Design Goal: To design a Math-Amusement Park, Skateboard Park, or similar (must be approved) using concepts from this cl

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Design Goal To Design A Math Amusement Park Skateboard Park Or Similar Must Be Approved Using Concepts From This Cl 1 (165.51 KiB) Viewed 26 times

Design Goal: To design a Math-Amusement Park, Skateboard Park, or similar (must be approved) using concepts from this class. Objectives: To demonstrate an understanding of vector-valued functions, functions of several variables, their respective derivatives and integrals, and applications. The Assignment: You will design a scale model of your park that will include the required shapes described below. All shapes must be in 3-dimensions. You can decide what these shapes represent. The ground level will be considered the xy-plane. Each object will have a description of the "ride" and the equation to scale. For calculation purposes, each object can have its own origin. You must also include a 2-dimensional layout of the park, showing where each "ride" is located. The layout should not have any 3-d images. You do not need to describe the mechanics of the rides, nor do they need to be able to exist in real life. Requirements: Layout: • A scale image of the "park" using the footprint of each ride or feature. • 2-dimensional "looking down" view. • Do not include any 3d images. Remember, the ground will be considered the xy-plane. . In otherwards, this is a projection into the xy-plane. • Each object can be modeled with its own xy-origin. That is, there does not need to be an absolute starting place common to every object. • You may use feet or meters as the units. Make sure these are consistently used. Vector-valued Functions: (5) • A minimum of five different types of curves. These may include quadradic, cubic, and sinusoidal curves, to name a few. There can be no two with the same shape. • All curves must be 3-d. That is, no component can be a constant. • No lines can be used. • To name them, use a vector-valued function, F(t) =. None of the components can be constant. • For each curve, you must set up the integral that will calculate the length, even if you can find a formula for length. • Then estimate the length of the curve to the nearest hundredth. You do not need to show work for the calculations. You may use an integral calculator. Functions of Several Variables: (5) • A minimum of five different types of surfaces. These may include cylindrical, and quadratic surfaces, as well as unnamed surfaces. There can be no two with the same shape, or part of the same shape. • For example, if you have an ellipsoid, you cannot also include a sphere. If you have one type of cylinder, you cannot have another type. • You cannot use planes. • For each surface, you must set up the triple integral that will calculate the volume enclosed by the surface, even if you can find a formula for volume. If the surface does not enclose a volume, find the volume between it and the xy-plane. • Then estimate the volume to the nearest hundredth.