An oll storage tank ruptures at time t = 0 and oil leaks from the tank at a rate of r(t) = 95e-0.02t liters per minute. How much oll leaks out (In liters) during the first hour? (Round yo answer to the nearest liter.) liters Neod Heln2

Q: Water is drained from a swimming pool at a rate given by |(-0.2)t R(t) = 100e' gallons per hour. If…

A: Solution : We have given the rate of water drain form a swimming pool is R(t) = 100e(-0.2)t…

Q: 10. A cylinder is being filled such that the height of its contents is increasing at a rate of 5 cm…

A: Explained below

Q: A tank initially holds 100 gallons of a brine solution containing 20 lb of salt. At t = 0, fresh…

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: Find the length of ladder when bottom of the ladder is increasing at the rate of 0.3m/s when bottom…

Q: A 10ft ladder is leaning against a vertical wall(see figure) when Jack begins pulling the foot of…

A:

Q: A tank contains 120 gal of brine made by dissolving 85 Ibs of salt in water. Pure water runs into…

A:

Q: A freshly brewed cup of coffee has temperature 95°C in a 20°C room. When its temperature is 63°C, it…

A:

Q: 2. The edge of a cube decreases at a rate of 2.5m/s. Find the rate at which the surface area…

A: Application of derivatives.

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: 1. A 1000 L tank is draining such that the volume V of water remaining in the tank after t minutes…

A: We will differentiate V with respect to t and evaluate the rate at t = 15

Q: Q.4 In some chemical reactions, the rate at which the amount of substance changes with time is…

A:

Q: An oil storage tank ruptures at time t = 0 and oll leaks from the tank at a rate of r(t) = 70e-0.05t…

A: Given: rt=70e-0.05t

Q: The population of a town grows at a rate proportional to the population present at time t. The…

A: Y(t)=Population in year tY(0)=700Y(15)=700+20%700=700+140=840

Q: Initially a tank contains 10 lb of salt dissolved in 100 gal of water. Assume that brine containing…

A: Given that Initially a tank contains 10 lb of salt dissolved in 100 gal of water. Let x(t) be the…

Q: The volume of a cube is changing at a rate of 24 cm3/sec. How fast is the side expanding when each…

A: V= s3 is given , we can differentiate with respect to time at substitute each value to get at what…

Q: The height of a rectangular box is 10 in. Its length increases at the rate of 2 in./sec; its width…

A: Volume of rectangular box = l b hwhere, l = length of boxb= width of boxh = height of boxRate of…

Q: A tank contains 7000 L of pure water. Brine that contains 35 g of salt per liter of water is pumped…

A:

Q: The number of bacteria in a culture is growing at a rate of 3000e²/5 per unit of time t. At t= 0,…

A: Given that the number of bacteria in a culture is growing at a rate 3000e2t/5 per unit of time t. At…

Q: An object is moving so that it's velocity after t hours is v(t)=te^-t^2 mph. How far does it travel…

A: Hey the equation of velocity that you have written is v(t)=t·e-t2mph following is the solution to…

Q: Q: Suppose we have a rectangular aquarium with dimensions of length 8m, width 4m and height 3m.…

A: we are given for rectangular aquarium length l=8 m width w=4 m height h=3 m dVdt=0.4m3/sec

Q: 1. A tank initially holds 100 gallons of brine solution containing 20 lbs. of salt. At t = 0, fresh…

A: Solution...

Q: A brine solution of salt flows at a constant rate of 6 L/min into a large tank that initially held…

A: given, brine solution of salt flows at a constant rate of 6 Lmin the tank initially had 100 L of…

Q: m³ The volume of a large spherical balloon is increasing at a rate of 64 balloon's surface area…

A:

Q: A large tank holds (400) gallons of brine solution with (50) pounds Q5: of salt. A concentration of…

A:

Q: The number of bacteria in a culture is growing at a rate of 2500e2t/5 per unit time t. Find the…

A:

Q: d. In which direction is the instantaneous rate of change the maximum from (1,0)? What is the…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

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

A:

Q: 15. Sand is falling off a conveyor belt at a rate of 12 cubic feet per minute into a conical pile.…

A: Since solve the first question for you. If you want any specific question to be solved then please…

Q: evaporation As a spherical raindrop falls, it reachesa layer of dry air and begins to evaporate at a…

A:

Q: 70. If r'(t) represents the rate of growth of a dog in pounds per year, what does r(t) represent?…

A: r(t) is the weight of the dog after t years.

Q: The edge of a cube decreases at a rate of 1.5m/s. Find the rate at which the surface area decreases…

A:

Q: What is the period of time ''t'' required for the initial infection rate ''I(t=0)'' to double in…

A:

Q: 10. A ladder 15 feet long leans against a vertical wall. Suppose that when the bottom of the ladder…

A: In the question we have to find the rate of rising of top end.

Q: A 13-foot ladder is leaning against a vertical wall (see figure) when Jack begins pulling the foot…

A:

Q: 12. A snowball melts in such a way that the rate of change in its volume is proportional to its…

A: Let us find the required time for the snow ball to disappear in the the following steps.

Q: Exercise 4 Water drains from the conical tank at the rate of 5 fi / min shown as in figure. (i) What…

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: Q3: Water is being poured into a hemispherical bowl of radius 3 inches at the rate of 1 in/s. How…

A: Solve

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 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: 3) Water is running from a vertical cylindrical tank 3 m in diameter at the rate of 3ayh , where h…

A: Given, Diameter of the cylindrical tank=3m Radius of the cylindrical tank, r=32=1.5m Volume of the…

Q: A brine solution of salt flows at a constant rate of 3 L/min into a large tank that initially held…

A:

Q: l edges of a cube are expanding at a rate of 4 centimeters per second. (a) How fast is the surface…

A:

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

A:

Q: A 20 m³ tank is full of brine with 40 kg of dissolved salt. Pure water enters the tank at a rate of…

A: The  given problem we can be formulated as  a differential equation and solve.

Q: A 30 m³ tank is full of brine with 40 kg of dissolved salt. Pure water enters the tank at a rate of…

A: Volume of the tank is 30 m3 The tank is full of brine with 40 kg of dissolved salt. Pure water…

Q: 150 liters of fluid in which 20 grams of salt is dissolved. Pure water is then pumped into the tank…

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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…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.