In order to stay awake during class, a professor keeps a 200 ounce capacity coffee maker in his office that contains 40 ounces of coffee containing 500 mg of caffeine. After developing a tolerance to such a small amount of caffeine, he begins to brew espresso containing 60 mg of caffeine per ounce at a rate 20 ounces per hour. If he consumes the coffee espresso mixture at a rate of 10 ounces per hour, then determine the amount of caffeine in the coffee mixture when the coffee maker contains 300 ounces

Q: A 250 mg per L solution of drug is adminstered intravenously at a rate of 50 ml. per hr to a patient…

A: 1st we will make differential equation for amount of drug in the body and then solve it to get exact…

Q: A tank that can hold 500 gal. originally contains 200 gal. of water with 100 Ibs. of salt in…

A: please comment if you need any clarification. If you find my answer useful please put thumbs up.…

Q: A 200-gal tank is half full of distilled water. At time t=0, a solution containing 0.5 Ib/gal of…

A:

Q: A 600 litre tank initially contains 200 litres of water in which 10 grams of salt are dissolved.…

A: (a) A 600 litre tank initially contains 200 liters of water. 10 grams of salt are dissolved in it.…

Q: Elena has a washing machine with a 20 gallon capacity. She always uses a 20 gram measure of soap for…

A: Let x(t) be the amount of a substance at time t. The concentration of the substance can be modeled…

Q: A tank contains 200 gallons of fresh water. Brine containing 2 lbs/gal of salt enters the tank at 4…

A:

Q: In a mixing vat there are initially 100 litres of volatile liquid. 3 litres of fresh liquid are…

A: Solution

Q: A tank with a capacity of 5000 kg of water is initially half full. Twenty kilogram per minute is…

A: Given that the capacity of the tank is 5000 kg. Let Q be the quantity of water in the tank after t…

Q: Initially a tank holds 100 gal of a brine solution containing 4 lb of salt. At t = 0, brine…

A: We will find out the required time.

Q: A 1,000-liter tank initially contains 200 liters of brine containing 100 kg of salt. Brine…

A: Given that, A 1,000-liter tank initially contains 200 liters of brine containing 100 kg of salt.…

Q: A tank initially holds 80 gallons of brine solution containing 1/8 Lb of salt per gallon. At t = 0,…

A:

Q: a 400 gal tank initially contains 100 gal of brine containing 25 lb of salt. Brine containing 2 lb…

A: A real-life scenario can be described mathematically through a differential equation. By solving the…

Q: A 100-gallon tank contains 50 gallons of water. Brine, containing 2 lbs of salt per gallon, flows…

A: Given that, A 100-gallon tank contains 50 gallons of water. Brine, containing 2 lbs of salt per…

Q: A tank contains 80 galloons (gal) of pure water. A brine solution with 2 lb/gal of salt enters at 2…

A: Given that, A tank contains 80 galloons (gal) of pure water. A brine solution with 2 lb/gal of salt…

Q: A tank contains 10m^3 of free water, brine having a concentration of 15kgsalt/m^3 is sent into the…

A:

Q: Tank A contains 274 litres of brine holding 123 N of dissolved salt, and tank B contains 274 litres…

A:

Q: The cost of installing insulation in a particular two-bedroom home is $2400. Present monthly heating…

A: Given: The cost of installing insulation in a particular two-bedroom home is $2400. Present monthly…

Q: the radiator in a car is filled with a solution of 60% antifreeze and 40% water. the manufacturer of…

A: In a 3.6 L radiator, the quantity of antifreeze is given by: In a 3.6 L radiator, the quantity of…

Q: Worker A is a loader and worker B is an unloader. Worker A can load a truck in 10mins, while worker…

A: The time taken by worker A to load the truck is = 10 min  The time taken by the worker B to unload…

Q: A tank contains 1,000 gal of brine in which 500 lb of salt are dissolved. Fresh water runs into the…

A: Form the first order differential equation and solve using separation of variables.

