Note: There were no math problems for Monday 10/5/26.

Question 1

Compute \(\int \frac{\sec^2(3x)}{1 + \tan(3x)} \space dx\) for a transformed variable in a model.

# install.packages(c("ggformula","mosaicCalc"))
library(ggformula)
## Warning: package 'ggformula' was built under R version 4.5.2
## Loading required package: ggplot2
## Loading required package: scales
## Loading required package: ggiraph
## Warning: package 'ggiraph' was built under R version 4.5.2
## Loading required package: ggridges
## Warning: package 'ggridges' was built under R version 4.5.2
## 
## New to ggformula?  Try the tutorials: 
##  learnr::run_tutorial("introduction", package = "ggformula")
##  learnr::run_tutorial("refining", package = "ggformula")
library(mosaicCalc)
## Warning: package 'mosaicCalc' was built under R version 4.5.2
## Registered S3 method overwritten by 'mosaic':
##   method                           from   
##   fortify.SpatialPolygonsDataFrame ggplot2
## 
## Attaching package: 'mosaicCalc'
## The following object is masked from 'package:stats':
## 
##     D
f <- makeFun((1 / (cos(3 * x))^2) / (1 + tan(3 * x)) ~ x)
anti_f <- antiD(f(x) ~ x)
anti_f
## function (x, C = 0) 
## {
##     F <- makeF((1/(cos(3 * x))^2)/(1 + tan(3 * x)))
##     evalFun(F, x = x, .const = C)
## }
## <environment: 0x000001551766ee00>

Question 2

A growth model is \(P(t) = 4(t^3 - 2t)\). What is \(P''(t)\)?

# install.packages("Deriv")
library(Deriv)
P <- function(t) {
  4 * (t^3 - 2 * t)
}
P_prime <- Deriv(P)
P_double_prime <- Deriv(P_prime)
P_double_prime
## function (t) 
## 24 * t

Question 3

Write the number 32 in words.

# install.packages("english")
library(english)
## Warning: package 'english' was built under R version 4.5.2
## 
## Attaching package: 'english'
## The following object is masked from 'package:scales':
## 
##     ordinal
words(32)
## [1] "thirty-two"

Question 4

Create a magic square of size 10.

# install.packages("pracma")
library(pracma)
## 
## Attaching package: 'pracma'
## The following objects are masked from 'package:Matrix':
## 
##     expm, lu, tril, triu
magic(n = 10)
##       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
##  [1,]   92   99    1    8   15   67   74   51   58    40
##  [2,]   98   80    7   14   16   73   55   57   64    41
##  [3,]    4   81   88   20   22   54   56   63   70    47
##  [4,]   85   87   19   21    3   60   62   69   71    28
##  [5,]   86   93   25    2    9   61   68   75   52    34
##  [6,]   17   24   76   83   90   42   49   26   33    65
##  [7,]   23    5   82   89   91   48   30   32   39    66
##  [8,]   79    6   13   95   97   29   31   38   45    72
##  [9,]   10   12   94   96   78   35   37   44   46    53
## [10,]   11   18  100   77   84   36   43   50   27    59