A company designs microphones for use in conference rooms. A new microphone needs to focus on the person speaking and not the voices of other people in the room. Which polar equation would best match the desired audible range of the microphone?

A microphone that focuses on one speaker should have a directional pattern: strong sensitivity toward the speaker and reduced sensitivity in other directions. The equation r = 3 + 3cos(θ) is a cardioid, with one main lobe and a point where the range falls to zero in the opposite direction. This makes it better suited than the circle, which represents equal range in every direction, or the multi-lobed patterns.

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