an ice cube is shrinking uniformly at a rate of 8 cubic inches per hour. when the cube has a volume of 27 cubic inches, at what rate is each side shrinking?

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Q: If a snowball melts so that its surface area decreases at a rate of 3 cm2/min, find the rate at…

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Q: Water is pumped from a tank at constant rate, and no more water enters the tank. If the tank…

A: To solve the following problem and find the amount of water left at 6:10pm.

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Q: A truck travelling southwards at 40kph and a car traveling eastward at a rate of 60kph ar headed for…

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Q: If the work required to stretch a spring 5 feet beyond its natural length is 15 foot-pounds, how…

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

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Q: The requirement for computer server capacity at a particular company is expected to increase at a…

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Q: If the length of the edge of a cube is increasing at a rate of 3cm/s, how fast is the volume of the…

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A: A geometric series is convergent if common ratio is less than 1. Sum of infinite geometric series is…

Q: If a snowball melts so that its surface area decreases at a rate of 9 cm2/min, find the rate at…

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Q: Consider an object in a surrounding with constant temperature of 25°C. If the temperature of the…

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Q: Water is pumped from a tank at constant rate, and no more water enters the tank. If the tank…

A: Given: The amount of water at 3:56 PM is 10452 L and amount of water at 4:12 PM on same day  is 8092…

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: Based on the figure below, how much water is stored after 20 minutes in each of the tanks? How long…

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Q: Consider three connected lakes, A, B, and C, where lake B has a volume of 2650 km, and water flows…

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Q: The volume of a cube is growing at a rate of 225 ft3/min, and the length of a side is 5 ft. What is…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

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

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Q: A safety inspector determines that contamination from an abandoned factory site is spreading through…

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Q: The side of a cube decreases at a rate of 9 m/sec Find the rate at which the volume changes, when…

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Q: If the volume of a cube is increasing at a rate of 24 in'/min and each edge is increasing at 2…

A: The volume of cube is given by V=a3 where a edge of cube. Given that volume of cube increasing at a…

Q: (d) If the ornithologists observe that birds of a certain species reach the shore at a point 3 km…

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Q: Consider three connected lakes, A, B, and C, where lake B has a volume of 2650 km3, and water flows…

A: Here we have consider 3 lakes. i.e A,B and C.                               Volume of lake B=2650…

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 simple pendulum, consisting of a mass of 8.237 kg, is attached to the end of a 2.68 m length of…

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Q: The side of a cube decreases at a rate of 7 m/sec. Find the rate at which the volume changes, when…

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Q: If the tank is completely full, how much is overflowing if 530 GPM is being taken off the bott

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Q: The side of a cube increases at a rate of 7 meter /second. Then the rate at which the volume of the…

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Q: What will happen to the density of a bar of iron if it is cut into 4 equal pieces? The density will…

A: Solution:-  Density:- Density of any material is the mass per unit Volume of the substance.…

Q: Consider three connected lakes, A, B, and C, where lake B has a volume of 2650 km2, and water flows…

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Q: The side of a cube decreases at a rate of 7 m/sec. Find the rate at which the volume changes, when…

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Q: A country with one of the highest population densities is San Wan​, where approximately 34,000…

A: Population density is the number of people divided by the size of the area. Here, number of…

Q: A large mixing tank initially contains 500 gallons of water in which 40 pounds of salt have been…

A: Given, A large mixing tank initially contains 500 gallons of water in which 40 pounds of salt have…

Q: A cube is expanding in such a way that the length of its diagonal is increasing at a rate of 5…

A: Let y be the diagonal, x be the length of an edge and V be the volume of the cube at any time t.…

Q: At a constant pressure, what temperature must be reached to increase the volume of a 100mL samples…

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Q: ular settling tank are: Length 24, Width 6 m and depth 3 m. If 3 hours detention time for tank is…

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Q: The smaller tank in the photograph has a capacity of 1400 m3​ ​and the larger tank has a capacity of…

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Q: The side of a cube is increasing at a rate 9m/s, then the rate at which the volume of the cube…

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

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Q: What is the flushing time in days for an estuary that has a volume of 6x10^9 m^3 and discharge of…

A: Dividing the volume by discharge rate, answer is obtained

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: was an earthquake in South America with magnitude 4.3 that caused only minor damage. How many times…

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Q: A 25-liter gas cylinder contains 80% oxygen and 20%   helium. If helium is added at a rate of 0.2…

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Q: Each side of a square is increasing at a rate of 3 cm / s . At what rate (in cm^ 2 /s) is the area…

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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: A process tank is being filled at a rate of 1200 GPM. If the tank is completely full, how much is…

A: In flow rate is 1200 GPM. Out flow rate is 320 GPM.

Q: The requirement for computer server capacity at a particular company is expected to increase at a…

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Q: Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A…

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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.