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I don't have any information on how to power supply a kCSWA900 Kenwood subwoofer. However, I can tell you that the Kenwood KSC-SW10 compact powered subwoofer has a built-in amplifier with a 38 watts RMS power and a wired remote for control over volume level, variable low-pass crossover (50-120 Hz), and selectable phase control (0°, 180°) . The subwoofer comes with a power/ground wiring harness and preamp (RCA) and speaker-level inputs .
Hopefully there's enough of the wires left to see their colors.
Here's a link to the manual. Other than the speaker level inputs, there's only 3 wires you need to be concerned with. Yellow is main power, black is ground, and blue is remote.
Yes, you can use RCA cables. Just wire in a "low-level" converter.
Using RCA's is really the best way, allowing you to run shielded wiring to the sub, making it less likely that the wiring will pick up electrical interference. I'd install the converter on the rear speaker wires behind the dash.
If you do not want to convert the speaker output, you can drive the Kenwood directly from the speaker wires. The diagram in the install manual shows the connections coming off the rear speakers.
Here's a link to one output converter. This one will convert all 4 speakers.
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