Questions from General Calculus

Q: A certain small country has $10 billion in paper currency in

A certain small country has $10 billion in paper currency in circulation, and each day $50 million comes into the country’s banks. The government decides to introduce new currency by having the banks...

Q: A tank contains 1000 L of brine with 15 kg of dissolved

A tank contains 1000 L of brine with 15 kg of dissolved salt. Pure water enters the tank at a rate of 10 L/min. The solution is kept thoroughly mixed and drains from the tank at the same rate. How muc...

Q: The air in a room with volume 180m3 contains 0.15

The air in a room with volume 180m3 contains 0.15% carbon dioxide initially. Fresher air with only 0.05% carbon dioxide flows into the room at a rate of 2 m3/min and the mixed air flows out at the sam...

Q: A vat with 500 gallons of beer contains 4% alcohol (

A vat with 500 gallons of beer contains 4% alcohol (by volume). Beer with 6% alcohol is pumped into the vat at a rate of 5 gal/min and the mixture is pumped out at the same rate. What is the percentag...

Q: A tank contains 1000 L of pure water. Brine that contains

A tank contains 1000 L of pure water. Brine that contains 0.05 kg of salt per liter of water enters the tank at a rate of 5 L/min. Brine that contains 0.04 kg of salt per liter of water enters the tan...

Q: When a raindrop falls, it increases in size and so its

When a raindrop falls, it increases in size and so its mass at time t is a function of t, namely m (t). The rate of growth of the mass is km (t) for some positive constant k. When we apply New ton’s L...

Q: An object of mass m is moving horizontally through a medium which

An object of mass m is moving horizontally through a medium which resists the motion with a force that is a function of the velocity; that is, Where v = v (t) and s = s (t) represents the velocity...

Q: Allometric growth in biology refers to relationships between sizes of parts of

Allometric growth in biology refers to relationships between sizes of parts of an organism (skull length and body length, for instance). If L1 (t) and L2 (t) are the sizes of two organs in an organism...

Q: Find the radius of convergence and interval of convergence of the series

Find the radius of convergence and interval of convergence of the series.

Q: Let x = 0.99999… (a). Do

Let x = 0.99999… (a). Do you think that x < 1 or x = 4? (b). Sum a geometric series to find the value of x. (c). How many decimal representations does the number 1 have? (d). Which numbers have more t...