# Lesson 9Summing Up Sand CastlesSolidify Understanding

The height of an arrow shot upward from the earth’s surface at an initial velocity of can be modeled by the function .

### 1.

Calculate the number of seconds the arrow will be in the air.

### 2.

If you used completing the square on to find the elapsed time in problem 1, your work would have looked something like this:

Use to explain why the maximum height of the arrow is meters and the height was attained at seconds.

Use the following information for problems 3–5.

The height of an arrow shot upward from the earth’s surface at an initial velocity of can be modeled by the function .

1. Calculate the number of seconds the arrow will be in the air for the given velocity.

2. Use completing the square to find the maximum height of the arrow and the time it takes to reach its maximum.

### 3.

#### a.

Calculate the number of seconds the arrow will be in the air.

#### b.

Use completing the square to find the maximum height of the arrow and the time it takes to reach its maximum.

### 4.

#### a.

Calculate the number of seconds the arrow will be in the air.

#### b.

Use completing the square to find the maximum height of the arrow and the time it takes to reach its maximum.

### 5.

#### a.

Calculate the number of seconds the arrow will be in the air.

#### b.

Use completing the square to find the maximum height of the arrow and the time it takes to reach its maximum.

## Set

For each of the following:

1. Write out the sum of terms represented by the notation.

2. Use the formula you derived in class today for the sum of a geometric series to find the total of the sum of terms without adding each term individually.

### 6.

#### a.

Write out the sum of terms represented by the notation.

#### b.

Use the formula you derived in class today for the sum of a geometric series to find the total of the sum of terms without adding each term individually.

### 7.

#### a.

Write out the sum of terms represented by the notation.

#### b.

Use the formula you derived in class today for the sum of a geometric series to find the total of the sum of terms without adding each term individually.

### 8.

#### a.

Write out the sum of terms represented by the notation.

#### b.

Use the formula you derived in class today for the sum of a geometric series to find the total of the sum of terms without adding each term individually.

### 9.

#### a.

Write out the sum of terms represented by the notation.

#### b.

Use the formula you derived in class today for the sum of a geometric series to find the total of the sum of terms without adding each term individually.

### 10.

#### a.

Write out the sum of terms represented by the notation.

#### b.

Use the formula you derived in class today for the sum of a geometric series to find the total of the sum of terms without adding each term individually.

### 11.

Based on problems , estimate the sum of this geometric series:

## Go

Prove the following.

Prove

Given: bisects

### 13.

Prove

Given: and bisects

Prove

Prove