Johannes kepler used decades of tycho brahe's observational data to formulate an accurate description of planetary motion. kepler spent almost 30 years of his life trying to develop a simple description of planetary motion based on a heliocentric model that fit tycho's data. what conclusion did kepler eventually come to that revolutionized the heliocentric model of the solar system?

The second largest public utility in the nation is the sole provider of electricity in 32 counties of southern florida. to meet the monthly demand for electricity in these counties, which is given by the inverse demand function p = 1,200 – 4q, the utility company has set up two electric generating facilities: q1 kilowatts are produced at facility 1, and q2 kilowatts are produced at facility 2 (so q = q1 + q2). the costs of producing electricity at each facility are given by c1(q1) = 8,000 + 6q12 and c2(q2) = 6,000 + 3q22, respectively. determine the profit-maximizing amounts of electricity to produce at the two facilities, the optimal price, and the utility company’s profit