Lesson 12 Sim City Solidify Understanding

Ready

$A = [\begin{array}{rrr} - 1 & 2 & - 6 \\ 3 & - 1 & 4 \end{array}] B = [\begin{array}{rr} - 6 & 4 \\ - 2 & 3 \\ 1 & - 4 \end{array}] C = [\begin{array}{rrr} 1 & - 3 & 2 \\ - 5 & 4 & - 7 \\ 6 & 3 & - 2 \end{array}] D = [\begin{array}{rrr} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 14 \end{array}]$

1.

Let $k = - 4$ . Find $k A$ .

2.

Find $A B$ , if possible.

3.

Find $C D$ , if possible.

4.

What is another name for matrix $D$ ?

5.

Let $E = [\begin{array}{rr} 1 & 4 \\ 2 & 9 \end{array}]$ and $F = [\begin{array}{rr} 9 & - 4 \\ - 2 & 1 \end{array}]$ . Find $E F$ .

6.

What is the relationship of matrix $F$ to matrix $E$ ?

Set

7.

For student body elections, a school’s statistics class samples $120 students$ and asks them who they will vote for. Of those surveyed, $72 students$ stated if the election were held today, they would vote for Juvenal for student body president. Create an interval of plausible values for the actual proportion of students in the entire school who would vote for Juvenal for president.

8.

If the statistics class were to double the sample size, what would likely happen to the interval of plausible values? Would you expect the interval to increase, decrease, or stay the same? Why?

9.

Based on your interval of plausible values (problem 7), is it likely that Juvenal will win the election? Why or why not?

10.

Suppose the actual proportion of students in the school who would vote for Juvenal is really $p = 0.52$ . If the statistics students were to create a sampling distribution by taking repeated samples of size $120$ and identify the proportion of students who would vote for Juvenal for each sample, what would be the shape, center, and standard deviation of this distribution?

11.

If the actual proportion of students who would vote for Juvenal is really $p = .52$ , what is the probability of taking a sample of $120 students$ and finding that $72$ or more of them would vote for Juvenal?

Go

A boat is being pulled towards a dock by means of a winch located $5 feet$ above the deck of the boat. Let $θ$ be the angle of elevation from the boat to the winch (in radians) and let $r$ be the length of the rope from the winch to the boat.

12.

Write $θ$ as a function of $r$ .

13.

Find $θ$ when $r = 18 ft$ .

14.

Find $θ$ when $r = 35 ft$ .

A spotlight is being set up so that its beam shines directly on the top of a flag pole. The light is located $15 feet$ away from the bottom of the pole.

Solve for $θ$ where $(0 < θ \leq \frac{π}{2})$ .

15.

$θ = \sin^{- 1} (\frac{\sqrt{2}}{2})$

16.

$θ = \cos^{- 1} (\frac{\sqrt{3}}{2})$

17.

$θ = \tan^{- 1} (1)$