4. In the class, you learn a bunch of tools. But, in the homework, I need you to be a little bit creative and use all you have learned to solve a seemingly random problem. Let us consider semi-circular paper of radius 2. The area of the whole paper is 2π ≈ 6.28. We want to cut a chord(red line) from this paper such that the area of the leftover paper(shown in blue) is 4.0. Where should I cut the chord (find the value of a where the red line should be such that the area of the blue region is 4.0? Try to get a decent answer. If you are good with geometry you can actually figure this one out analytically, but I want you to do it numerically using what we have learned so far. return sqrt(r**2 - ***2) ▷ 1 def circ_top(x, r=2.): 2 3 4 5 [3] def circ_bot(x, r=2.): return -sqrt(r**2 6 x=np.linspace(0,2,100) ***2) 7 y_top= [circ_top(xx) for xx in x] 8 y_bot = [circ_bot(xx) for xx in x] 9 ax= plt.figure(figsize=(4,4)) 10 plt.gca().set_aspect('equal') #get current axis and set aspect ratio 11 plt.plot(x, y_top, 'k-') 12 plt.plot(x, y_bot, 'k-') 13 plt.axvline (1.1, color='red') 14 plt.fill_between(x,y_top,y_bot, where=x>1.1, alpha=0.3) 2.0 15 10 0.5 0.0 -0.5 -1.0 -1.5 -2.0 1 00 05 10 15 20 Python Python

4. In the class, you learn a bunch of tools. But, in the homework, I need you to be a little bit creative and use all you have learned to solve a seemingly random problem. Let us consider semi-circular paper of radius 2. The area of the whole paper is 2π ≈ 6.28. We want to cut a chord(red line) from this paper such that the area of the leftover paper(shown in blue) is 4.0. Where should I cut the chord (find the value of a where the red line should be such that the area of the blue region is 4.0? Try to get a decent answer. If you are good with geometry you can actually figure this one out analytically, but I want you to do it numerically using what we have learned so far. return sqrt(r2 - 2) ▷ 1 def circ_top(x, r=2.): 2 3 4 5 [3] def circ_bot(x, r=2.): return -sqrt(r2 6 x=np.linspace(0,2,100) 2) 7 y_top= [circ_top(xx) for xx in x] 8 y_bot = [circ_bot(xx) for xx in x] 9 ax= plt.figure(figsize=(4,4)) 10 plt.gca().set_aspect('equal') #get current axis and set aspect ratio 11 plt.plot(x, y_top, 'k-') 12 plt.plot(x, y_bot, 'k-') 13 plt.axvline (1.1, color='red') 14 plt.fill_between(x,y_top,y_bot, where=x>1.1, alpha=0.3) 2.0 15 10 0.5 0.0 -0.5 -1.0 -1.5 -2.0 1 00 05 10 15 20 Python Python

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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