When a fork is placed in a hot piece of lasagna, thermal energy is transferred up the fork by

When a vertical beam of light passes through a transparent medium, the rate at which its intensity i decreases is proportional to i(t), where t represents the thickness of the medium (in feet). in clear seawater, the intensity 3 feet below the surface is 25% of the initial intensity i0 of the incident beam. what is the intensity of the beam "10" feet below the surface? (give your answer in terms of i0. round any constants or coefficients to five decimal places.)

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

Consider a u-tube whose arms are open to the atmosphere. now equal volumes of water and light oil (ρ = 49.3 lbm/ft3) are poured from different arms. a person blows from the oil side of the u-tube until the contact surface of the two fluids moves to the bottom of the u-tube, and therefore, the liquid levels in the two arms are the same. if the fluid height in each arm is 30 in, determine the gage pressure exerted by the person on the oil by blowing.