Math Project Part 2.doc - Introduction Throughout the calculus course our class has been working on a project base on the geography of the Manhattan

# Math Project Part 2.doc - Introduction Throughout the...

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Introduction Throughout the calculus course, our class has been working on a project base on the geography of the Manhattan, then we apply what we have learn to the project. In Part I of the project, we already choose three point of the triangle on Manhattan, then we apply our calculation to the triangle. This is Part II of the project; first we find the contour points and intersection points of all three sides of the triangle. Then we use the Big Book form 42 nd Street library to find the elevation of these points. For every side of the triangle, we make a table to graph, x represents the distance (in millimeter) form started point, y represents the elevation of the point above sea level. Then we find the best fit function to connect these points, the function we can use is linear function (two points), power function (two points), exponential function (two points), power function (three or more points), exponential function (three or more points), logarithmic function (three or more points), natural logarithmic function (three or more points), and the polynomial function of first degree, second degree, third degree, and fourth degree. For every graph, we do a piecewise function and function breakdown. Piecewise function is about finding the elevation above sea level of the midpoint and random point of the graph using the function. For function breakdown, every function needs to define, show the work of how you obtain the function, domain and range of the function, roots, x-intercept, y-intercept, and a rough sketch of the graph. This kind of project is very important because in real life, it helps the architecture to have a better understanding of where has a high elevation and has low elevation. They can predict the elevation of a place using the functions and decide what to build there.
A(x) x (Distance in millimeter) y (Elevation in feet) .1 53.11 19 50 28 50 41 60 47 67.1 77.5 70 95 75 99 70 102 60 107 50 128 40.8 137 40 173 30 185 18.8 200 20 224 18.1 237 14 2
Piecewise function for A(x) .0190353867x 2 - .6133526137x + 53.44611511 .1 ≤ x < 47 (1)D2 60.06101939(1.002216961) x 47≤ x <95 (2) A(x)= 56698.74303x -1.475707031 95≤ x < 173 (3)MR 1.180637442 E 17x -6. 9681296 173≤ x < 185 (4)A -.08833x + 36.406856 185 ≤ x 237 (5)D1 A(x) evaluates the elevation in feet, above sea level between point A: 65 th Street Park Avenue and point B: intersection of Spring Street and Hudson Street.

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• Spring '14
• DanielMcKinney

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