SOLVE STEP BY STEP IN DIGITAL FORMAT A steel bar is taken out of a furnace at a temperature of 900 °C and allowed to quench in air for 60 minutes, reaching a temperature of 50 °C. If the environment is at 20 °C and th rate of change of the temperature of the bar with respect to time is proportional to the temperature difference between the bar and the environment, determine: a) the proportionality constant b) the time it takes for the steel bar to reach 35 °C

Hooke's law states that the distance a spring stretches varies directly as the weight on the spring. Let d represent the distance (in inches) the spring stretches, let wrepresent the weight (in pounds) on the spring, and let k be the constant of proportionality. Write an equation that relates d to w. d =     A weight of 50 pounds stretches a spring 8 inches.     Use the equation that relates d to w and the known information to find k. k =   How far (in inches) will a weight of 120 pounds stretch the spring? in

A certain amount of an indissoluble substance containing 2 kg of salt in its pores is subjected to the action of 30 liters of water. After 5 min, 1 kg of salt dissolves. Within how long will 99% of the initial amount of salt dissolve? The rate of dissolution is proportional to the amount of salt that does not dissolve and to the difference between the concentration at the given instant and the concentration and the concentration of the saturated solution (1 kg for 3 litres). Give the result in minutes. The Answer should be: 10.47

The rate of conversion of a certain substance is proportional to the square root of the amount m of unconverted substance. Use k as the proportionality constant. Show that the substance will disappear in finite time and determine the time.