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^ab
(xa)^b
3x^3+2x2+1

x = 1
a = 2.2
b = 3.3

z = x^a^b
print(z)

## [1] 1

z = (x^a)^b
print(z)

## [1] 1

z = 3*(x^3) + 2*(x^2) + 1
print(z)

## [1] 6

Problem 2

**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)**

s = c((seq(from=1,to=8)), (seq(from=7,to=1)))
print(s)

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

s = c(rep(1,1),rep(2,2),rep(3,3),rep(4,4),rep(5,5))
print(s)

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

s = c(rep(5,1),rep(4,2),rep(3,3),rep(2,4),rep(1,5))
print(s)

##  [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 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.

n = c(runif(2))
print(n)

## [1] 0.7273111 0.6777043

y = atan(n[2]/n[1])
print(y)

## [1] 0.7501059

x = sqrt((n[1]^2)+(n[2]^2))
print(x)

## [1] 0.994115

x=r, y=theta

Problem 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 = append(queue, "serpent")
print(queue)

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

queue = queue[-1]
print(queue)

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

queue = append(queue, "donkey", after = 0)
print(queue)

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

queue = queue[-5]
print(queue)

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

queue = queue[-3]
print(queue)

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

queue = append(queue, "aphid", after = 2)
print(queue)

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

The aphid is 3rd in line!

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.

v = c(seq(from=1,to=100,by=1))

v2 = which(v %% 3 != 0 & v %% 7 != 0 & v %%  2 != 0)

print(v2)

##  [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