Activity 1 ("20-30 min): 1When 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 and the boundary of the optimal pickup region is given by the cardioid , where r is measured in meters and 1' =4 + 45in H 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. [For evaluating the actual integral, you may use Maple]. Hint: Start by writing the line representing the front of the stage in polar form and nding its intersection with the cardioid