Algebra Polynomials Degree & Calculus Questions

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