# Lesson 11Music to My EarsPractice Understanding

Recall that the three manipulations we can perform on the equations in a system.

• Replace an equation in the system with a constant multiple of that equation

• Replace an equation in the system with the sum or difference of the two equations

• Replace an equation with the sum of that equation and a multiple of the other

For each combination of matrices, write out the justification that allows you to write the new matrix.

Example: “I replaced the first row of matrix by multiplying the first row by .

## Set

### 5.

Marian works as a trainer for dogs. One of the tricks she has the dogs do is run through an obstacle course. As a prize for running the course successfully, she gives them a treat at the end. She is wondering if the type of treat will impact how fast the dogs get through the course. To test this, she randomly separates her into groups of and times how many seconds it takes to race through the course to get the treat at the end. The results are given below.

Group A

 $37$ $39$ $45$ $42$ $40$

Group B

 $35$ $43$ $34$ $37$ $39$

Is there convincing evidence the type of treat at the end of the course impacts the times of the dogs? Design and carry out a simulation to answer this question.

## Go

### 6.

Fill in the blanks to complete the definition of the inverse sine function.

The equation means “find the , on the interval , such that .”

### 7.

Sketch a graph of .

### 8.

Explain why the range of the inverse sine function is .

### 9.

Explain why the range of the inverse cosine function is .

### 10.

Sketch a graph of .

### 11.

Sketch the graph of . Sketch in your asymptotes with dotted lines.

### 12.

Sketch a graph of .