Boyle's Law states that when a sample of gas is compressed at a constant temperature, the pressure P and volume V satisfy the equation PV = C, where Cis a constant. Suppose that at a certain instant the volume is 100 cm³, the pressure is 100 kPa, and the pressure is increasing at a rate of 40 kPa/min. At what rate is the volume decreasing at this instant? |× cm³/min

Q: One hundred strands of bacteria are placed in a nutrient solution in which a plentiful supply of…

A:

Q: A.) A perfectly spherical balloon is losing volume at a rate of 3 in3 per sec. How fast is the…

A: A perfectly spherical balloon is losing volume at a rate of 3 in3 per second. That is, dVdt=-3 Now…

Q: A tank contains 52 gallons of a solution composed of 85% water and 15% alcohol. A second solution…

A: Please see the answer below

Q: A bucket that has a mass of 10 kg when filled with sand needs to be lifted to the top of a 30 meter…

A: Mass of rope = 0.1kg/mMass of rope on bucket = 0.1kg/m*1m = .1kg…

Q: le's Law states that when a sample of gas is compressed at a constant temperature, the pressure P…

A:

Q: A tank contains 100 liters of brine, with 50 kg total dissolved salt. Saltwater, with a…

A:

Q: The metal frame of a rectangular box has a square base. The horizontal rods in the base are made out…

A: To find the rate of change of the volume of the box

Q: According to Newton's Law of cooling, the temperature of an object changes at a rate proportional to…

A:

Q: a tank initialy holds 80 gal. of a brine solution containing 1/8 lb of salt per gallon. at t=0,…

A:

Q: A tank contains 57 gallons of a solution composed of 85% water and 15% alcohol. A second solution…

A:

Q: 2. A large tank is partially filled with 100 gallons of fluid in which 10 pounds of salt is…

A:

Q: A radioactive material, such as the isotope thorium-234, disintegrates at a rate proportional to the…

A: Given: dQdt=-rQ for Q is the amount present at time t. 100 mg reduce to 82.04 mg in 1 week, the…

Q: A tank contains 100 liters of brine, with 50 kg total dissolved salt. Saltwater, with a…

A:

Q: 19. A leaky 10-kg bucket is lifted from the ground to a height of 12 m at a constant speed with a…

A: Given that a leaky bucket is lifted from ground to a height of 12 m at constant speed with rope that…

Q: A tank initially holds 410 liters of brine solution containing 7 kg of salt. At t=0, another brine…

A:

Q: The length l of a rectangle is decreasing at the rate of 2 cm/sec while the width w is increasing at…

A: Given:The length of rectangle is decreasing at rate 2cm/sec  The width  of rectangle is…

Q: A 2000 L tank initially contains 40 kg of salt dissolved in 1000 L of water. A brine solution…

A: Given capacity of tank =2000 L initial amount of water =1000 L rate of in flow of salt =50 L/min…

Q: A cylindrical can is partially filled with sand. The radius of the cylindrical can is 15 cm. The…

A: Let h be the height of thesand at any instant 't'∴vol at any time…

Q: A bucket that has a mass of 15 kg when filled with sand needs to be lifted to the top of a 25 meter…

A:

Q: 13. A motorcycle is moving at 30 m/s when the rider applies the brakes, giving Che motorcycle a…

A: Consider the given information. If the acceleration is constant then we can use these equations.…

Q: 4. A tank initially holds 80 gal of a brine solution containing 1/8 lb of salt per gallon. At t = 0,…

A:

Q: Suppose a water tank is being pumped out at 3 L/min. The water tank starts at 10 L of clean water.…

A:

Q: The rate of decay of a certain substance is directly proportional to the amount remaining. The…

A:

Q: A tank contains 100 liters of brine, with 50 kg total dissolved salt. Saltwater, with a…

A:

Q: A radioactive material, such as the isotope thorium-234, disintegrates at a rate proportional to the…