Q: A tank contains 4000 liters (L) of a solution consisting of 120 kg of salt dissolved in water. Pure…

A: Here, ri = 4, ci = 0, r0 = 5, The differential equation is There is no inflow of salt, thus the…

Q: A tank contains 1000 liters (L) of a solution consisting of 170 kg of salt dissolved in water. Pure…

A: The rate of change of a quantity with respect to time is the differential of that quantity. In a…

Q: Tank A contains 499 litres of brine holding 192 N of dissolved salt, and tank B contains 499 litres…

A:

Q: A tank contains 80 gallons of pure water. A brine solution with 2lb/gal of salt enters at 2 gal/min,…

A: Given: r1=2 galsmin., r2=2 galsmin.,  c1=2 lbsgal,, v0=80 gallons, x0=0

Q: A 450 gal tank initially contains 110 gal of brine containing 52 Ib of salt. Brine containing 1lb of…

A:

Q: A tank with a capacity of 400 gal originally contains 150 gal of water with 25 lb of salt in…

A:

Q: A tank with a capacity of 400 gal originally contains 100 gal of water with 200 lb of salt in…

A: A tank with a capacity of 400 gal originally contains 100 gal of water with 200 lb of salt in…

Q: A tank contains 200 gallon of salt water with 150 lbs of dissolved salt. Salt water with 5 lbs of…

A:

Q: Two large tanks, each holding 24 liters of a brine solution, are interconnected by pipes as shown in…

A: Let x(t) and y(t) be the mass of salt in tanks T1 and T2 respectively. Fresh water follows into tank…

Q: A group of fitness club members lose a combined total of 28 kilograms in 1 week. There are…

A:

Q: The radiator car is filled with a solution of 65% antifreeze and 35% water. The manufacturer of the…

A: The capacity of the radiator is 3.9L.Let x be the amount of coolant to be drained.

Q: A tank contains 1000 liters of brine. Brine containing 0.4 kg/liter of salt flows in at 10…

A: Let st= The amount of salt at time t. The brine flows in at the rate 10 liters/minute and flows out…

Q: The side of a cube is increasing at a rate 7m/8, then the rate at which the m³/s. volume of the cube…

A:

Q: A 100-gallon tank contains 5O gallons of water. Brine, containing 2 Ibs of salt per gallon, flows…

A: Ans =38

Q: A tank containing chocolate milk initially contains a mixture of 460 gallons of milk and 40 gallons…

A: Let yt be the amount of chocolate syrup in the tank at time t.  The rate of change of the amount of…

Q: The side of a cube is increasing at a rate 9m/s, then the rate at which the volume of the cube…

A: The function f(t) is a rule that associates or fixes a number to the particular point t. The…

Q: A tank initially contains 50 gal. of fresh water. Brine (water in which a certain number of pounds…

A:

Q: A tank contains 400L of fresh water. By mistake, 100kg of salt is poured into the tank instead of…

A:

Q: We have a mixing tank that contains 100 gallons of water into which 5 pounds of sugar have been…

A: According to question. Initial amount of water in tank= 100gallons Initial amount of sugar = 5 pound

Q: A vessel with 500 gallons of beer contains 4% alcohol (by volume). Beer with 7% alcohol is pumped…

A:

Q: In 30 minutes, a thousand eight hundred tank of water empties from the bottom.The amount of water…

A: Proceed as shown below

Q: A tank contains 1000 liters (L) of a solution consisting of 195 kg of salt dissolved in water. Pure…

A: Solution is given below:

Q: Assume that you are attending a patient receiving intravenous medication. The doctor orders 24 mls…

A:

Q: Elena has a washing machine with a 20 gallon capacity. She always uses a 20 gram measure of soap for…

A: To determine the time taken to correct the error of adding extra soap to the water, we have to…

Q: A tank with a capacity of 25 L originally contains 15 L of brine with a concentration of 5 g/L of…

A:

Q: A large mixing tank currently contains 300 gallons of water, into which 8 pounds of sugar have been…

A: given: Capacity of tank = 300 gallon Amount of sugar = 8 pounds Rate of pouring of water = 20…

Q: A tank initially holds 80 gal of a brine solution containing of salt per gallon. At t=0, another…

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.