_vec,times=my_vec1)

##  [1] 5 4 4 3 3 3 2 2 2 2 1 1 1 1 1

Question 3

x <- runif(1)
y <- runif(1)
r <- tan(y/x)
theta <- asin(y/r)
polar <- c(r,theta)
print(polar)

## [1] 0.1810562 0.3594020

Question 4

queue <-c("sheep","fox","owl","ant")

#Part a
queue <- c(queue, "serpent")
print(queue)

## [1] "sheep"   "fox"     "owl"     "ant"     "serpent"

#Part b 
queue <- queue[-1]
print(queue)

## [1] "fox"     "owl"     "ant"     "serpent"

#Part c
queue <- c("donkey",queue)
print(queue)

## [1] "donkey"  "fox"     "owl"     "ant"     "serpent"

#Part d
queue <- queue[-length(queue)]
print(queue)

## [1] "donkey" "fox"    "owl"    "ant"

#Part e
queue <- queue[-3]
print(queue)

## [1] "donkey" "fox"    "ant"

#Part f
queue <- c(queue[2],"aphid",queue[3])
print(queue)

## [1] "fox"   "aphid" "ant"

#Part g
aphid_pos <- which(queue == "aphid")
print(aphid_pos)

## [1] 2

Question 5

numbers <- 1:100
my_vec <- numbers[!(numbers %% 2 == 0 | numbers %% 3 == 0 | numbers %% 7 == 0)]
print(my_vec)

##  [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