The blades of a ceiling fan have a radius of 0.380 m and are rotating about a fixed axis with an angular velocity of +1.50 rad/s. when the switch on the fan is turned to a higher speed, the blades acquire an angular acceleration of +2.00 rad/s². after 0.500 s has elapsed since the switch was reset, what is (a) the total acceleration (in m/s²) of a point on the tip of a blade and (b) the angle ϕ between the total acceleration → a and the centripetal acceleration → a c ?

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