Assignment 5 - and the boundary of the optimal pickup...

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Assignment #5 DUE DATE: This assignment is to be submitted entirely on paper on Friday, March 20 th by 9pm in your TA’s drop box. Hand in one copy per pair. Learning Objectives: Questions 1 of this assignment is a neat application directly related to the work studied in class! Question 2 will test your skills in integrating over general regions. ASSIGNMENT (12 marks total): 1. (6 marks) When recording live performances, sound engineers often use a microphone with a cardioid pickup pattern because it suppresses noise from the audience. Suppose the microphone is placed 3 m from the front of the stage
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Unformatted text preview: and the boundary of the optimal pickup region is given by the cardioid θ sin 4 4 + = r , where r is measured in meters and the microphone is at the pole. The musicians want to know the area they will have on stage within the optimal pickup range of the microphone. Answer their question. Hint: Start by writing the line representing the front of the stage in polar form and finding its intersection with the cardioid. 2. (6 marks) Find the volume of the solid bounded by the cylinder 4 2 2 = + z y and the planes y x 2 = , = x , = z in the first octant....
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