The metal frame of a rectangular box has a square base. The horizontal rods in the base are made out of one metal and the vertical rods out of a different metal. If the horizontal rods expand at a rate of 0.004 cm/hr and the vertical rods expand at a rate of 0.008 cm/hr, at what rate is the volume of the box expanding when the base has an area of 81 cm2 and the volume is 1620 cm3? Enter the exact answer. The volume is changing at a rate of Enter your answer in accordance to the question statement centimeters3 per hour.

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Q: A container initially contains 15 L of water in which there is 30 g of salt dissolved. A solution…

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

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Q: The radius of a right circular cone is increasing at a rate of 1.1 in/s while its height is…

A: Given that, drdt=1.1 in/s and dhdt=-2.7 in/s. Also, it is given that r=102 in. and h=162 in. It is…

Q: A 40 gal tank initially contains 11 gal of fresh water. At t = 0, a brine solution containing 1.2 lb…

A: Given: The initial volume of water v(0)=11 gallons The initial amount of salt s(0)=1.2 lb Since rate…

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.

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 tank with a capacity of 5000 kg of water is initially half full. Twenty kilogram per minute is…

A: Given that the capacity of the tank is 5000 kg. Let Q be the quantity of water in the tank after t…

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: A ladder 10 ft. long rests against a vertical wall. If the bottom of the ladder slides away from the…

A: A ladder 10 ft. long If the bottom of the ladder slides away from the wall at a rate of 2 ft./sec.,…

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

A:

Q: Suppose the edges of a cube are increasing at a constant rate of 11 m/hr. Then, the volume of the…

A: Let the side of the cube = x Edges of the cube increasing rate dx/dt = 11 m/hr

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

A: We will find out the required time.

Q: A screen saver displays 3 cm x 5 cm and then expands it in such a way that the length of the longer…

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Q: A bucket that weighs 4 lb and a rope of negligible weightare used to draw water from a well that is…

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

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Q: A container that has 5 L of water with 1 kg salt dissolved is to be filled by pure water at a rate…

A: Solve by making differential equation

Q: A reservoir is 80m long and its cross section is an isosceles trapezoid having equal sides of 10m,…

A: Sol

Q: A ladder 8 m long leans against a model home. If the bottom of the ladder slides away from the…

A: Given- A ladder 8 m long leans against a model home. If the bottom of the ladder slides away from…

Q: Tank A contains 274 litres of brine holding 123 N of dissolved salt, and tank B contains 274 litres…

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

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Q: Worker A is a loader and worker B is an unloader. Worker A can load a truck in 10mins, while worker…

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Q: A tank with a capacity of 400 gal originally contains 150 gal of water with 25 lb of salt in…

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Q: A bucket that weighs 4 lb and a rope of negligible weight are used to draw water from a well that is…

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Q: A tank contains 1000 liters (L) of a solution consisting of 170 kg of salt dissolved in water. Pure…

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Q: Tank A contains 499 litres of brine holding 192 N of dissolved salt, and tank B contains 499 litres…

A:

Q: A reservoir is 80m long and its cross section is an isosceles trapezoid having equal sides of 10m,…

A: Given that the reservoir is 80m long whose cross-section is an isosceles trapezoid with sides of…

Q: A reservoir is 80m long and its cross section is an isosceles trapezoid having equal sides of 10m,…

A: Given that the reservoir is 80m long whose cross-section is an isosceles trapezoid with sides of…

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

A: Given: Let the rate of filling be Qin = 1250 GPM  the rate of draining be Qdrain = 530 GPM Because…

Q: In a water bottling process, one-liter bottles are filled through a system that provides filtered…

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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: Sand is being dumped from a conveyor belt at a rate of 20 ft3/min, and its coarseness is such that…

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Q: The sides of the square are increasing at a rate of 3 cm per second . When the sides are 5cm long ,…

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Q: Tank A contains 402 litres of brine holding 123 N of dissolved salt, and tank B contains 402 litres…

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

A: Question is solved.

Q: 1. Air is being pumped into a spherical balloon at a rate of 4 cm3/min. How fast is the radius of…

A: 1. Given:   The rate at which air is pumped into the spherical balloon = 4 cm3/min   Diameter of the…

Q: A 400-gal tank initially contains 100 gal of brine containing 75 lb of salt. Brine containing 2 Ib…

A: The solution of above question is written below.

Q: The length of a rectangle is increasing at a rate of 2 ft/s, and its width is increasing at a rate…

A: Here we have, The length of a rectangle is increasing at a rate of 2 ft/s, and its width is…

Q: A 150 mg per L solution of drug is administered intravenously at a rate of 30 mL per hr to a patient…

A: Given that: A 150 mg per L solution of drug is administered intravenously at a rate of 30 mL per hr…

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 100L-capacity tank initially holds 80L of fresh water. A brine solution is poured into the tank at…

A: A brine solution is poured into the tank at the rate of 4 L/hr, while the well-stirred mixture…

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: 2. Air is leaking from a spherical-shaped advertising balloon at the rate of 26 cubic feet per…

A: Let r be the radius and v be the volume of balloon, Given dvdt=26 cf/minuteswe know…

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

A:

Q: A spacecraft is launched from the surface of a 6.7 x 1024 kg planet. If the spacecraft is moving at…

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 5m long ladder has its upper end leaning against a vertical wall and lower end on a perfectly…

A: To determine the rate at which the ladder is moving down in cm/sec when the lower end is 3 m away…

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…

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.