Question 1

A signal is modeled by \(y(t) = te^{2t}\). What is \(y'(t)\)?

# install.packages("Deriv")
library(Deriv)
y <- function(t) {
  t * exp(2 * t)
}
y_prime <- Deriv(y)
y_prime
## function (t) 
## {
##     .e1 <- 2 * t
##     (1 + .e1) * exp(.e1)
## }

Question 2

What is the least common multiple of 12 and 20?

# install.packages("pracma")
library(pracma)
Lcm(a = 12,b = 20)
## [1] 60

Question 3

Which one of the following cannot be the size of a power set?

A. 32

B. 256

C. 502

D. 2048

Note: A power set always has \(2^n\) elements.

# install.packages("tidyverse")
library(tidyverse)
## Warning: package 'lubridate' was built under R version 4.5.2
## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ dplyr     1.1.4     ✔ readr     2.1.5
## ✔ forcats   1.0.1     ✔ stringr   1.5.2
## ✔ ggplot2   4.0.0     ✔ tibble    3.3.0
## ✔ lubridate 1.9.4     ✔ tidyr     1.3.1
## ✔ purrr     1.1.0     
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ purrr::cross()  masks pracma::cross()
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag()    masks stats::lag()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors
q3_data <- data.frame(Choice = LETTERS[1:4],
                      Number = c(32,256,502,2048))
correct_answer <- q3_data %>%
  mutate(Is_Power_Two = Number > 0 & bitwAnd(Number,Number - 1) == 0) %>% # checking for power two
  filter(Is_Power_Two == FALSE) %>%
  pull(Choice)
cat("The correct answer is:",correct_answer,"\n")
## The correct answer is: C