1. A tank initially holds 100 gallons of brine solution containing 20 lbs. of salt. At t = 0, fresh water is poured into the tank at the rate of 5 gal/min., while the well- stirred mixture leaves the tank at the same rate. Find the amount of salt in the tank at any time t.

Q: f. A truck travelling southwards at 40 kph and a car traveling eastward at a rate of 60 kph are…

A:

Q: We found that salt is added to the tank at a constant rate and it is removed from the tank at a rate…

A: There is no such introduction for the solution.I have explained it within the solution.Please go…

Q: In a simple electric circuit, Ohm's law states that V IR, where V is the voltage in volts, I is the…

A: From the given problem: dVdt=-0.01 volts per second ; dRdt=0.03 ohms per secondR=300 ohms ; I=0.04…

Q: Consider a reservoir with a volume of 8 billion cubic feet (ft^3) and an initial pollutant…

A:

Q: Cane sugar, when placed in water, converts to dextrose at a rate proportional to the amount of…

A: An ordinary differential equation is an equation containing independent variables, dependent…

Q: Let the rate of growth dN/dt of a colony of bacteria be proportional to the square root of the…

A: Let N(t) denotes the number bacteria present at time t. Use the proportionality constant k, to get…

Q: consider a tree with a tr

A:

Q: A certain radioactive material is known to decay at a rate proportional to the amount present. If…

A: given,     radioactive material is decay at a rate proportional to the amount present .initially 50…

Q: A culture of yeast grows at a rate proportional to its size. If the initial population is 4000 cells…

A: Let's find.

Q: A tank contains 300 gal of water and 100 gal of pollutants. Fresh water is pumped into the tank at…

A: Fresh water is pumped into the tank at the rate of 2 gal/min, and the well stirred mixtureleaves at…

Q: 2. A tank initially contains 1000 gallons of fresh water. Brine containing 3 lbs/gallon of salt…

A: The time taken for the quantity of salt to reach 100 lbs is 16.80555 minutes

Q: A certain radioactive material is known to decay at a rate proportional to the amount present. If…

A: Given data:   The initial value of the mass is mi=50 milligrams. The mass lost after two hours is…

Q: 2. Suppose that at some time t the mass of the tumor, M(t), is between 0 and K. What is the sign of…

A: We need to find sign of rate of change of M.

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

A: Given that the size of the tank is 200 gallon. Half of it is full, that means 200/2=100 gallon is…

Q: A tank is initially filled with 1000 gal. of salt solution containing 500 H of salt. Fresh water…

A: Let At the amount of salt at the time t Then the rate of change of the amount of salt dAdt=0lbL.10…

Q: A substance cools in moving air at a rate proportional to the difference between the temperature of…

A:

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

A:

Q: 5. A termite population begins with 150 termites and increases at a rate of m'(t) termites per week.…

A: Termite population starts with 150 termites and increases with the rate of m'(t) termites per week

Q: 1 If a spherical drop of liquid evaporates at a rate proportional to its area, if initially its…

A: Let the surface area be A So rate of evaporates is dA/dt, According to the question, dVdtαAdVdt=-kA…

Q: 1. (a) If V is the volume of a cube with edge length x and the cube expands as time passes, find…

A: Topic = Derivative

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: Suppose you have a 200-gallon tank full of fresh water. A drain is opened that removes 3 gal/sec…

A: Let the concentration of brine =x lb/gal Amount of salt entering in per minute = 2 gal1 min×x lb1…

Q: A certain radioactive material is known to decay at a rate proportional to the amount present. If…

A: Percentage : Percentage of the item is 100th part of the number.  It is denoted by x% or written as…

Q: When air expands adiabatically (without gaining or losing heat), its pressure P and volume V are…

A:

Q: A liquid solution is passing thru a conical filter 2 feet deep and 4/3 feet across the top, into a…

A: We have to find the rate at which the level of the solution in the cylinder rising.

Q: If 150 g of copper at initial temperature of 50 °C gains 6930 J of heat when it is cooled to 170°C.…

A:

Q: A certain population of microorganisms grows at a rate proportional to the amount present under a…

A: Given that, A certain population of microorganisms grows at a rate proportional to the amount…

Q: A mold grows at a rate that is proportional to the amount present. Initially there is 6oz of this…

A: The amount of mold at time 0 is m0. The amount of mold present after t hours is m. The rate of…

Q: 1. A tank contains 80 gallons (gal) of pure water. A brine solution with 2 Ib/gal of salt enters at…

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

Q: Under certain conditions, cane sugar in water is converted into dextrose at a rate proportional to…

A:

Q: 6. The mass of a cube in grams is M = x³ + 0.1x*, where x is the length of one side in centimeters.…

A: Explained below

Q: Suppose that electricity is draining from a capacitor at a rate that is proportional to the voltage…

A:

Q: 1.A culture has y,number of bacteria. At time t=2 hours, the number of bacteria is measured to be…

A: Given, Initial number of bacteria is y0. also, given at time t=2 hours, the number of bacteria is…

Q: When air expands adiabatically (without gaining or losingheat), its pressure and volume are related…

A: Given that When air expands adiabatically (without gaining or losing heat), its pressure and volume…

Q: A cup of coffee cools at rate proportional to the difference between the constant room temperature…

A:

Q: A certain radioactive material is known to decay at a rate proportional to the amount present. If…

A:

Q: The mass of a radioactive sample is given by M(t)=M010^-kt where t is the time in years, M0 is the…

A:

Q: Consider a tank that initially contains 100 gallons of a solution in which 50 pounds of salt are…

A: Here I am attaching image so that you understand each and every step.

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: 1) A pump is used to fill an inflatable mattress at a constant rate of 0.25 cubic feet per second.…

A:

Q: The half-life of a radioactive material whose rate of disintegration is proportional to the amount…

A: Given that, The half-life of a radioactive material whose rate of disintegration is proportional to…

Q: A tank contains 50 gallons of a solution composed of 90% water and 10% alcohol. A second solution…

A:

Q: Blood carries a drug into an organ at a rate of 3 cm3/sec and leaves at the same rate. The organ has…

A: Exponential growth/decay is given by dxdy=rici-r0vx here, ri=3= rate of drug entering. and r0=3=…

Q: A tank contains 200 liters of fresh water. Brine containing 2.5 N/L of dissolved salt runs into the…

A:

Q: Water is drained from a pool at a rate of R(t) = 50e-0.08t gallons per hour. If the drain is left…

A: 625 gal. water drains from the pool.

Q: If oil leaks from a tank at a rate of  r(t) gallons per minute attime t , what does ∫0120 r(t) dt…

A: Oil leaks from a tank at a rate of  r(t) gallons per minute at time t.

Q: A pitcher of buttermilk initially at 27°C is to be cooled by settling in on a place where the…

A: At time t=0 minutes, temperature of buttermilk = 270C   At time t=20 minutes, temperature of…

Q: A certain radioactive material is known to decay at a rate proportional to the amount present. If…

A: Image is attached with detailed solution.

Q: In a chemical reaction, substance A decomposes at a rate proportional to the amount of A present. It…

A: This decomposition reaction of first order, because rate is directly proportional to the…