Homework 4

1. Suppose x=1.1, a=2.2, and b=3.3. Assign each expression to the value of the variable z and print the value stored in z.

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

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

## [1] 3.61714

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

## [1] 1.997611

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

## [1] 7.413

2. Using the rep and seq functions, create the following vectors:

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

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

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

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

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

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

3. Create a vector of two random uniform numbers. In a spatial map, these can be interpreted as x and y coordinates that give the location of an individual (such as a marked forest tree in a plot that has been mapped). Using one of Rs inverse trigonometry functions (asin(), acos(), or atan()) convert these numbers into polar coordinates.

point <- runif(2)
print(point)

## [1] 0.1332241 0.7335557

r <- (point[1]^2 + point[2]^2)^(1/2)
print(r)

## [1] 0.7455553

theta <- atan(point[2]/point[1])
print(theta)

## [1] 1.39114

4. Create a vector queue <- c("sheep", "fox", "owl", "ant") where queue represents the animals that are lined up to enter Noah’s Ark, with the sheep at the front of the line. Using R expressions, update queue as: the serpent arrives and gets in line; the sheep enters the ark; the donkey arrives and talks his way to the front of the line; the serpent gets impatient and leaves; the owl gets bored and leaves; the aphid arrives and the ant invites him to cut in line. Finally, determine the position of the aphid in the line.

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

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

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

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

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

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

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

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

queue <- queue[-c(5)]
print(queue)

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

queue <- queue[-c(3)]
print(queue)

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

queue <- c(queue[1:2], "aphid", queue[3])
print(queue)

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

The aphid is third in line.

5. Use R to create a vector of all of the integers from 1 to 100 that are not divisible by 2, 3, or 7.

vector <- 1:100
vector <- which((vector %% 2) != 0 & (vector %% 3) != 0 & (vector %% 7 != 0))
print(vector)

##  [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