A jar of tea is placed in sunlight until it reaches an equilibrium temperature of 31.8 ◦C . In an attempt to cool the liquid, which has a mass of 161 g , 131 g of ice at 0.0 ◦C is added. At the time at which the temperature of the tea is 28.8 ◦C , find the mass of the remaining

Amichelson interferometer operating at a 600 nm wavelength has a 3.02-cm-long glass cell in one arm. to begin, the air is pumped out of the cell and mirror m2 is adjusted to produce a bright spot at the center of the interference pattern. then a valve is opened and air is slowly admitted into the cell. the index of refraction of air at 1.00 atm pressure is 1.00028.how many bright-dark-bright fringe shifts are observed as the cell fills with air?

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

1. explain how you calculate the net force in any direction on the box. 2. suppose an upward force of 15n is added to the box. what will be the net vertical force on the box? 3. what force could be applied to the box to make the net force in the horizontal direction zero? explain. 4. suppose a force of 25n to the right is added to the box. what will be the net force to the right?