# Chapter 3 Another Chapter

## 3.1 Generating Theorem Environments Using Pandoc Fence Code Blocks

Bookdown has a lua filter called “latex-div.lua” which handles theorem environments for latex.

If $$c$$ denotes the length of the hypotenuse and $$a$$ and $$b$$ denote the lengths of the other two sides, the Pythagorean theorem can be expressed as the Pythagorean equation: $a^2+b^2=c^2.$

If $$c$$ denotes the length of the hypotenuse and $$a$$ and $$b$$ denote the lengths of the other two sides, the Pythagorean theorem can be expressed as the Pythagorean equation: $a^2+b^2=c^2.$

If $$c$$ denotes the length of the hypotenuse and $$a$$ and $$b$$ denote the lengths of the other two sides, the Pythagorean theorem can be expressed as the Pythagorean equation: $a^2+b^2=c^2.$

For any angle $$\theta$$, we have $\sin^2\theta+\cos^2\theta=1$

For any angle $$\theta$$, we have $\sin^2\theta+\cos^2\theta=1$

For any angle $$\theta$$, we have $\sin^2\theta+\cos^2\theta=1$

By ??, we know that …. ??

Pandoc use ::: {#Id .Div_attributes} to start and ::: to end a Div block. Such a block can be converted to LaTeX environment using lua.

Let $$f$$ be a function differentiable over $$(a, b)$$. If $$f'(x)>0$$ for any $$x$$ in $$(a, b)$$, then $$f(a)<f(x)<f(b)$$\$ for any $$x$$ in $$(a,b)$$.

Find the hypotenuose for the right triangle whose legs are 4 and 3.

By ??, the hypothenuose is $\sqrt{3^2+4^2}=5.$

## 3.2 Practice

Simplify. Write with positive exponents.

1. $$(3a^2b^3c^2)(4abc^2)(2b^2c^3)$$
2. $$\dfrac{4y^3z^0}{x^2y^2}$$
3. $$(-2)^{-3}$$