An oil storage tank ruptures at time t = 0 and oil leaks from the tank at a rate of r(t) = 120e-0.05t liters per minute. How much oil leaks out during the first hour? (Round your answer to the nearest liter.) x liters

Q: The time rate of change of an alligator population P in a swamp is proportional to the square of P.…

A:

Q: Q4. A man 7 ft tall walks at a speed of 5 ft/sec toward a street lamp which is 15 ft above the…

A:

Q: A factory is dumping pollutants into a river at a rate given by  dx/dt = t3/4/100  tons per week,…

A: A factory is dumping pollutants into a river at a rate given by dxdt=t34100 tons per week. Integrate…

Q: The population of a slowly growing bacterial colony after t hours is given by p(t) 3t2 + 21t + 150.…

A: We are given the population function p(t)=3t2+21t+150 where t is measured in hours. Here, we need to…

Q: Q1. In a study of Bacterial Growth, it is assumed that, a culture initially has Po number of…

A: P0 → initially number of bacteria.at t= 2h, number of bacteria→52P0We can model the problem as :P(t)…

Q: Oil spilled from a ruptured tanker spreads in a circle whose area (A=pi r^2) increases at a constant…

A: according to our terms and condition i have solved first question for next question repost

Q: A population of bacteria is growing according to the equation P(t) = 650e0.2t. Estimate when the…

A:

Q: The number of bacteria in a culture is given by the function n(t) 990e0.15t where t is measured in…

A:

Q: The number of action potentials produced by a nerve, t seconds after a stimulus, is given by N(t) =…

A:

Q: a

A:

Q: During the first 45 seconds of a rocket flight, the rocket is propelled straight up so that in t…

A: In the question it is asked to calculate instantaneous velocity of the rocket at the instant when…

Q: The population of a town grows at a rate of r(t) 400 e0.2t people per year (where t is the time in…

A: The population of a town grows at a rate of rt=400.e0.2 t people per year.At time t=3, the town's…

Q: Q1. In a study of Bacterial Growth, it is assumed that, a culture initially has Po number of…

A: This is Separable differential question

Q: An arrow is shot vertically up into the air with an initial vertical velocity of 60 m/s, and its…

A: factor out -5 to do a complete square add and subtract 36

Q: As we learned previously, most fish are indeterminate growers, which means they continue growing…

A: Given: Growth in centimeters per year is given by: f(t) = 3e-0.4t  centimeters per year.…

Q: A population of bacteria is growing according to the equation P(t) = 1850e0.1t. Estimate when the…

A:

Q: A coal-burning electrical generating plant emits sulfur dioxide into the surrounding air. The…

A: Given C(x) = 0.3/x^2 Therefore, Derivative of C(x) = 0.3 (-2)(x^-3) = -0.6/x^3

Q: An evergreen nursery usually sells a certain shrub after 8 years of growth and shaping. dh The…

A:

Q: The depth of the water in a tank is changing at a rate of r)= 3 In(t). t centimeters per minute…

A: dh/dt = 3×t×lnt Solving this equation .

Q: the brakes on a car give the car a constant negative acceleration of 2k m/s2, where k is a positive…

A:

Q: Q1. In a study of Bacterial Growth, it is assumed that, a culture initially has Po number of 5…

A: The formula for exponential growth or decay is given by the expression: At = A0ekt Here, A(t) is…

Q: An oil tanker breaks apart and starts leaking. As time goes on, the rate at which the oil is leaking…

A:

Q: dx In the equation, x2 +y2 = 45, what is the value of the rate of change in y with respect to time t…

A:

Q: A 50-gallon barrel is filled completely with pure water and then salt water with a concentration of…

A:

Q: The number of bacteria in a culture is given by the function n(t) = 990e0.45t where t is measured in…

A:

Q: During the first 45 seconds of a rocket flight, the rocket is propelled straight up so that in t…

A:

