"Life is like a rollercoaster, literally"
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Our engineering team has decided to launch “8 Kartoos” this upcoming summer. The engineers and designers have worked collaboratively to design this thrilling but daring ride. We began this project by determining the maximum, and minimum height of the rollercoaster, and the total time of duration. We made ourselves familiar with the mathematical equations we are going to utilize to help bring our vision to actuality. There are 7 equations that we’ve decided to use to create our rollercoaster. These range from linear, quadratic, polynomial, degree 3 and above, rational, sinusoidal, exponential and logarithmic. Taking into consideration safety hazards, we were limited to making our maximum 300 and the total time duration 100 seconds (1:40) to avoid any conflict with the existing rides.. The engineers used standard equations to come up with the design of the rollercoaster, and applied transformations to match the design of the rollercoaster’s blueprint. We were influenced to keep our rollercoaster simple, but appealing to our desired riders. 8 Kartoos is a must ride that will definitely change the world of rollercoasters.
The most difficulties us engineers had for this project involved creating and transforming based on the restrictions given. We took standard equations and used them as a base or a guide. In regards to the background knowledge that we had, we were able use the process of trial and error on the desmos software to resemble and actual structure that actually looks like a rollercoaster.
A polynomial function is a function such as a quadratic, a cubic, a quartic, and so on, involving only non-negative integer powers of "x". The function used to create our roller coaster is a degree 3 function meaning it is a cubic. Our equation is a cubic polynomial which means it is a polynomial of degree 3. A cubic polynomial has the form f(x)=a3x^3 + a2x^3 + a1x +a0. In our equation, it has a reflection in the x-axis and a vertical translation 2.1219 units up. This is also the lengthiest part of our roller coaster. The riders experience our polynomial function for a total of 47 seconds between the timing 28 to 75 seconds.