Problem 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

Problem 2

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

a <- c(seq(from = 1, to = 8),seq(from = 7, to = 1))
print(a)
##  [1] 1 2 3 4 5 6 7 8 7 6 5 4 3 2 1
b <- rep(1:5, c(1,2,3,4,5))
print(b)
##  [1] 1 2 2 3 3 3 4 4 4 4 5 5 5 5 5
c <- rep(5:1, c(1,2,3,4,5))
print(c)
##  [1] 5 4 4 3 3 3 2 2 2 2 1 1 1 1 1

Problem 3

Create a vector of two random uniform number. 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

xy <- runif(2)
theta = atan(xy[2]/xy[1])
r = (xy[2]^2 + xy[1]^2)^0.5

Problem 4

#start: animals lined up to enter Noah’s Ark
queue <- c("sheep", "fox", "owl", "ant")
print(queue)
## [1] "sheep" "fox"   "owl"   "ant"
#a: the serpent arrives and gets in line 
queue <- c(queue,"serpent")
print(queue)
## [1] "sheep"   "fox"     "owl"     "ant"     "serpent"
#b: the sheep enters the ark 
queue <- queue[! queue %in% c('sheep')]
print(queue)
## [1] "fox"     "owl"     "ant"     "serpent"
#c: the donkey arrives and talks his way to the front of the line;
queue <- append(queue, "donkey", after = 0)
print(queue)
## [1] "donkey"  "fox"     "owl"     "ant"     "serpent"
#d: the serpent gets impatient and leaves;
queue <- queue[! queue %in% c('serpent')]
print(queue)
## [1] "donkey" "fox"    "owl"    "ant"
#e: the owl gets bored and leaves;
queue <- queue[! queue %in% c('owl')]
print(queue)
## [1] "donkey" "fox"    "ant"
#f: the aphid arrives and the ant invites him to cut in line.
queue <- append(queue, "aphid", after = 2)
print(queue)
## [1] "donkey" "fox"    "aphid"  "ant"
#g:Finally, determine the position of the aphid in the line.
which(queue == "aphid")
## [1] 3

Problem 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.

odd <- c(seq(from = 1, to = 100))
integers <- which(odd%%2 != 0 & odd%%3 !=0 & odd%%7 !=0)
print(integers)
##  [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