Assume that a snowball melts so that its volume decreases at a rate proportional to its surface area. If it takes three hours for the snowball to decrease to half its original volume, how much longer will it take for the snowball to melt completely?

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

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Q: The bacteria in a culture can be assumed to multiply at a rate that at any given moment is…

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Q: A body cools at the rate of 0.5°C per second when it is 500°C above the surroundings. What is the…

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Q: The volume of an ice cube is decreasing at a rate of 1.5 cm³/ sec. At what rate is a side of the ice…

A: We know that volume of a cube is given by V=a3 here V=volume of cube ,a=edge of cube Rate of change…

Q: How fast is the volume of a parallelepiped increasing if the length, width, and height of the…

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Q: A rocket, rising vertically, is tracked by a radar station that is on the ground 5 mi from the…

A: Given that: Rate of increase of distance from radar station = 2000 mi/hDistance between radar…

Q: The volume of a cube is decreasing at a rate of 24 cubic inches per minute. At the instant when an…

A: Given that  The volume of a cube is decreasing at a rate of 24 cubic inches per minute.…

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: The surface area of kelp near Monterrey Bay is 40,000 square acres, but after four years a red sea…

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Q: Suppose that the concentration of a bacteria sample is 60,000 bacteria per miliditer. f the…

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Q: A cube is heated in such a way that the volume increases at a rate of 1 mm/s. The rate of change of…

A: A cube is heated in way that volume increases at the rate of 1mm/s. the side of the cube is 7mm…

Q: a)How quickly is the water leaving the barrel over the first two seconds? b)Will the water drain…

A: The solution is given below in the next step:

Q: snowball melts so that its surface area decreases ata rate of 1cm^2/min, find the rate at which the…

A: Given query is to find the rate of chnage of diameter.

Q: Assume that Laguna Lake has a volume of 480km^3 and that its rate of inflow (from Lake Huron) and…

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Q: The rate of decay of radium is said to be proportional to the amount of radium present. If the…

A: Simple rate of decay of radium problem....

Q: The volume of an ice cube is decreasing at a rate of 1.5 cm³/sec. At what rate is a side of the ice…

A: option A is correct detailed solution with explanations given below

Q: A 400-gal tank initially contains 100 gal of brine containing 50 lb of salt. Brine containing 1 lb…

A: Schematic diagram of the given situation:…

Q: Initially 100 milligrams of a radioactive substance were present. After 6 hours the mass had…

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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: The rate of growth of a certain cell culture is proportional to its size. In 10 hours a population…

A: The rate of growth of a certain cell culture is proportional to its size. In 10 hours a population…

Q: A tank contains 2,000 L of brine. Brine containing 5 kg/L of salt flows in at 10 L/min, and the…

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Q: A yeast grows at a rate proportional to its present size. If the original amount doubles in two…

A: Let v(t) be size of yeast at t time Therefore, ds/dt  ∝ s(t) ds/dt  = ks   [k is proportionality…

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: A storage battery discharge at a rate which is proportional to the charge. If the charge is reduced…

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Q: The height of a right circular cylinder is 50 inches and decreases at the rate of 4 inches per…

A: Topic = Volume

Q: Initially 50 grams of radioactive substance was present. After 10 hours the mass had decreased by…

A: The rate of change of amount A with respect to time t can be denoted by dAdt. If x is directly…

Q: In a chemical reaction a substance decomposes at a rate proportional to the amount of substance…

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Q: air containing 30% oxygen passes slowly into a 3 gallon flask initially filled with pure oxygen and…

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Q: A wet towel hung from a clothesline to dry loses moisture through evap-oration at a rate…

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Q: A swimming pool is 20 ft wide, 40 ft long, 3 ft deep at the shallow end, and 9 ft deep at its…

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Q: A mold grows at a rate that is proportional to the amount present. Initially, there is 5 oz of this…

A:

Q: If the radius of a sphere is increasing at the constant rate of 3 inches per second, how fast is the…

A: Given dr/dt = 3

Q: A bunch of hooligans dump 164 pounds of  pizza boxes into a lake. If the pizza boxes dissipates at a…

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Q: A mold grows at a rate proportional to its present size. If the original amount doubles in one day,…

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Q: Initially 53 grams of radioactive substance was present. After 6 hours the mass had decreased by 6%.…

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Q: The rate at which bacteria multiply is proportional to the instantaneous Number Present. If the…

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Q: A spherical drop of liquid evaporates at a rate proportional to tis surface area. If a given drop…

A: Given: The drop evaporates to 18 of its volume in 5 minutes

Q: An ice cube that is 3 cm on each side is melting at the rate of 2 cubic cm per min. How fast is the…

A:

Q: A body cools at the rate of 0.5°C per second when it is 500°C above the surroundings. what is the…

A:

Q: The growth rate of a bacteria culture is proportional to the number of bacteria present. If a…

A:

Q: Assume that Laguna Lake has a volume of 480km^3 and that its rate of inflow (from Lake Huron) and…

A:

Q: an ice cube is shrinking uniformly at a rate of 8 cubic inches per hour. when the cube has a volume…

A: We are given the rate of change of volume of ice cube is shrinking uniformly at a rate of 8 cubic…

Q: How long (in hours) would it take to fill a city water tank that has an inside diameter of 120 feet…

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Q: The surface area of a balloon that is being filled with helium increases at a rate of 5 square feet…

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Q: A stream containing 80 grams per liter of a dye is pumped into a mixing tank with 400 liters of…

A: The answer is 32kg

Q: The number of germs in a certain culture increases at a rate proportional to the number present. If…

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Q: A solution with 35% ammonia is added at a rate of 5 liters per minute to a vat that initially…

A: Given: A solution with 35% ammonia is added at a rate of 5 liters per minute to a vat that initially…

Q: A culture of bacteria grows at a rate that is proportional to the present number. It is found that…

A:

Q: Consider that sugar dissolves in water at a rate proportional to the amount still un-dissolved.…

A: 50kgs of sugar is present and at 5-hour mark there's only 20kg of sugar is left.

Q: The homicide rate decreases at a rate of 3%/yr in a city that had 800 homicides/yr in 2018. At this…

A: dH / dt = rate of change of homicide rate = - 3% = - 0.03 x HPlease see the white board for…

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.