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 C  is a constant. Suppose that at a certain instant the volume is 600 cu. cm the pressure is 150 kPa , and the pressure is increasing at a rateof 20 kPamin. At what rate is the volume decreasing at this instant?

Q: The rate of decay of radium is proportional to the amount present at any time. If 60 mg of radium…

A: Given that rate of decay of radium is proportional to the amount present at that time.

Q: b) A certain radioactive material is known to decay at a rate proportional to the ам amount present…

A:

Q: In a simple electric circuit, Ohm's law states that V IR, where V is the voltage in volts, I is the…

A: From the given problem: dVdt=-0.01 volts per second ; dRdt=0.03 ohms per secondR=300 ohms ; I=0.04…

Q: A 200-gal tank is half full of distilled water. At time t=0, a solution containing 0.5 Ib/gal of…

A:

Q: In the absence of predators the population of mosquitoes in a certain area would increase at a rate…

A: Given initial population of mosquitos is 200000 and the get triple every week, Flock birds eats…

Q: Cane sugar, when placed in water, converts to dextrose at a rate proportional to the amount of…

A: An ordinary differential equation is an equation containing independent variables, dependent…

Q: When air expands adiabatically (without gaining or losing heat), its pre and volume V are related by…

A: For decreasing rate apply negative sign

Q: Under certain conditions, the number of diseased cetls N(t) at time t increases at a rate N'(t) = A…

A: Rate at which number of diseased cells N(t) are increasing at time t is given by N'(t)=Aekt.…

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

A: (b)

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

A: given that pressure and volume are related by the equation PV1.4=C and a certain instant of time…

Q: The Ideal Gas Law is PV = mRT where P is the pressure, V is the volume, m is the constant mass, R is…

A:

Q: At what rate in cubic centimeters per minute is the volume increasing at this instant?

A:

Q: A 200-gal tank is half full of distilled water. At time t = 0, a solution containing 0.5 lb /gal of…

A: Given that the size of the tank is 200 gallon. Half of it is full, that means 200/2=100 gallon is…

Q: Alice measures a radioactive sample at 1400 counts/minute on a Geiger counter. If the radioactive…

A: Given: Initial value, R0=1400 counts/min Ending value, R = 1000 counts/min Time that has passed, t =…

Q: a new substance C is to be formed by removing two units from each of two substances whose initial…

A: 1st we will formed a differential equation for amount of C and then solve it to get actual amount of…

Q: A certain population of bacteria grows such that its rate of change is always proportional to the…

A:

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

A: Given expression is PV1.4=C   ......1 Where P is pressure, V is volume and C is constant.  Pressure…

Q: Question 2 A tank is initially filled to capacity of 25 L with brine having a salt concentration of…

A:

Q: In a first order chemical reaction with no backorder reaction the concentration of the reactant is…

A: We solve for C(t)

Q: When air expands adiabatically (without gaining or losing heat), its pressure P C where C is a…

A:

Q: A tank contains 10m^3 of free water, brine having a concentration of 15kgsalt/m^3 is sent into the…

A:

Q: A particular specie of animal has a carrying capacity of K and a growth rate of r. From an initial…

A:

Q: Under certain conitions, the number of diseased cells N ( t ) at time t increases at a rate N ' ( t…

A:

Q: Suppose you have a 200-gallon tank full of fresh water. A drain is opened that removes 3 gal/sec…

A: Let the concentration of brine =x lb/gal Amount of salt entering in per minute = 2 gal1 min×x lb1…

Q: According to one hypothesis, the growth rate dV/dt of a cell’s volume V is proportional to its…

A:

Q: a. A tank holds 1000 liters of water, in which 15 kg of salt is dissolved. Pure water enters the…

A:

Q: A body of an unknown temperature is placed in a room which is held at a constant temperature of 30 .…

A: Given that, A body of an unknown temperature is placed in a room which is held at a constant…

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

A:

Q: A certain population of microorganisms grows at a rate proportional to the amount present under a…

A: Given that, A certain population of microorganisms grows at a rate proportional to the amount…

Q: A certain radioactive material is known to decay at a rate proportional to the amount present.…

A: Let,Decay rate = r = -dAdt                        negative because it's decaying/decreasingwhere, r…

Q: 5. Consider a scenario in which a 20ft tall lamppost lights up a street. (a) her shadow on the…

A:

Q: 1. A tank contains 80 gallons (gal) of pure water. A brine solution with 2 Ib/gal of salt enters at…

A: Given that, a tank contains 80 gallons (gal) of pure water. A brine solution with 2 lb/gal of salt…

Q: Under certain conditions, cane sugar in water is converted into dextrose at a rate proportional to…

A:

Q: 6. The mass of a cube in grams is M = x³ + 0.1x*, where x is the length of one side in centimeters.…

A: Explained below

Q: A radioactive element decomposes at a rate proportional to the amount present. The amount remaining…

A:

Q: The base x of a triangle is decreasing at the rate of 5 in./sec. and the height y of the triangle is…

A: Given Base = x  Height = y Rate of change of base = dx/dt = - 5 in/s Rate of change of height =…

Q: A cup of coffee cools at rate proportional to the difference between the constant room temperature…

A:

Q: A mathematical model for population growth over short intervals is given by P=P0ert​, where P0 is…

A:

Q: The mass of a radioactive sample is given by M(t)=M010^-kt where t is the time in years, M0 is the…

A:

Q: Two substances, A and B, are being converted into a single compound C. In the laboratory it has been…

A:

Q: The upper end of the ladder 5 m long leans against a vertical wall. Suppose the foot of the ladder…

A:

Q: 1) A pump is used to fill an inflatable mattress at a constant rate of 0.25 cubic feet per second.…

A:

Q: A 200-gal tank is half full of distilled water. At what time (t) = 0, a solution containing 0.5…

A: A 200-gal tank is half full of distilled water. At what time (t) = 0, a solution containing 0.5…

Q: A bacterial population B is known to have a growth rate proportional to B itself. If between 3pm and…

A:

Q: A tank contains 50 gallons of a solution composed of 90% water and 10% alcohol. A second solution…

A:

Q: A certain population of bacteria grows at a rate that is proportional to the number present. It is…

A: Given that: Growth rate of bacteria ∝ Number of bacteria presentNumber doubles in 2 hr

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: The width of a rectangle is increasing at rate of 2cm/sec while the length increases at 3cm/sec. At…

A:

Q: In a chemical reaction, substance A decomposes at a rate proportional to the amount of A present. It…

A: This decomposition reaction of first order, because rate is directly proportional to the…

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

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.