Homework4

#1 Assign values to variables

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

Compute each expr4ession and store it in z Expression 1:

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

## [1] 3.61714

Expression 2:

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

## [1] 1.997611

Expression 3:

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

## [1] 7.413

#2 Vector 1:

vec1 <- c(seq(1,8,1), seq(7,1,-1))
print(vec1)

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

Vector 2:

vec2 <- rep(1:5, times = 1:5)
print(vec2)

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

Vector 3:

vec3 <- rep(5:1, times = 1:5)
print(vec3)

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

#3 Generate 2 random uniform numbers (x,y) between 0 and 1

set.seed(42) #setting for reproducibility
coords <- runif(2, min=0, max=1)
x <- coords[1]
y <- coords[2]

Convert to polar coordinates (r, theta)

r <- sqrt(x^2 + y^2) #compute radius
theta <- atan2(y,x) #compute angle in radians

Print results

cat("Caresian Coordinates: (x,y) =", x, y, "\n")

## Caresian Coordinates: (x,y) = 0.914806 0.9370754

cat("Polar Coordinates: (r, theta) =", r, theta, "\n")

## Polar Coordinates: (r, theta) = 1.309573 0.7974229

#4 Initial queue

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

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

1. The serpent arrives and gets in line

queue <- c(queue, "serpent")
print(queue)

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

2. The sheep enters the ark (remove first element)

queue <- queue[-1]
print(queue)

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

3. The donkey arrives and talks his way to the front of the line

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

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

4. The serpent gets impatient and leaves

queue <- queue[queue != "serpent"]
print(queue)

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

5. The owel gets board and leaves

queue <- queue[queue != "owl"]
print(queue)

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

6. The aphid arrives, and the ant invites him to cut in line (aphid before ant)

queue <- append(queue, "aphid", after = match("ant", queue) -1)
print(queue)

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

7. Determine the position of aphid

aphid_position <- match("aphid", queue)
cat("The aphid is at position:", aphid_position, "\n")

## The aphid is at position: 3

#5 Generate sequence from 1 to 100

numbers <- 1:100

apply filtering condiiton

filtered_numbers <- numbers[numbers %% 2 != 0 & numbers %% 3 != 0 & numbers %% 7 != 0]

Print each condition’s TRUE/FALSE values

print(filtered_numbers)

##  [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