Math Problems 6/24/26

Question 1

Write the number 689 in words.

# install.packages("english")
library(english)

## Warning: package 'english' was built under R version 4.5.2

Words(x = 689)

## [1] "Six hundred eighty-nine"

Question 2

What is \(\int \sin(x) \cos(x)\)?

# 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

## 
## Attaching package: 'scales'

## The following object is masked from 'package:english':
## 
##     ordinal

## 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(sin(x) * cos(x) ~ x)
anti_f <- antiD(f(x) ~ x)
anti_f

## function (x, C = 0) 
## C - cos(-2 * x)/4