Lesson 14 Music to My Ears Practice Understanding

Ready

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 $A$ by multiplying the first row by $\frac{1}{6}$ .”

$\begin{matrix} A \\ [\begin{matrix} 6 & 6 & 45.00 \\ 3 & 2 & 19.00 \end{matrix}] \end{matrix} ⟹ \begin{matrix} B \\ [\begin{matrix} 1 & 1 & 7.50 \\ 3 & 2 & 19.00 \end{matrix}] \end{matrix}$

1.

$[\begin{matrix} - 5 & 2 & 9 \\ 10 & 4 & 8 \end{matrix}] ⟹ [\begin{matrix} - 15 & 6 & 27 \\ 30 & 12 & 24 \end{matrix}]$

2.

$[\begin{matrix} 8 & 12 & 5 \\ 1 & - 6 & 2 \end{matrix}] ⟹ [\begin{matrix} 10 & 0 & 9 \\ 1 & - 6 & 2 \end{matrix}]$

3.

$[\begin{matrix} 1 & 2 & 5 \\ 1 & 4 & 10 \end{matrix}] ⟹ [\begin{matrix} 1 & 2 & 5 \\ 0 & 2 & 5 \end{matrix}]$

4.

$[\begin{matrix} 16 & 22 & 19 \\ 10 & 44 & 38 \end{matrix}] ⟹ [\begin{matrix} 16 & 22 & 19 \\ 11 & 0 & 0 \end{matrix}]$

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 $10 dogs$ into $2$ groups of $5$ 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 $y = \sin^{- 1} x$ means “find the , on the interval , such that $\sin y =$ .”

7.

Sketch a graph of $y = \sin^{- 1} x$ .

8.

Explain why the range of the inverse sine function is $- \frac{π}{2} \leq x \leq \frac{π}{2}$ .

9.

Explain why the range of the inverse cosine function is $[0, π]$ .

10.

Sketch a graph of $y = \cos^{- 1} x$ .

11.

Sketch the graph of $y = \tan x$ . Sketch in your asymptotes with dotted lines.

12.

Sketch a graph of $y = \tan^{- 1} x$ .