5.39.3 Can you answer these questions?

5.39.3.1 Badness: why 100. z ^3 instead of 100 z^2?

https://tex.stackexchange.com/landing/r/digest?cta=question&id=517643

As written here on page 158, the badness penalty is 100|z|^3 instead of 100z^2. Why is "3" in the exponent when we take the absolute value of z? 
Here z=(L-w)/w^+, where L is the required width and w  ... 
[tex-core] [badness]
 

asked by user2925716 https://tex.stackexchange.com/landing/r/digest?cta=user&id=171927 1 vote

5.39.3.2 Why are parentheses needed in this TikZ calculation?

https://tex.stackexchange.com/landing/r/digest?cta=question&id=518194

I am creating a multi-page PDF with TikZ that will be used for an animation. While doing so, I get this error: 
! Missing number, treated as zero. 
<to be read again> 
Here is a minimal working  ... 
[tikz-pgf]
 

asked by Erdrick https://tex.stackexchange.com/landing/r/digest?cta=user&id=153908 1 vote

5.39.3.3 Enable hyphenated word breaking

https://tex.stackexchange.com/landing/r/digest?cta=question&id=517921

When I compile my LaTeX file to produce pdf, the word breaking is not happening. Instead the complete word moves to the next line and extra spaces are inserted between the words in the current line.  ... 
[line-breaking]
 

asked by Nagabhushan S N https://tex.stackexchange.com/landing/r/digest?cta=user&id=178369 1 vote