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.

xab

(xa)b

3x^3 + 2x^2 +1

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

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

(1,2,3,4,5,6,7,8,7,6,5,4,3,2,1) (1,2,2,3,3,3,4,4,4,4,5,5,5,5,5) (5,4,4,3,3,3,2,2,2,2,1,1,1,1,1)

y<- seq(from = 1, to = 8, by = 1)
a <-seq(from = 7, to = 1, by = -1)
z <- c(y,a)

print(z)
##  [1] 1 2 3 4 5 6 7 8 7 6 5 4 3 2 1
y <- seq(1:5)

d <- rep(y , time=y)

print(d)
##  [1] 1 2 2 3 3 3 4 4 4 4 5 5 5 5 5
d <- rep(rev(y) , time=y)

print (d)
##  [1] 5 4 4 3 3 3 2 2 2 2 1 1 1 1 1

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

x <- 5 #Set x coordinate
y <- 105 #Set y coordinate
Cartesian <- c(x,y)

print(Cartesian)
## [1]   5 105
r <- sqrt((x^2) +(y^2)) # Find r
Theta <- acos(x/r)

Polar <- c(r,Theta)


print(Polar)
## [1] 105.118980   1.523213

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 <- c(queue[2:5])
print(queue)
## [1] "fox"     "owl"     "ant"     "serpent"
queue <- c("donkey", queue [1:4])
print(queue)
## [1] "donkey"  "fox"     "owl"     "ant"     "serpent"
queue <- c(queue [1:4])
print(queue)
## [1] "donkey" "fox"    "owl"    "ant"
queue <- c(queue [1:2], queue [4])
queue <- c(queue[1:2], "aphid", queue [3])
print(queue)
## [1] "donkey" "fox"    "aphid"  "ant"
print (which( "aphid" == queue))
## [1] 3

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

a <- 1:100

b <- which((a%%2!=0) & (a%%3!=0) & (a%%7!=0))
print(b)
##  [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