A: If Q(t) is the amount present at time t, then dQ/dt = −rQ, where r > 0 is the decay rate.…

Q: The length of a rectangle is increasing at a rate of 5 cm per second and its width is decreasing at…

A:

Q: The mass of a cube in grams is M = x + 0.1x*, where x is the length of one side in centimeters. If…

A:

Q: A dock is 6 feet above water. Suppose you stand on the edge of the dock and pull a rope attached to…

A:

Q: How fast is the volume V of a rectangular box changing when its length L is 10 ft. and increasing at…

A:

Q: SHOW FULL SOLUTION. DIFFERENTIAL CALCULUS. To measure the area of a quadrangle, two students decided…

A: The objective of the question is evaluate the distance between A and B.

Q: A bucket that has a mass of 10 kg when filled with sand needs to be lifted to the top of a 20 meter…

A: Given: Mass of bucket = 10kg Mass of the rope = 0.1kg/m Height of the Building = 20 meter

Q: One hundred strands of bacteria are placed in a nutrient solution in which a plentiful supply of…

A:

Q: A bucket that has a mass of 10 kg when filled with sand needs to be lifted to the top of a 30 meter…

A: Given:    Mass of the bucket =10 kg   Mass of the rope =0.2 kg/m  Height of the building =30 m…

Q: An inverted pyramid is being filled with water at a constant rate of 70 cubic centimeters per…

A:

Q: 9. The altitude of a triangle is increasing at a rate of 2 cm/min while the area of the triangle is…

A: Area of triangle = 12×b×h Where b is base and h is height . And height of the triangle is equal to…

Q: A bucket that has a mass of 25 kg when filled with sand needs to be lifted to the top of a 20 meter…

A:

Q: A bucket that has a mass of 15 kg when filled with sand needs to be lifted to the top of a 20 meter…

A: We are given that the mass of the bucket is 15 kg, the height of the building is 20 meter, the…

Q: A bucket that has a mass of 25 kg when filled with sand needs to be lifted to the top of a 25 meter…

A: If an object moves in a straight line by a continuous force, F(x), the work done by the force from…

Q: A tank initially contains 50 gal of sugar water having a concentration of 2 lb of sugar for each gal…

A: Given:   A tank initially contains 50 gal of sugar water having a concentration of 2 lb of sugar for…

Q: 4. A tank initially holds 80 gal of a brine solution containing 1/8 Ib of salt per gallon. At t = 0,…

A:

Q: 6. In a tank there are 1000 gal of water with a concentration of 1 lb per gallon of pollutant. Water…

A: Rate of change of pollutant in the mixture = dp/dt

Q: When air expands adiabatically (without gaining or losing heat), its pressure Pand volume V are…

A: We have to find the rate at which volume is increasing. We will use product rule of differentiation…

Q: A tank originally contains 200 gal of fresh water. Then water containing 1/2 1b of salt per gallon…

A: A tank originally contains 200 gallons of fresh water. Then water containing 1/2 lb salt per gallon…

Q: A bucket that has a mass of 10 kg when filled with sand needs to be lifted to the top of a 10 meter…

A:

Q: A tank contains 45 liters of a chemical solution prepared by dissolving 80 g of a soluble substance…

A: Let's find.

Q: By Newton's Law of Cooling, the rate at which an object cools is directly proportional to the…

A: let T denote the temperature of an object and T0 the surrounding temperature. If t denotes time,…

Q: A tank contains 54 gallons of a solution composed of 85% water and 15% alcohol. A second solution…

A: Consider the given information. Let y is the number of gallons of alcohol in the tank with rate of…

Q: 2. A bacteria culture is known to grow at a rate proportional to the amount present. After one hour,…

A: We will use exponential growth Function Here.

Q: The metal frame of a rectangular box has a square base. The horizontal rods in the base are made out…

A: Given: horizontal rods expand at the rate of 0.004cm/hr. vertical rods expand at a rate of 0.008…