Suppose you are filling your car with gasoline at the local gas station. Unfortunately, the pump display is broken, so you cannot see how much gas you put in your car. While you pump gas, the gasoline flows into the car’s gas tank at a rate of f(t) = 10t cos(t/2) gallons/minute. If it takes you 2 minutes to fill the tank, which has a capacity of 16 gallons, how many gallons were in the tank when you started to pump gas?

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A:

Q: Over 4 years, researchers studied the growth of a fish population and found its growth rate to P'(t)…

A: hintddxtan-1x=11+x2 or,∫11+x2dx=tan-1x

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A: Given,

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A: Let's find.

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A: For decreasing rate apply negative sign

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A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

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A: Solve for the value

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A:

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A: Topic = Algebra

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A:

Q: 7) The rate of water flowing in a tank is given by: R(t) = 0.5t* + 20t Gallons/minutes. How much…

A:

Q: From the beginning of the year 2000, the annual world demand for oil has increased. To account for…

A: Let's find.

Q: Suppose that electricity isdraining from a capacitor at a rate that is proportional to the voltageV…

A: Given equation in the question is: Integrating both sides: We have, at t = t0, V  = V0 =>ln(V0)…

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A:

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A: NOTE: Refresh your page if you can't see any equations. . the water leaving the tank at a rate of…

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A: Introduction: The half-life is the amount of time it takes for a quantity to decline to half its…

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A:

Q: | Suppose that electricity is draining from a capacitor at a rate proportional to the voltage V…

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Q: Suppose an Egyptian mummy is discovered in which the amount of​ carbon-14 present is only about…

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A:

Q: Because of job outsourcing, a town predicts that its public school population will decrease at the…

A: Given,           Because of job outsourcing, a town predicts that its public school population will…

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A: Here we have a population of fruit flies that changes at a rate of g(t)=-4e0.04t…

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A:

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A:

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A: Here, the initial population given is 2000, and its doubles after 2 hours.

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A:

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A: Solved below

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A: One model for the time it will take for the world’s oil supply to be depleted is given by the…

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A:

Q: The half-life of Palladium-100 is 4 days. After 24 days a sample of Palladium-100 has been reduced…

A:

Q: Suppose that electricity is draining from a capacitor at a rate that is proportional to the voltage…

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Q: Consider a tank that initially contains 100 gallons of a solution in which 50 pounds of salt are…

A: Here I am attaching image so that you understand each and every step.

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A: Given that: The time required to double the amount of an investment at an interest rate r compounded…

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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.