A tank initially contains 17 pounds of salt dissolved in 450 gallons of water. Starting at to = 0, water that contains 2/5 pounds of salt per gallon is poured into the tank at a rate of 10 gallons per minute and the mixture is drained from the tank at the exact same rate. Assume the tank is uniformly mixed at all times. Use this information to answer the following questions. a) Find a differential equation for the quantity of salt in the tank at time t > 0 b) Solve the differential equation from part (a) to find Q (t)

Newton's Law of Cooling states that the rate at which the temperature of a cooling object decreases and the rate at which a warming object increases are proportional to the difference between the temperature of the object and the temperature of the surrounding medium. The differential equation formula is given as: dT = k (T – A) dt - T = temperature of object at time t А ambient temperature (aka temperature of the surrounding medium) k = constant of proportionality Okay, now here's the problem. A glass of delicious orange soda (with an initial temperature of 34°F) is placed in a room with a constant temperature of 72°F. One hour later, the temperature of the orange soda is 52°F. Find the exact simplified value of k. Hint: solve the differential equation for T and note that A is a constant.

Please help for c and d.

At time t = 0, 5 grams of salt are dissolved into 15 liters of water. Brine with concentration of salt 4 grams per liter is added at a rate of 2 liters per minute. The tank is well mixed and drained at 2 liters per minute. Let ɩ be the Q amount of salt, in grams, in the solution after ₺ minutes t have elapsed. Find a differential equation for the rate of change in the amount of salt, dQ/at, in terms of the amount of salt in the solution Q. dQ dt grams/minute