---
title: "Ch 1 Practice: Example homework"
author: "YOUR NAME HERE"
output: pdf_document
---
Each question asks you to write some code, some will also ask you to answer a question or write some math. Write your answer in a full complete sentence with reasonably acceptable grammar. Knit this file to PDF after each question. 

# 1. Let `x <- c(1,2,3)` and `y <- c(6,5,4)`. Explain the math that is happening to the numbers when you run each of the following statements.

```{r}

```

## a) $x^2$

```{r}

```

Delete this line and put your answer here. Notice there is a blank line both before this answer and after. 

## b) $xy$

```{r}

```



## c) $x_1y_2$

```{r}

```


\newpage

# 2. What is the sum of the squares of all numbers from 1 to 100 (e.g. $1^{2}+2^{2}+\cdots +100^{2}$)?

```{r}

```

\newpage

# 3. What is the sum of the first 100 positive integers? The formula for the sum of integers 1 through $n$ is $\frac{n(n+1)}{2}$.

*Hint: Define* $n=100$ and then use R to compute the sum of 1 through 100 using the formula.

```{r}

```

\newpage

# 4. Graph the function $f(p) = p(1-p)$ where $p$ is a continuous number between 0 and 1.

```{r}

```

\newpage

# 5. Switch to the visual editor for the next few questions.

## a. Insert a picture that you find inspiring


## b. Write an equation using both display math, and inline math. You can google 


## c. Insert a code chunk and do some math. 
