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1. This is question 1!

x <- 1.1 #Define variable
a <- 2.2
b <- 3.3
z <- x^(a^b) #run first equation
print(z) #print result
## [1] 3.61714
z <- (x^a)^b # run second equation
print(z)
## [1] 1.997611
z <- 3*x^3 +2*x^2 + 1 # run third equation
print(z)
## [1] 7.413

2. This is question 2!

v1 <- c(1:8, seq(7,1)) # set first vector
print(v1)
##  [1] 1 2 3 4 5 6 7 8 7 6 5 4 3 2 1
v2 <- rep(1:5, seq(1,5)) # set second vector
print(v2)
##  [1] 1 2 2 3 3 3 4 4 4 4 5 5 5 5 5
v3 <- rep(5:1, seq(1,5)) # set third vector
print(v3)
##  [1] 5 4 4 3 3 3 2 2 2 2 1 1 1 1 1

3. This is question 3!

vector <- runif(2) #create cartesian coordinate
x = vector[1] #isolate X coordinate
y = vector[2] # isolate y coordinate
print(x) #print coordinates
## [1] 0.6007011
print(y)
## [1] 0.058782
r = sqrt(x^2+y^2) #calculate r value for polar coordinates
theta = atan(y/x) # calculate angle value for polar coordinates
print(r) # print results
## [1] 0.6035703
print(theta)
## [1] 0.09754509

4. This is question 4!

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

# a. the serpent arrives and gets in line
queue <- c(queue, "serpent") # add serpent
print(queue)
## [1] "sheep"   "fox"     "owl"     "ant"     "serpent"
# b the sheep enters the ark
queue <- queue[-which(queue=="sheep")] #sheep  enters ark
print(queue)
## [1] "fox"     "owl"     "ant"     "serpent"
# c the donkey arrives and talks his way to the front of the line
queue <- c("donkey", queue) # donkey cuts line
print(queue)
## [1] "donkey"  "fox"     "owl"     "ant"     "serpent"
# d the serpent gets impatient and leaves
queue <- queue[-which(queue=="serpent")]
print(queue)
## [1] "donkey" "fox"    "owl"    "ant"
#e the owl gets bored and leaves
queue <- queue[-which(queue=="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 = which(queue=="ant")-1)
print(queue)
## [1] "donkey" "fox"    "aphid"  "ant"
#g Finally, determine the position of the aphid in the line
which(queue=="aphid")
## [1] 3

5. This is question 5!

q5 <- c(1:100) #set q5 to all integers 1-100
print(q5)
##   [1]   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15  16  17  18
##  [19]  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36
##  [37]  37  38  39  40  41  42  43  44  45  46  47  48  49  50  51  52  53  54
##  [55]  55  56  57  58  59  60  61  62  63  64  65  66  67  68  69  70  71  72
##  [73]  73  74  75  76  77  78  79  80  81  82  83  84  85  86  87  88  89  90
##  [91]  91  92  93  94  95  96  97  98  99 100
q5 <- q5[q5%%2!=0 & q5%%3!=0 & q5%%7!=0] #only select numbers that are not divisible by 2, 3, or 7
print(q5)                    
##  [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