June 22, 20XX
As many of us were provided with rooms as guests at Princess Peach's castle, I decided to explore this majestic historical foundation from this futuristic era's planet.
There were more memorabilia and advertisements on the halls' walls with lots of key sentences and quotes that popped out to me in where I wish to inquire more about it:
"Players can choose to play different Game & Watch games, such as "Fire," "Octopus," "Oil Panic," and more. Each game has its own set of objectives and challenges that players must complete to earn high scores. The game also introduces new characters and features multiplayer modes where players can compete against each other!"
"Mario as he embarks on a quest to rescue Princess Peach from the evil Bowser"
"Mario, Luigi, Peach, and Bowser, each with their own unique abilities and play styles compete in various golf tournaments and challenges across different courses"
"Players can participate in tournaments, improve their skills in training modes, and unlock new characters and courses. The game also includes role-playing elements where players can create and customize their own golfers and guide them through a story mode, earning experience points and improving their abilities over time!"
"Donkey Kong and his friends as they embark on a quest to rescue Donkey Kong's kidnapped banana hoard from the evil King K. Rool"
"This software allows users to create and manipulate digital artwork using various tools and brushes. Users can draw, paint, and apply different effects to their creations"
"This game is played on a virtual board game where players take turns rolling dice and moving around the board. The goal is to collect coins and stars, which can be obtained through various minigames and events on the board. The game features a wide variety of minigames, each with its own unique objective and gameplay mechanics. Players can compete against each other in multiplayer modes or play cooperatively in team-based minigames!"
"Users can design their own characters, give them different poses and animations, and even create short movies using these animated characters. The software also includes interactive features that let users play with their creations"
"Users can create digital postcards, messages, and animations and send them to other users via the internet or through special communication devices. It provides a platform for users to connect and share their creativity with each other"
"Mario, Luigi, Peach, and Bowser, each with their own unique playing style participates in various tournaments and challenges, aiming to become the tennis champion"
"The peaceful Mushroom Kingdom is thrown into chaos when the villainous Bowser kidnaps Princess Peach and steals the mystical Star Rod, granting him immense power"
"Players can use various tools to sculpt and texture their creations, providing a creative outlet for those interested in digital art and design!"
"Mario, Luigi, Toad, and Peach must defeat the evil Millennium Star to save the Mushroom Kingdom from chaos"
"Players traverse and advance through diverse levels filled with enemies, obstacles, and hidden secrets. Each character possesses unique abilities, adding depth to the gameplay with features updated visuals, improved controls, and additional bonus content, making it a must-play for fans of the original game and newcomers alike!"
"Mario and Luigi help Sonic the Hedgehog and his friends, Tails, Knuckles, and Amy, as they set out and advance to stop the evil Dr. Eggman from achieving his plans for world domination"
"Dr. Eggman returns with a new plan to conquer the world. This time, he has captured all of Sonic's animal friends and used them to power his ultimate weapon, the Eggman Device"
"Dr. Eggman has once again devised a plan to conquer the world, but this time he has enlisted the help of a mysterious being known as Gemerl"
"In the Sol Kingdom, where Sonic encounters a Mobian named Blaze the Cat"
"Sonic and Tails find themselves stranded on an unknown island in the middle of the ocean called Southern Island. They discover that the island is under the control of a group of pirates led by Captain Whisker and his robotic companion, Johnny. Sonic and Tails join forces with Blaze to stop the pirates and their plans to dominate the islands and discover the secrets of the mysterious "Jeweled Scepter"
"Dr. Eggman returns with a new plot to conquer the world, and Sonic sets out to stop him once again"
"Sonic teaming up with his old friend Tails to stop Dr. Eggman's latest evil plans"
"Sonic, Tails, and Knuckles join forces to stop Dr. Eggman and his new henchmen, the Hard-Boiled Heavies, from obtaining a powerful artifact known as the Phantom Ruby"
"Sonic and his superstar friends unite to stop the evil plans of Dr. Eggman"
Math Notes: (filled with academic musings)
Cylinder
Max Volume=?
SA=100 cm^2
V=Pi r^2 h (Main)
SA= 2 Pi r^2 + 2 Pi r h (Supplementary)
100 = 2 Pi r^2 + 2 Pi r h
h= 100 - 2 Pi r^2 / 2 Pi r
V= Pi r^2 (100-2 Pi r^2 / 2 Pi r)
V= r(50-Pi r^3)
V=50 r - Pi r^3
V ' = 50 - 3 Pi r^2
0=50 - 3 Pi r^2
-50 / 3 Pi = -3 Pi r^2 / -3 Pi
50 / 3 Pi = r^2
r= square root 50 / 3Pi
V= Pi (square root 50 / 3 Pi)^2 (100 - 2 Pi (square root 50 / 3 Pi)^2 / 2 Pi (square root 50 / 3 Pi))
V= Pi (50 / 3 Pi)(100 - 2 Pi (50 / 3 Pi) / 2 Pi (square root 50 / 3 Pi))
V=76.8
L'Hosptial Rule: Always derivate until it works
Lim x to 0: 3 sin (4x) / 5x
3 sin 4(0) / 5(0) = 3 sin (0) / 0
3 cos (4x) / 5
3 cos (4(0)) / 5
3 cos (0) / 5
=3/5
Lim x to Infinity: 4x^3 - 2x^2 + 6 / Pi x^3 + 4 = infinity/infinity
12x^2 - 4x / 3 Pi x^2 = infinity/infinity
24x - 4 / 6 Pi x
24 / 6 Pi
= 4/Pi
Do Not Optimize the Derivatives; Box
V=lwh
SA=2x^2 + 4xh
SA= 30 = 20x^2 + 4xh
h=30-2x^2 / 4x
V= x^2 h
=x^2 (30 - 2x)^2
= 1/4 (30-2x)^2
50cm^3
50 = 2x^2 + 4xh
SA = 2x^2 + 4xh
SA = 2x^2 + 4x (50/x^2)
SA ' = 2x^2 + 200/x^2
4x - 200/x^2 = 0
4x = 200/x^2
x^3 = 200/4
x^3 = 50
x = cubed root 50
V= (cubed root 50)^2 (50 / (cubed root 50)^2)
V=50
V= x^2 (h)
50 cm^3 = x^2 (h)
h= 50/x^2
Remember Cylinder Formulas: V=x^2 (h) and SA=2 Pi r^2 + 4xh
lim x to 0: 3sin(4x) / 5x
Derivative
3cos(4(0))(4) / 5
3cos(4(0))(4) / 5
3(1)4 / 5
=12/5
lim x to infinity: 4x^3 - 2x^2 + 6 / Pi x^3 +4
12x^2 - 4x / 3 Pi x^2
24x - 4 / 6 Pi x
24 / 6 Pi
=4/Pi
Indefinite Integrals
Integral -4sin(4x) dx
Integral -4sin(u)
u=4x
du/dx = 4
du=4dx
dx=du/4
Integral -4sin(u)(du/4)
-4/4 Integral sin(u)(du)
- Integral sin(u)(du)
- Integral -cos(u)(du
Integral Goes Away
-(-cos)(u) + c
cos(u)+c
cos(4x)+c
Integral (3x^-2 - 4x^2 + 1)dx
Integral x^n dx = x^n+1 / n+1 + c
Integral x^-1 dx = ln |x| +c
3(x^-1 / -1) - 4 (x^3 / 3) + 1x + c
-3x^-1 - 4x^3 / 3 + x + c