A tank with a capacity of 5000 kg of water is initially half full. Twenty kilogram per minute is charged into the tank and 14.5 kg per minute is withdrawn simultaneously at the bottom. How long will it take to fill the tank?

Q: If 6 J of work is needed to stretch a spring from 13 cm to 15 cm and another 10 J is needed to…

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Q: 1200ml of IV fluid must be administered to the patient over an 8 hour period, if the calibration…

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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: The largest bulldozer ever built had a mass of about 1.5 x 105 kg and a blade 7.4 m wide. Its two…

A: We  have,  a  lrgest  bulldozer  ever  built  had  amass  of  about  1.5×105 kg  and  a  blade…

Q: If 6 J of work is needed to stretch a spring from 10 cm to12 cm and another 10 J is needed to…

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Q: In a mixing vat there are initially 100 litres of volatile liquid. 3 litres of fresh liquid are…

A: Solution

Q: A tank contains 60 kg of salt and 1000 L of wa solution is mixed and drains from the tank at

A: Given: A tank contains 60 kg of salt and 1000 kg of water.

Q: Assume that the population of the greater roadrunner in the Guadelope Desert was 250 per hectare at…

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

A: first, we need to find the spring constant  W=∫0a fxdx here we have W=15 and a=5 feet 15=∫05 fxdx…

Q: A force of 10 Ib is required to hold a spring stretched 4 feet beyond its natural length. How much…

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Q: A sewage disposal plant has a big concrete holding tank of 100,000-gal capacity. It is % full of…

A: Let M(t) be the mass of the organic material in the tank at time t and Mt=CtVt, where C(t) and V(t)…

Q: How fast is a 1.5g bullet moving if it has a momentum of 1.2kg m/s?

A: If the particle has mass m kg and moving at a velocity of v m/s Then the momentum of the particle is…

Q: Consider a lake with a volume of 8 billion ft3 and an initial pollutant concentration of 0.25%. An…

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Q: A force of 10 lb is required to hold a spring stretched 4 feet beyond its natural length. How much…

A: F=10 lb  x=4 feet  F=kx  k=10/4=5/2

Q: the radiator in a car is filled with a solution of 60% antifreeze and 40% water. the manufacturer of…

A: In a 3.6 L radiator, the quantity of antifreeze is given by: In a 3.6 L radiator, the quantity of…

Q: A Styrofoam cooler contains ice at 0° C. The cooler is left outside where the temperature is 30.° C.…

A: Given data: The cooler contains ice at 0°C, i.e. 273K The outside temperature is 30°C, i.e. 30+273K,…

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

A: The time taken by worker A to load the truck is = 10 min  The time taken by the worker B to unload…

Q: How much work is required to pump all the water from a right circular cylindrical tank, that is 8…

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Q: An automobile uses gasoline at a rate of 12 kilometres per litre and has a 65 litre tank. How far…

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Q: 1000 liters of water per second is filled into the square prism-shaped tank with a base edge of 10…

A: We have to find the relating equation of volume with height and then differentiate it with respect…

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 tank with capacity of 2000 litre originally contains 50 kg of sugar dissolved in pure water. Pure…

A: The initial amount of the sugar in the water is x (0) = 50 kg   The pure water is entering into the…

Q: A Computer on the 4 Mbps network is regulated by a token bucket. The bucker is filled at a rate of…

A: Let T be the time taken by computer to transmit full 6Mbps Let c = initial capacity =8Mb r =filling…

Q: If 6 J of work is needed to stretch a spring from 10 cm to 12 cm and another 10 J is needed to…

A: let L is the natural length (actual length) of the spring. Now if the force (f) produces…

Q: A chain lying on the ground is 10 m long and its mass is80 kg. How much work is required to raise…

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Q: A diver who is 10.0 m underwater experiences a pressure of 202kPa. If the diver’s surface area is…

A: Pressure P = 202 kPa Surface area A = 1.50 m2

Q: An IV Piggyback of lincomycin containing 5 gms of drug in 175 mL is to be infused over a 1 hour…

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Q: A 450 gal tank initially contains 110 gal of brine containing 52 Ib of salt. Brine containing 1lb of…

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Q: If the work required to stretch a spring 3 ft beyond its natural length is 15 ft-lb, how much work…

A: Given that the work required to stretch a spring 3 ft beyond its natural length is 15 ft-lb.

Q: A block of wood is 2.5 feet long, 0.5 feet wide, and 0.25 feet tall. It weighs 16.5 pounds. To the…

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Q: A worker uses 450 inches of steel wire to make 300 springs of the same size. At this rate how many…

A: Let he needs ' x ' inches for making 1 spring.

Q: a plant is growing expotentially, inityially is 8cm tall and 4 days later it is 12 cm tall, how long…

A: Given, The initial height of the plant is 8cm 4 days later the plant height is 12cm How long it…

Q: A 1000-kg car traveling at 35 m/s takes 3 m to stop under full braking. The same car under similar…

A: We have given  initial velocity u=35m/s, final velocity v=0  and taking time t=3m=180 s we know that…

Q: The radiator car is filled with a solution of 65% antifreeze and 35% water. The manufacturer of the…

A: The capacity of the radiator is 3.9L.Let x be the amount of coolant to be drained.

Q: A cardboard box with the dimensions of 20*15*5 (lwh), is used by a compnay to package laptops. If…

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Q: The side of a cube is increasing at a rate 7m/8, then the rate at which the m³/s. volume of the cube…

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Q: A spring has a natural length of 10 cm. If it takes 5 J to stretch the spring from 10 cm to 15 cm.…

A: Consider the provided question, (16) Given, natural length of spring = 10 cm It takes 5 J to stretch…

Q: How much water should be evaporated from 40% v/v alcohol in order to prepare 3000 ml of 60% ( v/v)…

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Q: A tank has a total capacity of 100 L, but initially it contains 15 L of pure water. Water flows into…

A: Given :- The total capacity of tank = 100 L Initially amount of fresh water in a tank = 15 L Saline…

Q: If you leave a 100-W light bulb on for a week, how many joules of energy will be consumed?

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Q: One mole of gas expands isothermically to double its volume. If the gas temperature is 340 k what…

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Q: In a room containing of air 20,000 m3 of air, 600 m3 of fresh air flows in per minute, and the…

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Q: Suppose you ask a jeweller to form a gold in the shape of a sphere whose volume is * cm³. But you…

A: Intial volume of gold = 4π/3.

Q: An electric elevator with a motor at the top has a multistrand cable weighing 4.5 lb/ft. When the…

A: Given,

Q: If a force of 50 pounds is required to stretch a spring by 1 inch from its natural length of 10…

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Q: If. the.work.required to stretch a spring 3 ft beyond its natural length is 9 ft-lb, how much work…

A: We have the relation,   Work = ∫abfdx Where f is the force and dx is the distance. According to…

Q: A tank initially holds 80 gal of a brine solution containing of salt per gallon. At t=0, another…

A:

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.