Prove: if b ≠ 0, then the cross product term can be eliminated from the quadratic form ax² + 2bxy + cy² by rotating the coordinate axes through an angle θ that satisfies the equation cot 2θ = a-c/2b.

Dean and karlene get paid to write songs. dean is paid a one-time fee of $20 plus $80 per day. karlene is paid a one-time fee of $25 plus $100 per day. write an expression to represent how much a producer will pay to hire both to work the same number of days on a song.