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. All equations must be properly scaled. If you want something to be 100 feet tall, the equation must show this. Requirements: Vector-valued Functions: (5) . A minimum of five different types of curves. These may include quadratic, 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, r (t) = (x(t), y(t), z(t)). 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.Equations of Several Variables: (5) . A minimum of five different types of surfaces. . There can be no two with the same shape, or part of the same shape. For example, you cannot have a hyperboloid of one sheet in the the z direction and another in the y direction. . If you have one type of cylinder, you cannot have another type. You cannot use planes or any surfaces that have flat components on top. This includes absolute value pyramids. You cannot use a sphere. Each surface must include an equation in rectangular coordinates. Any shape that has a standard form must be written in standard form. For example, Hyperboloids of one or two sheets must be set equal to one. If the shape is a function, z must be solved for. (If z is squared, you cannot solve for it uniquely.) 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, or from the surface to a maximum value. Integrals may be set up in rectangular, cylindrical, or spherical notation. If in cylindrical or spherical, show the equation of the object in the same notation, as well as in rectangular. . Then estimate the volume to the nearest hundredth. 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.To Turn In: - Descripon and equation for each "ride" including a 3d picture of the shape. This can be computer generated. l suggest Geogebra. The image must be in standard position. The x-axis coming out towards the left and the y- axis towards the right. The z axis is vertical. - Equation of the shape. including any other restricons. . Curve length or volume integrals and estimates. (Work not required.) - Park Layout You may turn the entire assignment in as a PDF document. If you use Google Docs. you must download and upload the file to the assignment. You cannot invite me to edit