Question 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

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

  1. (1,2,3,4,5,6,7,8,7,6,5,4,3,2,1)
c(seq(1,8),seq(7,1))
##  [1] 1 2 3 4 5 6 7 8 7 6 5 4 3 2 1
  1. (1,2,2,3,3,3,4,4,4,4,5,5,5,5,5)
rep(x=seq(1,5),times=seq(1,5))
##  [1] 1 2 2 3 3 3 4 4 4 4 5 5 5 5 5
  1. (5,4,4,3,3,3,2,2,2,2,1,1,1,1,1)
rep(x=seq(5,1),times=seq(1,5))
##  [1] 5 4 4 3 3 3 2 2 2 2 1 1 1 1 1

Question 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 R’s inverse trigonometry functions (asin(), acos(), or atan()), convert these numbers into polar coordinates.

cartesian_coords <- runif(2)
print(cartesian_coords)
## [1] 0.9239772 0.3619797
r <- sqrt(cartesian_coords[1])^2 + (cartesian_coords[2])^2
theta <- atan(cartesian_coords[2]/cartesian_coords[1])
polar_coords <- c(r, theta)
print(polar_coords)
## [1] 1.055006 0.373385

Question 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:

queue <- c("sheep", "fox", "owl", "ant")
  1. the serpent arrives and gets in line;
queue <- c(queue, "serpent")
print(queue)
## [1] "sheep"   "fox"     "owl"     "ant"     "serpent"
  1. the sheep enters the ark;
queue <- queue[-1]
print(queue)
## [1] "fox"     "owl"     "ant"     "serpent"
  1. 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"
  1. the serpent gets impatient and leaves;
queue <- queue[-5]
print(queue)
## [1] "donkey" "fox"    "owl"    "ant"
  1. the owl gets bored and leaves;
queue <- queue[-3]
print(queue)
## [1] "donkey" "fox"    "ant"
  1. the aphid arrives and the ant invites him to cut in line.
queue <- c(queue[1:2], "aphid", queue[3])
print(queue)
## [1] "donkey" "fox"    "aphid"  "ant"
  1. Finally, determine the position of the aphid in the line.
print(length(queue[-1]))
## [1] 3

Question 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.

q5vector <- seq(1,100)
print(which(q5vector%%2 & q5vector%%3 & q5vector%%7))
##  [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