Q: The number of bacteria in a culture is given by the function n(t) = 925e0.5t where t is measured in…

A: The number of bacteria of culture is given by the functionnT=925e0.5 twhere t is measured in hours…

Q: The rate of growth, dP/dt of a population of bacteria is given by dP/dt=k sqrt of t, where P is the…

A:

Q: A factory is dumping pollutants into a river at a rate given by dx/dt = t3/4/600 tons per week,…

A: A factory is dumping pollutants into a river at a rate given by dxdt=t34600 tons per week, where t…

Q: A factory is dumping pollutants into a river at a rate given by dx/dt = 3/4/100 tons per week, where…

A:

Q: The number of bacteria in a culture is given by the function n(t) = 935e0.3t %3D where t is measured…

A: the given equation is  compare this equation with  so here we have so the continuous growth rate…

Q: The number of bacteria in a culture is given by the function n(t)=930e0.15tn(t)=930e0.15t where tt…

A: Comparing these two equations we get: P=930, r=0.15 So, continuous growth rate = 0.15= 15% And…

Q: The rate of change of the number of coyotes N(t) in a population is directly proportional to 650 −…

A: Consider N(t) as the population of the coyotes after t years. Consider the given statement as the…

Q: A factory is dumping pollutants into a river at a rate given by dx/dt = t3/4/600 tons per week,…

A: First we separate the variables

Q: An object is propelled vertically upward with an initial velocity of 20 meters per second. The…

A: (a) To find: The time when the object is 15 meters above the ground. Given: The distance in meter is…

Q: A factory is dumping pollutants into a river at a rate given by  dx/dt = t3/4/200 tons per week,…

A: Rate of dumping pollutants,  dxdt=t34200  dx=t34200dt

Q: A factory is dumping pollutants into a river at a rate given by dx/dt=t3/4/400 tons per week, where…

A: Given that A factory is dumping pollutants into a river at a rate dxdt=t34400

Q: A body whose temperature is 180°C is cooled by immersing in a liquid at 60°C. In one minute, the…

A: The given rate of change in temperature (T) at time t is: dTdt=-kT-60 Also, it is given that the…

Q: In the manufacture of printing ink, solvents are used to suspend or dissolve the pigments that give…

A: Rt=10t5t2+4

Q: Q.4 Suppose that electricity is draining from a capacitor at a rate that is proportional to the…

A:

Q: An oil storage tank ruptures at time t = 0 and oil leaks from the tank at a rate of r(t) = 65e-0.05t…

A:

Q: The top of a ladder slides down a vertical wall at a rate of 0.125 m/s. At the moment when the…

A:

Q: A cup of coffee is poured, and the temperature is measured t be 120 degrees Fahrenheit. The…

A: Given initial temperature of the coffee cup is 120 F

Q: A culture initially has P0 number of bacteria. At t=3 hour the number of bacteria is measured to be…

A:

Q: A culture initialy has N mumber of bacteria. At t = 1 hour the mumber of bacteria is measured to be…

A: Let N be the number of bacteria at time t. The rate of increase which is proportional to N = dNdt…

Q: a factory is discharging pollution into a lake at the rate of r(t) tons per year given below, where…

A:

Q: At time t = 0, a tank contains 20 oz of salt dissolved in 100 gallons of water. Then brine…

A: Given that:                        At t=0, Salt present = 20 oz in 100 gallons of water.Brine…

Q: At a time t hours after taking a tablet, the rate at which a drug is being eliminated is r(t) =…

A:

Q: A factory is discharging pollutants at a rate of R(t)=120 gal/day. Using enzymes and other remedies,…

A: Given- A factory is discharging pollutants at a rate of Rt = 120 gal/day. Using enzymes and other…

Q: A certain gas satisfies the equation PV1.4 = C, where C is a constant, P is the pressure, and V is…

A: Given equation : P = 20 kg/cm2   V = 32  cm3dVdt=-2 cm3/min