August 2016 Common Core Algebra II Regents Part 2

I don't usually post the answers to the Algebra II exam, but I've received enough requests that I've decided to post some of the open-ended questions.

August 2016, Algebra II Part 2

25.The volume of air in a person’s lungs, as the person breathes in and out, can be modeled by a sine graph. A scientist is studying the differences in this volume for people at rest compared to people told to take a deep breath. When examining the graphs, should the scientist focus on the amplitude, period, or midline? Explain your choice.

The scientist should focus on the amplitude because the height of the graph corresponds to the Volume of air in the lungs.

26. Explain how (3^1/5)² can be written as the equivalent radical expression "fifth root of 9".

Look at the illustration below:

The question says "explain" so you MUST include an explanation for full credit. You can't just write an equation.
The exponents can be be switched so you have 3 square to the one-fifth power. Three squared is 9. The one-fifth power is the same as taking the fifth root of the number. So (3^1/5)² is the same as the fifth root of 9.

27. Simplify xi(i - 7i)², where i is the imaginary unit.

Subtract i - 7i to get -6i. Square (-6i) to get 36i². Replace i² with -1, so you have xi(-36). Rewrite as -36xi.

Illustrated below.

to be continued.

Any questions?

Comments, corrections welcome.