Hi,

I already have the answers for the 3 problems, need to show stepwise solutions of how to arrive at the answers. All the details are in the attachments.

Thanks

Scene #1

Burj Khalifa –- Dubai, United Arab Emirates

Polly No-Meal went through all 163 floors of the world’s tallest building and stole the toilet

paper from every restroom. At this time, it is unclear to investigators how this will aid in the

World Conquering Device.

Here we are in one of the world’s most under-the-radar

countries, UAE. Although I have certain items I must steal, I

plan to explore this jewel and overwhelm you with advanced

math puzzles! I am kicking things off with fireworks atop the

world’s tallest building. You will need this formula:

1

ℎ = − 𝑔𝑡 ! + 𝑣” 𝑡 + ℎ”

2

where h is the current height, g is the acceleration due to

gravity (9. 8 m/s2), 𝑣! is the initial velocity, and ℎ! is the initial

height.

Fireworks are launched from atop Burj Khalifa, which is 830 m

tall, with an initial velocity of 68 m/s. Find the maximum height

of the fireworks and round to the nearest meter. This will be

equal to i.

i = ____

Scene #2

Jumeirah Archaeological Site –- Dubai, United Arab Emirates

Disguised as Indiana Jones, No-Meal snuck past a security fence and stole unearthed coin fragments.

After my archaeology dig I’m ready for everyone’s favorite game! I call it the “You Must

Understand Polynomials to Find My Coin” Game. And off we go with our 4 clues…

1. The degree of my polynomial is odd.

2. The lim 𝑓(𝑥) = ∞ and lim 𝑓(𝑥) = −∞

“→$

“→%$

…but my variable is not x.

3. My polynomial has only one real root.

4. My polynomial has a local maximum at x = -0.296…

but the variable is not x.

The variable used on the coin that meets these

requirements is equal to 10.

____ = 10

© Clark Creative Education

Scene #3

Dubai Aquarium — Dubai, United Arab Emirates

Dubai’s famous Aquarium and Underwater Zoo was robbed by a rogue scuba diver. A sand

tiger shark was lifted from the tank and investigators later found this note attached to a

stingray.

Inside one of the largest malls in the world, I came across the largest indoor aquarium! These

types of fish like to eat real roots. Not imaginary roots. Not synthetic roots. Real roots of

polynomials. You’ll find their favorite root is already on the hook. Use synthetic division to

find out which real roots will be available for the fish to eat. (CAUTION: A root may have a

multiplicity greater than 1)

The Aquarium

-3

x – 1 x7 – 13×6 – 3×5 + 295×4 + 515×3 – 39×2 – 513x – 243

-1

3

How many fish baits are real roots of this polynomial?

9

One

t=1

Two

a=2

Three

m=3

© Clark Creative Education

1.Here we are in one of the world’s most under-the-radar countries, UAE. Although I have certain items I

must steal, I plan to explore this jewel and overwhelm you with advanced math puzzles! I am kicking

things off with fireworks atop the world’s tallest building. You will need this formula: ℎ = − 1/2 gt2 +

v0t+h0 where h is the current height, g is the acceleration due to gravity (9. 8 m/s2), v0 is the initial

velocity, and ℎ0 is the initial height. Fireworks are launched from atop Burj Khalifa, which is 830 m tall,

with an initial velocity of 68 m/s. Find the maximum height of the fireworks and round to the nearest

meter. This will be equal to i.

i = 1,066

2. 1. The degree of my polynomial is odd. 2. The lim f(x) = ∞ and lim f(x) = −∞ …but my variable is not x.

3. My polynomial has only one real root.

4. My polynomial has a local maximum at x = -0.296… but the variable is not x. The variable used on the

coin that meets these requirements is equal to 10

T=10

3. Inside one of the largest malls in the world, I came across the largest indoor aquarium! These types of

fish like to eat real roots. Not imaginary roots. Not synthetic roots. Real roots of polynomials. You’ll find

their favorite root is already on the hook. Use synthetic division to find out which real roots will be

available for the fish to eat. (CAUTION: A root may have a multiplicity greater than 1)

x – 1 x7 – 13×6 – 3×5 + 295×4 + 515×3 – 39×2 – 513x – 243

Three- M=3