Water is drained from a pool at a rate of R(t) = 50e-0.08t gallons per hour. If the drain is left open indefinitely, how much water drains from the pool?

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

A: Solution :-

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: consider a tree with a tr

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

A: For decreasing rate apply negative sign

Q: A tank initially holds 10 gal of fresh water. At t=0, a brine solution containing lb of salt per…

A: We have to find amount and concentration.

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

A: Let "s" represents the quantity of salt in the tank. dSdt=(8×2.5)-8S200dSdt+0.04S=20   and S(0)=0…

Q: A freshly brewed cup of coffee has temperature 95°C in a  20°C room. When its temperature is 70°C,…

A: Given that, Initial temperature of coffee is T0=95°C, surrounding temperature is Ts=20°C. Also,…

Q: A rectangular box has its height increasing at a rate of 1m/s while its volume is decreasing at a…

A: We have to find the  rate of change of length.

Q: In some chemical reactions, the rate at which the amount of a substance changes with time is…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: A population of insects increases at a rate of 200 + 10t + 0.25t2 insects per day (t in days). Find…

A: Given that, The population of insects increases at a rate of 200 + 10t + 0.25t2 insects per day. At…

Q: A freshly brewed cup of coffee has temperature 95 ° C in a 20 ° C When its temperature is 70 ° C it…

A: The temperature of a freshly brewed coffee is 95°C and the temperature of the room is 20°C. When the…

Q: A bacteria population starts with 400 bacteria and grows at a rate of r(t)= 450.268 e ^1.12567t per…

A:

Q: In the absence of predators the population of mosquitos in a certain area would inccrease at a rate…

A: Let P(t) be the population of mosquitoes in the area with t in weeks, and k be the rate at whichthey…

Q: 7) The rate of water flowing in a tank is given by: R(t) = 0.5t* + 20t Gallons/minutes. How much…

A:

Q: The length of a rectangle is increasing at a rate of 11 cm/s and its width is increasing at a rate…

A: The area of a rectangle is the product of its length and width, A=l×w, where l is the length of the…

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 100 gallon tank is filled with brine containing 60 pounds of dissolved salt. Water runs into the…

A: As this is a multiple question according to the Bartleby Answering rule, only first question is to…

Q: Water leaks from a tank at a rate of 2 + 5t liters/hour (L/h), where t is the number of hours after…

A: Given, water leaks from a tank at a rate of 2 + 5t liters/hour (L/h), where t is the number of hours…

Q: 6) A 13 ft ladder is leaning against a wall. If the top of the ladder slips down the wall at a rate…

A:

Q: A weight W is attached to a rope 50 ft long which passes over a pulley at P, 20 ft above the ground.…

A: Given: - A weight W is attached to a rope 50 ft, long which passes over a pulley at P, 20 ftabove…

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: Water is discharged from an inverted cone-shaped tank with a height of 12 meters and a radius of 6…

A: Given: The height of the inverted cone-shaped tank, h = 12m. Also, its radius, r = 6m. From the…

Q: (A1) A ladder 11 feet long rests againt a certical wall. if the bottom of the ladder slides away…

A:

Q: 1. If the motor on a motorboat is started at t = 0 and the boat consumes gasoline at the rate of 6 –…

A:

Q: 3. When polluted water begins to flow into an unpolluted pond, the concentration of pollutant, C, in…

A: Given that The concentration of pollutant C in the pond at t hours is modelled by

Q: A tank contains 5000 liters (L) of a solution consisting of 182 kg of salt dissolved in water. Pure…

A:

Q: A tank contains 100 L of water. A salt solution containing 2 kg of salt per liter flow in at the…

A:

Q: The air in a small room 12 ft by 8 ft by 8 ft is 5% carbon monoxide. Starting at t = 0, fresh air…

A: Let v(t) be the volume of CO in the room at time t, and let V be the total volume of the room.The…

Q: A 100 gallon tank is filled with brine containing 60 pounds of dissolved salt. Water runs into the…

A: Form the differential equation of first order and solve to get the answer.

Q: A 50 – gal tank initially contains 10 gal of fresh water. At t = 0, a brine solution containing 1 lb…

A: Remaining capacity of tank is 50-10 = 40 gallons.

Q: A radioactive element decomposes at a rate proportional to the amount present. The amount remaining…

A:

Q: D. A ladder 10 feet long rests against a vertical wall. If the top of the ladder slides down at a…

A: Make a diagram according to the situation.

Q: The kinetic energy K of a mass is proportional to the square of its velocity y. If K = 12,960 joules…

A: To determine the kinetic energy.

Q: Consider a rectangular metal box without a top lid which, because of being heated, is increasing in…

A:

Q: After a foreign substance is introduced into the blood, the rate at which antibodies are made is…

A: Please see the below picture for detailed solution.

Q: A tank contains 200 liters of fluid in which 30 grams of salt is dissolved. Brine containing 1 gram…

A: Question is solved.

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

A:

Q: Water flows from the bottom of a storage tank at a rate of r(t) = 4(50 − t)e −0.05t liters per…

A: Given:  rt=450-te-0.05t    , 0≤t≤50    1 We need to find the amount of water that flows from the…

Q: A 20-foot ladder is leaning against a vertical wall. Suppose the base of the ladder slides away from…

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 initially holds 10 gal of fresh water. At t = 0, a brine solution containing ¼pounds of salt…

A: Given that , Initially fresh water in tank = 10 gal At t=0 , the solution containing 14 pounds of…

Q: A 50 gallons tank initially contains 10 gal of fresh water. At t = 0, a brine solution  containing 1…

A: It is given that a 50 gallon tank initially contains 10 gallon fresh water. A brine solution with 1…

Q: The top ladder slides down a vertical wall at a rate of 0.15m/S. At what moment when the bottom of…

A: Given that the top ladder slides down a vertical wall at a rate of 0.15m/s. the bottom of the ladder…

Q: If a tank holds 3000 gallons of water, which drains from the bottom of the tank in 20 minutes, then…

A:

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 tank contains 2000 liters (L) of a solution consisting of 182 kg of salt dissolved in water. Pure…

A:

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: A 50L tank initially contains 5L of brine solution where 3kg of salt have been dissolved. At t = 0,…

A: According to the given information,

Q: A flag is raised vertically from a pole at a constant rate of 1 m/s. A point B on the ground is…

A: solution:- draw a right angle triangle:-

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

A: